AXISYMMETRIC DROP SHAPE ANALYSIS (ADSA) by · PDF file2.3 Double Injection Capability ......

AXISYMMETRIC DROP SHAPE ANALYSIS (ADSA)AND LUNG SURFACTANT

by

Sameh Mossaad Iskander Saad

A thesis submitted in conformity with the requirementsfor the degree of Doctor of Philosophy

Graduate Department of Mechanical and Industrial EngineeringUniversity of Toronto

Copyright c© 2011 by Sameh Mossaad Iskander Saad

AXISYMMETRIC DROP SHAPE ANALYSIS (ADSA)

AND LUNG SURFACTANT

Sameh Mossaad Iskander Saad

Doctor of Philosophy

Graduate Department of Mechanical and Industrial Engineering

University of Toronto

2011

Abstract

The objective of this thesis was to further develop a methodology for surface tension

measurement called Axisymmetric Drop Shape Analysis (ADSA) and to adapt it to

studies of lung surfactants, i.e. the material that coats and facilitates the functioning

of the lungs of all mammals. The key property of a functioning lung surfactant is its

surface tension, which can reach extremely low values below 1 mJ/m2. Such values are

difficult to measure; but a certain configuration of ADSA, using a constrained sessile

drop (ADSA–CSD), is capable of performing such measurements.

Clinically, lung surfactant films can be altered from both sides, i.e. from the airspace

as well as from the bulk liquid phase that carries the film. Therefore, being able to

access the interface from both sides is important. Here, ADSA–CSD was redesigned to

be used as a micro film balance allowing access to the interface from both gas- and liquid-

side. This allows deposition from the gas side as well as complete exchange of the bulk

liquid phase. The new design was used to study lung surfactant inhibition and inhibition

reversal.

A dynamic compression-relaxation model (CRM) was developed to describe the me-

chanical properties of lung surfactant films by investigating the response of surface tension

to changes in surface area. The model evaluates the quality of lung surfactant prepara-

tions – beyond the minimum surface tension value – and calculates the film properties,

i.e. elasticity, adsorption and relaxation, independent of the compression protocol.

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The accuracy of the surface tension measurement can depend on drop size. A detailed

analysis of drop shapes and accuracy of measured surface tension values was performed

using a shape parameter concept. Based on this analysis, the design of ADSA–CSD was

optimized to facilitate more accurate measurements. The validity analysis was further

extended to the more conventional pendant drop setup (ADSA–PD) in which accuracy

near ±0.01 mJ/m2 is now possible.

An overall upgrade of both hardware and software of ADSA–CSD, together with

extensive numerical work, is described and applied to facilitate a more efficient operation.

Finally, it is noted that the ADSA–CSD setup developed here can be used for a wide

range of colloid and surface chemical applications.

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†

“I can do all things through Christ who strengthens me.”

(Philippians 4:13)

To my Lord, God and Savior JESUS CHRIST.

To Marie, my parents and my siblings.

To my beloved homeland, Egypt.

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Acknowledgements

“Trust in the LORD with all your heart, and lean not on your own understanding;

in all your ways acknowledge Him, and He shall direct your paths.” (Proverbs 3:5-6).

I would like to express my sincere gratitude to my supervisor Professor A. Wilhelm

Neumann to whom I owe a great debt of gratitude for his patience, inspiration and

support. I would also like to thank my co-supervisor Professor Edgar J. Acosta for his

advice and support. I wish to thank my supervisory committee, Professor Michael L.

Hair and Professor Markus Bussmann, for their priceless suggestions, continuous support

and encouragement.

The experimental assistance of Ms. Zdenka Policova was invaluable and much appre-

ciated. Additional thanks to Dr. Robert David for his technical and fruitful discussions

and to my colleague Ali Kalantarian for his friendship and help. I wish to thank the

summer and co-op students: Wojciech Gryc, Regina Park, Simon Lee, Andrew Dang,

Maria Quadir and Carl Cheng, for their effort. I wish also to thank everyone in the

Laboratory of Applied Surface Thermodynamics.

I am grateful to the Provincial Government of Ontario for its financial support through

the Ontario Graduate Scholarship (OGS). I am also grateful to the University of Toronto

for awarding me an Open Fellowship and to the Department of Mechanical and Industrial

Engineering for several Teaching Assistant positions, which provided not only financial

support but also an important learning experience. I would like to thank BLES Biochem-

icals Inc. for the generous donation of the BLES samples. Part of this work is supported

by a grant from the Natural Sciences and Engineering Research Council (NSERC) of

Canada (Grant No. 8278) and part is supported by a grant from the Canadian Institutes

of Health Research (CIHR) (MOP-11 38037).

Finally, I would also like to extend a sincere thanks to all my friends, whose names

will not be written here for risk of leaving someone out, for making my sojourn in Canada

a profitable and enjoyable one. Most importantly I would like to thank my parents for

always offering support and love.

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Contents

1 Introduction 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Evaluation of Surface Tension . . . . . . . . . . . . . . . . . . . . 41.2.2 Pulmonary Surfactants . . . . . . . . . . . . . . . . . . . . . . . . 15

1.3 Scope and Purpose of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 ADSA-CSD as a Micro Film Balance 192.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Deposition Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.2 Results for Pure Monolayers . . . . . . . . . . . . . . . . . . . . . 302.2.3 Discussion for Pure Monolayers . . . . . . . . . . . . . . . . . . . 372.2.4 Results for Mixed Monolayers . . . . . . . . . . . . . . . . . . . . 432.2.5 Discussion for Mixed Monolayers . . . . . . . . . . . . . . . . . . 48

2.3 Double Injection Capability . . . . . . . . . . . . . . . . . . . . . . . . . 522.3.1 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . 532.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3 Dynamic Surface Tension Model 763.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.2 Previous Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.2.1 Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.2.2 Kinetic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.2.3 Adsorption-Limited Model . . . . . . . . . . . . . . . . . . . . . . 83

3.3 Development of Compression–Relaxation Model . . . . . . . . . . . . . . 853.3.1 Adsorption Process (Spreading) . . . . . . . . . . . . . . . . . . . 853.3.2 Desorption Process (Relaxation) . . . . . . . . . . . . . . . . . . . 863.3.3 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.3.4 Collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.3.5 The Integrated Model . . . . . . . . . . . . . . . . . . . . . . . . 88

3.4 CRM Applied to Sample Experiments . . . . . . . . . . . . . . . . . . . . 893.4.1 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . 893.4.2 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . 91

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3.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

3.5 Effect of Concentration, Compression Ratio and Compression Rate . . . 1043.5.1 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . 1053.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1063.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1213.5.4 Range of Insensitivity . . . . . . . . . . . . . . . . . . . . . . . . . 126

4 Accuracy and Shape Parameter 1304.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1304.2 Drop Shapes and Shape Parameter . . . . . . . . . . . . . . . . . . . . . 137

4.2.1 Dimensional Analysis of Axisymmetric Drop Shapes . . . . . . . . 1374.2.2 Shape Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . 1404.2.3 Sample Constrained Sessile Drops . . . . . . . . . . . . . . . . . . 1414.2.4 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . 1484.2.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 151

4.3 Pendant Drop Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1584.3.1 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . 1704.3.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 171

4.4 Universality of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

5 Summary of Progress and Outlook 185

Bibliography 191

Appendix A Commercial Lung Surfactants 219A.1 Natural Surfactant Extracts . . . . . . . . . . . . . . . . . . . . . . . . . 219

A.1.1 Alveofact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221A.1.2 BLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224A.1.3 Infasurf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224A.1.4 Curosurf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225A.1.5 Surfacten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225A.1.6 Survanta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

A.2 Synthetic Surfactants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226A.2.1 ALEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228A.2.2 Exosurf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228A.2.3 Surfaxin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228A.2.4 Venticute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

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List of Tables

2.1 Experimental parameters used for different monolayer types . . . . . . . 262.2 Collapse pressure (mJ/m2) from different runs of different monolayer types

and the average value along with the standard deviation . . . . . . . . . 352.3 Ultimate collapse pressure (mJ/m2) and film elasticity (mJ/m2) at room

temperature of 24oC from different runs of different DPPC:DPPG mixtureratios and the average value along with the standard deviation. . . . . . 45

3.1 Summary of the dynamic parameters (mean and standard deviation) cal-culated from the compression-relaxation model for different preparationsat 20% compression and 3 seconds per cycle. . . . . . . . . . . . . . . . 98

3.2 Summary of the dynamic parameters for BLES at 37C and 100% R.H. atdifferent conditions. Asterisks show range of insensitivity (explained in fig-ure 3.17): * range of insensitivity bigger than 0.2, ** range of insensitivitybigger than 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

3.3 Summary of the range of insensitivity of CRM to each of the dynamicparameter (explained in figure 3.17) for BLES at 37C and 100% R.H. atdifferent conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.1 Summary of results of constrained sessile drop experiments using differentliquids and different holder sizes. . . . . . . . . . . . . . . . . . . . . . . 154

4.2 Summary of results of pendant drop experiments using different liquidsand different holder sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

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List of Figures

1.1 Schematic diagram of a Langmuir-Wilhelmy Balance (LWB). . . . . . . 51.2 Schematic diagram of a Pulsating Bubble Surfactometer (PBS). . . . . . 81.3 Schematic diagram of a Captive Bubble Surfactometer (CBS). . . . . . . 91.4 Schematic diagram of different constellations of Axisymmetric Drop Shape

Analysis (ADSA). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 Schematic diagram of ADSA–CSD experimental setup. . . . . . . . . . . 242.2 The change of surface tension with time after the deposition of octadecanol

in heptane/ethanol solution. . . . . . . . . . . . . . . . . . . . . . . . . 252.3 The process of solution deposition on a constrained sessile drop: (a) the

drop at the full size (∼80µl) before deposition; (b) the drop at half size(∼40µl) before deposition; (c) solution deposition (5µl) where more thanone solution drop falls from the needle over the apex; (d) part of the solu-tion is still attached to the needle; (e) the needle is moved closer withoutpenetrating the interface; (f) the sessile drop after complete deposition; (g)expansion of the sessile drop back to the full size right after deposition;(h) the sessile drop after complete solvent evaporation (∼2min). . . . . 27

2.4 The change of surface tension, drop surface area, drop volume and radiusof curvature at the apex with time of a constrained sessile drop of anoctadecanol monolayer. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5 The change of surface pressure with area per molecule of a constrainedsessile drop of an octadecanol monolayer: (a) the full isotherm for differentruns; (b) the isotherm of five different runs in the vicinity of the collapsepressure (only two points per second shown). . . . . . . . . . . . . . . . 31

2.6 The change of surface pressure with area per molecule of a constrainedsessile drop of a DPPC monolayer: (a) the full isotherm; (b) the isothermin the vicinity of the collapse pressure (only two points per second shown). 32

2.7 The change of surface tension and drop surface area with time of a con-strained sessile drop of a DPPC monolayer: (a) in the vicinity of initialepisodes of collapse; (b) in the vicinity of the ultimate collapse pressure(raw data acquired at the rate of ten images per second shown). . . . . 34

2.8 The change of surface pressure with area per molecule of a constrainedsessile drop of a DPPG monolayer: (a) the full isotherm; (b) the isothermin the vicinity of the collapse pressure (only two points per second shown). 36

2.9 The change of surface pressure with area per molecule of a constrainedsessile drop of a DPPC monolayer for different runs. . . . . . . . . . . . 43

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2.10 The change of surface pressure with area per molecule of a constrained ses-sile drop of mixed DPPC/DPPG monolayers for different mixture ratios:(a) 100:0; (b) 90:10; (c) 80:20; (d) 70:30; (e) 60:40; (f) 50:50; (g) 0:100. . 44

2.11 The change of surface pressure with area per molecule on successive com-pressions and expansions of a constrained sessile drop of mixed DPPC/DPPGmonolayers for different mixture ratios: (a) 100:0; (b) 90:10; (c) 80:20. . 47

2.12 Schematic diagram of double injection ADSA–CSD experimental setupand an illustration of the exchange process. . . . . . . . . . . . . . . . . 55

2.13 Detailed engineering drawing of double injection ADSA–CSD. . . . . . . 56

2.14 Change in surface tension with time and with relative surface area duringdynamic cycling: (a) 2.0 mg/ml BLES and 0.2 mg/ml protasan (basicpreparation); (b) After replacing the bulk phase with salt solution. Allcompressions/expansions are performed at 3 s/cycle periodicity in humidair (100% R.H.). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.15 Change in surface tension with time and with relative surface area duringdynamic cycling: (a) 2.0 mg/ml BLES and 0.2 mg/ml protasan (basicpreparation); (b) After injecting 0.15 ml/ml serum into the bulk phase;(c) 2.0 mg/ml BLES and 0.2 mg/ml protasan and 0.15 ml/ml serum mixedin a separate single injection experiment. All compressions/expansions areperformed at 3 s/cycle periodicity in humid air (100% R.H.). . . . . . . . 61

2.16 Minimum surface tension (end of compression) as a function of protasanconcentration for different batches of BLES (2.0 mg/ml). All compressions(20%) are performed at 3 s/cycle periodicity in humid air (100% R.H.). 62

2.17 Change in surface tension with time and with relative surface area duringdynamic cycling: (a) After injecting 0.30 ml/ml serum into the bulk phaseof 2.0 mg/ml BLES and 0.2 mg/ml protasan; (b) 2.0 mg/ml BLES and0.2 mg/ml protasan and 0.30 ml/ml serum mixed in a separate singleinjection experiment. All compressions/expansions are performed at 3s/cycle periodicity in humid air (100% R.H.). . . . . . . . . . . . . . . . 63

2.18 Change in surface tension with time and with relative surface area duringdynamic cycling: (a) After injecting 40 mg/ml albumin into the bulk phaseof 2.0 mg/ml BLES and 0.2 mg/ml protasan; (b) 2.0 mg/ml BLES and0.2 mg/ml protasan and 40 mg/ml albumin mixed in a separate singleinjection experiment. All compressions/expansions are performed at 3s/cycle periodicity in humid air (100% R.H.). . . . . . . . . . . . . . . . 64

2.19 Change in surface tension with time and with relative surface area duringdynamic cycling: (a) After injecting 3.0 mg/ml fibrinogen into the bulkphase of 2.0 mg/ml BLES and 0.2 mg/ml protasan; (b) 2.0 mg/ml BLESand 0.2 mg/ml protasan and 3.0 mg/ml fibrinogen mixed in a separatesingle injection experiment. All compressions/expansions are performedat 3 s/cycle periodicity in humid air (100% R.H.). . . . . . . . . . . . . 65

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2.20 Change in surface tension with time and with relative surface area duringdynamic cycling: (a) After injecting 0.284 mg/ml cholesterol into the bulkphase of 2.0 mg/ml BLES and 0.2 mg/ml protasan; (b) 2.0 mg/ml BLESand 0.2 mg/ml protasan and 0.284 mg/ml cholesterol mixed in a separatesingle injection experiment. All compressions/expansions are performedat 3 s/cycle periodicity in humid air (100% R.H.). . . . . . . . . . . . . 66

2.21 Comparison of minimum surface tension for different inhibitors injectedor mixed into a basic preparation of 2.0 mg/ml BLES and 0.2 mg/mlprotasan. The dashed line shows the minimum surface tension of thebasic preparation. All compressions (20%) are performed at 3 s/cycleperiodicity in humid air (100% R.H.). . . . . . . . . . . . . . . . . . . . 67

2.22 Comparison of elasticity of compression for different inhibitors injectedor mixed into a basic preparation of 2.0 mg/ml BLES and 0.2 mg/mlprotasan. The dashed line shows the elasticity of compression of the basicpreparation. All compressions (20%) are performed at 3 s/cycle periodicityin humid air (100% R.H.). . . . . . . . . . . . . . . . . . . . . . . . . . . 68

2.23 Change in surface tension with time and with relative surface area duringdynamic cycling: (a) 0.01 ml/ml serum; (b) After injecting 2.0 mg/mlBLES and 0.2 mg/ml protasan into the bulk phase. All compressions/ex-pansions are performed at 3 s/cycle periodicity in humid air (100% R.H.).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.1 The change of surface tension and surface area with time of one cycle for2.0 mg/ml BLES at wet conditions, 37C, and 20% compression ratio witha periodicity of 3 seconds per cycle. . . . . . . . . . . . . . . . . . . . . 78

3.2 The response of surface tension to a trapezoidal change in surface areausing the new compression-relaxation model for a good (solid line) anda bad (dashed line) system: (a) the trapezoidal change of surface areawith time; (b) the response of surface tension with time for both systems;(c) the change of surface tension with the relative surface area for bothsystems. The good system (solid line) is generated using parameters: εc= 150 mJ/m2, εe = 150 mJ/m2, kr = 0.1 s−1, ka = 5 s−1. The bad system(dashed line) is generated using parameters: εc = 70 mJ/m2, εe = 70mJ/m2, kr = 0.3 s−1, ka = 0.1 s−1. . . . . . . . . . . . . . . . . . . . . . 90

3.3 The change of surface tension with the relative surface area of one cyclefor four different preparations of diluted and concentrated BLES in humid(H) and dry (D) conditions. The compression-relaxation model (CRM)predictions is compared to the experimental points. . . . . . . . . . . . . 94

3.4 The change of surface tension with time of one cycle for four differentpreparations of diluted and concentrated BLES in humid (H) and dry(D) conditions. The compression-relaxation model (CRM) predictions iscompared to the adsorption-limited model (ALM), the diffusion model(DM), and the experimental points. . . . . . . . . . . . . . . . . . . . . 95

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3.5 A special case of collapse at high surface tension of diluted BLES mixedwith albumin in humid (H) condition: (a) the change of surface tensionwith the relative surface area of one cycle; (b) the change of surface tensionand surface area with time of one cycle. CRM: compression-relaxationmodel, ALM: adsorption-limited model, DM: diffusion model. . . . . . . 97

3.6 Comparison between the goodness of fit (mean and standard deviation) ofdifferent models. CRM: compression-relaxation model, ALM: adsorption-limited model, DM: diffusion model. . . . . . . . . . . . . . . . . . . . . . 99

3.7 Comparison between the predicted value of elasticity (mean and standarddeviation) using different models. CRM: compression-relaxation model,ALM: adsorption-limited model, DM: diffusion model. . . . . . . . . . . . 100

3.8 The minimum surface tension, γmin, measured for four different concen-trations of BLES (2, 8, 15, 27 mg/ml) at different compression ratios(10%, 20%, 30%) and different cycling conditions (1, 3, 9 s/cycle). Theerror bars indicate the standard deviation between runs repeated underthe same conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

3.9 The change in surface tension with time and with relative surface areaduring dynamic cycling of BLES at 10% compression and different con-centrations and periodicities: (a) 2 mg/ml and 1 s/cyc; (b) 2 mg/ml and9 s/cyc; (c) 27 mg/ml and 1 s/cyc; (d) 27 mg/ml and 9 s/cyc. Sym-bols show the measured surface tension values and lines show the valuesobtained from CRM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

3.10 The change in surface tension with time and with relative surface areaduring dynamic cycling of BLES at 30% compression and different con-centrations and periodicities: (a) 2 mg/ml and 1 s/cyc; (b) 2 mg/ml and9 s/cyc; (c) 27 mg/ml and 1 s/cyc; (d) 27 mg/ml and 9 s/cyc. Sym-bols show the measured surface tension values and lines show the valuesobtained from CRM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

3.11 The goodness of fit for CRM measured for four different concentrationsof BLES (2, 8, 15, 27 mg/ml) at different compression ratios (10%, 20%,30%) and different cycling conditions (1, 3, 9 s/cycle). The error barsindicate the standard deviation between runs repeated under the sameconditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

3.12 The elasticity of compression, εc, calculated from CRM for four differentconcentrations of BLES (2, 8, 15, 27 mg/ml) at different compressionratios (10%, 20%, 30%) and different cycling conditions (1, 3, 9 s/cycle).The asterisks show the range of insensitivity (explained in figure 3.17):* indicate points with range of insensitivity bigger than 0.2, ** indicatepoints with range of insensitivity bigger than 0.5. . . . . . . . . . . . . . 116

3.13 The relaxation coefficient, kr, calculated from CRM for four different con-centrations of BLES (2, 8, 15, 27 mg/ml) at different compression ratios(10%, 20%, 30%) and different cycling conditions (1, 3, 9 s/cycle). Theasterisks show the range of insensitivity (explained in figure 3.17): * indi-cate points with range of insensitivity bigger than 0.2, ** indicate pointswith range of insensitivity bigger than 0.5. . . . . . . . . . . . . . . . . . 117

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3.14 The elasticity of expansion, εe, calculated from CRM for four differentconcentrations of BLES (2, 8, 15, 27 mg/ml) at different compressionratios (10%, 20%, 30%) and different cycling conditions (1, 3, 9 s/cycle).The asterisks show the range of insensitivity (explained in figure 3.17):* indicate points with range of insensitivity bigger than 0.2, ** indicatepoints with range of insensitivity bigger than 0.5. . . . . . . . . . . . . . 118

3.15 The adsorption coefficient, ka, calculated from CRM for four differentconcentrations of BLES (2, 8, 15, 27 mg/ml) at different compressionratios (10%, 20%, 30%) and different cycling conditions (1, 3, 9 s/cycle).The asterisks show the range of insensitivity (explained in figure 3.17):* indicate points with range of insensitivity bigger than 0.2, ** indicatepoints with range of insensitivity bigger than 0.5. . . . . . . . . . . . . . 119

3.16 Contour lines of the range of insensitivity for each of the parameters: (a)εc, (b) εe, (c) kr, (d) ka, at different periodicities, compression ratios andconcentrations. The calculation of the range of insensitivity is explainedin figure 3.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

3.17 Calculation of the range of insensitivity for the elasticity of the compressionεc and the adsorption coefficient ka of one cycle for 2.0 mg/ml BLES at20% compression ratio with a periodicity of 9 seconds per cycle: (a) Thechange of goodness of fit with the change of εc around the calculated valuewhile keeping the rest of the parameters (εe, kr, ka) constant. (b) Thechange of goodness of fit with the change of ka around the calculatedvalue while keeping the rest of the parameters (εc, εe, kr) constant. (c)The relative change of sensitivity with the relative change of εc. (d) Therelative change of sensitivity with the relative change of ka. The range ofinsensitivity is the range of percentage change of the parameter in whichthe sensitivity is below 1. . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.1 The change of surface tension with drop volume of a constrained sessiledrop of OMCTS formed on top of a holder with outer diameter of 7.86 mm.131

4.2 Schematic of projected areas of a pendant drop profile and a circle. . . . 135

4.3 The change of the apex curvature of a constrained sessile drop with surfacetension and drop volume for two different holder sizes: (a) outer radius of3 mm, and outer radius of (b) 6 mm. . . . . . . . . . . . . . . . . . . . 142

4.4 The change of the dimensionless apex curvature of a constrained sessiledrop with Bond number and dimensionless drop volume. The same rela-tionship can be obtained using any holder size. . . . . . . . . . . . . . . 144

4.5 The shape of a constrained sessile drop for different holder sizes and surfacetension values. Bond number is indicated on top of every figure. Theopen symbols indicate a drop profile with a small volume, while the solidsymbols symbols that with a large volume. The lines indicate the bestcircle that fit the profile. . . . . . . . . . . . . . . . . . . . . . . . . . . 145

4.6 The change of the shape parameter of a constrained sessile drop withBond number and dimensionless drop volume. The same relationship canbe obtained using any holder size. . . . . . . . . . . . . . . . . . . . . . 147

xiii

4.7 Schematic diagram of ADSA–CSD experimental setup. . . . . . . . . . . 149

4.8 The change of surface tension, drop surface area, drop volume, and thecurvature at drop apex with time of a constrained sessile drop of OMCTSformed on top of a holder with outer diameter of 7.86 mm. . . . . . . . 150

4.9 The error in surface tension measured by ADSA as a function of the shapeparameter for different drop sizes of a constrained sessile drop of OMCTSformed on top of a holder with outer diameter of 7.86 mm. For a maximumerror of ±0.1 mJ/m2, the critical shape parameter is 0.018. . . . . . . . 152

4.10 The error in surface tension measured by ADSA as a function of the shapeparameter for different drop sizes of a constrained sessile drop of: (a)OMCTS formed on top of a holder with outer diameter of 6.55 mm, and(b) DEP formed on top of a holder with outer diameter of 7.86 mm. Fora maximum error of ±0.1 mJ/m2, the critical shape parameters are 0.026and 0.027, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

4.11 The critical shape parameter as a function of the Bond number. Theexperimental points were fitted to a linear function (continuous line). . . 156

4.12 The change of the apex curvature of a pendant drop with surface tensionand drop volume for two different holder sizes: (a) outer radius of 1.5 mm;(b) outer radius of 3 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . 160

4.13 The change of the dimensionless apex curvature, bd, of a pendant dropwith Bond number, Bo, and dimensionless drop volume, Vd. The Bondnumber, Bo = ∆ρgR2

h/γ, is the ratio of body forces (gravitational) tosurface tension forces using the holder’s radius as the length scale. . . . . 161

4.14 The shape of a pendant drop for different holder sizes and surface tensionvalues. Bond number is indicated on top of every figure. The symbolsindicate the drop profile, and the lines indicate the best circle that fit theprofile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

4.15 The change of the shape parameter of a pendant drop with Bond numberand dimensionless drop volume. . . . . . . . . . . . . . . . . . . . . . . 164

4.16 The change of (a) the maximum dimensionless drop volume, and (b) theapparent contact angle of a pendant drop with Bond number. . . . . . . 166

4.17 The shape of a pendant drop with the maximum dimensionless drop vol-ume for different Bond numbers. The symbols indicate the drop profile,and the lines indicate the best circle that fit the profile. . . . . . . . . . 168

4.18 The change of the shape parameter of pendant drops with the maximumdimensionless drop volume with Bond number. . . . . . . . . . . . . . . 169

4.19 Schematic diagram of ADSA–PD experimental setup. . . . . . . . . . . 170

4.20 The change of surface tension, drop surface area, drop volume, and thecurvature at drop apex with time of a pendant drop of hexadecane formedusing a holder with outer diameter of 6.25 mm. . . . . . . . . . . . . . . 172

4.21 The error in surface tension measured by ADSA as a function of the shapeparameter for different drop sizes of a pendant drop of hexadecane formedusing a holder with outer diameter of 6.25 mm. For a maximum error of±0.1 mJ/m2, the critical shape parameter is 0.04. . . . . . . . . . . . . 173

xiv

4.22 The error in surface tension measured by ADSA as a function of the shapeparameter for different drop sizes of a pendant drop of: (a) hexadecaneformed using a holder with outer diameter of 4.24 mm, and (b) DEPformed using a holder with outer diameter of 4.24 mm. For a maximumerror of ±0.1 mJ/m2, the critical shape parameters are 0.052 and 0.039,respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

4.23 The critical shape parameter as a function of the Bond number. Theexperimental points were fitted to a linear function (continuous line). . . 177

4.24 The change of surface tension with time of a pendant drop of hexadecaneformed using a holder with outer diameter of 6.25 mm. The calculationsare repeated using different software options; ADSA: the default optionsusing Canny for edge detection and Levenberg-Marquardt for optimiza-tion; ADSASUS: SUSAN is used instead of Canny; ADSANM : Nelder-Mead is used instead of Levenberg-Marquardt; TIFA: theoretical imagefitting analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

4.25 The error in measured surface tension as a function of the shape parameterfor different drop sizes of a pendant drop of hexadecane formed using aholder with outer diameter of 6.25 mm. The calculations are repeatedusing different software options; ADSA: the default options using Cannyfor edge detection and Levenberg-Marquardt for optimization; ADSASUS:SUSAN is used instead of Canny; ADSANM : Nelder-Mead is used insteadof Levenberg-Marquardt; TIFA: theoretical image fitting analysis. . . . . 183

A.1 General classification of commercial lung extracts. . . . . . . . . . . . . 220A.2 Extraction procedure for surfactants extract of lung lavage. . . . . . . . 221A.3 Extraction procedure for surfactants extract of lung tissue. . . . . . . . 222A.4 Composition of natural surfactants extracts. . . . . . . . . . . . . . . . . 223A.5 Composition of synthetic surfactants. . . . . . . . . . . . . . . . . . . . 227

xv

Chapter 1

Introduction

1.1 Overview

The significance of interfacial and capillarity phenomena in surface science has been

increasingly recognized in recent years. These phenomena occur whenever a liquid is

in contact with another fluid or solid. Common examples are menisci, liquid drops

formed in either air or another liquid, and thin films such as soap bubbles. Surface

phenomena play an important role in many engineering applications and technologies

including biotechnology, surface engineering, and micro/nanotechnology.

In the present context, the goal is to adapt a methodology for surface tension measure-

ment called Axisymmetric Drop Shape Analysis (ADSA) to a biomedical development in

the area of lung physiology, specifically lung surfactant, i.e., the material that coats and

facilitates the functioning of the lungs of all mammals. A brief overview of lung surfactant

is given first followed by a discussion of surface tension measurement techniques.

Lung surfactants are mixtures of lipids and proteins which form a thin surface film or

a monolayer at the alveolar liquid-air interface. The key property of a functioning lung

surfactant is its surface tension. This film modulates the surface tension of the lung,

lowering the normal air-water surface tension of approximately 70 mJ/m2 to extremely

1

Chapter 1. Introduction 2

low values below 1 mJ/m2. By lowering and varying the surface tension during breathing,

lung surfactant reduces the work needed for respiration and stabilizes the alveoli against

collapse and overexpansion [1]. The extremely low surface tension values are difficult to

measure; but certain techniques are capable of performing such measurements.

Deficiency of the lung surfactant, due to injury or lack of development in premature

babies, is a relatively frequent cause of death. The lack of effective surfactant in pre-

mature babies results in neonatal respiratory distress syndrome (nRDS). This is usually

treated clinically by surfactant replacement therapy using surfactant preparations such as

Bovine Lipid Extract Surfactant (BLES). Acute respiratory distress syndrome (ARDS) is

a frequent, life-threatening disease in which a significant increase in alveolar surface ten-

sion has been observed. However, in this case, it is known that poor performance of the

surfactants used for ARDS patients is due to inhibition or inactivation of the surfactant

by plasma proteins and lipids.

Drop shape techniques, based on the shape of a pendant drop, sessile drop or captive

bubble, are extensively used for surface tension measurement. Early efforts in the analysis

started by understanding the shapes of pendant drops and predicting the shapes for a

given surface tension value [2]. Later, certain dimensions of the shape were tabulated

along with the corresponding surface tension value. Consequently, the surface tension can

be calculated through interpolation using these tables [3]. A more sophisticated method

was later developed based on comparing a number of selected and measured points on the

drop periphery to calculated drop shapes and hence determine the surface tension [4, 5].

An alternative method uses a semi-empirical equation to approximate surface tension

from the total height and maximum diameter of a sessile drop or captive bubble [6].

The shape of the drop/bubble depends on the balance between gravity and surface

tension. The balance between surface tension and external forces, e.g. gravity, is reflected

mathematically in the Laplace equation of capillarity. When gravitational and surface

tension effects are comparable, then, in principle, one can determine the surface tension


from an analysis of the shape of the drop/bubble. The surface tension tends to round the

drop, whereas gravity deforms it, i.e. gravity elongates a pendant drop or flattens a sessile

drop. Whenever the surface tension effect is much higher than the gravitational effect, the

shape tends to become spherical in the case of both pendant and sessile drops/bubbles.

Theoretically, each drop shape corresponds to a certain surface tension value.

Axisymmetric Drop Shape Analysis (ADSA) [7–11] is a drop shape technique now

extensively used for surface tension and contact angle measurement. ADSA, based on

the shape of liquid/fluid interfaces, is complex but is adaptable to a variety of experi-

mental circumstances including pendant drops, sessile drops and bubbles. Briefly, ADSA

matches the drop/bubble profile extracted from experimental images to a theoretical

Laplacian curve for known surface tension values using a nonlinear optimization pro-

cedure [7–9]. An objective function is used to evaluate the discrepancy between the

theoretical Laplacian curve and the actual profile. This objective function is the sum

of the squares of the normal distances between the measured points (i.e. experimental

curve) and the calculated curve [9]. The optimization procedure minimizes the objective

function and, hence, finds the surface tension value corresponding to the extracted profile

from experimental images.

In this thesis, the goal is to adapt ADSA to biomedical lung surfactant development.

Certain configurations of ADSA are capable of measuring the extremely low surface ten-

sion values which are observed. Although these configurations are capable and most

suitable for surface tension measurement of lung surfactants, they had unexplored po-

tential to allow for more extensive evaluation of surface properties. Three main needs

arise in this area: First, access to the interface through the gas and liquid phases is

needed to evaluate the role that lipids, gases and inhibitors play in the surface activity

of lung surfactants. Second, a method to identify a set of characteristic properties of

the surfactant preparations is needed in a way that they are independent of compression

conditions and that can be used to compare the surface activity of different formula-


tions. Finally, given that the surface tension of lung surfactants changes in a dynamic

experiment, it is necessary to confirm the accuracy of the surface tension measurements

obtained via ADSA. Therefore, three main areas are developed in this thesis in response

to these needs: First, the hardware is redesigned to allow complete access to the interface

from both the air and liquid sides. Second, a detailed analysis of the dynamic surface

tension measurements is used to evaluate the intrinsic properties of the lung surfactant

film. These film properties are elasticity, relaxation and adsorption. Finally, the accuracy

of the surface tension measurements is analyzed and has been re-evaluated. Based on

this analysis, the design of certain configurations of ADSA can be optimized to facilitate

more accurate surface tension measurements.

1.2 Background

In this section a detailed background is provided for the different techniques of surface

tension measurements and natural lung surfactant. In Section 1.2.1, various in vitro tech-

niques for the evaluation of surface tension of lung surfactants are discussed. Section 1.2.2

provides more background on the composition of natural lung surfactant.

1.2.1 Evaluation of Surface Tension

Various methods and techniques have been developed for evaluating the surface activity

of lung surfactants. These methods usually belong to one of three categories: in vitro,

in situ, and in vivo techniques. In vivo techniques involve experimentation done on

the living lung of an animal. In contrast to the surface tension as an output from in

vitro and in situ techniques, the main outputs of in vivo techniques are usually the lung

compliance (the ability of the lungs to stretch due to a change in volume as a function of

an applied change in pressure) and blood oxygenation (the partial pressure of oxygen in

blood sample). Different animal models have been developed to evaluate the efficiency


Figure 1.1: Schematic diagram of a Langmuir-Wilhelmy Balance (LWB).

of a lung surfactant preparation on premature and adult animals. In situ techniques are

used to estimate the alveolar surface tension in excised lungs, i.e. in its natural setting

without moving it to some special medium. In situ techniques are usually considered as

an intermediate between in vivo and in vitro.

The focus of this thesis is the in vitro techniques for the evaluation of surface tension

of lung surfactants. These are the most commonly used techniques for assessing their

performance. In such techniques, the surface properties (such as the minimum surface

tension and adsorption rates at a specific cycling conditions) of the lung surfactants are

assessed by measuring the surface tension in a controlled environment experiment. In

this section, various in vitro techniques are discussed.

1.2.1.1 Langmuir-Wilhelmy Balance

In a Langmuir-Wilhelmy Balance (LWB) [12–17] an insoluble surfactant monolayer is

spread on top of a liquid subphase filling a trough, and then compressed by means of

hydrophobic barriers on the surface. During compression, surface pressure is typically

monitored by a Wilhelmy plate system as shown in figure 1.1.


The net force acting on the Wilhelmy slide is the sum of forces from surface tension,

gravity and buoyancy; this net force can be calculated as follows:

F = 2γ(W + T ) cos θ + (WTL)ρsg − (WTh)ρwg (1.1)

where W , T , and L are the width, thickness and length of the slide, h is the wetted

height of the slide, γ is the surface tension of the interface, θ is the contact angle, g is the

gravitational acceleration, ρs is the density of the slide material, and ρw is the density of

the subphase.

More commonly, a modified expression is used giving the difference in force (∆F ) be-

tween the case of the slide in pure subphase (no surfactant) and the case where surfactant

is present at the interface,

∆F = 2(γo − γ)(W + T ) cos θ (1.2)

where γo is the surface tension of the pure subphase and γ is the surface tension of

subphase with surfactant at the interface. This modified expression can also be expressed

in terms of surface pressure,

π = γo − γ =∆F

2(W + T ) cos θ(1.3)

Equation 1.3 is usually simplified by assuming the the slide thickness T is negligible

compared to the slide width W , and by assuming complete wetting so that the contact

angle is zero, i.e. cos θ = 1.

The Langmuir film balance has been widely used to study the π-A isotherm of many

spread monolayers including octadecanol [18], dipalmitoyl-phosphatidyl-choline (DPPC)

[19, 20], and dipalmitoyl-phosphatidyl-glycerol (DPPG) [21, 22]. It has been also used

for adsorbed films [14, 17]. The main advantages of this method are accurate control


of molecular area, easy integration with microscopy techniques such as Brewster Angle

Microscopy (BAM) and Atomic Force Microscopy (AFM), and wide commercial avail-

ability.

However, the Langmuir film balance has some limitations. First, it requires a rel-

atively large amount of liquid sample, usually no less than several tens of milliliters.

Second, it only allows relatively slow compression-expansions approximately 5 minutes

per cycle [1] as fast cycling creates waves at the air-water interface, which interfere with

the surface tension measurement. This limitation becomes significant in the study of

lung surfactant where experiments should mimic the frequency of the normal breathing,

i.e. human respiration action, at high rates of approximately 1.5 to 3 seconds per cycle

[1].

The third limitation is film leakage. Since lung surfactant and phospholipid films can

reach very low surface tensions (e.g. < 5 mJ/m2) under dynamic compression, the liquid

subphase is able to wet even very hydrophobic materials such as Teflon, the material out

of which most film balances are constructed. Film leakage may occur both at the trough

walls and at the barriers, either above the water level (at the air-solid interfaces) or below

the water level (at the liquid-solid interfaces, in the case of soluble surfactants). Leakage

at the air-solid interfaces can be reduced using tightly fitted barriers [23] or continuous

Teflon ribbons [14, 24]. Leakage at the liquid-solid interfaces can be reduced by priming

the Teflon walls with an alcoholic solution of lanthanum-chloride and long-chain satu-

rated phosphatidyl-choline [16]. A fourth limitation is the difficulty of controlling the

environmental conditions (temperature and humidity) during the experimentation [25].

1.2.1.2 Pulsating Bubble Surfactometer

In a Pulsating Bubble Surfactometer (PBS) [26–32] an air bubble is formed in a surfactant

suspension by drawing atmospheric air through a capillary tube as shown in figure 1.2.

After adsorption of surfactant, the bubble is pulsated between two set positions. The


Figure 1.2: Schematic diagram of a Pulsating Bubble Surfactometer (PBS).

bubble radius is usually monitored, while the pressure in the subphase is measured by

a pressure transducer. The surface tension, γ, is calculated from the measured values

of the pressure drop, ∆P , and the bubble radius, R, using the Laplace equation and

assuming a spherical shape,

γ =(∆P )R

2. (1.4)

This method has several advantages: it is a simple setup and easy to use, it requires

only a small volume of subphase, and it is available commercially. PBS allows fast cycling

to mimic the physiological conditions. A further development of a bulk phase exchange

system for PBS facilitates the study of the effect of a specific inhibitor on a preformed

surfactant film [33]. This system has been used to characterize the inhibition mechanisms

of different inhibitors [33–35].

However, film leakage from the bubble surface into the capillary tube at low surface

tensions is again a common complication [36]. Other limitations are the inaccurate

calculation of low surface tension values due to the spherical shape assumption [27], and


Figure 1.3: Schematic diagram of a Captive Bubble Surfactometer (CBS).

the difficulty of controlling the environmental conditions (specially humidity) which are

essential in lung surfactant studies.

1.2.1.3 Captive Bubble Surfactometer

In a Captive Bubble Surfactometer (CBS) [28, 37–43] an air bubble is formed in a closed

chamber filled with surfactant suspension. The air bubble floats against a hydrophobic

ceiling coated with 1% agarose gel as shown in figure 1.3. After film formation (spreading

or adsorption), the bubble can be dynamically compressed by changing the chamber

pressure.

In this case, the bubble is not expected to be spherical due to the relatively large

size compared to PBS. The shape of the interface is controlled by the balance between

surface tension forces and gravity as given by the Laplace equation,

γ(1

R1

+1

R2

) =2γ

R0

+ (∆ρ)gz (1.5)

where R1 and R2 are the principal radii of curvature at a point on the interface, R0 is


the symmetric radius of curvature at the apex point of the interface, ∆ρ is the density

difference across the interface, g is the local gravitational acceleration, and z is the

vertical distance between the apex point and the point on the interface. Therefore, the

surface tension value, γ, can be determined from the shape of the interface. In CBS, the

height-to-diameter ratio of the bubble is used to calculate surface tension, bubble area,

and volume [40].

The CBS has all the advantages of the PBS setup and solves the problem of leakage

because the bubble is not in contact with any solid surfaces. Interpretation of CBS

does not assume a spherical shape. Nevertheless, the captive bubble film balance has

some limitations. First, any study that requires spreading of a monolayer on the bubble

interface is not trivial. Second, the small volume of the air bubble complicates the

evaporation of the spreading solvent in the study of spread films; the non-evaporated

portion of the solvent will influence the performance of the monolayer at the interface

[44, 45]. Also, controlling the humidity in a captive bubble is relatively difficult and it

is known that such environmental conditions are vital and have significant effect on lung

surfactant films [46, 47]. Another limitation is that it is inoperable at the high surfactant

concentrations used clinically due to visual opaqueness of lung surfactant preparations

at high concentrations (> 3 mg/ml) [48]. Recent experiments use sub-phase spreading

of highly concentrated suspensions near the interface [49]; however, the validity of that

approach is yet to be determined particularly in the presence of water-soluble/dispersable

surfactant inhibitors.

1.2.1.4 ADSA–CB

Axisymmetric Drop Shape Analysis (ADSA) has been used for measuring surface tension

and contact angles [7–9]. Currently, there exist three constellations of ADSA for surface

tension measurements: a captive bubble (ADSA–CB), a pendant drop (ADSA–PD) and

a constrained sessile drop (ADSA–CSD) as shown in figure 1.4. There is also the un-


Fig

ure

1.4:

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constrained sessile drop constellation (ADSA–SD) that is used mainly for contact angle

measurements [50–52]. As mentioned earlier, ADSA software extracts an experimental

drop profile from a digitized drop/bubble image and uses an optimization procedure to

match the extracted profile to a theoretical one calculated from the Laplace equation

of capillarity. The surface tension of the bubble/drop is then calculated based on the

matched theoretical profile. Other outputs of ADSA are drop volume, drop surface area,

contact angle (if applicable), and radius of curvature at the drop/bubble apex.

The first embodiment of ADSA working in conjunction with a Captive Bubble (ADSA–

CB) [41, 46, 47, 53–56] has a very similar setup compared to CBS as shown in figure 1.4.

However, ADSA–CB uses the more accurate and automatic ADSA software for deter-

mining the surface tension, surface area and volume from a bubble image, rather than

just using the height-to-diameter ratio of the bubble needed in CBS. The technique has

now been widely used for soluble films [46, 47], and also as a film balance, especially for

DPPC [44, 45, 57, 58].

ADSA–CB has the same advantages as CBS but provides a greater accuracy in the

calculation of the surface tension and faster data acquisition and processing. On the other

hand, ADSA–CB has the same limitations as CBS: the setup is not trivial especially for

spread films, it is inoperable at the high surfactant concentrations (> 3 mg/ml) used

clinically as the solutions are usually opaque, and controlling the humidity is relatively

difficult.

1.2.1.5 ADSA–PD

A second embodiment of ADSA working in conjunction with a Pendant Drop (ADSA–

PD) [59–63] has also been developed. In this method, a pendant drop of surfactant

suspension is formed at the end of a teflon capillary tube as shown in figure 1.4. Surface

tension, surface area and drop volume are calculated by ADSA. Alternatively, a small

flat circular holder (inverted pedestal) with a sharp-knife edge is used instead of the


capillary [59, 64]. This holder was introduced originally in the constrained sessile drop

constellation as will be explained later, and was later used in ADSA–PD for studying

surfactant films at the interface to prevent the film from spreading on to the solid surface

at low surface tension. In addition to the apparent advantages of simplicity and flexibility,

the pendant drop method is believed to have very high accuracy [59].

ADSA–PD has been used extensively to study the π-A isotherm of several monolayers

including octadecanol [59, 65], Dipalmitoyl-phosphatidyl-choline (DPPC) [62, 66–69],

and Dipalmitoyl-phosphatidyl-glycerol (DPPG) [70]. In this method, a pendant drop is

formed at the end of a teflon capillary tube and a known amount of insoluble substance

is spread onto its surface. The π − A isotherms are generated by changing the drop

volume in a controlled manner causing a decrease in the drop surface area and hence

compression of the film. ADSA–PD is able to achieve high rates of compression and

hence has advantages over a Langmuir film balance for certain studies. Nevertheless, the

method still has some limitations. The deposition procedure used in the pendant drop

constellation is not straightforward. This deposition can be performed in one of two ways;

in both strategies, the surfactant solution is delivered through a micro syringe needle. In

one strategy, the needle is brought as close as possible to the side of the hanging drop;

but apparently, penetration of the needle into the bulk phase was inevitable [67] and the

molecules are deposited into the bulk phase and it is uncertain whether they all diffuse

to the surface. In the alternative procedure, the needle is used to deposit the surfactant

solution on the teflon capillary above the pendant drop. The solution then flows down

over the drop surface. Remaining surfactant molecules on the teflon capillary can lead

to overestimation of the number of molecules deposited [68].

ADSA–PD was further developed to be used as a penetration film balance using an

arrangement of two co-axial capillaries connected to two branches of a microinjector [60].

This system allows the bulk phase exchange after forming a stable film and was used to

study the interfacial hydrolysis of mixed phospholipid monolayers by porcine pancreatic


phospholipase A2 [60]. Although ADSA–PD eliminates the surfactant concentration

limitation, it can suffer from film leakage at low surface tensions [59]. Another limitation

at low surface tension values is that although gravity assures a well deformed drop shape,

it also tends to detach the drop from the capillary holder in the case of big drops [71].

1.2.1.6 ADSA–CSD

A third embodiment of ADSA working in conjunction with a Constrained Sessile Drop

(ADSA–CSD) [48, 72–75] is now extensively used for determining the dynamic surface

tension of lung surfactants. In this setup, a sessile drop is formed on top of a small

flat pedestal (holder) with a circular sharp knife edge preventing uncontrolled spreading

and hence film leakage (figure 1.4). The sharp edge acts as a barrier to spreading. The

mechanism of this barrier is readily understood in terms of what may be called Young’s

inequality, a generalization of the Young equation: If the three phase line approaches

an edge, Young’s equation will be obeyed. When reaching the edge, motion of the three

phase line will cease and the contact line will not move until the drop has become much

larger. During this time, the apparent contact angle increases. When the contact angle

becomes so large that it becomes equal to the Young angle on the adjacent surface, motion

of the three phase line will continue, and, from the point of view of the surface tension

measurement, undesirable processes occur, such as film spreading. However, there will be

a large range of drop sizes over which the volume of the drop can be changed at virtually

constant drop diameter, offering an opportunity for film balance type of work. Hence,

the apparent contact angle will change with the drop volume.

This holder was introduced originally for the study of density and surface tension of

polymer melts [73]. Due to the presence of the sharp edge, ADSA–CSD proved to be

very suitable for a wide range of surface tension measurements including very low values,

down to below 1 mJ/m2, that are difficult to measure with other setups. ADSA–CSD

is used to perform dynamic cycling by successive compression/expansion of the drop via


programmed cycling of the drop volume. This is usually done through several cycles

(normally 20) with prescribed periodicity and compression ratio (percentage of surface

area reduction). In such experiments, a large amount of data is collected including the

surface tension as a function of time as well as the change of the drop surface area and

volume.

ADSA–CSD has been used so far only for the study of films adsorbed from solution

(soluble films). Matters such as the effect of humidity on film formation [25], and the

development of polymeric additives for clinical lung surfactants [76] have been considered.

ADSA–CSD studies were performed at the high rates of compression which mimic human

breathing and which are not achievable using a Langmuir setup. A specially-designed

environmental control chamber for ADSA–CSD facilitates the control of gas composition,

temperature and humidity to mimic the physiologically relevant conditions.

ADSA–CSD is believed to be free of all restrictions and limitations of other conven-

tional methods. The main advantages are that it is very simple to setup and is easy

to use and only small liquid volumes (microliter drops) are required to perform very

accurate surface tension measurements. In the context of lung surfactants, ADSA–CSD

is capable of simulating physiological conditions in the lungs, i.e. the cycling rate to

simulate breathing, environmental and temperature conditions. However, ADSA–CSD

has no concentration limitation of surfactant suspension. Other unexplored potentials:

it is possible to perform high frequency cycling and it is possible to access the air/liquid

interface from both sides to allow spreading and bulk replacement. Although such poten-

tial would be useful, especially in the lung surfactant context, it has not been explored

so far.

1.2.2 Pulmonary Surfactants

Pulmonary surfactants are mixtures of lipids and proteins forming a monolayer at the

alveolar liquid-air interface. Pulmonary surfactant consists of about 90% lipids and about


10% proteins. Four surfactant apoproteins are present in native surfactants, called SP-A,

SP-B, SP-C, and SP-D. Approximately 10-20% of the lipids are neutral, and the rest (80-

90%) are phospholipids (PL). Phosphatidylcholine (PC) is the predominant PL species

(about 80%) followed by phosphatidylglycerol (PG) which comprises more than 10% of

PL. Dipalmitoylphosphatidylcholine (DPPC) comprises about 50% of PC, i.e. about

40% of the total PL. The other main lipid component is dipalmitoylphosphatidylglycerol

(DPPG) which comprises almost 10-40% of PG [1, 36, 77, 78]. Native human lung

surfactant is near the high end of these percentages. [78]

A brief review of the commercial exogenous lung extracts is also provided in Ap-

pendix A. Commercial lung extracts are divided into two main categories according to

the source of the preparation: natural lung surfactants which contain exogenous lung

extracts from animals and synthetic lung surfactants which do not contain any natural

extracts. In this thesis, a clinical exogenous lung surfactant called Bovine Lipid Extract

Surfactant (BLES) is chosen as a model lung surfactant. BLES is made from lung sur-

factant lavaged from cows and is produced locally in Canada. A detailed list of other

clinically used lung surfactants worldwide is given Appendix A. It is noted that DP-

PC/PG mixtures are used as the main component of many clinical synthetic exogenous

lung surfactants, e.g. ALEC (artificial lung expanding compound) [79–81], Surfaxin (KL4

or lucinactant) [82–84], and Venticute (Recombinant SP-C or lusupultide) [85–87].

1.3 Scope and Purpose of Thesis

The objective of this thesis is to further develop and automate ADSA–CSD to allow fur-

ther studies of lung surfactants. As discussed in Section 1.2.1, ADSA–CSD can be applied

– in principle – to lung surfactant studies at relevant physiological conditions which in-

clude appropriate temperature, relative humidity, gas composition, pollution, surfactant

concentration, respiration periodicity, and compression ratio. Until now, ADSA–CSD


has been used only for the study of films adsorbed from solution (soluble films) and

matters such as the effect of humidity on film formation [25], and the development of

polymeric additives for clinical lung surfactants [76] have also been considered. However,

ADSA–CSD had some unexplored and undiscovered potential which will be addressed

here. The use of ADSA as a film balance was so far done using the pendant drop constel-

lation and there were considerable experimental difficulties [59] that can be avoided in a

constrained sessile drop setup. In this thesis, ADSA–CSD is redesigned to allow access

to the air-liquid interface from either side.

In clinical reality, lung surfactant films can be altered from both the airspace and the

bulk liquid phase that carries the film. Contaminations (pollution) affect the surfactant

interface from the air side and treatment (surfactant therapy for premature babies) is

instilled from the air side, while leakage of plasma and blood proteins usually occurs from

the liquid side, causing severe lung injury. Such inhibitors degrade the surface activity

of the surfactant by impairing the adsorption and the surface tension lowering abilities

of the surfactant. Therefore, accessing the lung surfactant interface from both sides is a

necessary feature in a general in vitro technique used for the assessment of the surface

activity of lung surfactant. In Chapter 2, ADSA–CSD is redesigned to be used as a micro

film balance allowing access to the interface from both the gas-side and the liquid-side.

This allows deposition from the gas side as well as complete exchange of the bulk liquid

phase. The key feature of the design is the insertion of a second capillary into the bulk

of the drop to facilitate addition or removal of a secondary liquid. The new design is

used to study lung surfactant inhibition resistance (subphase injection of inhibitor under

an uninhibited film) and inhibition reversal (subphase injection of surfactant under an

inhibited film). The access from the air-side is illustrated by a series of experiments of

the collapse surface pressure of spread pure monolayers of DPPC and DPPG (the main

constituents of lung surfactants).

To asses the performance of surfactant preparations subject to dynamic compres-


sion/expansion, typically only the minimum surface tension at the end of compression is

reported. While the minimum surface tension is useful for a preliminary assessment, it

must be realized that it depends on the compression protocol [46]. Therefore, it is neces-

sary to concentrate on the properties of the film itself such as its elasticity, its formation

(adsorption) and its stability (or relaxation tendency) in addition to, if not in place of,

the minimum surface tension. In Chapter 3, a dynamic compression-relaxation model

(CRM) is developed to describe the mechanical properties of lung surfactant films by

investigating the response of surface tension to changes in surface area. The model treats

the compression/expansion with the conventional definition of dilatational elasticity of

insoluble surfactants, and treats the relaxation and adsorption of the film as first order

processes driven by the excess surface free energy of the film. The model is used to eval-

uate the quality of lung surfactant preparations based on calculating the film properties

independent of the compression protocol used.

The accuracy of the determined mechanical properties of lung surfactant films depends

on the accuracy of the measured response of surface tension to changes in surface area.

Therefore, high accuracy surface tension measurements are necessary in such studies. It

is well documented that the accuracy of the surface tension determined by ADSA can

depend on drop size, unless all drops of different sizes are well deformed and far from

spherical [64]. A detailed analysis of constrained sessile drop shapes and the accuracy

of the measured surface tension values is developed using a shape parameter concept in

Chapter 4. Dimensional analysis is used to describe similarity in constrained sessile drop

shapes and to express the problem using appropriate dimensionless groups. Based on this

analysis, the design of ADSA–CSD is optimized to facilitate more accurate surface tension

measurements. The validity analysis is further extended to the pendant drop (ADSA–

PD). This setup is the most frequently used and most accurate drop shape technique for

surface tension measurement outside the area of lung surfactants.

Chapter 2

ADSA-CSD as Micro Film Balance∗

2.1 Introduction

ADSA–CSD has been extensively used for the study of lung surfactants [91]. Matters such

as the effect of humidity on film formation [25], and the choice of polymeric additives for

clinical lung surfactants [76] have been considered. ADSA–CSD studies were performed

at high rates of compression (to mimic human breathing in lung surfactant studies). A

specially-designed environmental control chamber for ADSA–CSD facilitates the control

of gas composition, temperature and humidity to mimic the physiologically relevant con-

ditions [25]. ADSA–CSD is believed to be free of all restrictions and limitations of other

methods as mentioned in detail in Chapter 1.

However, certain studies cannot be readily performed using the current ADSA–CSD

setup. In the lung surfactant context, certain insoluble molecules such as DPPC and

DPPG are closely related to the surface activity of pulmonary surfactant as shown in

Chapter 1. The study of these insoluble molecules is essential in understanding the

surface properties of lung surfactants. Studying lung surfactant inhibition is also an

important aspect. Such studies are introduced here by removing the bulk phase, after

∗Portions of this chapter were previously published in Refs. [88–90], reproduced with permission.

19

Chapter 2. ADSA-CSD as a Micro Film Balance 20

forming a sessile drop of a basic lung surfactant preparation, and exchanging it for one

containing different inhibitors. This mimics the leakage of plasma and blood proteins into

the alveolar spaces altering the surface activity of lung surfactant in a phenomenon called

surfactant inhibition. These studies cannot be performed using the current ADSA–CSD

setup.

In response to these needs, two main capabilities are added to the ADSA–CSD setup.

The first one is the deposition capability allowing deposition of molecules onto the air/wa-

ter interface from the air side. This allows the study of the collapse of deposited films

through the study of pure monolayers as well as mixed monolayers. DPPC and DPPG

monolayers are studied here to characterize the role of such molecules in maintaining

stable film properties and surface activity of lung surfactant preparations. The second

capability is the double injection, facilitating the complete exchange of the subphase of

a spread or adsorbed film from the liquid side. This feature allows certain studies rele-

vant to lung surfactant research that cannot be readily performed by other means. The

development will be illustrated through studies concerning lung surfactant inhibition.

The redesigned ADSA–CSD is a versatile tool for surface tension measurements that

has a wide range of applications outside the scope of the lung surfactant research area.

For example, the deposition capability allows for the study of properties of insoluble films

such as film relaxation and collapse and interfacial dilational elasticity. The double in-

jection capability allows studies on the interaction between a monolayer and a surfactant

dissolved in the subphase.

2.2 Deposition Capability

The collapse pressure is the highest surface pressure to which a monolayer can be com-

pressed without detectable expulsion of molecules into a new phase [92]. Experimen-

tally, it was found that many monolayers can be compressed to pressures considerably


higher than their equilibrium spreading pressure [1, 92, 93]. Eventually, however, it was

found impossible to increase the surface pressure further. If compression continues, the

monolayer collapses ejecting surfactant molecules into one or more surface or subsurface

collapse structures or phases [1, 93]. Monolayer collapse is accompanied by a change in

slope or by a horizontal plateau in the surface pressure/area π-A isotherm. The surface

pressure, π, can be computed by calculating the difference between the surface tension

of the pure liquid (without an insoluble monolayer spread at the interface), γo, and the

surface tension with the monolayer spread at the interface, γ, i.e. π = γo − γ.

These isotherms are measured with a surface balance or a film balance. Film balances

have been used to study monolayer properties for different substances, such as the collapse

pressure. The collapse pressure is used as an indication of the monolayer stability; the

higher the collapse pressure, the more stable the monolayer. The first film balance was

developed by Langmuir [12] and modified subsequently by others [92, 93]. The Langmuir

film balance suffers from three main limitations as indicated in detail in Chapter 1. First,

it requires a relatively large amount of liquid sample. Second, it only allows relatively

slow compression-expansions. Third, it suffers from film leakage especially at very low

surface tensions (very high surface pressures). These limitations become significant in

the study of lung surfactant.

The pendant drop and the captive bubble techniques have also been used to study

the π-A isotherm of several monolayers as shown in Chapter 1. Nevertheless, both

techniques have one or more of the following limitations when used as as film balance.

In both techniques, the deposition procedure to spread a monolayer on the bubble/drop

interface is neither straightforward nor trivial. In the pendant drop technique, film

leakage usually occurs at low surface tensions (high surface pressures); and gravity tends

to detach the drop from the capillary holder in the case of big drops [71]. In the captive

bubble technique, controlling the humidity is a difficult matter. More details regarding

these limitations were given in Chapter 1.


ADSA–CSD has been used so far only for the study of films adsorbed from solution

(soluble films). Here, the usage of ADSA–CSD as a film balance is illustrated. The fact

that the drop is sitting on a pedestal makes the deposition near the drop apex much

easier compared to the case of the pendant drop. Another feature is that gravity will

cause the drop to be well deformed at very low surface tension values; this guarantees

high accuracy of ADSA calculations, especially in the vicinity of the collapse pressure,

where very low surface tension values exist. Using ADSA–CSD, the collapse region will

be studied carefully to gain insight into the collapse details of three different monolayers:

octadecanol, dipalmitoyl-phosphatidyl-choline (DPPC), and dipalmitoyl-phosphatidyl-

glycerol (DPPG).

The reason for choosing DPPC and DPPG is their relevance to pulmonary surfactant

studies as shown in Chapter 1. In the literature, a DPPC/DPPG mixture ratio of 80:20

was used in several studies to mimic natural lung surfactant lipids [94–98]. This ratio

is usually selected because it is similar to the ratio found in a variety of mammalian

lung surfactant extracts. Other studies have used a ratio of 70:30 [99, 100]. Most of

these studies (using a ratio of 80:20 or 70:30) have focused on investigating the effect of

surfactant proteins (SP-A, SP-B, and SP-C) on the properties of a model lung surfactant

composed of only DPPC and DPPG at the specified ratio. Properties at the very high

surface pressures which occur in the lungs were not investigated in any of these studies.

DPPC/PG mixtures are also used as the main component of many clinical synthetic

exogenous lung surfactants, e.g. ALEC (artificial lung expanding compound) [79–81],

Surfaxin (KL4 or lucinactant) [82–84], and Venticute (Recombinant SP-C or lusupultide)

[85–87]. In ALEC, DPPC (70%) is the main component for lowering surface tension,

while egg PG (30%) is used to improve adsorption and spreading [79].

There appears to be no systematic study to date to study the effect of increasing

the DPPG content in a DPPC/DPPG mixture on the ultimate collapse pressure. Here,

ADSA–CSD is also used to study spread monolayers of mixed DPPC/DPPG films. Com-


pression isotherms were obtained for different DPPC/DPPG mixture ratios with special

focus on the ultimate collapse pressure, film elasticity and film hysteresis for every mix-

ture ratio.

2.2.1 Experimental Details

2.2.1.1 Materials and Methodology

1-Octadecanol was purchased from Sigma-Aldrich (Fluka) Co. (cat. 74720) with a purity

≥99.0%; dipalmitoyl-phosphatidyl-choline (DPPC) from Sigma-Aldrich Co. (cat. P-

4329) with a purity ≥99.0%; and dipalmitoyl-phosphatidyl-glycerol [ammonium salt]

(DPPG) from Sigma-Aldrich Co. (cat. P-5650) with a purity ∼99.0%. All amphiphilic

substances were used without further purification.

Heptane, ethanol, chloroform and methanol were used as spreading agents. Heptane

was purchased from EMD Co. (cat. HX0082-1) with a purity 99.6% (99.95% saturated

C7 hydrocarbons); ethanol from Commercial Alcohols Inc. (cat. UN-1170); chloroform

from Sigma-Aldrich Co. (cat. 36,692-7) with a purity ≥99.8%; and methanol from

Sigma-Aldrich Co. (cat. 27,047-4) with a purity 99.93%.

Ocatadecanol was dissolved in a heptane/ethanol (9:1 v/v) mixture to form a stock

solution with a concentration of 1.2270 mg/ml and then diluted in heptane only to a

concentration of 0.0258 mg/ml. DPPC was dissolved in a heptane/ethanol (9:1 v/v)

mixture to form a stock of concentrated solution and then diluted in a heptane/ethanol

(9:1 v/v) mixture to different concentrations in the range of 0.0025 to 0.0250 mg/ml.

DPPG was dissolved in a chloroform/methanol (9:1 v/v) mixture to form a stock of

concentrated solution and then diluted in a heptane/ethanol (9:1 v/v) mixture to different

concentrations in the range of 0.0025 to 0.0250 mg/ml. The stock and dilute solutions

were always freshly prepared on the day of experiment and subsequently mixed (in the

case of the mixed monolayers study) to give the required mixture DPPC/DPPG ratio


Diff

user

Light Source

Microscope CCD

Stepping MotorSyringe

Glass Cuvette

Figure 2.1: Schematic diagram of ADSA–CSD experimental setup.

and used in the experiments. The water used as the subphase in the experiments is

demineralized and glass distilled (pH ' 5); the ionic strength is almost negligible.

A schematic diagram of the experimental setup for ADSA–CSD is shown in figure 2.1.

As shown, a constrained sessile drop is formed on a stainless steel pedestal with an outside

diameter of 6.2 mm and an inside diameter of 1.5 mm. A Cohu 4800 monochrome camera

is mounted on a Wild-Apozoom 1:6 microscope. The video signal of the constrained

sessile drop is transmitted to a digital video processor, which performs the frame grabbing

and the digitization of the image.

A computer is used to acquire images from the image processor and to perform image

analysis and computation. The rate of image acquisition for the present experiments is

ten images per second. ADSA software extracts an experimental drop profile from the

digitized image and uses an optimization procedure to match the extracted profile to a

theoretical one calculated from the Laplace equation of capillarity. The surface tension of

the constrained sessile drop is then calculated based on the matched theoretical profile.

Other outputs of ADSA are radius of curvature, drop volume and drop surface area. The

fact that we can measure changes in surface area makes this methodology suited for film

balance experiments.

The volume of the drop is controlled by a syringe connected to a stepper motor.

By moving the syringe plunger, changing the volume changes the surface area of the

constrained sessile drop. Although the surface area is changed indirectly, this change is


0 20 40 60 80 100 12040

45

50

55

60

65

70

75

Time, t (s)

Sur

face

Ten

sion

, γ (

mJ/

m2 )

Figure 2.2: The change of surface tension with time after the deposition of octadecanolin heptane/ethanol solution.

essentially linear for the relatively small changes in volume [59].

2.2.1.2 Experimental Procedure

A drop of pure water was formed on the stainless steel pedestal which is connected to

the syringe and the stepper motor. A few images were acquired and analyzed by ADSA,

providing the surface tension of the pure water subphase, γo. All experiments were

performed at room temperature of 24oC.

Using a Hamilton microliter syringe with 0.01% accuracy and a micro-manipulator, a

known amount (typically 5 µl) of the diluted surfactant solution was deposited on top of

the sessile drop. After the deposition, complete evaporation of the spreading agent takes

place in approximately 60 seconds. This is shown is figure 2.2, where the surface tension


Table 2.1: Experimental parameters used for different monolayer types

MonolayerVolume Concentration 10−14 × No. Area Rate Area Rate

(µl) (mg/ml) of Molecules (cm2/min) (A2/molecule·min)

Octadecanol 5.0 0.0258 2.87 0.19 6.65DPPC 5.0 0.0250 1.03 0.19 18.94DPPG 5.0 0.0250 1.02 0.19 19.47

of pure water decreases after deposition of octadecanol in heptane/ethanol solution and

then drifts back up again as the spreading agent evaporates. In the actual experiments,

3 minutes are allowed to elapse to ensure complete evaporation of the spreading agent

before the actual compression is started.

A crucial part of the experiment is the deposition of the insoluble surfactant onto the

drop surface. The constrained sessile drop constellation used here makes the deposition

procedure much easier compared to deposition methods in the pendant drop constellation.

A detailed description of the deposition method used in the current experiments is shown

in figure 2.3. Increasing the size of the drop after the deposition promotes complete

spreading of a monolayer over the whole surface of the drop. After measuring the surface

tension of a pure water drop at full size, the size of the drop is decreased from the full

size (∼80µl) to half size (∼40µl) before deposition. Then the solution deposition (5µl) is

performed from the syringe needle over the water drop apex. Two or more solution drops

fall from the needle onto the drop, causing more than one minimum in the surface tension

in figure 2.2. In some cases, part of the solution dose remains attached to the needle as a

pendant drop; in such cases the needle is moved closer to the drop without penetrating

the interface. The sessile drop is expanded back to full size right after deposition.

At this point, the constrained sessile drop carries an insoluble monolayer and is then

covered with a glass cuvette to isolate the drop from the environment and to prevent

contamination. The surface area was then decreased by reducing the drop volume with

the motor-controlled syringe. For the first study of pure monolayers, table 2.1 summa-


(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 2.3: The process of solution deposition on a constrained sessile drop: (a) thedrop at the full size (∼80µl) before deposition; (b) the drop at half size (∼40µl) beforedeposition; (c) solution deposition (5µl) where more than one solution drop falls fromthe needle over the apex; (d) part of the solution is still attached to the needle; (e)the needle is moved closer without penetrating the interface; (f) the sessile drop aftercomplete deposition; (g) expansion of the sessile drop back to the full size right afterdeposition; (h) the sessile drop after complete solvent evaporation (∼2min).


rizes the amounts of deposition as well as the compression rates for different surfactant

types calculated based on equations 2.1 and 2.2 below. For the second study of mixed

monolayers, the deposition amount for all mixtures used is 5.5 µl volume with a mix-

ture concentration of 0.025 mg/ml. The compression rate is fixed at 0.19 cm2/min for

all experiments. During the compression, images were acquired and saved for further

analysis.

All acquired images were analyzed by ADSA, providing the surface tension value,

γ, the drop surface area, A, the drop volume, V , and the radius of curvature at the

apex, Rc. Figure 2.4 shows a typical result of ADSA for the deposition of octadecanol

in heptane/ethanol solution on a water drop. The number of molecules deposited can be

calculated

Molecules =CVdAvMw

(2.1)

where C is the concentration of the dilute solution used, Vd is the volume used in the

deposition, Av is Avogadro’s number, and Mw is the molecular weight of the specific

surfactant. The change of the surface area with time is used to calculate the rate of

molecular area compression

Area

Molecules×Minutes=

(1

Molecules

)(Area

Minutes

)(2.2)

The parameters of all experiments are summarized in Table 2.1. The value of the surface

pressure, π, can be readily computed by calculating the difference between γo and γ, i.e.

π = γo − γ (2.3)

For the mixed monolayer study, there was an interest to see the effect of mixing

DPPC and DPPG on the film elasticity. The dilatational elasticity, ε, is defined as the

magnitude of surface tension reduction (or surface pressure increase) for a given reduction


0

20

40

60

80

Sur

face

Ten

sion

, γ (

mJ/

m2 )

0.4

0.5

0.6

0.7

0.8

Are

a, A

(cm

2 )

0

20

40

60

80

Vol

ume,

V (

*10−

3 cm

3 )

0 50 100 1500.5

1

1.5

2

2.5

3

Rad

ius

of C

urva

ture

, Rc (

cm)

Time, t (s)

Figure 2.4: The change of surface tension, drop surface area, drop volume and radius ofcurvature at the apex with time of a constrained sessile drop of an octadecanol monolayer.


of the relative surface area of the film. The film elasticity can be calculated from the

change in surface pressure resulting from a small change in drop surface area:

ε =

∣∣∣∣ dπ

d lnA

∣∣∣∣ =

∣∣∣∣Ad(γo − γ)

dA

∣∣∣∣ (2.4)

where π is the surface pressure, γ and γo are the surface tension values in the presence

and absence of a phospholipid film, respectively, and A is the drop surface area.

2.2.2 Results for Pure Monolayers

Figure 2.5 shows the change of surface pressure with area per molecule for an octadecanol

monolayer at a compression speed of 0.19 cm2/min (6.65 A2/molecule·min). Figure 2.5(a)

shows two runs, illustrating reproducibility. Although ten images were acquired every

second, here only two points per second are shown to enhance graph readability. This

applies for figures 2.5, 2.6 and 2.8. However, figure 2.7 shows the raw data acquired

from ADSA–CSD at the rate of ten images per second. As shown in figure 2.5(a), the

surface pressure starts near 0 mJ/m2 and reaches approximately 61 mJ/m2 as the film

is compressed. Further compression did not raise the surface pressure. A plateau is

observed indicating collapse of the monolayer at this limiting surface pressure. Further

inspection shows that there is a change in the isotherm slope (in the domain of rapid

increasing area, i.e. the liquid condensed phase) starting well below the limiting collapse

pressure. Figure 2.5(b) shows the isotherm of five different runs in the vicinity of the

collapse pressure, where point A indicates the point where the slope of the isotherms

starts to change.

Figure 2.6 shows the change of surface pressure with area per molecule for a DPPC

monolayer with a compression speed of 0.19 cm2/min (18.94 A2/molecule·min). Fig-

ure 2.6(a) shows a typical DPPC isotherm; the surface pressure starts at approximately

5 mJ/m2 and reaches about 70 mJ/m2 as the film is compressed. A plateau is observed


10 15 20 25 300

10

20

30

40

50

60

70

Area per Molecule, Am

(Å2/molecule)

Sur

face

Pre

ssur

e, π

(m

J/m

2 )

Run 1Run 2

(a)

16.5 17 17.5

50

55

60

Run 1

A

16.5 17 17.5

Run 2

A

16.5 17 17.5

Run 3

A

16.5 17 17.5

Run 4

A

16.5 17 17.5

Run 5

A


(Å2/molecule)

Sur

face

Pre

ssur

e, π

(m

J/m

2 )

(b)

Figure 2.5: The change of surface pressure with area per molecule of a constrainedsessile drop of an octadecanol monolayer: (a) the full isotherm for different runs; (b) theisotherm of five different runs in the vicinity of the collapse pressure (only two points persecond shown).


25 30 35 40 45 50 55 60 65 70 750

10

20

30

40

50

60

70


(Å2/molecule)

Sur

face

Pre

ssur

e, π

(m

J/m

2 )

(a)

25 30 35 4045

50

55

60

65

70


(Å2/molecule)

Sur

face

Pre

ssur

e, π

(m

J/m

2 )

A

(b)

Figure 2.6: The change of surface pressure with area per molecule of a constrained sessiledrop of a DPPC monolayer: (a) the full isotherm; (b) the isotherm in the vicinity of thecollapse pressure (only two points per second shown).


indicating the collapse of the monolayer at this very high limiting surface pressure (very

low surface tension, approximately 2 mJ/m2). Such low surface tension was not achiev-

able using a pendant drop [62, 66–69], where gravity will detach the drop at very low

surface tension values. Further inspection shows that there is a change in the isotherm

slope starting at pressures well below the limiting collapse pressure. This is illustrated

in figure 2.6(b) which shows the isotherm in the vicinity of the collapse pressure, where

point A (' 52.8 mJ/m2) indicates the point where the isotherm slope changes.

As shown in figure 2.6(b), the isotherm shows a continuous change starting from

point A till the horizontal plateau indicated by the dotted line. To further understand

the isotherm behaviour in this region, we show in figure 2.7 the change of surface tension

and drop surface area with time in two key regions; the first is the vicinity of point A

shown in figure 2.7(a) and the other is the vicinity of the isotherm horizontal plateau

shown in figure 2.7(b).

In the first region, figure 2.7(a), the surface tension shows episodes of collapse in

terms of sudden changes. The curve before the time window shown is quite smooth.

These changes are in the range of 2 mJ/m2, while it was shown [101] that the error of

the measurement is less than 0.1 mJ/m2. These episodes of collapse are accompanied

by a slight decrease in the drop surface area. The reason is that for the same drop

volume, when the surface tension increases at a collapse episode, the drop becomes more

spherical, decreasing the drop surface area at a given volume.

In the second region, figure 2.7(b), the surface tension is almost constant at a very low

value corresponding to the horizontal plateau in the surface pressure isotherm. The most

interesting part in this figure is the change of drop surface area with time at this very

low surface tension. In this region, further compression cannot increase the surface pres-

sure anymore indicating an ultimate collapse pressure. However, due to the continuous

compression, the drop surface area shows sudden drops. This suggests that molecules are

leaving the interface to the bulk causing a sudden drop in the surface area. This aspect


20

24

28

32

Sur

face

Ten

sion

, γ (

mJ/

m2 )

115 116 117 118 119 120 121 122 123 124 125

0.35

0.36

0.37

Are

a, A

(cm

2 )

Time, t (s)

(a)

4

8

12

16

Sur

face

Ten

sion

, γ (

mJ/

m2 )

145 146 147 148 149 150 151 152 153 154 155

0.28

0.29

0.30

Are

a, A

(cm

2 )

Time, t (s)

(b)

Figure 2.7: The change of surface tension and drop surface area with time of a constrainedsessile drop of a DPPC monolayer: (a) in the vicinity of initial episodes of collapse; (b)in the vicinity of the ultimate collapse pressure (raw data acquired at the rate of tenimages per second shown).


Table 2.2: Collapse pressure (mJ/m2) from different runs of different monolayer typesand the average value along with the standard deviation

Monolayer Run 1 Run 2 Run 3 Run 4 Run 5 AverageStandardDeviation

Initial Episode of Collapse

Octadecanol 54.8 53.5 54.5 55.7 54.1 54.5 0.37DPPC 52.8 48.5 44.8 44.2 - 47.9 1.98DPPG 57.8 58.5 59.7 57.4 - 58.4 0.51

Ultimate Collapse Pressure

Octadecanol 61.5 62.1 61.9 60.7 60.3 61.3 0.34DPPC 70.5 70.2 70.1 70.0 - 70.2 0.12DPPG 59.9 58.2 60.7 57.2 - 59.0 0.80

will be treated in more detail in the discussion section.

Figure 2.8 shows the change of surface pressure with area per molecule for a con-

strained sessile drop of a DPPG monolayer with a compression speed of 0.19 cm2/min

(19.47 A2/molecule·min). Figure 2.8(a) shows a typical DPPG isotherm; the surface

pressure starts at approximately 3 mJ/m2 and reaches about 59 mJ/m2 as the film is

compressed. A plateau is observed indicating the collapse of the monolayer at this lim-

iting surface pressure. In contrast to octadecanol and DPPC, DPPG did not show a

sudden change in the isotherm slope before the ultimate collapse pressure. Figure 2.8(b)

shows the isotherm in the vicinity of the collapse pressure, where point A (' 58.5 mJ/m2)

indicates the first point of the change of the isotherm slope.

To illustrate the reproducibility of the results, every experiment was repeated 4 or

5 times. Table 2.2 summarizes the values of the first episode of collapse as well as the

ultimate collapse pressure from different runs for the different monolayers (Octadecanol,

DPPC and DPPG) and the average values along with the standard deviation.


25 30 35 40 45 50 55 60 65 70 750

10

20

30

40

50

60

70


(Å2/molecule)

Sur

face

Pre

ssur

e, π

(m

J/m

2 )

(a)

33 34 35 36 37 38 39 40 41 4250

52

54

56

58

60

62


(Å2/molecule)

Sur

face

Pre

ssur

e, π

(m

J/m

2 )

A

(b)

Figure 2.8: The change of surface pressure with area per molecule of a constrained sessiledrop of a DPPG monolayer: (a) the full isotherm; (b) the isotherm in the vicinity of thecollapse pressure (only two points per second shown).


2.2.3 Discussion for Pure Monolayers

2.2.3.1 Problem of leakage

The results of compressing an octadecanol monolayer are in good agreement with pre-

vious experiments with the pendant drop constellation [59, 65]. The new methodology

proves to be comparable with existing methods with respect to accuracy and reproducibil-

ity. ADSA–CSD shares certain advantages with ADSA–PD over Langmuir film balances.

One of the key advantages is the ability to use higher compression rates, and just as the

Langmuir balance, there is no lower limit for the rate of compression and expansion. An-

other potential strength is that environmental control (contamination, humidity, pressure

and temperature) is straightforward and easy to integrate with the current setup; this

will be a necessity, e.g. for lung surfactant studies [25, 76]. Other advantages are that

only small quantities of liquid and insoluble surfactants are required, and that a very

simple setup is needed and could be integrated with microscopy systems, e.g. BAM or

AFM, for further studies. Compared to ADSA–PD, ADSA–CSD has an easier deposition

procedure.

However, the main advantage here of ADSA–CSD over ADSA–PD and Langmuir

balance is that leakage is eliminated completely. Leakage in the pendant drop can affect

the manifestation of the collapse pressure as a horizontal plateau in the surface pres-

sure/area isotherm. For example, previous results using a pendant drop [65] have shown

the presence of the horizontal plateau for some octadecanol isotherms, while a sudden

decrease in the surface pressure after a certain point was shown for higher compression

speeds. This point was originally considered as the collapse pressure. However, the ef-

fect was recently attributed to monolayer leakage on the teflon capillary supporting the

pendant drop [88]. In fact, all of the studies performed using a pendant drop with a

teflon capillary [59, 62, 65–70] could not achieve any surface pressures larger than about

62 mJ/m2. Although leakage in pendant drops can be eliminated by using a sharp edge


holder as will be discussed in Chapter 4, the problem with low surface tension values is

partially due to the fact that the gravity forces are more pronounced at these low surface

tension values (high surface pressure values) and would act to detach the drop from the

holder. The current constrained sessile drop setup is free of any of these shortcomings.

It has the ability to measure very low surface tension values as shown in the DPPC re-

sults, and it features much easier deposition procedure and leak-proof design. A further

merit of ADSA–CSD is the ability of performing high rates of compression, e.g. for lung

surfactant studies [25, 76], see Chapter 3.

2.2.3.2 Onset of collapse versus ultimate collapse pressure

Disagreements between investigators about collapse pressure has been considerable [65].

Some consider the surface pressure at which the isotherm slope starts to change to be

the starting point of ejection of molecules from the interface as the collapse pressure in

agreement with the definition given in the introduction [92]. Others would consider a

horizontal plateau in the isotherm as the collapse pressure, while an intermediate point

in between those two case is sometimes also considered [1].

The results presented here show a distinctive difference between the onset of collapse

and the ultimate collapse pressure (ultimate strength) of these films. For example, com-

pression of a DPPC monolayer causes the isotherm to change its slope at a certain point

as shown in figure 2.6(b). This change in the isotherm slope reflects the existence of

some interaction between molecules at the interface causing some episodes of collapse.

This point is called here the onset of collapse. Upon further compression, the mono-

layer adapts and sustains higher surface pressure until reaching a maximum or ultimate

strength or an ultimate collapse pressure. Thus, a collapse region can be defined to start

with an initial episode of collapse (onset of collapse) and to end when the ultimate (or

maximum) collapse pressure is reached, manifested in a horizontal plateau in the surface

pressure/area isotherm. From an applied perspective, e.g. for lung surfactant, we are


mostly interested in knowing if the film can sustain high surface pressures (e.g. > 67

mJ/m2), i.e. surface tensions that prevent lung collapse.

Whereas a Langmuir film balance controls the surface area and measures the change

in surface pressure, ADSA–CSD measures the change of both surface area and surface

tension with time caused by the externally imposed change of drop volume. This fea-

ture allows ADSA–CSD to provide a detailed study of the collapse region, as shown in

figure 2.7 for DPPC. Figure 2.7(a) shows the change of surface tension and drop surface

area with time in the vicinity of the onset of collapse, while figure 2.7(b) focusses more

on the vicinity of the ultimate collapse pressure. Episodes of collapse occur as indicated

by the change of surface tension in the former; however, the surface tension is almost

constant in the latter. The change of drop surface area provides more information in

both figures.

In figure 2.7(a), the episodes of collapse are accompanied by some irregularities in the

surface area. In figure 2.7(b), while the surface tension is constant, the surface area shows

sudden decreases at some points. The sudden decrease in area suggests squeeze out of

some molecules from the interface. The decrease in surface area can be used to estimate

the size of regions and the number of molecules that are being pushed into the subphase.

For example, from figure 2.7(b) at time 148 seconds the area suddenly drops from 0.300

cm2 to 0.295 cm2. Since the surface tension is essentially constant, this suggests that a

region (or regions) of accumulative area equal to approximately 0.005 cm2 or 5×1013 A2

have been pushed out to the subphase. The minimum area per DPPC molecule is known

[1] to be in the range of 35 to 40 A2/molecule; this gives an estimate of the number of

molecules that have to leave the interface as in the order of 1012 molecules, i.e. 1% of

the total material deposited. Such information might be of specific interest, e.g. for lung

surfactant systems. Obviously, such information cannot be obtained by a Langmuir film

balance.


2.2.3.3 Comparison of the three systems

Table 2.2 summarizes the values obtained for onset of collapse and ultimate collapse

pressure for the three systems studied here: octadecanol, DPPC and DPPG. Octadecanol

and DPPC show a distinctive difference between the onset of collapse and the ultimate

collapse pressure, while both values are very close for DPPG. In fact, some of the DPPG

runs (run 2 and 4) did not show any sudden change in the isotherm slope until the

ultimate collapse pressure was reached, i.e. there was no separate distinctive onset of

collapse for these runs, as shown in figure 2.8. The values for the ultimate collapse

pressure were well reproducible for all three systems. However, the onset of collapse is

harder to reproduce especially for the DPPC monolayer as reflected in the high value of

the standard deviation.

Octadecanol was found to have an ultimate collapse pressure of 61.3 mJ/m2, DPPC

of 70.2 mJ/m2, and DPPG of 59.0 mJ/m2. The superior ability of DPPC to sustain such

a high pressure may help to understand why it is the main component of lung surfactant.

The difference between the ultimate collapse pressure of these three systems is believed

to be due to several factors, including the molecular structure, the chain length, and

the properties of the head group. DPPC [C40H80NO8P] has two aliphatic chains with

a large choline head group, compared to octadecanol molecules [CH3(CH2)17OH] with a

single alkyl chain and only a small head group. DPPG [C38H75O10P·NH3] has a similar

molecular structure to DPPC; however, unlike DPPC which is zwitterionic, DPPG is

anionic. Further discussion of the collapse of each system is given below.

Results of Brewster Angle Microscopy (BAM) of octadecanol monolayers have shown

that under the usual spreading conditions, irregularly shaped islands of condensed phase

are distributed in a continuous gaseous phase [65]. Upon compression, these islands even-

tually touch each other and start to coalescence and rearrange. With increasing surface

pressure, the condensed phase becomes a continous phase with irregular areas of the

residual gaseous phase [65]. However, results presented here suggest that the interaction


between these islands starts earlier than the maximum surface pressure achieved as indi-

cated by point A in figure 2.5(b). After a small transition period, the monolayer reaches

the “ultimate” collapse pressure. At this area, the islands of the condensed phase fill the

interface completely. Compressing the monolayer further does not yield any increase in

the surface pressure, but allows for more rearrangements at the interface. It is observed

that the surface pressure measured here is kept constant by further compression and does

not fall to lower values as suggested by other studies [65].

DPPC was chosen here for two reasons; it is the main component of lung surfactant

and it can achieve very low surface tension (very high surface pressure) values upon

compression. This is shown in the results of the collapse pressure values presented here

which are in good agreement with values in the literature [14, 20]. Upon compression,

DPPC monolayer forms flexible domains in the coexistence region of low density and

condensed phases. The ability of DPPC to adjust to an area reduction is attributed to

the change in the orientation of the hydrophobic tails of the DPPC molecule [102–104].

When the average area per molecule for the polar head decreases, the tilt angle of the

tail also decreases and the orientation becomes more vertical. However, the large head

group prevents the complete erection of the chains. These processes are responsible for

some of the irregularities in the vicinity of the collapse area as shown in figure 2.6(b).

Comparing figures 2.5(a) and 2.6(a), the results confirm that the range of area per

molecule over which the compression occurs is broader for DPPC than for octadecanol.

Because of the higher flexibility of the domains, a DPPC monolayer may be compressed

over a larger area per molecule range. This was attributed to the ordering of the DPPC

tails towards vertical orientation which requires more energy, extending the range of area

per molecule over which the compression occurs [66].

DPPG is a lipid found in lung surfactant where it represents 5-10% of the total

phospholipid content. Unlike DPPC (the main lipid in lung surfactant), DPPG is ionic

and forms charged monolayers on aqueous electrolyte subphases. The collapse pressure


depends on the nature of the subphase used. The values reported here are in good

agreement with previous results, where DPPG was deposited on an air/water interface

[21]. Other studies show a different collapse pressure value when DPPG was deposited

onto subphases composed of solutions of sodium bicarbonate with varying NaCl salt

concentrations [22].

Apart from the collapse pressure value, the DPPG isotherm has a similar shape to that

of DPPC. However, figure 2.8(b) shows no signs of collapse prior to reaching the collapse

pressure value. The change of the isotherm slope occurs at the collapse pressure as shown

in figure 2.8(b). Further compression causes squeeze out from the DPPG monolayer. This

squeezed out material organizes as aggregates in the subphase decreasing the surface

pressure [22]. More compression will cause the surface pressure to increase again until

another portion of the material is squeezed out. This would explain the irregularities in

the isotherm in the vicinity of the collapse pressure as shown in figure 2.8(b). Studies

using Brewster Angle Microscopy (BAM) and Atomic Force Microscopy (AFM) reveal

that the squeezed out aggregates diffuse away from the monolayer at low ionic strength

and remain in the subphase; at high ionic strength, they remain attached to the monolayer

and reincorporate again into the monolayer when the film is expanded [22].

In conclusion, the use of a constrained sessile drop constellation (ADSA–CSD) as a

film balance is illustrated. It was shown that it has certain advantages over conventional

methods. It is a very simple setup and only small quantities of liquid are required. The

ability to measure very low surface tension values, easier deposition procedure and leak-

proof design makes the constrained sessile drop constellation a better choice than the

pendant drop for studies of both soluble or insoluble monolayers.

The fact that ADSA–CSD measures the change of both surface area and surface

tension with time allows a detailed study of the collapse region. Changes in surface area

in the vicinity of the ultimate collapse pressure allow an estimate of the size of regions

and the number of molecules that are being pushed into the subphase. Such information


20 30 40 50 60 700

10

20

30

40

50

60

70

Area per Molecule, Am (Å2/molecule)

Sur

face

Pre

ssur

e, π

(m

J/m

2 )

Run aRun bRun c

Figure 2.9: The change of surface pressure with area per molecule of a constrained sessiledrop of a DPPC monolayer for different runs.

is of specific interest for lung surfactant systems and cannot be obtained by a Langmuir

film balance.

The results of compression isotherms for different systems show distinctive differences

between the onset of collapse and the ultimate collapse pressure (ultimate strength) of

these films. ADSA–CSD allows detailed study of this collapse region.

2.2.4 Results for Mixed Monolayers

Figure 2.9 shows the change of surface pressure with area per molecule for a DPPC

monolayer at a compression speed of 0.19 cm2/min (19 A2/molecule·min). The figure

shows three different runs, illustrating reproducibility. The surface pressure starts at


25 30 3545

50

55

60

65

70

75DPPC:DPPG

100:0(a)

Sur

face

Pre

ssur

e, π

(m

J/m

2 )

25 30 35

DPPC:DPPG90:10

(b)

25 30 35

DPPC:DPPG80:20

(c)

25 30 35

DPPC:DPPG70:30

(d)


25 30 35

DPPC:DPPG60:40

(e)

25 30 35

DPPC:DPPG50:50

(f)

25 30 35

DPPC:DPPG0:100

(g)

Figure 2.10: The change of surface pressure with area per molecule of a constrainedsessile drop of mixed DPPC/DPPG monolayers for different mixture ratios: (a) 100:0;(b) 90:10; (c) 80:20; (d) 70:30; (e) 60:40; (f) 50:50; (g) 0:100.

approximately 5 mJ/m2 and reaches about 70 mJ/m2 as the film is compressed. A

plateau is observed indicating the collapse of the monolayer at this ultimate collapse

surface pressure (very low surface tension, approximately 2 mJ/m2). Further inspection

shows that there is a slight change (not readily apparent in the figure) in the isotherm

slope starting at pressures round 48 mJ/m2, well below the ultimate collapse pressure.

This point was denoted in the previous section as the onset of collapse.

The change of surface pressure with area per molecule of a constrained sessile drop of

mixed DPPC/DPPG monolayers for different mixture ratios are compared in Figure 2.10

in the vicinity of the collapse pressure. The ratios studied here ranges from 100 to 50%

DPPC (with 10% increments) in the mixture in addition to pure DPPG. It can be seen

from the figure that for ratios 90:10 and 80:20, the DPPC/DPPG mixture can achieve a

very high ultimate collapse pressure, similar to pure DPPC. When the ratio of DPPG in

the mixture is increased, the ultimate collapse pressure is decreased slightly for the ratios

70:30 and 60:40. Upon further increase of DPPG (50% or more), the ultimate collapse

pressure is decreased to approximately 60 mJ/m2, similar to pure DPPG.

Every experiment for a specific mixture ratio was repeated at least 4 times. The

reproducibility of the results shown in Figure 2.9 for the case of pure DPPC is not


Table 2.3: Ultimate collapse pressure (mJ/m2) and film elasticity (mJ/m2) at roomtemperature of 24oC from different runs of different DPPC:DPPG mixture ratios andthe average value along with the standard deviation.

DPPC:DPPG Run 1 Run 2 Run 3 Run 4 AverageStandardDeviation

Ultimate Collapse Pressure

100:0 70.7±0.03 70.6±0.07 70.6±0.14 70.7±0.04 70.6 0.0290:10 70.5±0.11 70.4±0.25 70.5±0.24 70.2±0.13 70.4 0.0580:20 70.9±0.24 70.5±0.29 70.8±0.26 70.7±0.21 70.7 0.0770:30 68.7±0.23 69.0±0.41 68.1±0.44 67.4±0.82 68.3 0.2860:40 68.6±0.80 69.9±0.61 70.0±0.36 67.2±0.58 68.9 0.5050:50 60.8±1.39 60.4±1.10 60.2±0.99 61.0±1.90 60.6 0.150:100 60.8±1.12 59.6±1.68 60.0±1.42 59.2±1.82 59.9 0.25

Film elasticity at π = 50 mJ/m2

100:0 227.5±1.4 236.4±2.0 225.2±0.7 221.5±1.7 227.6 2.490:10 243.7±1.0 209.4±5.3 257.5±4.4 255.7±4.0 241.6 8.480:20 212.4±1.5 214.1±1.6 203.5±2.7 207.8±1.0 209.4 1.870:30 209.3±1.7 224.8±2.8 198.9±1.1 263.0±2.1 224.0 10.660:40 191.9±1.7 214.8±1.6 208.8±1.0 224.7±2.3 210.1 5.250:50 199.2±1.4 250.4±3.1 168.5±1.3 227.3±1.2 211.3 13.40:100 774.6±31.8 755.3±38.2 717.8±18.7 736.4±59.9 746.0 9.2


always guaranteed. A summary of calculated ultimate collapse pressure for different

mixture ratios is shown in Table 2.3 along with an average value and standard deviation.

To illustrate the reproducibility of the results for different mixture ratios, Table 2.3 shows

the ultimate collapse pressure values obtained for all runs of every mixture ratio. The

table shows that adding a limited amount of DPPG (up to 20%) to DPPC monolayer does

not alter the ultimate collapse pressure. Increasing the DPPG content in the mixture

(30% or 40%) shows a transition region, where the ultimate collapse pressure is decreased

to values ranging between 66 and 70 mJ/m2. The variations of values obtained for the

ultimate collapse pressure in this regions are not small, indicating a low reproducibility.

However, further increase of DPPG content in the mixture (50% and beyond) causes a

sharp decrease in the ultimate collapse pressure to values close to the pure DPPG. It is

noted that the reproducibility in this region is much better than that of the transition

region.

Further insight into the differences between the mixture ratios can be gained by

calculating the surface dilatational elasticity from the measured isotherms. For reason of

comparison, elasticity values are calculated at the same surface pressure, i.e. 50 mJ/m2,

for all the measured isotherms. This value is chosen for two reasons; first, it is below

the ultimate collapse pressure for the isotherms in this study. Second, this value is close

to the equilibrium surface pressure for lung surfactant systems, thus eliminating any

effects of relaxation or adsorption that could alter the calculated value of film elasticity.

A summary of calculated film elasticity values for different mixture ratios is shown in

Table 2.3 along with an average value and standard deviation. It can be seen that for

all ratios studied here, the elasticity values are around 220 mJ/m2, very close to pure

DPPC. Increasing the DPPG content in the mixture does not increase the film elasticity.

However, the pure DPPG film has a much higher elasticity of approximately 750 mJ/m2,

i.e. a better film property.

Thus far, experiments were performed by only compressing the film once and record-


15 20 25 30 35 40 45 5045

50

55

60

65

70

75


Sur

face

Pre

ssur

e, π

(m

J/m

2 )

DPPC:DPPG100:0

1st comp2nd comp

3rd comp4th comp

(a)

15 20 25 30 35 40 45 5045

50

55

60

65

70

75


Sur

face

Pre

ssur

e, π

(m

J/m

2 )

DPPC:DPPG90:10

1st comp2nd comp

3rd comp4th comp

(b)

15 20 25 30 35 40 45 5045

50

55

60

65

70

75


Sur

face

Pre

ssur

e, π

(m

J/m

2 )

DPPC:DPPG80:20

1st comp2nd comp

3rd comp4th comp

(c)

Figure 2.11: The change of surface pressure with area per molecule on successive com-pressions and expansions of a constrained sessile drop of mixed DPPC/DPPG monolayersfor different mixture ratios: (a) 100:0; (b) 90:10; (c) 80:20.


ing the change of surface pressure. A different set of experiments were performed, where

after the full compression of the monolayer (different mixture ratios), the monolayer was

then expanded and compressed again. This compression/expansion cycle was then re-

peated, i.e. 3 compression/expansion cycles for each mixture ratio. Figure 2.11 shows

the different compression/expansion cycles for three different mixture ratios, i.e. pure

DPPC, 90:10 and 80:20 DPPC/DPPG. These ratios were selected because all of them

reach the same high ultimate collapse pressure shown in Table 2.3. The second com-

pression of pure DPPC was slightly shifted to the left compared to the first compression

as shown in Figure 2.11(a). This indicated that recompression of pure DPPC causes a

small loss of molecules between the first and second compression. For the case of 10%

DPPG (Figure 2.11(b)), after the first compression, the shape of the compression/ex-

pansion isotherms is very similar to the pure DPPC isotherm. This suggests that during

the first compression, most of the DPPG was ejected from the interface leaving a pure

DPPC monolayer for the following compression/expansion cycles. However, increasing

the DPPG content to 20% (Figure 2.11(c)) shows a change in the shape of the cycle.

After the first compression, the shape of the subsequent compressions did not change.

Every compression in this case shows a slight shift to the left. It is noted that the shape

here is different from that of pure DPPC for all 4 compressions.

2.2.5 Discussion for Mixed Monolayers

2.2.5.1 Ultimate Collapse Pressure of Mixed Monolayers

As the main component of lung surfactant, DPPC is known to achieve very low surface

tension (very high surface pressure) values upon compression. This is shown in the results

of the collapse pressure values for pure DPPC presented here in Figure 2.9 and Table 2.3.

These results are in good agreement with values in the literature [14, 20, 88]. Unlike

DPPC, the collapse pressure of DPPG depends on the nature of the subphase used. The


values for pure DPPG reported here in Table 2.3 are in good agreement with previous

results, where DPPG was deposited on an air/water interface [21, 70, 88].

Results presented in Table 2.3 show that adding a limited amount of DPPG (up to

20%) to DPPC does not alter the ability of the monolayer to reach a very high ultimate

collapse pressure. With further increase of the amount of DPPG in the mixture, the

ultimate collapse pressure goes through a transition region followed by a decrease in the

ultimate collapse pressure to values close to that of the pure DPPG (for ratios of 50% and

beyond). These results suggest that an increased amount of DPPG (beyond 30%) would

adversely affect the ability of the mixture to reach high surface pressure (low surface

tension) values.

2.2.5.2 Film Elasticity of Mixed Monolayers

In addition to the high collapse pressure, a good monolayer would also have a high

elasticity value. The elasticity can be calculated from the slope of a π − A isotherm as

shown in Table 2.3. The monolayer elasticity is a measure of the film resistance (change

in the film surface pressure) to a change in the area per molecule. The results show that

the monolayer elasticity calculated at 50 mJ/m2 surface pressure is around 220 mJ/m2

for pure DPPC, and around 750 mJ/m2 for pure DPPG. The value for pure DPPC is in

good agreement with previous results [105], and the value for pure DPPG is in agreement

with values calculated from previously measured isotherms [88]. Some of the calculated

elasticity values measured from previously measured isotherms [70, 106] are somewhat

lower (between 350 and 600 mJ/m2) than the value measured here, but still higher

than that of pure DPPC. However, the resolution in the current data in the vicinity of

50 mJ/m2 surface pressure is much better than in other techniques. As elasticity is a

function of compression rate, it should be kept in mind that the compression rate for all

experiments was fixed at 0.19 cm2/min, as indicated earlier. The relatively large error for

DPPG elasticity in Table 2.3 is due to the fact that the experimental isotherms are very


steep, i.e. approaching a slope of infinity. All DPPC/DPPG mixture ratios studied here

(90 to 50% DPPC) have elasticity values very close to pure DPPC. It is clear that pure

DPPG films have better elasticity than DPPC films. However, increasing the DPPG

content in the mixture does not improve the film elasticity.

2.2.5.3 Repeated Compression Cycles

In the first set of experiments, after spreading, the monolayer was continuously com-

pressed until collapse, at which point the experiment ended. In the second set of exper-

iments, the monolayer was spread, then compressed until collapse occurred. The mono-

layer was then expanded and compressed again. Three compression/expansion cycles

were performed for every experiment. The difference between the first and the following

compressions usually gives an indication of the number of molecules lost between com-

pressions. Three DPPC/DPPG mixture ratios are compared in Figure 2.11. For the case

of pure DPPC (Figure 2.11(a)), the results suggest that some molecules were not able to

reincorporate at the interface after the first compression. The successive compressions

did not show significant change. For the case of 10% DPPG in the mixture, the shape

of the compression/expansion cycles after the first compression is essentially the same

as that of pure DPPC as shown in Figure 2.11(b). This suggests that the 10% DPPG

content was squeezed out from the interface during the first compression and was not able

to reincorporate back. The interface after the first compression is probably composed of

DPPC only. On the other hand, increasing the DPPG content to 20% (Figure 2.11(c))

shows a change in the shape of the compression/expansion cycles. Every compression in

this case shows a slight shift to the left, indicating a continuous ejection of molecules. It

is noted that the shape here is different from that of pure DPPC for all compressions.

This suggest that, at this mixture ratio, DPPG is still present at the interface at the

high ultimate collapse pressure.


2.2.5.4 Implications for Lung Surfactant Development

Conceptually, it is possible to define qualitatively a set of surface properties that are nec-

essary for the respiratory function of lung surfactants. These surface properties include

the ability to adsorb to the air/water interface, the ability to reach very low surface ten-

sion values during dynamic cycling, the ability to reach such low surface tension values

with minimum amount of area reduction (high elasticity), and the ability to respread

at the interface during expansion [1]. No single component of the complex compound

of lung surfactant has all these necessary surface properties. However, different compo-

nents interact to achieve the required system behaviour. As shown in the literature, and

reported here as well, DPPC alone (zwitterionic phospholipid) can reach extremely high

surface pressures (low surface tensions below 2 mJ/m2). However, DPPC adsorbs very

slowly to the air/water interface [1, 36], has a relatively low elasticity compared to DPPG

as shown in Table 2.3, and respreads poorly in compression/expansion cycles as shown in

Figure 2.11(a). Fluid phospholipids, neutral lipids and surfactant proteins (SP-A, SP-B,

and SP-C) cannot reach high surface pressures but have a significant effect on improving

adsorption and respreading [61, 62, 107].

The presence of anionic phospholipids, e.g. DPPG, in lung surfactant is well estab-

lished; however, their quantitative contribution to surface activity is less clear. Results

presented here suggest that an increased content of DPPG will adversely affect the sur-

face tension lowering ability of DPPC. However, it is also shown that DPPG has better

film elasticity and respreading properties in compression/expansion cycles. It is widely

believed that their association with one or more surfactant proteins may make a con-

tribution to the surface activity [96–100, 108–115]. As mentioned before a DPPC/PG

mixture has been repeatedly used to mimic natural lung surfactant [94, 95], and has also

been used as the main component of many clinical synthetic exogenous lung surfactants,

e.g. ALEC [79], Surfaxin [82], and Venticute [85].

In conclusion, results here suggest that DPPG improves the respreading properties


of the mixture and may improve the film elasticity. The only drawback of increasing the

content of DPPG is the adverse effect on the ultimate collapse pressure. However, the

low collapse pressure of DPPG is limited only to pure water as subphase. Other studies

showed that DPPG can in fact achieve very high collapse pressure values (similar to pure

DPPC) when deposited onto subphases composed of solutions of sodium bicarbonate

mixed with NaCl [22]. This leads to the expectation that DPPG may play an important

role in the future of lung surfactant development.

2.3 Double Injection Capability

Lung surfactant inhibition or inactivation is a phenomenon caused by processes that

degrade the surface activity of the surfactant [1]. Direct interaction with endogenous in-

hibitors is a main reason for such phenomena. Some inhibitors can impair the adsorption

and the surface tension lowering abilities of the surfactant. Examples of such inhibitors

include plasma and blood proteins (such as albumin, fibrinogen, and hemoglobin) [116–

122], unsaturated cell membrane phospholipids [121, 123], lysophospholipids [34, 124],

fluid free fatty acids (such as oleic acid) [35, 125], meconium [126, 127], and cholesterol

when present at high concentrations [128, 129]. Other inhibitors, usually released during

lung inflammation or injury, can chemically react with and degrade the functional compo-

nents of the surfactant. Examples include lytic enzymes (proteases and phospholipases)

[33, 130] and reactive oxidant species [131, 132].

The surface activity of lung surfactants can be assessed with various methods as

shown in Chapter 1. Most of the methods suffer from one or more of the following

limitations: inability to perform fast cycling, film leakage, uncontrolled environmental

conditions, inaccurate calculation of low surface tension values, inoperability at the high

surfactant concentrations. These limitations must be removed in the in vitro study of

lung surfactants that should mimic the conditions of normal breathing. ADSA–CSD


is believed to be free of all restrictions and limitations of other conventional methods

mentioned before. However, it is not possible yet to use ADSA–CSD as a penetration

film balance that would allow the access to the interface from the liquid side.

The purpose of this section is to present a modified design for ADSA–CSD featuring

a secondary injection system facilitating access to the interface from the liquid side.

The study of the effect of a specific inhibitor on a preformed lung surfactant film is a

good illustration of this capability. After forming a sessile drop of a basic surfactant

preparation, the bulk phase can be exchanged and different inhibitors such as serum,

albumin, fibrinogen, and cholesterol can be introduced. Results are compared, below,

with the case where the inhibitor and the surfactant preparation are premixed and co-

adsorb. This modified design can be used to evaluate lung surfactant inhibition, resistance

and reversal under completely controlled physiological conditions. The modified design

can also be used for bulk liquid sampling and on-site mixing.



The lung surfactant used, Bovine Lipid Extract Surfactant (BLES), was provided by

BLES Biochemicals Inc. (London, Ontario, Canada) at a concentration of 27 mg/ml

and was used without further purification. BLES was divided into 1 ml glass vials in Ar

atmosphere and stored at -20 C. On the day of the experiment, one vial was maintained

at 37.5 C water bath for one hour before diluting it to 2.0 mg/ml by a salt solution of

0.6% NaCl and 1.5 mM CaCl2. The pH value of the diluted BLES preparation ranged

from 5 to 6.

A potential lung surfactant additive, protasan (UP CL 213, chitosan chloride, deacety-

lation 75-90%), was purchased from NovaMatrix (Norway). More details about protasan

can be found elsewhere [133, 134]. Protasan was dissolved in the NaCl/CaCl2 salt solu-


tion on the day of the experiment and then diluted to the final concentration (ranging

from 0.05 to 0.50 mg/ml according to the required preparation) and mixed with 2.0

mg/ml BLES suspension. The pH of these BLES-protasan mixtures ranged from 5 to

5.5.

Here, a preparation of BLES and protasan is chosen as the basic preparation, i.e.

a basis for comparison. Through accumulated experience in the Laboratory of Applied

Surface Thermodynamics, it was observed that the minimum surface tension of BLES

alone, without any additives, varies significantly from batch to batch [91], at least at

low BLES concentrations. The minimum surface tension, i.e. the lowest surface tension

obtainable upon 20% area reduction, varied from 5.5 mJ/m2 to 20.4 mJ/m2 in 100%

relative humidity [91]. Parenthetically, it is noted that typically these minimum surface

tensions are much lower at non-physiological lower humidities. Therefore, in order to

study whether a certain inhibitor has the capability of raising the surface tension above

the physiologically interesting range of 1 to 5 mJ/m2, we need a standard enhancing

additive to guarantee an initial low surface tension, prior to any challenge of the surfactant

film by an inhibitor. The choice of additive here is protasan (chitosan chloride). A similar

procedure was described previously for the case of chitosan as a surfactant additive [91].

Serum (bovine, cat. B8655), albumin (from bovine serum, fatty acid free, globulin

free, ≥99%, cat. A0281), fibrinogen (from bovine plasma, type I-S, 65-85% protein, cat.

F8630), and cholesterol (≥99%, cat. C8667) were purchased from Sigma-Aldrich Co.

Serum was diluted in the NaCl/CaCl2 salt solution to a final concentration, ranging from

0.01 to 0.30 ml/ml according to the required preparation. Albumin was dissolved in the

NaCl/CaCl2 salt solution to a concentration of 40.0 mg/ml. Fibrinogen was dissolved

in a salt solution of 0.85% NaCl and 1.5 mM CaCl2 and adjusted to a concentration

of 3.0 mg/ml. Cholesterol was dissolved in 10 mg/ml ethanol and diluted to a final

concentration of 0.284 mg/ml. The pH value of the diluted serum preparations was near

7, while the pH value of the other inhibitor preparations ranged from 5 to 6.


Figure 2.12: Schematic diagram of double injection ADSA–CSD experimental setup andan illustration of the exchange process.


The design for a modified ADSA–CSD including a secondary injection was developed

and manufactured. The details of the design and operation of the original ADSA–CSD

were described elsewhere [25, 46, 48]. A schematic diagram of the new design is shown

in figure 2.12 and a detailed engineering drawing is shown in figure 2.13. The modified

design features a capillary needle fitted concentrically in the opening of the main pedestal

(holder) to facilitate secondary liquid injection. The capillary needle is connected to a

separate syringe with a dedicated motor equipped with a controller.

The details of the modified ADSA–CSD are as follows: the primary fluid (lung sur-

factant preparation) is delivered from the first syringe to form a sessile drop on a circular

horizontal stainless steel pedestal. The secondary fluid (inhibitor) is injected from the

second syringe into the preformed sessile drop through a capillary needle. The base of

the pedestal is designed to accommodate a reservoir, which is used to ensure a constant


Figure 2.13: Detailed engineering drawing of double injection ADSA–CSD.


temperature.

During the experiment, the setup is enclosed in an environmental control chamber

that facilitates the control of gas composition and temperature. The humidity inside the

chamber was kept constant at 100% relative humidity at 37 C. Two stepping motors

(controller 18705/6, Oriel Instruments, Stratford, CT) were used, one for each fluid, to

facilitate the fluid volume injection/extraction and the compression/expansion during the

dynamic cycling part of the experiment. A CCD camera (model 4815-5000, Cohu Corp.,

Poway, CA) mounted on a microscope (type 400076, Wild Heerburgg, Switzerland) was

used to acquire images throughout the experiment at a rate of 20 images per second.

The images were digitized using a digital video frame grabber (Snapper-8, Active Silicon

Ltd., Iver, UK) and stored in a workstation (SunBlade 1500, Sun Microsystems, Santa

Clara, CA) for further analysis by ADSA.

The experimental procedure for a double injection experiment is as follows: First,

the capillary needle is filled with the secondary fluid (inhibitor). Then, the primary fluid

(lung surfactant) is used to form a sessile drop on the pedestal. The surface tension

is tracked until the film reaches the equilibrium surface tension (within 180 seconds).

Thereafter, dynamic cycling is performed by successive compression/expansion of the

drop. This is normally done through 20 cycles with a periodicity of 3 seconds per cycle

and a compression ratio (percentage of surface area reduction) of 20% to simulate normal

human breathing conditions [1, 25]. Unless stated otherwise, compression conditions in

all results in this work are the same (20% surface area reduction at 3 s/cycle periodicity)

in humid air (100% R.H.).

At this point, the volume replacement procedure begins. The secondary fluid is in-

jected continuously through the inner capillary needle. During the injection, the primary

fluid is simultaneously and continuously withdrawn using the other syringe and motor

controller. The volume exchanged is 5 times the drop volume to ensure a complete bulk

replacement of the primary fluid by the secondary fluid [60]. This minimum exchange


volume depends on flow dynamics as shown earlier [135]. To corroborate the recommen-

dations of Cabrerizo-Vılchez et al. [60], the volume exchange process was tested using

two miscible liquids with the same density but with different interfacial tensions, namely

dimethylsulfoxide (DMSO) and 1-chlorobenzene (CB). It was found that complete bulk

replacement can be ensured after only 2 volumes exchange for the specific dynamic flow

condition used here.

The volume replacement is performed slowly (120 seconds) to avoid film disturbance.

After completing this step, the drop is left for 180 seconds to reach equilibrium again.

Finally, the dynamic cycling part is repeated (20 cycles, 3 seconds per cycle, 20% com-

pression). The results from the two dynamic cycling parts (before and after injection)

are further analyzed and compared to evaluate the effect of injecting the secondary fluid

(usually an inhibitor) under a preformed film of the primary fluid (the basic preparation).

One of the main parameters that reflects the effect of injection is the minimum surface

tension, γmin, obtained at the end of compression in each cycle during the two dynamic

cycling parts. The reported values here are those averaged over the 20 cycles during a

specific dynamic part along with the standard deviation. The measured value of minimum

surface tension depends on the compression conditions. Another important parameter is

the dilatational elasticity as defined in equation 2.4. The elasticity can be calculated in

a similar fashion to equation 2.4 but written in terms of surface tension [25, 45, 47, 62,

107, 136],

ε =

∣∣∣∣ dγ

d lnA

∣∣∣∣ (2.5)

where γ is the surface tension of the film at any time, and A is the drop surface area

at any time. The change of surface tension with the relative surface area during the

compression part of every cycle is fitted to a fourth order polynomial and the slope is

evaluated at the midpoint of the compression [91]. The calculated slope and the value

of the relative surface area are used to calculate the dilatational elasticity according to

equation 2.5.


10

20

30

40

50

Su

rfa

ce

Te

nsio

n, γ

(m

J/m

2) (a) BLES and Protasan only

180 190 200

10

20

30

40

50

Time, t (s)

Su

rfa

ce

Te

nsio

n, γ

(m

J/m

2) (b) After Bulk Replacement

0.8 0.9 1

Relative Surface Area, Ar

Figure 2.14: Change in surface tension with time and with relative surface area duringdynamic cycling: (a) 2.0 mg/ml BLES and 0.2 mg/ml protasan (basic preparation);(b) After replacing the bulk phase with salt solution. All compressions/expansions areperformed at 3 s/cycle periodicity in humid air (100% R.H.).

2.3.2 Results

Figure 2.14 shows a solvent exchange experiment. The change of surface tension, γ,

with time during the first few cycles in the dynamic cycling of a basic preparation of 2.0

mg/ml BLES and 0.2 mg/ml protasan is shown in figure 2.14(a). The figure also shows

the change of surface tension with relative surface area, Ar, for one of the cycles (the

fifth cycle). Figure 2.14(b) shows the surface tension response for the same compression

conditions but after replacing the bulk with salt solution only (bulk wash-out). The

minimum surface tension after bulk replacement did not change. Both cases have the

same γ−Ar response with similar elasticity. The consistency of the surface activity after

bulk replacement suggests effectively irreversible adsorption. This is consistent with the


spreading of lung surfactant vesicles described in the literature [137–139].

Figure 2.15(a) shows the change of surface tension, γ, with time during the first few

cycles in the dynamic cycling of a basic preparation of 2.0 mg/ml BLES and 0.2 mg/ml

protasan. The rest of the 20 cycles did not show a significant difference from the first few.

The figure also shows the change of surface tension with relative surface area, Ar, for one

of the cycles (the fifth cycle). The open circles show the change during the compression

part of the cycle, while the solid circles give the surface tension during the expansion

part. The minimum surface tension is 2.9 ±0.3 mJ/m2. Figure 2.15(b) shows the surface

tension response for the same compression conditions but after injecting 0.15 ml/ml

serum into the bulk of the basic preparation. The minimum surface tension after the

injection is 3.5 ±0.6 mJ/m2. Comparing figures 2.15(a) and 2.15(b) show that injecting

serum under a preformed film of BLES and protasan has little effect on the minimum

surface tension. However, the γ − Ar isotherms show a significant change in the cycle

hysteresis and also in the slope of the compression part of the cycle.

Figure 2.15(c) shows the change of surface tension with time and with relative surface

area for the mixture of the inhibitor (0.15 ml/ml serum) and the basic preparation (2.0

mg/ml BLES and 0.2 mg/ml protasan) in a separate single injection experiment. In

this experiment, the mixture is used to form a sessile drop on the pedestal. Then, the

surface tension is tracked until the film reaches the equilibrium surface tension (within 180

seconds). After that, dynamic cycling is performed under standard conditions [25]. The

minimum surface tension for the mixture is 15.6 ±0.3 mJ/m2, which differs significantly

from the value achieved after the injection in the double injection experiment. The γ−Ar

isotherms show that the cycle hysteresis and the slope of the compression is also different

from figures 2.15(a) and 2.15(b).

The choice of the basic preparation in that experiment needs further comment. To

determine a suitable concentration of protasan to be added to BLES, different concen-

trations were tested and the minimum surface tension obtained for two different BLES


10

20

30

40

50

Surf

ace T

ensio

n, γ

(m

J/m

2) (a) BLES and Protasan only

10

20

30

40

50

Surf

ace T

ensio

n, γ

(m

J/m


180 190 200

10

20

30

40

50

Time, t (s)

Surf

ace T

ensio

n, γ

(m

J/m

2) (c) Mixed with Inhibitor

0.8 0.9 1


Figure 2.15: Change in surface tension with time and with relative surface area duringdynamic cycling: (a) 2.0 mg/ml BLES and 0.2 mg/ml protasan (basic preparation); (b)After injecting 0.15 ml/ml serum into the bulk phase; (c) 2.0 mg/ml BLES and 0.2mg/ml protasan and 0.15 ml/ml serum mixed in a separate single injection experiment.All compressions/expansions are performed at 3 s/cycle periodicity in humid air (100%R.H.).


0 0.1 0.2 0.3 0.4 0.50

5

10

15

Min

imu

m S

urf

ace

Te

nsio

n, γ

min (

mJ/m

2)

Protasan Conentration (mg/ml)

BLES 2.0 mg/ml (batch 1)

BLES 2.0 mg/ml (batch 2)

Figure 2.16: Minimum surface tension (end of compression) as a function of protasanconcentration for different batches of BLES (2.0 mg/ml). All compressions (20%) areperformed at 3 s/cycle periodicity in humid air (100% R.H.).


10

20

30

40

50

Su

rfa

ce

Te

nsio

n, γ

(m

J/m

2) (a) After Bulk Replacement

180 190 200

10

20

30

40

50

Time, t (s)

Su

rfa

ce

Te

nsio

n, γ

(m

J/m

2) (b) Mixed with Inhibitor

0.8 0.9 1


Figure 2.17: Change in surface tension with time and with relative surface area duringdynamic cycling: (a) After injecting 0.30 ml/ml serum into the bulk phase of 2.0 mg/mlBLES and 0.2 mg/ml protasan; (b) 2.0 mg/ml BLES and 0.2 mg/ml protasan and 0.30ml/ml serum mixed in a separate single injection experiment. All compressions/expan-sions are performed at 3 s/cycle periodicity in humid air (100% R.H.).

batches (2.0 mg/ml) was plotted in figure 2.16. These values were obtained during the

dynamic cycling of single injection experiments. It is clear that the minimum surface ten-

sion of BLES alone, without any protasan, differs in these two batches from 5.5 mJ/m2

to 11.0 mJ/m2. It is also clear that adding a small concentration of protasan reduces the

minimum surface tension of both BLES batches; this is similar to the effect of chitosan

on different BLES batches [91]. In view of this figure, a preparation of 2.0 mg/ml BLES

and 0.2 mg/ml protasan is used as the basic preparation.

Figure 2.17(a) shows the change of surface tension, γ, with time during the first few

cycles in the dynamic cycling after injecting a higher concentration of serum, i.e. 0.30

ml/ml, into the bulk of the basic preparation (2.0 mg/ml BLES and 0.2 mg/ml protasan).


10

20

30

40

50

Su

rfa

ce

Te

nsio

n, γ

(m

J/m


180 190 200

10

20

30

40

50

Time, t (s)

Su

rfa

ce

Te

nsio

n, γ

(m

J/m


0.8 0.9 1


Figure 2.18: Change in surface tension with time and with relative surface area duringdynamic cycling: (a) After injecting 40 mg/ml albumin into the bulk phase of 2.0 mg/mlBLES and 0.2 mg/ml protasan; (b) 2.0 mg/ml BLES and 0.2 mg/ml protasan and 40mg/ml albumin mixed in a separate single injection experiment. All compressions/ex-pansions are performed at 3 s/cycle periodicity in humid air (100% R.H.).

The figure also shows the change of surface tension with relative surface area, Ar, for

one of the cycles. Figure 2.17(b) shows the change of surface tension with time and with

relative surface area for the mixture of the inhibitor (0.30 ml/ml serum) and the basic

preparation (2.0 mg/ml BLES and 0.2 mg/ml protasan) in a separate single injection

experiment. Figures 2.18, 2.19, and 2.20 show similar results for different inhibitors:

40.0 mg/ml albumin, 3.0 mg/ml fibrinogen, and 0.28 mg/ml cholesterol, respectively.

Results for injecting an inhibitor under a preformed film of the basic preparation and

mixing the inhibitor with the preparation (letting them adsorb together to form a film)

show a similar pattern for a wide range of inhibitors.

Results for albumin (figure 2.18) show that mixing with the basic preparation causes


10

20

30

40

50

Su

rfa

ce

Te

nsio

n, γ

(m

J/m


180 190 200

10

20

30

40

50

Time, t (s)

Su

rfa

ce

Te

nsio

n, γ

(m

J/m


0.8 0.9 1


Figure 2.19: Change in surface tension with time and with relative surface area duringdynamic cycling: (a) After injecting 3.0 mg/ml fibrinogen into the bulk phase of 2.0mg/ml BLES and 0.2 mg/ml protasan; (b) 2.0 mg/ml BLES and 0.2 mg/ml protasanand 3.0 mg/ml fibrinogen mixed in a separate single injection experiment. All compres-sions/expansions are performed at 3 s/cycle periodicity in humid air (100% R.H.).

an increase in the minimum surface tension and a decrease in film elasticity during

compression. On the other hand, the injection of albumin under a preformed surfactant

film did not change the minimum surface tension. However, injecting albumin caused an

increase in the film elasticity during compression, leading to a minimum surface tension

at a lower compression ratio, i.e. at approximately 12%, compared to the standard 20%.

Further compression caused film collapse (no further decrease in surface tension) leading

to film hysteresis as shown in figure 2.18(a).

Results for fibrinogen (figure 2.19) show a dramatic increase in the minimum surface

tension and a corresponding decrease in film elasticity during compression when fibrino-

gen was mixed with the basic preparation. However, when fibrinogen is injected under


10

20

30

40

50

Su

rfa

ce

Te

nsio

n, γ

(m

J/m


180 190 200

10

20

30

40

50

Time, t (s)

Su

rfa

ce

Te

nsio

n, γ

(m

J/m


0.8 0.9 1


Figure 2.20: Change in surface tension with time and with relative surface area duringdynamic cycling: (a) After injecting 0.284 mg/ml cholesterol into the bulk phase of 2.0mg/ml BLES and 0.2 mg/ml protasan; (b) 2.0 mg/ml BLES and 0.2 mg/ml protasanand 0.284 mg/ml cholesterol mixed in a separate single injection experiment. All com-pressions/expansions are performed at 3 s/cycle periodicity in humid air (100% R.H.).

a preformed film, the minimum surface tension in the first cycle was very close to that

of the basic preparation. Starting with the second cycle, the minimum surface tension

increased slightly and stayed constant during the rest of the 20 cycles. In this case, it

can be seen that the film elasticity during compression has decreased as well.

Results for cholesterol (figure 2.20) show an increase in the minimum surface tension

and a decrease in film elasticity during compression when cholesterol was mixed with

the basic preparation. On the other hand, when injected under a preformed surfactant

film, cholesterol does not tend to change the minimum surface tension, and in fact tends

to improve the film elasticity during compression. This can be seen from the increased

slope of the γ−Ar isotherm shown in figure 2.20(a) when compared to the corresponding


0

10

20

30

40

Min

imu

m S

urf

ace

Te

nsio

n, γ

min (

mJ/m

2)

Serum0.15ml/ml

Serum0.30ml/ml

Albumin40mg/ml

Fibrinogen3.0mg/ml

Cholesterol0.284mg/ml

After Bulk Replacement

Mixed with Inhibitor

Figure 2.21: Comparison of minimum surface tension for different inhibitors injected ormixed into a basic preparation of 2.0 mg/ml BLES and 0.2 mg/ml protasan. The dashedline shows the minimum surface tension of the basic preparation. All compressions (20%)are performed at 3 s/cycle periodicity in humid air (100% R.H.).

isotherm of the basic preparation shown in figure 2.15(a).

A comparison of minimum surface tension obtained during dynamic cycling for dif-

ferent inhibitors injected or mixed into the basic preparation of 2.0 mg/ml BLES and 0.2

mg/ml protasan is shown in figure 2.21. For all the inhibitors tested here, the minimum

surface tension of the basic preparation (before injection) did not change significantly

after injecting the inhibitor. However, when the same inhibitors are mixed with the

basic preparation and adsorb together to form a film, the minimum surface tension is

significantly higher as shown in figure 2.21.

The corresponding comparison for the dilatational elasticity, ε, obtained during dy-

namic cycling for different inhibitors injected as well as mixed into the basic preparation


0

50

100

150

200

Ela

sticity o

f C

om

pre

ssio

n,

εcom

(m

J/m

2)

Serum0.15ml/ml

Serum0.30ml/ml

Albumin40mg/ml

Fibrinogen3.0mg/ml

Cholesterol0.284mg/ml

After Bulk Replacement

Mixed with Inhibitor

Figure 2.22: Comparison of elasticity of compression for different inhibitors injected ormixed into a basic preparation of 2.0 mg/ml BLES and 0.2 mg/ml protasan. The dashedline shows the elasticity of compression of the basic preparation. All compressions (20%)are performed at 3 s/cycle periodicity in humid air (100% R.H.).


10

20

30

40

50

Su

rfa

ce

Te

nsio

n, γ

(m

J/m

2) (a) Serum only

180 200 220

10

20

30

40

50

Time, t (s)

Su

rfa

ce

Te

nsio

n, γ

(m

J/m


0.8 0.9 1


Figure 2.23: Change in surface tension with time and with relative surface area duringdynamic cycling: (a) 0.01 ml/ml serum; (b) After injecting 2.0 mg/ml BLES and 0.2mg/ml protasan into the bulk phase. All compressions/expansions are performed at 3s/cycle periodicity in humid air (100% R.H.).

of 2.0 mg/ml BLES and 0.2 mg/ml protasan is shown in figure 2.22. The trends here are

similar to the comparison of the minimum surface tension. For the cases of serum and

albumin, the elasticity of the film of the basic preparation did not change significantly

after injecting the inhibitor. However, for the case of fibrinogen, the injection caused the

elasticity to decrease to reach a value close to that obtained from the mixture. Interest-

ingly, cholesterol apparently increased the elasticity (improved the film properties) after

being injected under the preformed film of the basic preparation.

So far, only the effect of injecting an inhibitor under a preformed film of an active

basic preparation has been studied. Another important aspect that can be studied using

this new technique is inhibition reversal, i.e. the ability to restore the normal surface

activity of an inhibited lung surfactant film. An experiment illustrating this concept is


shown in figure 2.23. In this experiment, a film was originally formed using 0.01 ml/ml

serum only (as the basic preparation in this case). Changes of surface tension with time

and with relative surface area during the dynamic cycling are shown in figure 2.23(a);

the minimum surface tension obtained in this case is 38.0 ±0.2 mJ/m2. A preparation

of 2.0 mg/ml BLES and 0.2 mg/ml protasan is subsequently injected into the preformed

film of serum, and the change of surface tension with time during the dynamic cycling

(after the injection) is shown in figure 2.23(b). This figure shows 12 cycles out of a total

of 20 cycles performed, the rest of the cycles did not show significant further changes.

The change of surface tension with relative surface area is shown for the twelfth cycle.

The minimum surface tension obtained after 12 cycles is 5.7±0.6 mJ/m2. This effectively

shows that a film of dilute serum can be replaced at least partially by a preparation of

BLES and protasan.

2.3.3 Discussion

2.3.3.1 Methodology Evaluation

In order to manipulate and intervene with a lung surfactant film in vitro, it is desirable

to have access to the film from both the liquid and the air side. In ADSA–CSD, access

from the air side is quite easy, as shown in Section 2.2. A deposition procedure to

spread films on the interface was developed and used. But access from the liquid side is

also possible and the necessary development has been described above. As the present

development does not affect any core parts of ADSA–CSD, the results have the same

reliability as those of previous studies [25, 48, 76, 88, 91]. The vehicle chosen here to

illustrate capabilities of bulk substrate manipulation is the resistance of existing lung

surfactant films against inhibitors and, briefly, to document the possibility of reversing

inhibition, i.e. the removal of inhibitors from the surface film.

A key feature of ADSA–CSD is the ability to use relevant physiological conditions in


terms of compression rates and environmental control (contamination, humidity, pressure

and temperature). Other conventional methods also have some of these features, but

typically not all. For example, a hypophase exchange system was used in conjunction

with a Pulsating Bubble Surfactometer to study the effect of albumin as an inhibitor on

a preformed lung surfactant film [34]. However, film leakage from the bubble surface into

the capillary tube at low surface tension values is a common complication [36]. Other

limitations are the inaccurate calculation of low surface tension values due to spherical

shape assumption [27], and the difficulty of controlling the environmental conditions.

2.3.3.2 Inhibition Study: Effect of Film Formation

The leakage of plasma and blood proteins into the alveolar spaces is a common cause of

severe lung injury. The results presented here show a distinctive difference between the

inhibition of a specific inhibitor when mixed with and when injected under a preformed

surfactant film. Generally, all the inhibitors studied here (serum, albumin, fibrinogen,

and cholesterol) were not able to penetrate the film or affect the lowering surface tension

ability of the chosen basic preparation film (BLES and protasan), while all of them can

alter the surface activity when mixed with the preparation. Figure 2.21 compares the

minimum surface tension achieved in both cases for every inhibitor. On the other hand,

changes in the elasticity of the film during compression (i.e. the inverse of film com-

pressibility) gives useful insight into the effect of every inhibitor. Some of the inhibitors

studied here have altered the film compressibility without showing any changes in the

minimum surface tension measured during the dynamic cycling. Detailed discussion for

every inhibitor is given below.

Two concentrations of serum were studied here, 0.15 and 0.30 ml/ml. They show a

similar pattern when mixed with the basic preparation (BLES and protasan). The min-

imum surface tension values measured for both concentrations was significantly higher

and the elasticity of film compression was much lower than that for the basic preparation


alone. On the other hand, when the bulk phase of the basic preparation was replaced

with serum (under a preformed film), the minimum surface tension did not change signif-

icantly. It can be seen from figures 2.15(b) and 2.17(a) that the first cycle after the bulk

replacement can go to a very low surface tension value (indicating a good film at this

point). Starting with the second cycle, the minimum surface tension increased slightly.

Comparison of the γ −Ar isotherms in the same two figures with figure 2.15(a) suggests

that having serum under a preformed lung surfactant film does not change the minimum

surface tension but it does increase the hysteresis as shown in the figures. Obviously,

this increase in film hysteresis must be due to change in film properties other than the

minimum surface tension. Such properties include the film elasticity during the compres-

sion part as shown in figure 2.22. Another important property is the film relaxation at

the end of the compression, where further decrease in film area causes an increase in the

surface tension. It is apparent that the characterization of inhibition mechanisms will

require other surface properties in addition to the minimum surface tension; this will be

discussed further in Chapter 3.

Results obtained here from premixing albumin and BLES shows the inhibition of the

lung surfactant when it is to co-adsorb with albumin as shown in figure 2.18(b). The

minimum surface tension was increased and the elasticity was decreased. However, for

the case of introducing albumin under a preformed film of lung surfactant, results here

suggest that the dynamic surface tension lowering ability of the film was not altered.

Similar results were obtained before for a lower range of albumin concentrations (3 to 6

mg/ml) than used here using the hypophase exchange system with PBS [34]. However,

since we have here complete information about the change of surface tension and area

during the cycling, we are able to report that the elasticity of the film has changed as

shown in figure 2.18(a). In this figure, the minimum surface tension was reached at a

lower degree of area reduction. This suggests a slight increase in the film elasticity in

this case.


Results obtained here suggest that fibrinogen is more potent than other inhibitors

when mixed with lung surfactant preparations as shown in figure 2.21, causing a very

significant increase in the minimum surface tension during the dynamic cycling. The

severe inhibition effect of fibrinogen has been reported in previous studies [116, 117, 120,

122, 140]. However, results show that injecting fibrinogen under a preformed film of

lung surfactant did not significantly change the minimum surface tension. As shown

in figure 2.19(a), the first cycle after the bulk replacement can go to a very low surface

tension value, but the minimum surface tension increased slightly starting from the second

cycle. It is important to note that fibrinogen reduces the film elasticity much more

severely than other inhibitors when injected under a preformed surfactant film as shown

in figure 2.22.

Similar to the other inhibitors, cholesterol increases the minimum surface tension

when mixed with lung surfactant preparation. Results show that the effect of the same

concentration of cholesterol is different for the case of introducing the cholesterol to the

subphase of a preformed film versus premixing with the lung surfactant preparation prior

to film formation. When injected under a preformed film, cholesterol did not significantly

change the minimum surface tension and it actually improved the film elasticity as shown

in figures 2.21 and 2.22. Cholesterol, which is removed from complete lung surfactant

in the preparation of BLES, is one of the main neutral lipids in lung surfactant with

a concentration of around 10% of the surfactant lipids [141, 142]. Until recently, lung

surfactant inhibition has been attributed to factors other than cholesterol. However, it

was reported that elevated levels of cholesterol have the ability to impair and inhibit lung

surfactant, affecting its ability of dynamic surface tension lowering [128, 129, 143–145].

2.3.3.3 Inhibition Reversal

The methodology developed above allows study of inhibition reversal, i.e. the restoration

of the normal surface activity of an inhibited lung surfactant film. This is illustrated in


figure 2.23. While a mixture of BLES and protasan has been used to form the initial

film so far, in this experiment a film was originally formed using serum only as the basic

preparation. The serum was allowed to adsorb first to form a film at the interface and the

dynamic surface tension was measured as shown in figure 2.23(a). Then the serum bulk

was replaced by a preparation of BLES and protasan and the dynamic surface tension

was measured again as shown in figure 2.23(b). The first few cycles are close to those

before bulk replacement. Starting from the sixth cycle the minimum surface tension

started to decrease from 38.0 ±0.2 mJ/m2 to 5.7±0.6 mJ/m2. Beyond the twelfth cycle

there was no further significant change in the minimum surface tension. The changes

from cycles 6 to 12 indicate that the preparation of BLES and protasan was able to

replace serum components at the interface, effectively reversing the serum inhibition. A

low concentration of serum (0.01 ml/ml) was used in this experiment just to illustrate

the capacity of the new methodology proposed here. More detailed investigations can be

readily performed.

In a recent study, spreading experiments using a Langmuir trough showed that serum

(with concentrations as low as 0.0017 ml/ml) alone adsorbs to the air-water interface

[118]. When a clinical lung surfactant (Curosurf) was spread on top of the adsorbed

serum film, only minimal decreases in surface tension were observed. This is similar to

what is seen in figure 2.23 where the equilibrium surface tension did not change before

and after the bulk replacement. However, in that previous study, only adsorption time

could be investigated, not the dynamic cycling.

In conclusion, a novel methodology for studying adsorbed or spread surfactant films

before and after replacing one bulk subphase with another possibly also containing sur-

face active material was presented. This technique allowed lung surfactant films to be

formed by adsorption from a surfactant subphase and to be studied on a new subphase

containing inhibitor molecules rather than surfactant. Such studies were performed at

physiologically relevant conditions, mimicking the leakage of plasma and blood proteins


into the alveolar spaces. The main advantage of the new method, in addition to com-

plete leakage elimination and controlled physiologically relevant conditions inherent in

ADSA–CSD, is the ability to exchange the subphase after forming adsorbed or spread

films.

Chapter 3

Dynamic Surface Tension Model∗

3.1 Introduction

A key property of lung surfactants is their dynamic surface tension response to film com-

pression and expansion. To assess the performance of surfactant preparations subject

to dynamic compression/expansion, typically only the minimum surface tension at the

end of compression is reported. While the minimum surface tension is useful for a pre-

liminary assessment, it has to be realized that it depends on the method of compression

[46]. Increasing the extent of compression or the speed of compression may significantly

change the value of the minimum surface tension achieved [25]. In fact, this makes the

comparison of different literature values difficult in the case of different compression pro-

tocols. Therefore, there is a need to concentrate on the properties of the film itself such

as the elasticity and the relaxation as proposed in the literature [25, 147] rather than

simply reporting the minimum surface tension achieved. In this chapter, a new approach

to evaluate the quality of lung surfactant preparations is developed – beyond the γmin

value as the only quantitative characteristic – based on determining the film properties

for any compression protocol.

∗A portion of this chapter was previously published in Ref. [146], reproduced with permission.

76

Chapter 3. Dynamic Surface Tension Model 77

In ADSA–CSD experiments, a large amount of data is collected including the surface

tension as a function of time as well as the change of the drop surface area and vol-

ume. Such results can provide valuable information about various properties of the film.

ADSA–CSD is used to perform dynamic cycling by successive compression/expansion of

the drop via programmed cycling of the drop volume. This is normally done through 20

cycles with a periodicity of 3 seconds per cycle and a compression ratio (percentage of

surface area reduction) of 20% to simulate normal human breathing.

A typical experimental result for 2.0 mg/ml BLES at 100% relative humidity and

37C is shown in figure 3.1. Dynamic cycling starts after an equilibrium surface tension

value due to adsorption is reached. The response of surface tension for a trapezoidal

change of drop surface area is shown. Parenthetically, the trapezoidal perturbation of

the drop volume is a consequence of the backlash of the stepping motor controlling the

syringe. The fluid mechanics rounds off the corner of the trapezoidal perturbation as

shown in the figure. In region A, the drop volume is decreased causing a decrease in

drop surface area and a corresponding decrease in surface tension due to compression.

In region B, the drop volume is kept constant while the motor is reversing its direction;

therefore, the surface area is almost constant. The surface tension in this region starts to

increase towards the equilibrium value. In region C, the drop volume is increased causing

an increase in drop surface area and a corresponding increase in surface tension due to

expansion. In region D, the drop volume is kept constant while the motor is reversing its

direction to start a new cycle; therefore, the surface area is almost constant. The surface

tension in this region starts to decrease towards the equilibrium value again.

The response of surface tension for every part of the trapezoidal area change is useful

to understand different film properties. For regions A and C in figure 3.1, the response

of surface tension to a continuous decrease (A) or increase (C) in surface area gives an

indication of the dilatational elasticity of the surfactant film. For regions B and D in

figure 3.1, the response of surface tension to a constant surface area gives an indication


Figure 3.1: The change of surface tension and surface area with time of one cycle for 2.0mg/ml BLES at wet conditions, 37C, and 20% compression ratio with a periodicity of3 seconds per cycle.


of the interfacial adsorption/desorption of the surfactant film. If the surface tension is

above the equilibrium value, adsorption is dominant (region D) and promotes a decrease

in the surface tension towards the equilibrium value. However, if the surface tension is

below the equilibrium value, desorption is dominant (region B) and promotes an increase

in the surface tension towards the equilibrium value.

It is important to note that near the end of region A, there are two simultaneous

effects: elasticity (due to the continuous decrease in surface area) and desorption (because

the surface tension is below the equilibrium value). Similarly, near the end of region C,

there are two simultaneous effects: elasticity (due to the continuous increase in surface

area) and adsorption (because the surface tension is above the equilibrium value).

It is necessary to quantify the dynamic surface tension responses in regions A, B, C,

and D through adequate models that can reflect elasticity of the lung surfactant film as

well as adsorption and desorption at the interface. Such phenomena have been studied,

separately, by different groups. The most relevant studies are reviewed here. However,

for the case of pulmonary surfactant films, it is expected that more than one of these

phenomena are acting at any given time. The combined effect can be evaluated by simple

addition of individual effects. This idea is introduced and evaluated in this chapter.

The simplest possible model is considered here to explain the changes in the sur-

face tension during the dynamic cycling based on three main well known processes:

adsorption/spreading, desorption/relaxation, and elasticity/compressibility. The proce-

dure developed in this chapter is to evaluate the quality of lung surfactant preparations

– beyond the γmin value as the only quantitative characteristic – based on calculating the

film properties independent of the compression protocol used. The results show that the

proposed models can explain the performance of different lung surfactant preparations

based on the chosen effective dynamic parameter.

The structure of this Chapter is as follows: Previous dynamic models are reviewed

and summarized in Section 3.2. A proposed model called Compression–Relaxation Model


(CRM) is introduced and developed in detail in Section 3.3. Sample experiments are used

with the previous models and the new developed CRM in Section 3.4 for comparison pur-

poses. The computational details of CRM and how to use the model with experimental

data are explained in the same section. Section 3.5 shows a detailed study of the dynamic

surface tension (using CRM) of a lung surfactant preparation, BLES, at concentrations,

compression ratios and compression rates relevant to current exogenous surfactant ther-

apies. A detailed sensitivity study of CRM is also presented in the same section.

3.2 Previous Models

There are two approaches to describe the dynamics of adsorption at liquid/air interfaces.

The diffusion controlled model assumes that the diffusional transport of interfacially

active molecules through the bulk is the rate limiting process and that the adsorption

is instantaneous. In the kinetic model, the adsorption and desorption steps are the rate

limiting processes.

3.2.1 Diffusion Model

One of the available diffusion models assumes that the surface tension relaxation is dom-

inated by a translational-diffusion mechanism [136]. According to this mechanism, the

surfactants diffuse through the subphase to reach the air/water interface, so that the

magnitude of surface tension reduction (∆γ) is:

∆γ1(t) =Ωεo2ωo

exp (2ωot) erfc(√

2ωot)

+Ωεo√t√

2πωo− Ωεo

2ωo0 < t ≤ t1 (3.1a)

∆γ2(t) = ∆γ1(t)−∆γ1(t− t1) t1 < t ≤ t2 (3.1b)

∆γ3(t) = ∆γ2(t)−∆γ2(t− t2) t2 < t ≤ t3 (3.1c)

∆γ4(t) = ∆γ3(t)−∆γ3(t− t3) t > t3 (3.1d)


where Ω is the area constant, εo is the elasticity constant, and ωo is the diffusion constant:

Ω =d lnA

dt=

1

t1ln

(1− ∆A

Ao

), εo = − dγ

d ln Γ, ωo =

D

2

(dc

dΓ

)2

(3.2)

where Γ and c are the surface and bulk concentrations, and D is the diffusion coefficient.

This surface tension response is based on a trapezoidal change in surface area where t1,

t2 and t3 are the limits of different time domains associated with this change as shown

in regions A, B, C, and D in figure 3.1.

The model parameters εo and ωo (defined above) are surface thermodynamic proper-

ties. Their values, obtained from fitting different surfactants, depend on the concentra-

tion c and on the surface activity dγ/dc. This model was compared to experiments using

a variety of soluble surfactants: n-dodecyl-dimethyl-phosphine oxide (DC12PO), sodium

bis(2-ethylhexyl)-sulfo-succinate (DESS), and n-octadecyl-trimethyl-ammonium bromide

(STAB). Good agreement was obtained between experimental data and the theoretical

curves for the selected soluble surfactants [136]. Other models were also developed for

soluble surfactants [148, 149]. However, the diffusion model may not be the most ap-

propriate for insoluble surfactant systems, like lung surfactants, where the exchange of

matter with sub-surface material controls the dynamic of these systems [150].

3.2.2 Kinetic Model

As mentioned above, other models exist beside the diffusion-controlled one to describe

the adsorption kinetics and exchange of matter. Most of them are based on the Langmuir

hypothesis about the nature of the adsorbed layer considering that there is an equilibrium

between the subsurface and the bulk of the solution. The rate of adsorption can be written

as the difference between adsorption and desorption as follows [151]:

dΓ

dt= k1c

(1− Γ

Γ∗

)− k2

Γ

Γ∗ (3.3)


where Γ is the surface concentration, Γ∗ is the maximum equilibrium surface concentra-

tion, c is the bulk concentration, k1 is the adsorption coefficient, and k2 is the desorption

coefficient.

A model for an adsorption layer relaxation was derived [151] by considering the time-

dependent square pulse area A(t). In this model, the interfacial tension response can be

calculated as:

∆γ1(t) = εo∆A

Aoexp (−Kt) 0 < t ≤ t1 (3.4a)

∆γ2(t) = ∆γ1(t)−∆γ1(t− t1) t > t1 (3.4b)

where t1 is time range of the square pulse cycle while the area is compressed, ∆A/Ao is

the relative area change, εo is the elasticity coefficient and K is the sorption coefficient

(Langmuir Isotherm).

εo = − dγ

d ln Γ= RTΓ∗ Γ/Γ∗

1− Γ/Γ∗ , K =k1c

Γ∗ +k2Γ∗ (3.5)

Equation 3.4 can be used to interpret experimental data by the use of a fitting proce-

dure. It is important to note that equation 3.4 suggests that adsorption and relaxation

are first order processes. The resulting values for εo and K are obtained independently

of any knowledge of the parameters of the equilibrium adsorption isotherm. On the

other hand, both parameters contain specific constants of the adsorption isotherm and

are therefore of interest also from this point of view.

The results of relaxation experiments of human albumin (HA) adsorbed at the aque-

ous solution/air interfaces [152] were discussed on the basis of the diffusion model as

shown in equation 3.1. The resulting diffusion coefficients were found to be two to three

orders of magnitude higher than the physically expected value. It was concluded that

the adsorption layer of human albumin at the aqueous solution/air interface shows a dy-


namic behaviour similar to that of surfactants, while relaxations after area disturbances

are reversible and controlled by a mechanism other than diffusion.

The same experimental data were interpreted using both models [151]: the diffusion

model (equation 3.1) and the kinetic model (equation 3.4). It was shown that the kinetic

model yields values of the parameters which are rather consistent (considering different

cycles of the same run) while those obtained from the diffusion model are more scattered.

3.2.3 Adsorption-Limited Model

In another model, transport of surfactant to the interface is assumed to be adsorption-

limited as opposed to diffusion-limited [153]. Several assumptions were adopted; one

is that there exists a maximum surfactant concentration to which the interface can be

dynamically packed, and when interfacial area is reduced from this point, surfactant is

squeezed out from the surface. Another assumption is that transport of surfactant to the

interface is adsorption rather than diffusion limited. When the interfacial concentration

of surfactant is less than its maximum equilibrium value, adsorption and desorption are

controlled by Langmuir kinetics, while for interfacial surfactant concentrations between

the maximum equilibrium value and the maximum packing concentration, the surfactant

is frozen in the surface and can neither adsorb nor desorb. The kinetics of adsorption

and desorption were defined in this model by three interfacial surface concentration (Γ)

regimes:

d(AΓ)

dt= A [k1C(Γ∗ − Γ)− k2Γ] Γ < Γ∗ (3.6a)

d(AΓ)

dt= 0 Γ∗ < Γ < Γmax (3.6b)

d(AΓ)

dt= −Γmax

dA

dtΓ = Γmax (3.6c)

where k1 is the adsorption coefficient, k2 is the desorption coefficient, C is the bulk

concentration, Γ∗ is the maximum equilibrium surface concentration, and Γmax is the


maximum dynamic surface concentration (collapse).

The relationship between the normalized interfacial concentration, Γ/Γ∗, and the

surface tension, γ, is the compression isotherm. The compression isotherm is modeled

as two straight lines that meet at Γ = Γ∗, the slopes for both regions are m1 and m2.

Therefore, surface tension can be calculated as follows:

γ = γo −m1Γ

Γ∗Γ

Γ∗ < 1.0 (3.7a)

γ = γ∗ −m2

(Γ

Γ∗ − 1

)ΓmaxΓ∗ ≥

Γ

Γ∗ ≥ 1.0 (3.7b)

where γo is the water surface tension, γ∗ is the equilibrium surface tension, m1 is the

isotherm slope for γ > γ∗, and m2 is the isotherm slope for γmin < γ < γ∗.

This model [153] was used to characterize the dynamic behaviour of lung surfactant

fractions [154], containing: (1) phospholipids (PL) only, (2) PL and hydrophobic apopro-

teins (HA), (3) PL and HA and surfactant protein A (SP-A), and (4) PL and HA and

SP-A and neutral lipids (NL). The results were compared to those of native surfactant

and dipalmitoyl-phosphatidyl-choline (DPPC). The effect of individual components on

the surface activity (minimum surface tension, adsorption, film compressibility) of the

mixture was evaluated by comparing the experimental results to the model predictions.

It was noted that the model produces predictions that are qualitatively but not quanti-

tatively close to the experimental results for most of the cases.

The adsorption-limited model [153] was later extended to characterize the initial tran-

sient behaviour (that occurs upon initiation of pulsation, before steady-state was reached)

by including the effects of diffusion in the bulk phase and comparing the results to both

transient and steady-state oscillatory data [155]. It was concluded that at steady-state

cycling conditions, diffusion-limited transport is most relevant. While there are a num-

ber of situations in which the extended model gives significantly improved predictions,

steady-state oscillatory data at high bulk concentration are still adequately modeled by


an adsorption-limited model, which is computationally more efficient. When compared

to previous experimental data [154], both models yield results that are very close to each

other but are far from the experimental results.

3.3 Development of Compression–Relaxation Model

As inferred from the dynamic experiments, there are four main factors that affect the

response of the dynamic surface tension: adsorption or spreading, desorption or relax-

ation, elasticity during compression and elasticity during expansion. In the proposed

model, the adsorption and relaxation rates depend on how far the surface tension is from

the equilibrium value while the elasticity for both compression and expansion depends

on changes in the surface area of the interface. The main feature is to allow the surface

tension to change due to simultaneous effects of one or more of these parameters.

3.3.1 Adsorption Process (Spreading)

Based on the Langmuir hypothesis, the rate of adsorption can be written as the difference

between adsorption and desorption as shown in equation 3.6a. As mentioned before, Γ∗ is

the maximum equilibrium interfacial concentration, i.e. the limiting value of Γeq reached

as c (concentration) is increased. Also, Γeq can be calculated as [153]

ΓeqΓ∗ =

k1c

k1c+ k2(3.8)

Note that equation 3.6a predicts adsorption for surface concentration less than the

equilibrium concentration, Γeq, and desorption for concentrations greater than this. There-

fore, for surface concentration less than Γeq (surface tension greater than γeq) and for a

given concentration and constant surface area, that equation can be simplified to

dΓ

dt= k(Γeq − Γ) (3.9)


where k is a coefficient for the dynamic adsorption and desorption. This indicates that

both rates of adsorption/spreading and desorption/relaxation are proportional to the

difference between the surface coverage at any time and the equilibrium surface coverage.

However, since the mechanisms of adsorption and desorption for pulmonary surfactant

compounds are different, we use here two coefficients, one for adsorption and another for

desorption.

Assuming a linear relationship between the surface concentration and the surface

pressure in the region above the equilibrium surface tension (equivalent to the assump-

tions behind equation 3.7 in the adsorption-limited model [153]), equation 3.9 can be

further simplified to

dγ

dt= ka(γeq − γ) for γ ≥ γeq (3.10)

where ka is the adsorption coefficient.

It is important to note that the above equations were derived for a single component

system. It is assumed here that it is also valid for multi-component systems, where

the coefficient now has to be understood as an effective constant for the system, not any

specific material. The comparison between experimental results and the developed model

will show whether this assumption is reasonable.

3.3.2 Desorption Process (Relaxation)

As mentioned earlier, equation 3.6a predicts adsorption for surface concentration less

than the equilibrium concentration, Γeq, and desorption for concentrations greater than

this. Therefore, for surface concentration greater than Γeq (surface tension less than γeq)

and constant surface area, a simplified desorption relation similar to that of equation 3.10

can be used,

dγ

dt= kr(γeq − γ) for γ ≤ γeq (3.11)

where kr is the desorption or relaxation coefficient.


Non-equilibrium surface pressures occurring during dynamic compression are believed

to indicate the formation of metastable surface states within phospholipid films [1]. When

the compression is stopped (the surface area is kept constant), the dynamic surface

pressure relaxes towards the equilibrium values. Relaxation has also been studied [156–

158] in terms of a nucleation mechanism [159–161] through which a similar expression to

equation 3.11 can be derived. After compression beyond collapse, the dynamic surface

pressure becomes more stable and remains in the vicinity of the dynamic collapse value

over an extended time scale [162].

3.3.3 Elasticity

The dilational interfacial elasticity is defined by [136, 151],

εo = − dγ

d lnA(3.12)

which is equivalent to

dγ

dt= −εo

(1

A

dA

dt

)(3.13)

If we consider different elasticities for compression and expansion, the above equation

becomes,

dγ

dt=

εc

(1

A

dA

dt

)for

dA

dt≤ 0

εe

(1

A

dA

dt

)for

dA

dt≥ 0

(3.14)

3.3.4 Collapse

It is well known that many surfactant layers at the interface can be compressed to pres-

sures considerably higher than their equilibrium spreading pressure [1, 92, 93]. As dis-

cussed in Chapter 2, if compression continues beyond an ultimate collapse pressure, the

surfactant layers collapse ejecting surfactant molecules into one or more surface or subsur-


face collapse structures or phases [1, 93]. Therefore, once the ultimate collapse pressure,

i.e. the minimum surface tension, is reached, the surface tension can not be further

decreased by more compression. This can be formulated as follows

dγ

dt= 0 for γ ≤ γmin (3.15)

3.3.5 The Integrated Model

Combining equations 3.10, 3.11, 3.14, and 3.15 and allowing the surface tension to change

due to simultaneous effects of relaxation/adsorption and elasticity, we obtain:

dγ

dt=

dγ1dt

+dγ2dt

if γ ≥ γmin

0 if γ ≤ γmin

(3.16a)

where

dγ1dt

=

ka (γeq − γ) if γ ≥ γeq

kr (γeq − γ) if γ ≤ γeq

(3.16b)

dγ2dt

=

εc

(1

A

dA

dt

)ifdA

dt≤ 0

εe

(1

A

dA

dt

)ifdA

dt≥ 0

(3.16c)

According to this model better lung surfactant preparations can be identified as having

faster adsorption rate (higher ka), slower relaxation rate (lower kr), and higher elasticity

of compression and expansion (higher εc and εe). Figure 3.2 shows a comparison between

two hypothetical dynamic surface tension responses, where one has desired dynamic

properties and the other does not. The figure shows schematics based on an assumed,

i.e. exact, trapezoidal change in surface area. However, it is important to note that the

proposed model does not assume any specific perturbation waveform and can be applied


to various perturbations including trapezoidal and sinusoidal.

These dynamic parameters are actually very similar to those used in the previous

models. The elasticities of compression and expansion, εc and εe, are defined in the same

fashion as the elasticity constant, εo, in both the diffusion model [136] and the kinetic

model [151]. The adsorption coefficient, ka, is similar to that used in the adsorption-

limited model [153]. Thus, the equations involving these parameters are not novel, but

it is the simultaneous solution for these parameters that makes this model unique. The

model introduces the possibility of simultaneous compression and relaxation effects. It

is important to note that the calculations of these parameters in the current model are

based directly on the surface tension rather than the surface concentration. This allows

the direct use of ADSA output (changes in surface tension and surface area with time)

in the fitting procedure to estimate the film properties.

3.4 CRM Applied to Sample Experiments


Details about the experimental setup and procedure were given in Chapter 2. During the

experiment, the setup is enclosed in an environmental control chamber that facilitates the

control of gas composition and temperature. The humidity inside the chamber was kept

constant (wet at 100% relative humidity or dry < 20% relative humidity) at 37C. The

dynamic cycling experiments were carried out by periodically injecting/withdrawing liq-

uid from the drop. After reaching the equilibrium surface tension value, dynamic cycling

is started. The dynamic cycling consists of four sub-stages: compression, relaxation,

expansion and re-adsorption, as indicated in the discussion of figure 3.1. Throughout

Section 3.4, the compression conditions were: compression periodicity of 3 s/cycle, and

compression ratio (fraction of surface area reduction) of 20% to simulate normal breathing

conditions [1, 163].


Surf

ace A

rea, A

Time, t

(a)

Su

rfa

ce

Te

nsio

n, γ

Time, t

(b)

Su

rfa

ce

Te

nsio

n, γ


(c)

Figure 3.2: The response of surface tension to a trapezoidal change in surface area usingthe new compression-relaxation model for a good (solid line) and a bad (dashed line)system: (a) the trapezoidal change of surface area with time; (b) the response of surfacetension with time for both systems; (c) the change of surface tension with the relativesurface area for both systems. The good system (solid line) is generated using parameters:εc = 150 mJ/m2, εe = 150 mJ/m2, kr = 0.1 s−1, ka = 5 s−1. The bad system (dashedline) is generated using parameters: εc = 70 mJ/m2, εe = 70 mJ/m2, kr = 0.3 s−1, ka =0.1 s−1.


It was shown in recent studies [25, 46, 47] that BLES films are less stable in humid

environments than in dry ones and tend to have lower surface activity compared to BLES

films in dry air. To further investigate the effect off humidity, five formulations were used

for model comparisons: 0.5 mg/ml BLES (humid air) [25, 91], 0.5 mg/ml BLES (dry air)

[25, 91], 2.0 mg/ml BLES (humid air) [91], 2.0 mg/ml BLES (dry air) [91], and 0.5 mg/ml

BLES mixed with 2.5 mg/ml Albumin (humid air) [47]. The last formulation is chosen

to illustrate the effect of a known inhibitor on the surface activity and film properties of

BLES.

3.4.2 Computational Details

The proposed compression/relaxation model, as summarized in equation 3.16, is able

to predict the surface tension response of a surfactant preparation for a given change

in surface area with time, assuming an a priori knowledge of the above mentioned four

dynamic parameters: adsorption coefficient (ka), desorption coefficient (kr), elasticity of

compression (εc), and elasticity of expansion (εe). The numerical procedure for determin-

ing these four parameters requires three steps: First, the differential equation 3.16 must

be solved using numerical integration to generate a surface tension response. Second,

initial guesses for the four parameters are needed; the experimental results are analyzed

to calculate approximate values (initial guesses) for these parameters. Third, an opti-

mization procedure is required to compare the calculated surface tension values with the

experimentally measured values, and modifying the parameter values until a matched

surface tension response is obtained. These three steps are explained in detail below.

3.4.2.1 Numerical Integration

Equation 3.16 is considered as a set of ordinary differential equations and can be solved

using an initial value problem solver for given values of the four dynamic parameters.

A variable order Adams-Bashforth-Moulton PECE solver [164] is implemented for the


numerical integration. This method is considered more efficient than the Runge-Kutta

solver at stringent tolerances and when the ordinary differential equations set is particu-

larly expensive in computation time. This solver is a multi-step solver; it normally needs

the solutions at four preceding time points to compute the solution at a specific point in

time. The first point is usually the first surface tension value measured experimentally.

The following three points are usually calculated using the Runge-Kutta solver and then

the Adams-Bashforth-Moulton solver is used afterwards.

3.4.2.2 Initial Guess

As mentioned earlier, an initial guess for the dynamic parameters is required for the

curve fitting module. Simple methods previously used to calculate dilatational elasticity,

adsorption, and relaxation rates in the literature [25, 47, 91] are used to estimate initial

values.

For the elasticity of compression and expansion, the change of surface tension with the

relative surface area during the compression/expansion part of every cycle is fitted to a

fourth order polynomial and the slope is evaluated at the midpoint [91]. The calculated

slope and the value of the relative surface area are used to calculate the dilatational

elasticity according to equation 3.12. This is similar to what was used in Chapter 2.

For the adsorption and desorption coefficients, the surface tension increase/decrease

with time (region B and D in figure 3.1) is fitted to a fourth order polynomial and the

slope is evaluated at the midpoint [91]. The calculated slope and the difference between

the surface tension value and the equilibrium surface tension value are used to calculate

the adsorption and desorption coefficients according to equations 3.10 and 3.11.

3.4.2.3 Curve Fitting (Optimization Procedure)

Once the initial guesses for the dynamic parameters are calculated, the numerical in-

tegration is performed and the calculated surface tension response is compared to the


experimental values using a curve fitting module (optimization procedure). Multidimen-

sional unconstrained nonlinear minimization (Nelder-Mead) is used to find the minimum

of a fitting residual function, < (see equation 3.17 below), using the simplex derivative-

free search method [165]. This is a direct search method that does not use numerical or

analytic gradients. At the end of this module, the four dynamic parameters are obtained

from the experimental result of a specific cycle. The same procedure is applied for differ-

ent cycles (typically 20 cycles) and the values reported below are the average value and

the standard deviation for a specific preparation.

3.4.3 Results

The proposed compression-relaxation model for dynamic characterization is implemented

using the above mentioned numerical details. Four preparations (high and low concentra-

tion of BLES with humid and dry conditions) were selected to illustrate the significance

of different parameters. Figure 3.3 shows the change of surface tension with the relative

surface area of one cycle for these preparations. The compression/expansion cycles of

surface layers are commonly used for qualitative and quantitative data analysis as pro-

posed in the literature [166]. The model predictions fit most of the experimental points

well. Figure 3.4 shows the change of surface tension and surface area with time for the

same four preparations. In the same figure, the compression-relaxation model is com-

pared to other models, i.e. the adsorption-limited model and the diffusion model. The

kinetic model was considered but can not be compared because it was designed to work

only with square pulse changes in surface area, which is not the case for the experiments

considered here. The results in figure 3.4 show that the proposed compression-relaxation

model has better quantitative agreement with experimental results than other models.

A special case is shown in figure 3.5, where the film has collapsed at a high surface

tension due to the presence of albumin in BLES. The proposed compression-relaxation

model shows again a better fit with the experimental points compared to other models.


0.8 0.9 10

10

20

30

40BLES 0.5 mg/ml (H)


Surf

ace T

ensio

n, γ

(m

J/m

2)

Exp.

CRM

(a)

0.8 0.9 10

10

20

30

40BLES 0.5 mg/ml (D)


Surf

ace T

ensio

n, γ

(m

J/m

2)

Exp.

CRM

(b)

0.8 0.9 10

10

20

30



Surf

ace T

ensio

n, γ

(m

J/m

2)

Exp.

CRM

(c)

0.8 0.9 10

10

20

30



Surf

ace T

ensio

n, γ

(m

J/m

2)

Exp.

CRM

(d)

Figure 3.3: The change of surface tension with the relative surface area of one cycle forfour different preparations of diluted and concentrated BLES in humid (H) and dry (D)conditions. The compression-relaxation model (CRM) predictions is compared to theexperimental points.


211 212 213 2140

10

20

30


Time, t (s)

Surf

ace T

ensio

n, γ

(m

J/m

2)

Exp.

CRM

ALM

DM

(a)

211 212 213 2140

10

20

30


Time, t (s)

Surf

ace T

ensio

n, γ

(m

J/m

2)

Exp.

CRM

ALM

DM

(b)

211 212 213 2140

10

20

30


Time, t (s)

Surf

ace T

ensio

n, γ

(m

J/m

2)

Exp.

CRM

ALM

DM

(c)

211 212 213 2140

10

20

30


Time, t (s)

Surf

ace T

ensio

n, γ

(m

J/m

2)

Exp.

CRM

ALM

DM

(d)

Figure 3.4: The change of surface tension with time of one cycle for four different prepa-rations of diluted and concentrated BLES in humid (H) and dry (D) conditions. Thecompression-relaxation model (CRM) predictions is compared to the adsorption-limitedmodel (ALM), the diffusion model (DM), and the experimental points.


A summary of the four dynamic parameters calculated from the compression-relaxation

model for the different five preparations is shown in table 3.1. The third column of

the table shows the values of elasticity of compression calculated from an elementary

procedure used previously in the literature [91] and in Chapter 2. The values in this

table will be discussed in detail in the next section.

Figure 3.6 compares the values of the fitting residual function from different models

as an indication of the goodness of fit. The fitting residual function is defined as:

< =√∑

|γe − γm|2 (3.17)

where γe is the experimentally measured surface tension value and γm is the predicted

surface tension value from the respective model. Five cases (the four cases of diluted

and concentrated BLES in humid and dry conditions shown in figure 3.3 and the case

of adding albumin shown in figure 3.5) were considered here. It is apparent that the

compression-relaxation model gives the best fit for all five cases. The adsorption-limited

model performed very well in the second case (film collapse at low surface tension with

minimum relaxation) but performed poorly in the third case (relaxation process with no

collapse).

Figure 3.7 shows a comparison between the calculated values of elasticity between

different models. In the proposed compression-relaxation model, two different values

were considered (one for compression and another for expansion). It is noted that the

difference between calculated elasticity values are not very big except for the diffusion

model in two of the five cases.


211 212 213 2140

10

20

30

40BLES 0.5 mg/ml & Albumin 2.5 mg/ml (H)

Time, t (s)

Su

rfa

ce

Te

nsio

n, γ

(m

J/m

2)

Exp.

CRM

ALM

DM

(a)

0.8 0.9 10

10

20

30

40BLES 0.5 mg/ml & Albumin 2.5 mg/ml (H)


Su

rfa

ce

Te

nsio

n, γ

(m

J/m

2)

Exp.

CRM

(b)

Figure 3.5: A special case of collapse at high surface tension of diluted BLES mixedwith albumin in humid (H) condition: (a) the change of surface tension with the relativesurface area of one cycle; (b) the change of surface tension and surface area with time ofone cycle. CRM: compression-relaxation model, ALM: adsorption-limited model, DM:diffusion model.


Tab

le3.

1:Sum

mar

yof

the

dynam

icpar

amet

ers

(mea

nan

dst

andar

ddev

iati

on)

calc

ula

ted

from

the

com

pre

ssio

n-r

elax

atio

nm

odel

for

diff

eren

tpre

par

atio

ns

at20

%co

mpre

ssio

nan

d3

seco

nds

per

cycl

e.

Pre

par

atio

n

Ref

.[9

1]C

RM

Hum

idit

yE

last

icit

yof

Ela

stic

ity

ofE

last

icit

yof

Rel

axat

ion

Adso

rpti

onC

ondit

ion

Com

pre

ssio

nC

ompre

ssio

nE

xpan

sion

Coeffi

cien

tC

oeffi

cien

tε c

(mJ/m

2)

ε c(m

J/m

2)

ε e(m

J/m

2)

kr

(s−1)

ka

(s−1)

BL

ES

0.5

mg/

ml

Hum

id99

.8±

2.9

125.

1±3.

815

7.8±

2.5

0.54

7±0.

018

2.47

4±0.

264

BL

ES

0.5

mg/

ml

Dry

105.

9±3.

811

2.7±

1.4

120.

0±3.

10.

001±

1e-4

2.78

3±0.

380

BL

ES

2.0

mg/

ml

Hum

id49

.1±

8.7

126.

3±2.

813

6.0±

15.3

3.75

1±0.

184

4.99

1±0.

570

BL

ES

2.0

mg/

ml

Dry

108.

9±5.

312

3.1±

2.1

129.

9±1.

40.

006±

0.00

10.

712±

0.12

6

BL

ES

0.5

mg/

ml

&H

um

id10

.3±

2.6

72.4±

10.6

77.6±

3.0

2.50

1±0.

400

1.55

9±0.

052

Alb

um

in2.

5m

g/m

l

*E

xp

erim

enta

lre

sult

suse

dher

ew

ere

take

nfr

omth

elite

ratu

re[2

5,47

,91

].


0

10

20

30

40

50

Fittin

g R

esid

ua

l, ℜ

(m

J/m

2)

BLES (H)0.5 mg/ml

BLES (D)0.5 mg/ml

BLES (H)2.0 mg/ml

BLES (D)2.0 mg/ml

BLES 0.5 mg/ml (H)Albumin 2.5 mg/ml

CRM

ALM

DM

Figure 3.6: Comparison between the goodness of fit (mean and standard deviation) ofdifferent models. CRM: compression-relaxation model, ALM: adsorption-limited model,DM: diffusion model.


0

100

200

300

400

500

600

Ela

sticity, ε

(m

J/m

2)

BLES (H)0.5 mg/ml

BLES (D)0.5 mg/ml

BLES (H)2.0 mg/ml

BLES (D)2.0 mg/ml

BLES 0.5 mg/ml (H)Albumin 2.5 mg/ml

CRM (comp)

CRM (exp)

ALM

DM

Figure 3.7: Comparison between the predicted value of elasticity (mean and standard de-viation) using different models. CRM: compression-relaxation model, ALM: adsorption-limited model, DM: diffusion model.


3.4.4 Discussion

3.4.4.1 Comparison of Models

The compression-relaxation model presented here shows better fitting than other models

for the five experimental cases shown here. The model can quantify the dynamic pa-

rameters that affect the response of the dynamic surface tension: adsorption coefficient,

desorption or relaxation coefficient, and dilatational elasticity of compression and expan-

sion. The main feature in this model is that more than one process is occurring at any

given time (compared to different regions of specific mechanism for each). This is evident,

for example, in the experimental result of humid concentrated BLES, figure 3.3(c), where

the surface tension starts to increase near the end of the compression stage indicating a

relaxation process occurring during the change in area not only when the area is constant.

This suggests a combined and simultaneous effect of relaxation and elasticity. A similar

effect is observed near the end of the expansion stage of the same experiment, where

the surface tension starts to decrease, suggesting that surfactant adsorption is already

occurring during expansion.

The diffusion model did not show good agreement with most of the experimental

results. The main assumption in that model is that the diffusion of surfactant molecules

through the subphase to reach the interface is the dominant physical phenomenon. In

this model, the diffusion coefficient is the same for diffusion to or from the interface.

This would apply to soluble surfactants like DC12PO, DESS and STAB [136]. However,

pulmonary surfactants are insoluble surfactants suspended as vesicles or other aggregates

and spread at the interface forming possibly multilayers [137–139, 167].

The adsorption-limited model did show a reasonable agreement with experimental

results for some of the cases. However, for humid diluted and humid concentrated BLES,

the adsorption-limited model was not able to capture the desorption/relaxation phe-

nomenon. According to this model, the surfactant can only collapse, i.e. be squeezed


out, but can neither adsorb nor desorb below the minimum equilibrium surface tension,

γ∗. The better agreement with experimental results for dry diluted and concentrated

BLES is likely due to the fact that relaxation is not pronounced in these cases.

3.4.4.2 Calculated Dynamic Parameters

Besides the minimum surface tension value, the calculated dynamic properties can be

considered a measure of the quality of the lung surfactant preparation. For example,

with respect to the calculated elasticity value for all five preparations shown in figure 3.7

and table 3.1, results suggest that there is not much variation in the elasticity values

calculated for humid and dry, diluted and concentrated BLES. However, when albumin

is added to BLES, the elasticity value is markedly decreased from approximately 125 to

75 mJ/m2, indicating surfactant inactivation or inhibition. This conclusion agrees with

findings in the literature [34, 76, 116, 117, 122, 168–170] that albumin poisons surface

activity of lung surfactant preparations.

For most of the preparations studied, the values obtained for the elasticities of com-

pression and expansion are quite close except for the case of diluted BLES at high hu-

midity. The difference between the values of elasticity calculated during compression and

expansion may suggest that the film composition during compression is not the same as

during expansion, which is consistent with the hypothesis that some less surface active

material is squeezed out of the film [1, 171, 172]. Such changes in the film composition

may happen during the course of compression or just at the end of the compression.

These possibilities should be further investigated. A hydration-film fluidization mech-

anism has been proposed to explain the effect of humidity on the film elasticity [25].

However, this effect is minimal when the compression periodicity is short enough for the

hydration effects not to take place(∼3 s/cycle) and the elasticity remains almost constant

[25].

The desorption (relaxation) coefficient calculated here is also an important quality


measure for lung surfactant preparations. Comparing the calculated values for diluted

and concentrated BLES in table 3.1, it is clear that the relaxation coefficient increases

with the increase of concentration for both humid and dry conditions. However, there is

a distinctive effect of humidity on the calculated value of the relaxation coefficient. For

both diluted and concentrated BLES, the dry condition causes a more stable preparation;

the relaxation coefficient is two orders of magnitude smaller than in the case of humid

conditions. This indicates that little or no significant relaxation is experienced by BLES

films in dry air as suggested in the literature on the basis of the hydration-film fluidization

mechanism [25]. Comparing the diluted humid BLES to the same preparation mixed with

albumin, the increase of the relaxation coefficient is another indication of lung surfactant

inhibition.

In summary, the dynamic compression-relaxation model is used to describe the me-

chanical properties of insoluble pulmonary surfactant films by investigating the response

of surface tension to changes in surface area. This model introduces the possibility of

simultaneous compression and relaxation effects. The model is able to fit different exper-

imental results of diluted and concentrated BLES preparation evaluated in humid and

dry air, as well as BLES and albumin mixtures. The calculated dynamic parameters

confirm the known effect of albumin on changing the elasticity and desorption of BLES

preparations. The effect of humidity on the desorption process is illustrated by the huge

increase in the relaxation coefficient in humid conditions, indicating that the dry condi-

tion causes a more stable surfactant films. Since the humid conditions are physiologically

relevant to lung surfactant studies, the effect of humidity introduces some doubts and

questions regarding the optimistic results of lung surfactant films in dry conditions in

the literature.


3.5 Effect of Concentration, Compression Ratio and

Compression Rate

In this section, ADSA–CSD is used to measure the dynamic surface tension of a lung sur-

factant preparation, BLES, at concentrations, compression ratios and compression rates

relevant to current exogenous surfactant therapies. The results are analyzed using CRM

to evaluate the effect of surfactant concentration, compression ratio and compression rate

on the surface activity and dynamic properties (elasticity, adsorption and relaxation) of

BLES preparations.

As indicated in Chapter 1 exogenous surfactant replacement therapy, in which either

synthetic or modified natural pulmonary surfactant (extracted from bovine or porcine

sources) is delivered into the patients’ lungs, has been established as a standard therapeu-

tic intervention for patients with nRDS [173]. Surfactant therapy has shown only limited

therapeutic effect on ARDS patients [174–177]. In these therapies, high concentrations of

the exogenous surfactant are commonly used to reach an effective dose, i.e. the surfactant

dose to recover the mechanical properties of the lungs. The dose is usually in the range

of 8 mg/ml [1, 178, 179]. Some other formulations, e.g. bovine lipid extracted surfactant

(BLES) preparations, are used in surfactant replacement therapy with larger doses of 27

mg/ml [25]. However, there is a lack of in vitro studies for these high concentrations

due to limitations of methodologies used. For these studies, the maximum surfactant

concentration is usually restricted to no more than 3 mg/ml. This restriction arises from

optical limitations since surfactant suspensions become murky and eventually opaque at

increased concentrations.

Although there is promising evidence for surfactant therapy in ARDS, the effec-

tiveness of high doses of commercial surfactant preparations has been inconsistent in

clinical trials [177, 180–184]. However, surfactant concentration is only one strategy

to address the problem. High frequency low tidal volume ventilation, henceforth sim-


ply referred to as high frequency ventilation (HFV) has been shown to reduce, even if

marginally, the mortality of ARDS [181, 185–189]. To simulate normal breathing, cy-

cling frequencies of 0.1 - 0.5 Hz and a reduction in surface area to near 20% are necessary

[1, 25, 36, 172, 190, 191]. However, for high frequency ventilation it is necessary to

produce cycling frequencies higher than 1 Hz [192].

As indicated in Chapter 1, ADSA–CSD is capable of measuring surface tension of

lung surfactants at a wide range of concentrations, compressions ratios and frequencies.

In fact, in contrast to other methodologies, there is no upper limit to the surfactant

concentration that can be used in ADSA–CSD. In this section, ADSA–CSD is used in

conjunction with CRM to measure the effective dynamic properties of BLES at condi-

tions relevant to conventional (high concentration) and high frequency surfactant thera-

pies. Results show that CRM is generally sensitive to all the parameters, i.e., elasticity,

adsorption and relaxation, at any concentration at physiological conditions of 20% com-

pression and 3 seconds per cycle. The model is also very sensitive to all the parameters

at any concentration at low compression ratios and high frequency cycling. These later

conditions are relevant to the clinical practice of high frequency ventilation.


Details about preparation of BLES, the experimental setup and procedures are given in

Chapter 2. During the experiment, the setup is enclosed in an environmental control

chamber that facilitates the control of gas composition and temperature. The humidity

inside the chamber was kept constant at 100% relative humidity at 37C. Drop images

were acquired throughout the experiment at a rate of 20 images per second for cycling

speeds of 3 or 9 seconds per cycle and at a rate of 30 images per second for a cycling

speed of 1 second per cycle.

The experimental procedure was as follows: First, the sessile drop was quickly formed

(within 0.5 s) on the pedestal. The drop was then left undisturbed to allow adsorption


of the lung surfactant film. The surface tension was tracked until the film reaches the

equilibrium surface tension (within 180 seconds for all cases). Thereafter, dynamic cycling

was performed by successive compression/expansion of the drop. This is normally done

through 20 cycles with the required periodicity (1, 3, or 9 seconds per cycle) and the

required compression ratio (percentage of surface area reduction) of 10%, 20%, or 30%.

During every experimental run, images were acquired, stored and later analyzed with

ADSA. All experiments were reproduced at least in triplicate. A typical experimental

result for 2.0 mg/ml BLES at 100% relative humidity, 20% compression, 3 seconds per

cycle and 37C is shown in figure 3.1 showing an example of ADSA outputs as a function

of cycling time. It can be seen that cycles repeat very well. Using the change of surface

tension and area with time during dynamic cycling, dynamic parameters are calculated

using the compression-relaxation model (CRM).

3.5.2 Results

The dynamic cycling for a specific concentration is performed by successive compression/-

expansion of the drop with the prescribed periodicity and the preselected compression

ratio (percentage of surface area reduction). In this section, 36 experiments are reported:

4 concentrations (2, 8, 15, or 27 mg/ml), 3 periodicities (1, 3, or 9 seconds per cycle),

and 3 compression ratios (10%, 20%, or 30%); each experimental run contains 20 cycles

and is repeated at least 3 times. In total, 108 runs were performed.

During every experimental run, images are acquired continuously at a rate of 30

images per second (for periodicity of 1 second per cycle) or 20 images per second (for

periodicities of 3 and 9 seconds per cycle). A typical run contains approximately 600

images (20 cycles, 1 second per cycle and 30 images per second), 1200 images (20 cycles, 3

second per cycle and 20 images per second) or 3600 images (20 cycles, 9 second per cycle

and 20 images per second). Thus, results reported here rely on almost 200,000 individ-

ual surface tension measurements, involving the analysis of that number of drop images.


These images are stored and later analyzed with ADSA. For every image, ADSA calcu-

lates the surface tension, the surface area, and the drop volume as shown in figure 3.1.

The reproducibility between cycles is apparent from figure 3.1.

To deal with such a huge number of data, an overall upgrade of the numerical work

was performed to facilitate the efficient operation and post-analysis functions. After

running all the acquired images through ADSA, an output file was created; this file

needs some careful data analysis. The objectives of the data analysis are editing the

ADSA output file, plotting the change of the surface tension, area and volume with time,

and some preliminary analysis. This includes separating the compression and expansion

parts of every cycle, plotting the change in the surface tension with the relative area

for every half cycle and calculating minimum surface tension values in the cycling part.

These tasks were so far performed manually consuming more than a complete day to

produce the required plots and calculations for a cycling experiment. A Matlab code was

developed to perform the data analysis and plotting for ADSA output files rapidly and

efficiently. The code was designed to process more than one ADSA output file (batch

mode for processing different experimental runs, so all input data are preselected by the

user through script parameters). The outputs from this code are two plots that are saved

in the same folder of the ADSA output files, and an output structure that contains:

the alphabetic run indicator, compression ratio, minimum surface tension mean value,

minimum surface tension standard deviation, maximum surface tension mean value and

maximum surface tension standard for the specified run. The code was also extended to

include the calculated dynamic parameters from CRM.

The minimum value for surface tension for every cycle can be obtained by inspection

from the output of ADSA. A typical run includes 20 values for the minimum surface

tension. The reported minimum surface tension value is the average value within a par-

ticular run. For a specific condition (concentration, compression ratio, and compression

rate), at least three runs were performed. From every run, an average minimum surface


0 5 10 15 20 25 300

5

10

15

20

BLES Concentration (mg/ml)

γm

in (

mJ/m

2)

10% compression

1 s/cyc

3 s/cyc

9 s/cyc

(a)

0 5 10 15 20 25 300

5

10

15

20


γm

in (

mJ/m

2)

20% compression

(b)

0 5 10 15 20 25 300

5

10

15

20


γm

in (

mJ/m

2)

30% compression

(c)

Figure 3.8: The minimum surface tension, γmin, measured for four different concentra-tions of BLES (2, 8, 15, 27 mg/ml) at different compression ratios (10%, 20%, 30%)and different cycling conditions (1, 3, 9 s/cycle). The error bars indicate the standarddeviation between runs repeated under the same conditions.


tension is reported in figure 3.8.

Figure 3.8 shows the average minimum surface tension, γmin, measured for four dif-

ferent concentrations of BLES (2, 8, 15, 27 mg/ml) at different compression ratios (10%,

20%, 30%) and different cycling conditions (1, 3, 9 s/cycle). The standard deviation

indicated by the error bars shows good reproducibility between runs repeated under the

same conditions.

At higher concentration, the minimum surface tension is sensitive to changes in pe-

riodicity only at small compression ratios. At 10% compression, the minimum surface

tension decreases with the increase of concentration and with the increase with cycling

rate. For 20% compression and above, the minimum surface tension decreases in the

range of 2 mg/ml to 8 mg/ml but stays essentially constant at higher concentrations.

However, for concentrations above 8 mg/ml, there is no significant change in minimum

surface tension. In clinical practice, high concentration BLES of 27 mg/ml is used [1, 178].

and it is believed to be diluted after delivery to lungs to a concentration close to 8 mg/ml

[179, 193–199].

Generally, increasing the extent of compression produces lower minimum surface ten-

sion values. This agrees with previous investigations of BLES at 0.5 and 5 mg/ml and

cycling speeds of 3 and 10 seconds per cycle [25]. At high concentrations, the speed of

cycling does not have a significant effect on the minimum surface tension. The decrease

of minimum surface tension with the increase of the speed of compression at low concen-

trations agrees with previous investigations in the literature of BLES 0.5 mg/ml and 20%

compression [25]. This dependence of minimum surface tension on speed is probably due

to the fact that the speed of compression seems to be fast enough to prevent, in part,

the hydration of the surfactant film [25].

The surface tension measurements of BLES at these high concentrations are now pos-

sible due to the features of the ADSA–CSD methodology as mentioned before. It is also

important to note that ADSA–CSD studies can be performed readily at high rates of


compression (to mimic human breathing at 3 seconds per cycle). In this study, higher

rates are also reported (up to 1 second per cycle or 1 Hz). Even higher rates of com-

pression will become achievable after hardware upgrades for both the liquid control and

image acquisition systems. It is noted that flow conditions and viscosity may introduce

errors in the measurement of surface tension via drop/shape methods when the cycling

frequencies are 10 Hz or larger [27, 200–202]. Therefore, an upper limit of 10 Hz exists

for the high frequency studies.

Using the output of ADSA for every experimental run, the change of surface tension

and surface area with time are analyzed using CRM following the procedure explained

in section 3.4.2. As mentioned earlier, a typical experimental run consists of 20 cycles.

From every cycle, the four dynamic parameters of CRM are evaluated, i.e. elasticity of

compression (εc), elasticity of expansion (εe), desorption/relaxation coefficient (kr), and

adsorption coefficient (ka). An indication of the goodness of fit is also calculated for

every cycle. The goodness of fit is defined below in equation 3.18, indicating the relative

error between the predicted surface tension response from CRM and the experimentally

measured surface tension response. Smaller values for the goodness of fit indicate a better

fit.

Figures 3.9 and 3.10 show sample experimental results of the change in surface ten-

sion with time and with relative surface area during dynamic cycling. Figure 3.9 shows

results of BLES concentrations 2 and 27 mg/ml at 10% compression and periodicities of

1 and 9 seconds per cycle. Figure 3.10 shows corresponding results at 30% compression.

The figures illustrate the quality, or “goodness of fit” of CRM to the experimental data.

In these figures, the symbols represent the measured experimental results and the con-

tinuous lines represent the best-fit CRM curves, the four parameters (εc, εe, kr, and ka)

determined from the experimental points having been used for the calculation of CRM

curves. It can be seen that the calculated curves match the experimental points well.

Generally, results shown in figures 3.9 and 3.10 show that CRM fits almost all exper-


0 0.2 0.4 0.6 0.8 10

10

20

30

40

Surf

ace T

ensio

n, γ

(m

J/m

2)

Normalized Time, tn

0.9 0.95 1


(a) BLES 2 mg/ml − 10% comp − 1 s/cycle

0 0.2 0.4 0.6 0.8 10

10

20

30

40

Surf

ace T

ensio

n, γ

(m

J/m

2)

Normalized Time, tn

0.9 0.95 1


(b) BLES 2 mg/ml − 10% comp − 9 s/cycle

0 0.2 0.4 0.6 0.8 10

10

20

30

40

Surf

ace T

ensio

n, γ

(m

J/m

2)

Normalized Time, tn

0.9 0.95 1


(c) BLES 27 mg/ml − 10% comp − 1 s/cycle

0 0.2 0.4 0.6 0.8 10

10

20

30

40

Surf

ace T

ensio

n, γ

(m

J/m

2)

Normalized Time, tn

0.9 0.95 1


(d) BLES 27 mg/ml − 10% comp − 9 s/cycle

Figure 3.9: The change in surface tension with time and with relative surface area duringdynamic cycling of BLES at 10% compression and different concentrations and period-icities: (a) 2 mg/ml and 1 s/cyc; (b) 2 mg/ml and 9 s/cyc; (c) 27 mg/ml and 1 s/cyc;(d) 27 mg/ml and 9 s/cyc. Symbols show the measured surface tension values and linesshow the values obtained from CRM.


0 0.2 0.4 0.6 0.8 10

10

20

30

40S

urf

ace T

en

sio

n, γ

(m

J/m

2)

Normalized Time, tn

0.7 0.75 0.8 0.85 0.9 0.95 1


(a) BLES 2 mg/ml − 30% comp − 1 s/cycle

0 0.2 0.4 0.6 0.8 10

10

20

30

40

Surf

ace T

ensio

n, γ

(m

J/m

2)

Normalized Time, tn

0.7 0.75 0.8 0.85 0.9 0.95 1


(b) BLES 2 mg/ml − 30% comp − 9 s/cycle

0 0.2 0.4 0.6 0.8 10

10

20

30

40

Surf

ace T

ensio

n, γ

(m

J/m

2)

Normalized Time, tn

0.7 0.75 0.8 0.85 0.9 0.95 1


(c) BLES 27 mg/ml − 30% comp − 1 s/cycle

0 0.2 0.4 0.6 0.8 10

10

20

30

40

Surf

ace T

ensio

n, γ

(m

J/m

2)

Normalized Time, tn

0.7 0.75 0.8 0.85 0.9 0.95 1


(d) BLES 27 mg/ml − 30% comp − 9 s/cycle

Figure 3.10: The change in surface tension with time and with relative surface areaduring dynamic cycling of BLES at 30% compression and different concentrations andperiodicities: (a) 2 mg/ml and 1 s/cyc; (b) 2 mg/ml and 9 s/cyc; (c) 27 mg/ml and 1s/cyc; (d) 27 mg/ml and 9 s/cyc. Symbols show the measured surface tension values andlines show the values obtained from CRM.


imental conditions (high and low concentrations, cycling rates and compression ratios)

very well. It can be concluded that the model using only four adjustable parameters is

capable of capturing the main features of the dynamic cycling for different conditions.

However, there is a slight inconsistency between the model and the experimental results

at the high surface tension range in some cases, e.g. figures 3.10(b) and 3.10(d). This

disagreement only appears at the highest compression ratio (30%) and the lowest com-

pression rates (9 seconds per cycle). In these cases, the compression is slow, and hence

the details of the adsorption and elasticity effects are pronounced near the highest sur-

face tension values. As the area is increased, the surface tension increases due to the

film elasticity; however, if the surface tension exceeds the equilibrium value, the surface

tension tends to decrease at the same time due to adsorption to the interface. Since

the compression is slow in these cases, the surface tension shows some fluctuations near

the highest surface tension range. The adsorption in such cases is much quicker than

the speed of compression, causing these fluctuations to be very pronounced. Such low

compression rates are not really relevant clinically; however, this lack of agreement is

considered in more detail below.

The same procedure of extracting the dynamic parameters from every cycle is applied

for all 20 cycles in every experimental run. An effective value for each of the parameters

is formed by the multi-variable optimization for every cycle. 20 values for each of the four

dynamic parameters and the goodness of fit are calculated for every run. From every run,

average values are calculated. For a specific condition (concentration, compression ratio,

and compression rate), at least three runs were performed. For each of the 36 different

experimental conditions considered, the values of the goodness of fit and the four dynamic

parameters reported below in figures 3.11 to 3.15 are the average values of the parameter

plotted on the ordinate across repeated runs and the standard deviation. The average

values of the four dynamic parameters for different conditions are also summarized in

table 3.2.


0 5 10 15 20 25 300

0.5

1

1.5


GF

(−

)

10% compression

1 s/cyc

3 s/cyc

9 s/cyc

(a)

0 5 10 15 20 25 300

0.5

1

1.5


GF

(−

)

20% compression

(b)

0 5 10 15 20 25 300

0.5

1

1.5


GF

(−

)

30% compression

(c)

Figure 3.11: The goodness of fit for CRM measured for four different concentrations ofBLES (2, 8, 15, 27 mg/ml) at different compression ratios (10%, 20%, 30%) and differentcycling conditions (1, 3, 9 s/cycle). The error bars indicate the standard deviationbetween runs repeated under the same conditions.


The visual judgement of a good fit between experimental points and calculated curves

can be quantified by means of a “goodness of fit”. Figure 3.11 compares the values of the

goodness of fit from CRM calculated at different experimental conditions. The goodness

of fit is defined as:

GF =

√∑∣∣∣∣γe − γmγe

∣∣∣∣2 (3.18)

where γe is the experimentally measured surface tension value and γm is the predicted

surface tension value from CRM. Smaller values for the goodness of fit indicate a better

fit. It turns out that CRM fits almost all experimental conditions (high and low concen-

trations, cycling rates and compression ratios) very well except for a few points at higher

compression ratios. The best results for the goodness of fit are at any concentration

at low compression ratios and high frequency cycling. These conditions are relevant to

clinical practice of high frequency ventilation. The goodness of fit gives an indication of

the conditions where CRM works best. This point of the applicability of the model to

certain conditions is considered in more detail below.

Figures 3.12 and 3.14 show the calculated elasticity of compression, εc, and elasticity

of expansion, εe, obtained at different experimental conditions. Figure 3.13 and 3.15

show the calculated relaxation coefficient, kr, and adsorption coefficient, ka, obtained at

different experimental conditions. A detailed inspection of every parameter will follow

below. In these four figures, the values reported are the average values across repeated

runs and the standard deviation. Asterisks are used in these figures to highlight points

where CRM is less sensitive to one or more of the parameters. The quantification of the

sensitivity of the model is described in section 3.5.3.2.


0 5 10 15 20 25 300

50

100

150

200


ε c(m

J/m2 )

10% compression

1 s/cyc3 s/cyc9 s/cyc

****

(a)

0 5 10 15 20 25 300

50

100

150

200

BLES Concentration (mg/ml)ε

c (

mJ/m

2)

20% compression

(b)

0 5 10 15 20 25 300

50

100

150

200


ε c(m

J/m2 )

30% compression

**

*

(c)

Figure 3.12: The elasticity of compression, εc, calculated from CRM for four differentconcentrations of BLES (2, 8, 15, 27 mg/ml) at different compression ratios (10%, 20%,30%) and different cycling conditions (1, 3, 9 s/cycle). The asterisks show the rangeof insensitivity (explained in figure 3.17): * indicate points with range of insensitivitybigger than 0.2, ** indicate points with range of insensitivity bigger than 0.5.


0 5 10 15 20 25 300

1

2

3

4

5


k r(s−1 )

10% compression


**

**

(a)

0 5 10 15 20 25 300

1

2

3

4

5

BLES Concentration (mg/ml)k

r (s

−1)

20% compression

(b)

0 5 10 15 20 25 300

1

2

3

4

5


k r(s−1 )

30% compression

****

(c)

Figure 3.13: The relaxation coefficient, kr, calculated from CRM for four different con-centrations of BLES (2, 8, 15, 27 mg/ml) at different compression ratios (10%, 20%,30%) and different cycling conditions (1, 3, 9 s/cycle). The asterisks show the rangeof insensitivity (explained in figure 3.17): * indicate points with range of insensitivitybigger than 0.2, ** indicate points with range of insensitivity bigger than 0.5.


0 5 10 15 20 25 300

50

100

150

200


εe (

mJ/m

2)

10% compression

1 s/cyc

3 s/cyc

9 s/cyc

(a)

0 5 10 15 20 25 300

50

100

150

200

BLES Concentration (mg/ml)ε e

(mJ/

m2 )

20% compression

* * **

(b)

0 5 10 15 20 25 300

50

100

150

200


ε e(m

J/m2 )

30% compression

*

**

*

** **

**

******

(c)

Figure 3.14: The elasticity of expansion, εe, calculated from CRM for four differentconcentrations of BLES (2, 8, 15, 27 mg/ml) at different compression ratios (10%, 20%,30%) and different cycling conditions (1, 3, 9 s/cycle). The asterisks show the rangeof insensitivity (explained in figure 3.17): * indicate points with range of insensitivitybigger than 0.2, ** indicate points with range of insensitivity bigger than 0.5.


0 5 10 15 20 25 300

2

4

6

8

10


k a(s−1 )

10% compression


*

* * *

(a)

0 5 10 15 20 25 300

2

4

6

8

10

BLES Concentration (mg/ml)k a

(s−1 )

20% compression

*

**

*

****

**

**

**

**

**

(b)

0 5 10 15 20 25 300

2

4

6

8

10


k a(s−1 )

30% compression

**

*

**

**

****

**

****

**

(c)

Figure 3.15: The adsorption coefficient, ka, calculated from CRM for four different con-centrations of BLES (2, 8, 15, 27 mg/ml) at different compression ratios (10%, 20%,30%) and different cycling conditions (1, 3, 9 s/cycle). The asterisks show the rangeof insensitivity (explained in figure 3.17): * indicate points with range of insensitivitybigger than 0.2, ** indicate points with range of insensitivity bigger than 0.5.


Table 3.2: Summary of the dynamic parameters for BLES at 37C and 100% R.H. atdifferent conditions. Asterisks show range of insensitivity (explained in figure 3.17): *range of insensitivity bigger than 0.2, ** range of insensitivity bigger than 0.5.

Elasticity of Elasticity of Relaxation AdsorptionConc. Comp. Freq. Compression Expansion Coefficient Coefficient

(mg/ml) (%) (s/cyc) εc (mJ/m2) εe (mJ/m2) kr (s−1) ka (s−1)

2

101 145.4±2.8 144.4±3.2 3.36±0.12 2.51±0.273 151.6±3.8 162.7±5.1 0.94±0.12 1.11±0.099 103.3±5.6 131.8±4.2 0.90±0.08 0.93±0.02

201 137.6±1.3 151.8±3.5 1.91±0.19 5.36±0.463 134.3±2.8 134.9±2.7 1.61±0.15 * 2.10±0.199 93.9±23.6 93.5±7.9 0.84±0.10 ** 1.07±0.08

301 102.9±1.4 114.5±2.7 3.18±0.10 4.98±0.303 113.5±2.6 106.9±2.4 1.84±0.05 2.07±0.329 126.6±3.8 106.5±4.2 1.31±0.03 * 1.02±0.07

8

101 158.6±2.6 158.8±1.9 1.08±0.07 * 1.21±0.033 151.3±5.5 147.4±5.6 2.33±0.17 0.99±0.059 ** 147.6±6.9 153.3±3.8 ** 2.56±0.08 * 0.63±0.04

201 129.8±1.8 141.4±1.9 1.96±0.22 * 4.74±0.333 112.3±4.8 * 160.9±6.8 1.49±0.04 ** 4.11±0.339 144.8±2.3 * 132.6±3.4 0.55±0.02 ** 1.31±0.04

301 109.6±1.0 * 117.8±4.0 2.10±0.19 ** 9.43±0.743 136.6±3.0 ** 96.3±4.5 2.42±0.28 ** 3.84±0.249 148.7±3.6 ** 95.1±1.3 1.03±0.05 ** 1.38±0.03

15

101 155.4±2.3 168.0±3.8 2.45±0.34 2.45±0.373 167.9±8.1 182.1±5.7 3.75±0.61 2.66±0.139 ** 115.0±3.3 165.6±3.7 ** 2.03±0.07 * 0.91±0.03

201 130.4±2.3 141.4±2.0 1.61±0.27 ** 6.02±1.033 130.7±1.6 144.6±2.3 0.36±0.04 ** 1.77±0.549 135.4±2.4 * 126.5±1.7 0.34±0.01 ** 1.46±0.07

301 * 116.2±4.8 ** 98.9±4.8 ** 2.87±0.32 ** 6.95±0.533 114.8±3.7 * 152.2±8.6 1.25±0.08 ** 5.97±0.489 174.3±4.8 ** 58.2±1.9 1.41±0.05 ** 0.94±0.02

27

101 162.8±1.7 177.5±4.4 1.04±0.14 * 1.83±0.543 161.1±3.0 185.1±2.6 0.91±0.12 2.10±0.369 143.9±1.9 163.9±2.2 0.87±0.07 0.75±0.04

201 142.7±2.2 152.6±8.3 1.28±0.20 ** 4.32±1.173 139.4±1.3 * 149.0±3.6 1.09±0.10 ** 3.44±0.109 149.3±1.8 * 128.8±4.2 0.66±0.02 ** 1.27±0.03

301 ** 143.0±17.7 ** 117.8±8.2 ** 3.44±1.59 ** 8.32±1.083 131.5±3.0 ** 113.4±5.8 1.37±0.13 ** 4.31±0.329 153.2±3.3 ** 99.8±4.9 0.87±0.02 ** 1.35±0.14


3.5.3 Discussion

3.5.3.1 Dynamic CRM Parameters

The change of the elasticity of compression, εc, with concentration, compression ratio

and compression rate is shown in figure 3.12. It is expected that the elasticity is an

intrinsic property of the lung surfactant preparation that should not change with different

experimental conditions. The elasticity of compression did indeed remain almost the same

with concentrations above 8 mg/ml. There is also no significant change with compression

ratio or compression rate. This agrees with previous studies on BLES with concentrations

0.5 and 2 mg/ml at 20% compression and 3 seconds per cycle [146]. In previous studies of

DPPC spread films at compression ratios between 0.1 and 30% and frequencies 0.02, 0.05

and 0.1 Hz, the dilatational elasticities were found to be almost constant for compression

ratios higher than 1% and for all frequencies studied [203]. Spread films of of n-dodecyl

dimethyl phosphine oxide (DC12PO), at compression ratios in the range of 2% to 10%

and frequencies in the range of 0.015 to 0.57 Hz, did not show significant change in the

dilatational elasticities [166].

Elasticity of compression of BLES was previously evaluated using an elementary pro-

cedure [25]. The surface tension-relative area curve during the compression stage was

fitted to a fourth order polynomial equation, and the first derivative was used to calculate

the dilatational elasticity at the midpoint of the compression. Values obtained from that

method are in the range of 100 mJ/m2; these results are lower, but essentially in the same

order of magnitude as results presented here. However, it is important to note that the

main assumption in that procedure [25] is that the elasticity is the only active parameter

during the film compression and that any effects of relaxation during the compression

process are negligible.

Other studies of DPPC/SP-B, DPPC/SP-C, DPPC/SP-B/SP-C spread films did not

show any dependence of the elasticity on the compression speed [61, 62, 107, 147]. These


results support the concept that more flexible film structures are formed in the presence

of surfactant proteins [204]. It can be concluded that the elasticity parameter in CRM

is a property of the lung surfactant preparation. In fact, the addition of an inhibitor,

e.g. serum, albumin, fibrinogen, or excess cholesterol, to lung surfactant preparations is

known to significantly reduce the elasticity of compression of BLES [90].

The change of the relaxation coefficient, kr, with concentration, compression ratio

and compression rate is shown in figure 3.13. There is some variability but not a pro-

nounced dependence on surfactant concentration. There is no significant dependence on

concentrations at all compression ratios or compression rates except for a few points at

the 10% compression. There is a small increase in the relaxation coefficient when the

compression ratio is increased from 20% to 30%. This agrees with published results for

BLES [25]. The relaxation coefficient seems to depend also on the speed of compression;

the higher the frequency, the higher the relaxation rate. This agrees with other studies

of BLES [25] and DC12PO [166].

The change of the elasticity of expansion, εe, with concentration, compression ratio

and compression rate is shown in figure 3.14. Values are very close to the elasticity of

compression. Generally, there is no significant dependence on concentration, compression

ratio or compression rate. However, the sensitivity of the model to changes in εe of

most experiments at 30% compression is low. This leads to less reliable values at these

conditions. More details regarding the sensitivity of the model are given in section 3.5.3.2.

The change of the adsorption coefficient, ka, with concentration, compression ra-

tio and compression rate is shown in figure 3.15. There is some variability but not a

pronounced dependence on surfactant concentration. However, this variability is repro-

ducible as indicated by the error bars in the figure. The adsorption coefficient seems to

increase with the increase of the compression ratio and compression rate. However, the

sensitivity of most points at 20% and 30% compression is very low. This leads to less

reliable ka values at these conditions. More details regarding the sensitivity of the model


are given in section 3.5.3.2.

3.5.3.2 Sensitivity of CRM

For some experiments reported here, it is noticed that the fitting of CRM to the ex-

perimental results is not sensitive to one or more of the four dynamic parameters. To

further investigate this point, a detailed sensitivity study was performed. The details

of calculating the “range of insensitivity” for each parameter is given in section 3.5.4.

Briefly, it is attempted to identify for each parameter the range in which CRM is not

highly sensitive. The sensitivity of the model (in terms of the goodness of fit) to changes

in the respective parameter is calculated as the percentage change of the goodness of fit

divided by the percentage change of the parameter. For example, a sensitivity of 1 means

that a relative change of, say 20%, of a specific parameter yields a relative change of the

same amount, 20% in this case, of the goodness of fit. A sensitivity cut-off level of 1 is

chosen to differentiate between sensitive and insensitive values. The range of percentage

change of the parameter in which the sensitivity of the model is below 1 is called here

the “range of insensitivity” for a specific parameter. The procedure is applied for each

of the four parameters of CRM and the range of insensitivity is calculated for each in

all experiments. A summary of these calculations is shown in figure 3.16 and also in

table 3.3.

In this figure, the contour lines show the range of insensitivity for each parameter.

Higher values indicate that the model is less sensitive to a wider range for this specific

parameter. It can be seen that there are similarities between the insensitivity contours of

both elasticity of compression and relaxation coefficient and also between both elasticity

of expansion and adsorption coefficient.

From these contours, experimental conditions can be identified where CRM is less

sensitive to certain parameters. Such information can be very useful as recommendations

can be made to what experimental conditions are to be used if there is an interest in


5 15 25

10

20

30

0.010.05

0.2

0.5

Co

mp

resssio

n R

atio

(%

)

Concentration (mg/ml)

1 s/cycle

5 15 25

0.01

0.05


3 s/cycle

(a) Elasticity of Compression, εc (mJ/m

2)

5 15 25

0.01

0.0

1

0.05

0.0

5 0.2

0.5

1


9 s/cycle

5 15 25

10

20

30

0.01

0.0

1

0.05

0.20.5

1

1.5

Co

mp

resssio

n R

atio

(%

)


1 s/cycle

5 15 25

0.01

0.05

0.0

5

0.2

0.2

0.5

0.5

1


3 s/cycle

(b) Elasticity of Expansion, εe (mJ/m

2)

5 15 25

0.2

0.2

0.5

1

1.5


9 s/cycle

5 15 25

10

20

30

0.010.05

0.2

0.5

Co

mp

resssio

n R

atio

(%

)


1 s/cycle

5 15 25

0.01

0.01

0.05


3 s/cycle

(c) Relaxation Coefficient, kr (s

−1)

5 15 25

0.010.05

0.20.5

1


9 s/cycle

5 15 25

10

20

30

0.0

5

0.2

0.2 0.5

1

1.5

Co

mp

resssio

n R

atio

(%

)


1 s/cycle

5 15 25

0.05

0.2 0.5

1


3 s/cycle

(d) Adsorption Coefficient, ka (s

−1)

5 15 25

0.5

1

1


9 s/cycle

Figure 3.16: Contour lines of the range of insensitivity for each of the parameters: (a)εc, (b) εe, (c) kr, (d) ka, at different periodicities, compression ratios and concentrations.The calculation of the range of insensitivity is explained in figure 3.17.


Table 3.3: Summary of the range of insensitivity of CRM to each of the dynamic param-eter (explained in figure 3.17) for BLES at 37C and 100% R.H. at different conditions.

Elasticity of Elasticity of Relaxation AdsorptionConc. Comp. Freq. Compression Expansion Coefficient Coefficient

(mg/ml) (%) (s/cyc) εc (mJ/m2) εe (mJ/m2) kr (s−1) ka (s−1)

2

101 0.00 0.00 0.00 0.003 0.00 0.00 0.00 0.019 0.02 0.01 0.09 0.09

201 0.00 0.00 0.00 0.003 0.00 0.03 0.00 0.219 0.01 0.17 0.02 0.57

301 0.00 0.00 0.00 0.123 0.00 0.02 0.00 0.119 0.00 0.12 0.00 0.21

8

101 0.00 0.00 0.00 0.273 0.00 0.00 0.00 0.009 0.67 0.07 1.21 0.22

201 0.00 0.00 0.00 0.213 0.00 0.20 0.02 0.739 0.00 0.23 0.00 1.10

301 0.00 0.40 0.00 1.303 0.00 1.38 0.00 1.289 0.00 1.41 0.00 1.25

15

101 0.00 0.00 0.00 0.023 0.08 0.00 0.09 0.089 1.18 0.17 1.23 0.28

201 0.00 0.02 0.01 0.623 0.00 0.03 0.06 1.279 0.00 0.22 0.00 1.20

301 0.46 1.47 0.53 1.553 0.00 0.32 0.00 1.139 0.00 1.30 0.00 1.30

27

101 0.00 0.00 0.00 0.243 0.00 0.00 0.00 0.099 0.00 0.00 0.07 0.17

201 0.00 0.08 0.08 1.333 0.00 0.24 0.00 1.119 0.00 0.21 0.00 1.06

301 0.69 1.62 0.99 1.643 0.00 0.81 0.01 1.319 0.00 1.79 0.01 1.42


a specific parameter. For example, the elasticity of compression, εc, and the relaxation

coefficient, kr, are less sensitive at high concentrations, high compression ratios, and high

cycling rates. The fit is also less sensitive to εc and kr at low compression ratios and

low cycling rates; at these conditions the parameters εe and ka are more sensitive. The

elasticity of expansion, εe, and the adsorption coefficient, ka, are less sensitive at high

concentrations and high compression ratios.

It is important to note that CRM is generally sensitive to all the parameters at any

concentration at physiological conditions of 20% compression and 3 seconds per cycle.

The model is also sensitive to all the parameters at any concentration at low compression

ratios and high frequency cycling. These conditions are relevant to conventional and high

frequency ventilation.

Generally, the effect of the concentration on the four dynamic parameters is minimal

beyond 8 mg/ml. This is important for clinical therapeutic practice where it is believed

that increased concentration will improve the surfactant properties. As shown here,

increasing surfactant concentration does improve the dynamic properties only in the low

concentration range below 8 mg/ml. Although the dynamic properties of BLES-only

preparations do not improve significantly with increasing BLES concentration, the same

might not be true in the presence of inhibitors. For example, it was shown before [146]

that when albumin is added to BLES, the elasticity value is markedly decreased indicating

surfactant inactivation or inhibition. Using ADSA–CSD in combination with CRM, the

effect of relevant additives and/or inhibitors could be evaluated at appropriate conditions

of concentration, compression rate and compression ratio.

3.5.4 Range of Insensitivity

This section explains the calculations of the range of insensitivity for each parameter of

CRM. First, the change of goodness of fit (defined in equation 3.18) is recalculated after

changing the respective parameter around the calculated value while keeping the rest


0 20 40 60 80 100 120 140 160 180 2000

1

2

Go

od

ne

ss o

f F

it,

GF

(−

)

Elasticity of Compression, εc (mJ/m

2)

(a)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

Go

od

ne

ss o

f F

it,

GF

(−

)

Adsorption Coefficient, ka (s

−1)

(b)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2

4

6

range ofinsensitivity

Percentage change in εc, ∆ε

c/ε

c

Sensitiv

ity o

f ε

c, (∆

GF

/GF

)/(∆

εc/ε

c)

(c)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2

4

6

range ofinsensitivity

Percentage change in ka, ∆k

a/k

a

Se

nsitiv

ity o

f k

a,

(∆G

F/G

F)/

(∆k

a/k

a)

(d)

Figure 3.17: Calculation of the range of insensitivity for the elasticity of the compressionεc and the adsorption coefficient ka of one cycle for 2.0 mg/ml BLES at 20% compressionratio with a periodicity of 9 seconds per cycle: (a) The change of goodness of fit withthe change of εc around the calculated value while keeping the rest of the parameters(εe, kr, ka) constant. (b) The change of goodness of fit with the change of ka aroundthe calculated value while keeping the rest of the parameters (εc, εe, kr) constant. (c)The relative change of sensitivity with the relative change of εc. (d) The relative changeof sensitivity with the relative change of ka. The range of insensitivity is the range ofpercentage change of the parameter in which the sensitivity is below 1.


of the parameters constant. Two examples are shown in figures 3.17(a) and 3.17(b) for

one of the cycles of 2.0 mg/ml BLES at 20% compression ratio with a periodicity of 9

seconds per cycle. In figure 3.17(a), the change of goodness of fit is plotted versus the

change of one of the parameters (εc) around the calculated value while keeping the rest

of the parameters (εe, kr, ka) constant. In figure 3.17(b), the change of goodness of fit

is plotted versus the change of one of the parameters (ka) around the calculated value

while keeping the rest of the parameters (εc, εe, kr) constant.

The second step is to calculate the sensitivity of the model (in terms of the goodness

of fit) to changes in the respective parameter by calculating the percentage change of the

goodness of fit divided by the percentage change of the parameter. For example, for the

case of the adsorption coefficient, ka, the sensitivity of the model with respect to this

parameter is

S =

∣∣∣∣∆GF/GF∆ka/ka

∣∣∣∣ (3.19)

Samples are shown in figures 3.17(c) and 3.17(d) for the same experiment. In these

figure, the relative change of sensitivity is plotted versus the relative change of one of the

parameters (εc or ka).

The third step is to define the “range of insensitivity” based on the sensitivity cal-

culations. A cut-off level of 1 is chosen to differentiate between sensitive and insensitive

values. If the change in the respective parameter yields a sensitivity more than 1, the

model is considered sensitive to this parameter at this change level, and vice versa. Hence,

the range of insensitivity for this parameter is defined as the range of percentage change

of the parameter in which the sensitivity of the model is below 1.

In our example of figure 3.17(c), CRM is found to be insensitive to small changes in

this parameter, εc, in the range of roughly 98% to 102% of the calculated value for εc.

This means that the range of insensitivity of the model to the parameter εc is found to

be 0.04 in this experiment as shown in the figure. In figure 3.17(d), CRM is found to be

insensitive to small changes in this parameter, ka, in the range of roughly 82% to 133%


of the calculated value for ka. This means that the range of insensitivity of the model to

the parameter ka is found to be 0.51 in this experiment as shown in the figure.

The same procedure is applied for each of the four parameters of CRM and the

range of insensitivity is calculated for each in all the experiments. A summary of these

calculations is shown in figure 3.16 and also in table 3.3.

Chapter 4

Accuracy and Shape Parameter∗

4.1 Introduction

In Chapters 2 and 3 little is known about the accuracy of the surface tension measure-

ments. This is particularly critical in Chapter 3, because the accuracy of the determined

mechanical properties of lung surfactant films depends on the accuracy of the measured

response of surface tension to changes in surface area. Therefore, high accuracy surface

tension measurements are necessary in such studies.

As indicated in Chapter 1, drop shape techniques for surface tension measurement

are based on the shape of a pendant drop, sessile drop or captive bubble. Generally, the

shape of the drop/bubble depends on the balance between gravity and surface tension.

When gravitational and surface tension effects are comparable, then, in principle, one can

determine the surface tension from an analysis of the shape of the drop/bubble. Whenever

the surface tension effect is much larger than the gravitational effect, the shape tends to

become close to spherical in the case of pendant and sessile drops/bubbles. Theoretically,

each drop shape corresponds to a certain surface tension value. For well deformed shapes,

a slight change in surface tension causes a significant change in the shape. However, for

∗Portions of this chapter were previously published in Refs. [205, 206], reproduced with permission.

130

Chapter 4. Accuracy and Shape Parameter 131

0 10 20 30 40 50 60 70 8017

18

19

20

21

22

γ (

mJ/m

2)

V (µl)

Figure 4.1: The change of surface tension with drop volume of a constrained sessile dropof OMCTS formed on top of a holder with outer diameter of 7.86 mm.

nearly spherical drop/bubble shapes, a significant change in surface tension causes only

a slight change in the shape. Thus, the sensitivity of surface tension to changes in drop

shape is low.

Despite the general success and flexibility of ADSA, it is well-documented that, as the

drop/bubble shape becomes close to spherical, the performance of all drop shape tech-

niques, including ADSA, deteriorates [64]. The same problem has also been observed by

other researchers who are using numerical optimizations for the measurement of interfa-

cial tensions [207–209]. In their study, the surface tension values calculated from large

pendant drops of pure liquids are calculated consistently and accurately. However, as the

volume of the drop decreases, the surface tension value deviates from the true value.

An illustration of such limitation is shown in figure 4.1, where the surface tension

of a pure liquid, OMCTS, is measured in the ADSA–CSD setup while changing the

drop volume. The symbols represent the actual measurement, while the straight line

represents the literature value. It is clear that the surface tension is correct for the


large drops. However, as the drop volume decreases, the surface tension deviates from

the true value. The reason for choosing pure liquids for accuracy studies is that there

exists a unique constant value of surface tension for each liquid for all drop sizes; any

experimental deviation from that value is attributed to errors or limitations of ADSA. Of

course, this becomes more complicated in the case of surfactants, where surface tension

changes surface compression and compression rate as shown in Chapters 2 and 3. In

fact, two BLES constrained sessile drops of the same concentration and same volume

might have very different surface tension values. A serious implication would be clear

in case slopes of the surface tension with drop size (specifically drop surface area) are

to be calculated. Such slopes are required, for example, to calculate the elasticity of

lung surfactant films as shown in Chapter 2 (equation 2.5). A systematic error in the

calculations of these slopes should be expected if the surface tension calculated from

ADSA deviates systematically (with positive or negative slopes) from the correct value as

shown in figure 4.1. Therefore, an independent measure of the quality of the measurement

is needed to evaluate the validity of ADSA results using pure liquids. In the literature,

there are two different approaches for this problem.

The first approach to quantify the accuracy of the measurements uses a quantita-

tive criterion called “shape parameter” that was introduced to quantify the meaning of

“well-deformed” drops and “close-to-spherical” drops [64]. The shape parameter is a

dimensionless parameter that expresses quantitatively the difference in shape between a

given experimental drop and a spherical shape. A simple approach was used to calculate

the difference between the projected area of the drop and a circle with radius R0 (the

radius of curvature at the apex of the drop). The mathematical formulation of the shape

parameter was

Ps =

∣∣∣∣2π∫0

rθ∫0

rdrdθ − πR20

∣∣∣∣2π∫0

rθ∫0

rdrdθ

(4.1)


Experimentally, the volume of a sessile/pendant drop of pure liquids with known surface

tension values was changed from the smallest drop size for which the numerical scheme

converges to the largest drop size that a constellation can hold. The surface tension

values obtained from ADSA for these drop sizes were compared with the literature value

and a shape parameter value was calculated for each drop image. Typically, the error in

the surface tension measurement is presented as a function of the shape parameter. A

critical shape parameter was defined based on the minimum value of the shape parameter

that guarantees an error of less than, say, ±0.1 mJ/m2, or any other relative error. The

critical shape parameter determines the range of applicability of ADSA. In other words,

for a drop shape with a shape parameter larger than the critical value, ADSA performs

within an accuracy of ±0.1 mJ/m2 [64]. It was found that the critical shape parameter

does not depend on Bond number (defined as ∆ρgR20/γ using R0 as the characteristic

length scale in that study) [64].

The second approach reported is a sensitivity test of pendant drops and liquid bridges

to measure the interfacial tension [210]. The sensitivity was defined as the change in the

projected area of the drop profile due to a small change (5%) in the surface tension.

This analysis was applied to synthetic images with pre-defined surface tension values. It

was found that the sensitivity of both pendant drops and liquid bridges decreases as the

Bond number decreases [210]. The Bond number here was defined using the diameter

of the needle used for the pendant drop case or the diameter of the circular holder used

for the liquid bridge case as the characteristic length scale. It has to be noted that such

sensitivity results will depend on the size of the drop. In the same study, a different

approach was used when dealing with experimental images. Briefly, the images of liquid

drops of known surface tension values were analyzed using a drop shape technique called

TIFA (theoretical image fitting analysis) that fits whole drop images rather than drop

profile lines [211, 212]. The surface tension results were compared to the known value

for the liquid. A minimum volume was defined based on the minimum value of the drop


volume that guarantees an error of less than 1% in the surface tension measurement.

The minimum volume was found to increase for both configurations when the Bond

number decreases [210]. One concern with using this approach is that the output of

the drop shape technique for surface tension measurement is required to evaluate the

quality of the results obtained. The shape parameter, on the other hand, predicts the

appropriateness of the subsequent analysis solely based on the acquired drop image.

The idea of comparing a drop shape to a circle (a two dimensional projection of

a sphere) used earlier [64] is due to the fact that the shape of sessile/pendant drops

or bubbles will be spherical at zero gravity (Bond number of zero). Of course, the

sensitivity of any drop shape technique near the zero gravity shape is very limited and

approaches zero. Hence comparing the shape of a drop/bubble with the zero gravity

shape is an appropriate strategy to evaluate the quality of shape techniques. Therefore,

the approach of using a shape parameter [64], i.e. comparing to the case where the

sensitivity is effectively zero, is often preferable to using a local sensitivity measure [210]

that will change with the drop size. The shape parameter approach is also useful in

predicting, a priori, the quality of the measurement, i.e. without using the output of the

drop shape technique, and hence can be used to design surface tension setups.

For example, when studying lung surfactants using the ADSA–CSD constellation,

the surface tension depends both on time and rate of liquid surface area change. Surface

area change in turn depends on drop volume change. There are no pure liquids available

to mimic the surface tension response of such systems, e.g. near 1 mJ/m2, i.e. a range

critical in lung surfactant studies. The shape parameter approach can be used as an

experimental guideline to design surface tension setups; if the range of surface tensions

to be studied is known, a suitable holder size for the ADSA–CSD setup can be readily

selected.

In this chapter, a modified approach to the shape parameter is proposed. The previ-

ous definition of shape parameter is based on extracting the value of R0 (the radius of


Figure 4.2: Schematic of projected areas of a pendant drop profile and a circle.

curvature at the apex of the drop) from the experimental images and comparing projected

area of the drop to the circle of that radius R0. There are four points that suggest a re-

working of this approach. First, this circle (zero gravity shape) may not be the best fit to

the experimental profile. Better overall fits may well be obtainable with circles of slightly

incorrect R0. Second, comparing projected areas might not be the best way to compare

the drop profile and the best fit circle. The drop profile and the circle might have similar

projected areas and completely different shapes as can be seen from figure 4.2. A more

appropriate comparison can be achieved by minimizing the normal distances between

the profile and the circle. Third, when dealing with theoretical profiles generated by the

Laplace equation for a given value of surface tension and curvature at the drop/bubble

apex, experience has shown that the shape parameter values are usually overestimated

specially for very small drop volumes. The fourth point is that one would expect that the

shape parameter should depend on the Bond number (dimensionless number expressing

the ratio of body forces to surface tension forces) contrary to previous findings [64] but

in agreement with the above sensitivity test [210]. It is suspected that using R0 as the

length scale in the previous shape parameter study [64] is not appropriate.

To address these concerns a new definition for the shape parameter is proposed here,

in which the experimental drop shape is compared to the circle that fits best all the points


of the drop profile. The best fit circle is calculated by minimizing the normal distances

between the drop profile and the circle. Therefore, the drop profile can be compared to

the best fit zero gravity shape (circle in this case); such a circle is not restricted to a

specific radius, R0. Thus the search process for the best fit zero gravity shape will include

all possible variables, in a similar fashion to how ADSA searches for the best fit profile.

This definition will eliminate any dependence on the radius of curvature of the apex. In

this case, the circle can have any radius – not only R0 as previously considered [64] – to

fit all profile points.

As mentioned earlier, the circle (sphere, in three dimensions) is the zero gravity shape

for pendant and sessile drops/bubbles. These zero gravity shapes can be obtained under

different conditions. Examples are very low gravity, very high surface tension values,

and interfaces between fluids with similar densities. However for other configurations,

e.g. liquid bridges or sessile drops formed at the end of a capillary, the shape at zero

gravity is not spherical but will depend on the new contact conditions. These drops at

zero gravity may assume different shapes including cylindrical, nodoidal, unduloidal and

catenoidal. The definition of the shape parameter can be readily extended – in principle

– to these configurations by comparing the drop shape to the best fit zero gravity shape

that is appropriate to a specific configuration.

In this chapter, a simple strategy to construct the shape parameter is applied to

ADSA–CSD in Section 4.2, because of the need for it in Chapters 2 and 3. To under-

stand the relationship between the constrained sessile drop shape and the accuracy of

the surface tension measurement, dimensional analysis is used to describe similarity in

sessile drop shapes and to express the problem using appropriate dimensionless groups.

The proposed shape parameter (in dimensionless form) is found to depend only on two

dimensionless groups: the dimensionless volume (drop volume normalized by the cube of

the holder radius) and the Bond Number (using the holder’s radius as the length scale).

A set of experiments were performed with pure liquids to illustrate the change of


the critical shape parameter with the Bond number for the two different sessile/pendant

setups. To obtain a reasonable range of Bond numbers several pure liquids with known

surface tensions and several holder sizes were used as will be shown below. In every

experiment, the drop volume is varied and the error in the surface tension measurement

is presented as a function of the shape parameter following the same procedure as in

literature [64]. A critical shape parameter is defined as the minimum value of the shape

parameter that guarantees an error below a stipulated error limit. It will be shown

below that the critical shape parameter depends only on the Bond number. Based on

the analysis presented here, specific experimental design parameters are recommended

for accurate surface tension measurements using constrained sessile drops.

Since it turned out that the very same analysis is applicable to the pendant drops,

and since the pendant drop constellation is now the most frequently used surface tension

methodology, the analysis for the shape parameter was extended to the pendant drop

situation in Section 4.3. The universality of the results is examined is Section 4.4.

4.2 Drop Shapes and Shape Parameter

4.2.1 Dimensional Analysis of Axisymmetric Drop Shapes

Five, and only five, independent parameters affect the shape of the constrained sessile

drop: the surface tension of the drop, γ, the density difference between the drop and the

surrounding fluid, ∆ρ, the gravitational acceleration, g, the volume of the drop, V , and

the diameter of the holder, Rh. As discussed in Chapter 1, the apparent contact angle

neither affects nor defines the drop shape in this constrained sessile drop setup. The drop

takes a specific shape depending on only those five independent parameters so that the

drop assumes a specific curvature at the apex, b = 1/R0. Hence, it stands to reason that

b =1

R0

= F(Rh, V, γ,∆ρ, g) (4.2)


where R0 is the radius of curvature at the apex of the drop. Examples of this relationship

are shown below in Section 4.2.3.

Using standard dimensional analysis techniques [213], the parameters of equation 4.2

can be simplified to a set of dimensionless groups. The standard procedure can be

summarized briefly as follows: First, equation 4.2 can be rewritten as a relation between

parameters in the form

f(b, Rh, V, γ,∆ρ, g) = 0 (4.3)

There are 3 fundamental physical units in this equation: mass m, length l, and time t,

while there are 6 (n) dimensional variables: b [l−1], Rh [l1], V [l3], γ [m1 ·t−2], ∆ρ [m1 ·l−3],

and g [l1 · t−2]. The units of the dimensional quantities are indicated in brackets. The

dimensions of the variables in equation 4.3 can be arranged in the form of the following

dimensional matrix:

b Rh V γ ∆ρ g

m 0 0 0 1 1 0

l −1 1 3 0 −3 1

t 0 0 0 −2 0 −2

(4.4)

The rank of this dimensional matrix is r = 3. Thus, there are only n−r = 3 independent

dimensionless combinations (parameters), denoted π1, π2, π3, and equation 4.3 can be

re-expressed as

f(π1, π2, π3) = 0 (4.5)

At this point, any 3 (=r) of the variables can be selected as “repeating variables”,

that will be repeated in all of the dimensionless parameters. In this case, we choose

Rh (a characteristic length scale), γ, and g as the repeating variables. Although other

choices would result in a different set of dimensionless parameters, other complete sets

can be obtained by combining the ones already computed. Therefore, any choice of the

repeating variables is satisfactory.


Each dimensionless parameter is formed by combining the three repeating variables

with one of the remaining variables. For example, let the first dimensional product be

taken as

π1 = b ·Rah · γb · gc (4.6)

The exponents a, b, and c are obtained from the requirement that π1 is dimensionless.

This requires:

m0 · l0 · t0 = (l−1) · (l1)a · (m1 · t−2)b · (l1 · t−2)c (4.7)

By equating the indices, we obtain a = 1, b = 0, c = 0, so that

π1 = b ·R1h · γ0 · g0 = b ·Rh =

Rh

R0

= bd (4.8)

A similar procedure gives:

π2 = V ·Rah · γb · gc =

V

R3h

= Vd (4.9)

π3 = ∆ρ ·Rah · γb · gc =

∆ρgR2h

γ= Bo (4.10)

Therefore the dimensionless representation of equation 4.2 is of the form

bd =Rh

R0

= F(V

R3h

,∆ρgR2

h

γ) = F(Vd, Bo) (4.11)

Equation 4.11 shows that the dimensionless curvature, bd, (the apex curvature normal-

ized by the holder’s radius) of the drop apex depends only on two dimensionless groups.

The first one is the dimensionless volume, Vd, which is the drop volume normalized by

the cube of the holder’s radius. The second one is effectively the Bond Number, Bo,

using the holder’s radius as the length scale for this case. Examples of this relationship

are shown below in Section 4.2.3.


4.2.2 Shape Parameter

The proposed definition of the shape parameter for the ADSA–CSD setup is a comparison

of the drop profile with the circle that best fits all the points of the drop profile. Such

definition will eliminate any dependency on the radius of curvature of the apex. In this

case, the circle can have any radius – not only R0 as previously used – to fit all profile

points.

A simple and computationally inexpensive algebraic fit [214] can be used to find the

best fit circle for a number of points (i.e., digitized drop image). Here, the sum of squares

of algebraic distances is minimized

F(a, b, R) =n∑i=1

[(xi − a)2 + (zi − b)2 −R2

]2=

n∑i=1

(ei + Axi +Bzi + C)2 (4.12)

where a is the x-axis location for the circle center point, b is the z-axis location for

the circle center point, R is the circle radius, ei = x2i + z2i , A = −2a, B = −2b, and

C = a2 +b2−R2. Now differentiating F with respect to A, B, C yields a system of linear

equations that can be solved to yield A, B, C, and hence a, b, R can be computed. Other

algebraic fit methods exist to calculate the circle that best fits a list of points [215, 216].

Such methods were also tested in this context, and the results of the calculated shape

parameter yielded the same result.

Once the best fit circle is determined, the normal distances between every point in

the drop profile and the best fit circle can be simply calculated and used to define the

shape parameter as

P =

√√√√ 1

n

n∑i=1

[√(xi − a)2 + (zi − b)2 −R

]2(4.13)

To eliminate the effect of the size of the drop, it is desirable to define the shape pa-

rameter in dimensionless form. A non-dimensional form can be calculated by normalizing


the value calculated above with the radius of the best fit circle

Pc =1

R

√√√√ 1

n

n∑i=1

[√(xi − a)2 + (zi − b)2 −R

]2(4.14)

The main conclusion that can be drawn from the previous section is that all drop

shapes depend on only two dimensionless groups, i.e. the dimensionless drop volume

and the Bond number. Since the shape parameter depends only on the drop shape, we

postulate that the shape parameter, in its dimensionless form as defined in equation 4.14,

depends on the same two dimensionless groups, in a similar fashion as equation 4.11

Pc = F(V

R3h

,∆ρgR2

h

γ) = F(Vd, Bo) (4.15)

This means that every drop shape, and it’s associated shape parameter, depends only

on Vd and Bo. Similar shapes will have similar shape parameters. Examples of this

relationship are shown below in Section 4.2.3.

This should not be understood to mean that Pc is equivalent to bd. Pc is the shape

parameter as calculated from the digitized drop profile using equation 4.14. Pc is an

indication of the difference in shape between a given experimental drop profile and the

best fit circle. On the other hand, bd is the dimensionless curvature at the drop apex and

is used here as an indication of the drop shape.

4.2.3 Sample Constrained Sessile Drops

The relationship between the curvature of the drop apex and the independent parameters

affecting the shape of the constrained sessile drop as shown in equation 4.2 is further

illustrated here. Figure 4.3 shows the change of the curvature at the constrained sessile

drop apex with the drop volume for different holder sizes (outside radius of 3 and 6 mm)

and surface tension values (18, 36, and 72 mJ/m2). These results were obtained using


0 50 100 150 2000

0.5

1

1.5

2

2.5

3

Volume, V (µl)

Cu

rva

ture

, b

= 1

/R0 (

cm

−1)

Holder Size: Rh = 3 mm

γ = 72 mJ/m2

γ = 36 mJ/m2

γ = 18 mJ/m2

(a)

0 100 200 300 400 500 600 7000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Volume, V (µl)

Cu

rva

ture

, b

= 1

/R0 (

cm

−1)


γ = 72 mJ/m2

γ = 36 mJ/m2

γ = 18 mJ/m2

(b)

Figure 4.3: The change of the apex curvature of a constrained sessile drop with surfacetension and drop volume for two different holder sizes: (a) outer radius of 3 mm, andouter radius of (b) 6 mm.


the Axisymmetric Liquid Fluid Interface (ALFI) program [9], that predicts the shape of

a drop/bubble through numerical integration of the Laplace equation. The inputs for

the ALFI program are the apex curvature, b, and the capillary constant, c = ∆ρg/γ.

The outputs are the generated drop profile, drop surface area, drop volume, V , and the

contact angle at the end of the drop profile. The end condition for the integration is the

radius of the holder, Rh.

For the same holder size and the same surface tension value, as the drop volume

increases, the curvature at the drop apex increases initially, then decreases when passing

through the 90o contact angle. The same curvature can be reached twice on every curve,

one time for a small drop volume and another for a large drop volume. There exists a

maximum drop volume and a maximum curvature at the drop apex for a given holder

size and surface tension value. The maximum curvature at the drop apex corresponds

to the case of the 90 contact angle. For the same holder size, as the surface tension

increases, the maximum volume and the maximum apex curvature increase. As the

holder size increases, the range of possible drop volumes increases and the range of

possible curvatures at the drop apex decreases.

The dimensional analysis in Section 4.2.1 (equation 4.11) shows that the dimensionless

curvature, bd, of the constrained sessile drop apex depends only on two dimensionless

groups: the dimensionless volume, Vd, and the Bond Number, Bo. Figure 4.4 shows the

predicted change of the dimensionless curvature at the constrained sessile drop apex with

the dimensionless drop volume for different Bond number values (1.22, 2.44, and 4.89).

This figure is considered a general map of the relationship of the three dimensionless

groups for the constrained sessile drop problem. The effect of the holder size is effectively

integrated inside every one of the dimensionless groups.

For the same Bond number value, as the dimensionless drop volume increases, the

dimensionless curvature increases initially, then decreases. The same dimensionless cur-

vature can be obtained twice on every curve, one time for a small dimensionless drop


0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Dimensionless Volume, V/Rh

3

Dim

en

sio

nle

ss C

urv

atu

re,

Rh/R

0

Bo = 1.22

Bo = 2.44

Bo = 4.89

Figure 4.4: The change of the dimensionless apex curvature of a constrained sessiledrop with Bond number and dimensionless drop volume. The same relationship can beobtained using any holder size.

volume and another for a large dimensionless drop volume. There exists a maximum

dimensionless drop volume and a maximum dimensionless curvature at the drop apex for

a given Bond number value. As the Bond number decreases, the maximum dimensionless

volume and the maximum dimensionless apex curvature increase.

To further investigate similarity in drop shapes, figure 4.5 shows the predicted drop

profile shapes for different conditions. Figure 4.5(a) shows the shape of the constrained

sessile drop generated using ALFI for the case of surface tension of 6 mJ/m2, holder

radius of 3 mm, and apex curvature of 0.51 cm−1. This is equivalent to a Bond number

of 14.67 and a dimensionless curvature of 0.153. For the given curvature at the apex, there

exist two drop volumes that can satisfy these conditions. The dimensionless volumes for

the two drops are 0.412 and 1.598. The large volume corresponds to the case where

the maximum drop diameter is larger than the holder diameter. This case is indicated

with solid symbols in the figure. The other case of small volume is indicated with open


−0.5 0 0.5

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Rh = 3 mm, γ = 6 mJ/m

2, Bo = 14.67

x (cm)

z (

cm

)

(a)

−1.5 −1 −0.5 0 0.5 1 1.5

−0.5

0

0.5

1

1.5

Rh = 9 mm, γ = 54 mJ/m

2, Bo = 14.67

x (cm)

z (

cm

)

(b)

−0.5 0 0.5

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Rh = 3 mm, γ = 216 mJ/m

2, Bo = 0.41

x (cm)

z (

cm

)

(c)

−0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08

−0.04

−0.02

0

0.02

0.04

0.06

0.08

Rh = 0.5 mm, γ = 6 mJ/m

2, Bo = 0.41

x (cm)

z (

cm

)

(d)

Figure 4.5: The shape of a constrained sessile drop for different holder sizes and surfacetension values. Bond number is indicated on top of every figure. The open symbolsindicate a drop profile with a small volume, while the solid symbols symbols that with alarge volume. The lines indicate the best circle that fit the profile.


symbols. The continuous lines indicate the best fit circles that are fitted to all the drop

profile points; these are the circles used in the definition of the shape parameter as

shown in equation 4.14. It is clear that the large volume drop is well deformed, but the

small volume can be fitted to a circle and hence will not allow accurate surface tension

measurement with ADSA.

A case of the very same Bond number is considered in figure 4.5(b). In this case, the

drop shape is generated for a surface tension of 54 mJ/m2, holder radius of 9 mm, and

apex curvature of 0.17 cm−1. This is equivalent to the same Bond number of 14.67 and

the same dimensionless curvature of 0.153. For the given curvature at the apex, there

exist two drop volumes that can satisfy these conditions. The dimensionless volumes for

the two drops are exactly the same as before, i.e. 0.412 and 1.598. It is clear that the

drop shapes in figure 4.5(b) are similar to those in figure 4.5(a). The only difference is

the scaling factor. Therefore, it is expected that the shape parameter should be exactly

the same for both cases. Furthermore, ADSA should treat them similarly, i.e. ADSA will

process the well deformed drops (solid symbol) satisfactorily and will not work accurately

with the small volume drops (open symbols).

A higher surface tension case is considered in figure 4.5(c). In this case, the drop

shape is considered for the case of surface tension of 216 mJ/m2, holder radius of 3

mm, and apex curvature of 2.1 cm−1. This is equivalent to a Bond number of 0.41

and a dimensionless curvature of 0.63. For the given curvature at the apex, there exist

two drop volumes that satisfy these conditions. The dimensionless volumes for the two

drops are 0.613 and 8.734. It is clear that both drops can be fitted well to a circle and

hence will not work accurately with ADSA. A similar Bond number case is considered

in figure 4.5(d). In this case, surface tension is 6 mJ/m2, holder radius is 0.5 mm, and

apex curvature is 12.6 cm−1. This is equivalent to the same Bond number of 0.41 and

the same dimensionless curvature of 0.63. The dimensionless volumes for the two drops

are exactly the same as before, i.e. 0.613 and 8.734. It is clear that the drop shapes in


0 1 2 3 4 5 6 7 80

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Dimensionless Volume, V/Rh

3

Sh

ape

Pa

ram

ete

r, P

c

Bo = 1.22

Bo = 2.44

Bo = 4.89

Figure 4.6: The change of the shape parameter of a constrained sessile drop with Bondnumber and dimensionless drop volume. The same relationship can be obtained usingany holder size.

figure 4.5(d) are similar to those in figure 4.5(c). The only difference is the scaling factor.

Following the similarity between equations 4.11 and 4.15, a map similar to that of

figure 4.4 can be readily derived. Figure 4.6 shows the change of the dimensionless shape

parameter with the dimensionless drop volume for different Bond number values (1.22,

2.44, and 4.89). For the same Bond number value, as the dimensionless drop volume

increases, the value for Pc increases indicating more deformed drops. There exists a

maximum value for Pc for a given Bond number value. According to this definition of

the shape parameter, the minimum value for Pc is always zero. This indicates that very

small drops are not appropriate for surface tension measurement even for drops with small

surface tension values on large holders. This figure is considered a general map of the

relationship of the three dimensionless groups for the constrained sessile drop problem.

The same relationship can be obtained using any holder size.

It can be observed that forming the biggest drop possible on a specific holder size is


not always sufficient to obtain accurate results from ADSA. This is clear from the large

volume drops at low Bond number values as shown in figures 4.5(c) and 4.5(d). Although

the drop volume is large, the drop shape is still very close to a sphere preventing ADSA

from calculating accurate results. As the Bond number increases, the drop shape becomes

more deformed at large volume. Nevertheless, even at high Bond number values, the drop

volume has to be large enough to produce a well deformed drop.

At this point, it is appropriate to assume that at any Bond number, there is a critical

shape parameter above which the drop shape is considered well deformed. This critical

shape parameter corresponds to a critical volume that the drop has to exceed to be well

deformed. This critical shape parameter is expected to increase with the decrease in

Bond number. To further investigate this point, a set of experiments were performed to

illustrate the change of the critical shape parameter with the Bond number as illustrated

below.



Octamethylcyclotetrasiloxane (OMCTS) [C8H24O4Si4] was purchased from Sigma-Aldrich

Co. (cat. 74811) with purity ≥99.0%, Diethyl phthalate (DEP) [C12H14O4] from Sigma-

Aldrich Co. (cat. 524972) with purity ∼99.5%, and Water from Sigma-Aldrich Co. (cat.

95286). These three liquids were chosen because they have adequate vapour pressure and

cover a wide range of surface tension. OMCTS, DEP, and water have surface tensions of

approximately 18, 36, and 72 mJ/m2, respectively.

A schematic diagram of the experimental setup for ADSA–CSD is shown in Figure 4.7.

Details of the setup and how ADSA works were given before in Chapter 2. Two holder

sizes were used in this study, outer diameters of 6.55 and 7.86 mm. To ensure consistency,

the quality of the acquired images (or more specifically, the number of the pixels of the


Diff

user

Light Source

Microscope CCD

Stepping MotorSyringe

Glass Cuvette

Figure 4.7: Schematic diagram of ADSA–CSD experimental setup.

extracted drop profile) was maintained to be as constant as possible for all experiments.

This is done by using different magnifications for different holder sizes. If the same

magnification were used for all holders, the drops on the smaller holders would have fewer

pixels at the interface and the calculated surface tension values would be less accurate.


A large drop of the liquid (roughly 80 µl) was formed on the stainless steel pedestal which

is connected to the syringe and the stepper motor. All experiments were performed at

room temperature of 24oC. The constrained sessile drop is covered with a glass cuvette

to isolate the drop from the environment and to prevent contamination. Several images

were acquired and analyzed by ADSA, providing the surface tension of the pure liquid.

The drop volume was then decreased very slowly with the motor-controlled syringe and

then increased again. The rate of liquid withdrawal and addition was fixed at 0.6 µl/s,

for all experiments. During the volume reduction and enlargement, images were acquired

at the rate of two images per second and saved for further analysis.

All acquired images were analyzed by ADSA, providing a value for the surface tension,

γ, the drop surface area, A, the drop volume, V , and the curvature at the apex, b.

Figure 4.8 shows a typical result of ADSA for a constrained sessile drop of OMCTS

formed on top of a holder with outer diameter of 7.86 mm. This is the same experiment

shown previously in figure 4.1. As mentioned earlier, there exists a unique constant

value of surface tension for each liquid, any experimental deviation from that value is


17

18

19

20

21

22

γ (

mJ/m

2)

0.4

0.5

0.6

0.7

0.8

A (

cm

2)

0

20

40

60

80

V (

µl)

0 50 100 150 200 250 3000.4

0.6

0.8

1

1.2

1.4

b (

cm

−1)

Time, t (s)

Figure 4.8: The change of surface tension, drop surface area, drop volume, and thecurvature at drop apex with time of a constrained sessile drop of OMCTS formed on topof a holder with outer diameter of 7.86 mm.


attributed to errors or limitations of ADSA.

4.2.5 Results and Discussion

The surface tension values of large drops (at the beginning and at the end of every run) are

constant, i.e. they do not change with drop size, and they agree with the literature value.

However, values calculated from small drops are not constant and show irregular trends,

i.e. not just random errors, as shown in figure 4.8. All acquired images were analyzed

to calculate the shape parameter values according to equation 4.14. To calculate the

critical shape parameter for every experiment, the procedure proposed previously [64]

was followed. Briefly, the shape parameter values of every run are plotted against the

calculated surface tension for this run. The critical shape parameter is the value below

which the error in the calculated surface tension value exceeds a specific limit, usually

set at ±0.1 mJ/m2.

Figure 4.9 shows the error in surface tension measured by ADSA as a function of

the shape parameter for different drop sizes of OMCTS formed on a holder with outer

diameter of 7.86 mm. This case is equivalent to a Bond number of 7.91. For a maximum

error of ±0.1 mJ/m2, the critical shape parameter is 0.018. It is to be noted that for

large drop sizes (large shape parameter values), the measured surface tension is accurate

and consistent. It is also important to note that the overall error in surface tension for

this case did not exceed ±1 mJ/m2 for almost all drops in this run, except for very small

values of shape parameter below 0.005 where the drop is very small and is essentially a

spherical cap.

It was noted in figure 4.9 that there is a specific trend for the direction (positive or

negative) of the error in the surface tension measurements. Similar trends were also noted

in other cases. Figure 4.10(a) shows the error in surface tension of OMCTS formed on

a holder with outer diameter of 6.55 mm, while figure 4.10(b) shows the error in surface

tension of DEP formed on a holder with outer diameter of 7.86 mm. Both figures show


0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1

1.5

2

2.5

3

Shape Parameter, Pc

Err

or

in S

urf

ace

Te

nsio

n, ε

(m

J/m

2)

Figure 4.9: The error in surface tension measured by ADSA as a function of the shapeparameter for different drop sizes of a constrained sessile drop of OMCTS formed on topof a holder with outer diameter of 7.86 mm. For a maximum error of ±0.1 mJ/m2, thecritical shape parameter is 0.018.

similar – but not exactly the same – trends to that of figure 4.9. To further clarify this,

a series of synthetic profiles were generated from ALFI at the same conditions (same

surface tension, holder size, drop volumes) and were analyzed with ADSA. It was noted

that the error in this case has no tendency to take positive or negative values, i.e. there

are no systematic deviations from the correct value. Therefore, it can be concluded that

the systematic deviations observed experimentally is not an artifact of the optimization

procedure used. The deviations might be caused by the quality of the images and the

related optical conditions.

The same analysis was applied to experiments using the other two liquids, diethyl

phthalate (DEP) and water, using the two holders with outer diameters of 6.55 and 7.86

mm. All the results are summarized in Table 4.1. The first two columns of the table

list the holder size and the liquid used for every experiment. The third column lists

the presumably correct surface tension values as found in the literature and/or previous


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035−1

−0.5

0

0.5

1

1.5

2

2.5

3

Shape Parameter, Pc

Err

or

in S

urf

ace T

ensio

n, ε

(m

J/m

2)

(a)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04−1

−0.5

0

0.5

1

1.5

2

2.5

3

Shape Parameter, Pc

Err

or

in S

urf

ace

Te

nsio

n, ε

(m

J/m

2)

(b)

Figure 4.10: The error in surface tension measured by ADSA as a function of the shapeparameter for different drop sizes of a constrained sessile drop of: (a) OMCTS formed ontop of a holder with outer diameter of 6.55 mm, and (b) DEP formed on top of a holderwith outer diameter of 7.86 mm. For a maximum error of ±0.1 mJ/m2, the critical shapeparameters are 0.026 and 0.027, respectively.


Tab

le4.

1:Sum

mar

yof

resu

lts

ofco

nst

rain

edse

ssile

dro

pex

per

imen

tsusi

ng

diff

eren

tliquid

san

ddiff

eren

thol

der

size

s.

Hol

der

Liq

uid

γ(m

J/m

2)

Bo

γmeasured

(mJ/m

2)

Pcrit

(mm

)[2

17–2

19]

Run

1R

un

2R

un

3R

un

1R

un

2R

un

3

4.20

Wat

er72

.39

0.60

71.0

23±

0.01

170

.992±

0.01

271

.024±

0.01

0-

--

6.55

Wat

er72

.39

1.46

72.3

61±

0.01

572

.321±

0.01

772

.353±

0.01

60.

036

0.03

40.

035

7.86

Wat

er72

.39

2.10

72.3

54±

0.01

772

.313±

0.00

972

.323±

0.02

10.

035

0.03

40.

034

6.55

DE

P36

.95

3.18

36.8

61±

0.01

336

.865±

0.01

336

.878±

0.01

20.

032

0.03

30.

032

7.86

DE

P37

.95

4.58

36.9

36±

0.00

636

.913±

0.00

836

.900±

0.00

60.

029

0.02

70.

029

6.55

OM

CT

S18

.20

5.41

18.1

10±

0.00

918

.137±

0.00

618

.126±

0.00

60.

029

0.02

60.

028

7.86

OM

CT

S18

.20

7.91

18.1

77±

0.00

618

.206±

0.00

418

.189±

0.00

50.

018

0.01

80.

018


work [217–219]. The fourth column lists the Bond number for every experiment; a range

of Bond numbers between 0.60 and 7.91 is covered in this study. The following three

columns contain the calculated surface tension value (from the largest drop sizes) and

the accuracy of the calculation; more than 60 drops were used in the calculation of the

average value and the standard deviation. The last three columns contain the measured

critical shape parameter for every experimental run. These values were measured in a

similar procedure used in figure 4.9.

Inspection of table 4.1 shows that for all systems, except the first one listed, there is

excellent agreement from run to run, as well as with the standard values of column 3. It

is also noted that the differences from run to run could be due to ambient temperature

changes of the order of 0.1oC. The consistency from run to run and the accuracy of each

run are generally less for the first system, and the agreement with the standard values is

much poorer, out of the stipulated error range of ±0.1 mJ/m2. A critical shape parameter

does not exist for these cases. The reason of this difference in pattern is discussed in

detail below.

Figure 4.11 shows the change of the critical shape parameter as a function of the Bond

number for all the experiments of this study. In other words, the critical shape parameter

values for every run obtained in a similar fashion to figure 4.9 and summarized in the

last three columns of table 4.1 are used to calculate an average critical shape parameter

value for every Bond number as shown in figure 4.11.

Therefore, for a specific liquid, i.e. a specific surface tension value, and a specific

holder size, there exists a critical shape parameter value below which the error in the

calculated surface tension value exceeds a specific limit. If we use the same liquid with

a larger holder size, the drop shapes become more deformed and the calculated critical

shape parameter value is lower. A similar case exists when a different liquid with a

smaller surface tension value is used with the same holder size. The drop shapes become

more deformed and the calculated critical shape parameter value is lower. A larger holder


1 2 3 4 5 6 7 8 9

0.02

0.03

0.04

Bond Number, Bo

Critical S

ha

pe

Pa

ram

ete

r, P

crit

Experiments Results

Best Fit (Linear)

Figure 4.11: The critical shape parameter as a function of the Bond number. Theexperimental points were fitted to a linear function (continuous line).

or a liquid with a smaller surface tension value leads to a larger Bond number (using the

holder’s radius as the length scale).

As expected, figure 4.11 shows that the critical shape parameter decreases with in-

creasing Bond number. The critical shape parameter is equivalent to a critical dimen-

sionless volume (the drop volume normalized by the cube of the holder’s radius) that

the drop has to exceed to allow for accurate measurement of the surface tension. This

can also be understood from figure 4.6 which defines the relationship between the shape

parameter, dimensionless volume and Bond number. The critical shape parameter is

one point on every curve below which the drop shape is indistinguishable from the zero

gravity shape (circle in this case). For high Bond numbers (a low surface tension liquid

and/or a large holder), it is expected that small drop volumes are sufficient to have well

deformed shapes. On the other hand, for low Bond numbers (a high surface tension

liquid and/or a small holder), it is expected that very large drop volumes are needed to

make sure that the drop is well deformed.


It is expected that as the Bond number increases, the critical shape parameter will

decrease approaching the value of zero as the Bond number approaches infinity. On

the other hand, as the Bond number decreases and approaches zero, the critical shape

parameter will increase dramatically. However, it was found in this study that critical

shape parameters can not be established for Bond numbers below one, i.e. when the

diameter of holder becomes small and approaches zero. This is due to the fact that the

largest drop that can be formed on a given holder size is not big enough to calculate an

accurate surface tension value.

The relationship between the critical shape parameter and the Bond number can be

considered as a universal guide. Therefore, it was attempted to fit these points in this

range with a straight line as shown in the figure. Of course, on a wider range, it is

expected to have an exponential form. However, using a straight line in the experimental

range here seems sufficient. The best fit line is plotted in figure 4.11 as a continuous line.

Such a relationship is only applicable for a desired error of ±0.1 mJ/m2 in the measured

surface tension. Changing this value for the desired error to a higher or a lower value

would change the location of this curve downwards or upwards, respectively. However,

such change in the stipulated error will not have any effect on the shape of the curve.

The relation between the critical shape parameter and the Bond number should be

universal for this specific constrained sessile drop constellation. To further illustrate this

point, an additional experiment was performed using a fourth liquid, hexadecane (with

surface tension of 27 mJ/m2), and the holder with outer diameter of 7.86 mm. The

Bond number is 4.3 for this experiment, and the critical shape parameter is expected to

be 0.0331 from figure 8. The hexadecane experiment was repeated three times and the

measured critical shape parameter was found to be 0.034±0.0014. This value agrees with

the expected value and fits well with the other points shown in figure 4.11.

The relationship between the critical shape parameter and the Bond number can be

used in the design of a constrained sessile drop experiment for surface tension measure-


ment. Through the above relationship, we know that a high Bond number is always

preferable and will facilitate more accurate surface tension measurement. A high Bond

number is equivalent to a small surface tension value and/or a large holder size. If a

rough approximation of the surface tension is known, the right holder size can be easily

selected to produce accurate measurement.

For example, based on the calculations presented here and assuming a density differ-

ence of 1000 kg/m3 and gravity of 9.80 m/s2, designing an ADSA–CSD experiment to

measure surface tension values in the range of 0.5 to 38 mJ/m2 would require a minimum

holder diameter of 4 mm to ensure a maximum error of ±0.1 mJ/m2 throughout. Such

range of surface tension values is of interest in the case of lung surfactant studies, or

compressed soluble or insoluble films. Based on this analysis, results of Chapter 3 can

be confirmed to be within the ±0.1 mJ/m2 error range. It has to be noted that using a

smaller holder for this case will cause a larger error near the high end of this surface ten-

sion range. Generally, it is advisable to make the drop as large as possible to guarantee

accurate results especially near the high end of this range. Another example is designing

an experiment to measure surface tension in the range of 15 to 72 mJ/m2, e.g. common

liquids, which would require a minimum holder diameter of 6 mm. Based on this analysis,

results of Chapter 2 can be confirmed to be within the ±0.1 mJ/m2 error range. These

rough examples serve as a guide for selecting the right holder size to produce accurate

measurement, if a rough approximation of the surface tension is known. It is important

to emphasize that it is the largest surface tension values that dictate a minimum holder

size.

4.3 Pendant Drop Shapes

In the pendant drop setup, a drop is formed at the end of a needle. Alternatively, a

small flat circular holder (inverted pedestal) with a sharp-knife edge is used instead of


the capillary [59, 64] as indicated in Chapter 1. The dimensional analysis of Section 4.2.1

developed for the constrained sessile drop case is still applicable to the pendant drop

case because the same five independent parameters affects the shape of both the pendant

drop as well as the constrained sessile drop (Section 4.2.1). The definition of the shape

parameter presented in Section 4.2.2 can be also used for the pendant drop case, since

they both share the same zero gravity shape (sphere). This would not be appropriate,

e.g., in the case of a liquid bridge.

This section follows the same logic as that of Section 4.2. The relationship between

the curvature of the drop apex and the independent parameters affecting the shape as

shown in equation 4.2 is further illustrated here for the pendant drop. The change of the

curvature, b, at the pendant drop apex with the drop volume for different holder sizes

(outside diameter of 3 and 6 mm) and surface tension values (18, 36, and 72 mJ/m2) is

shown in figure 4.12. These results were obtained using ALFI as mentioned before in the

case of the constrained sessile drop.

For a given holder size and given surface tension value, as the drop volume increases,

the curvature at the drop apex increases initially, then decreases in some cases. There

exists a largest drop volume, V , and a largest apex curvature, b, for a given holder size

and a given surface tension value. Drop profiles can not be generated beyond these values.

This will be discussed in more detail below. For a given holder size, when a liquid with

a higher surface tension value is used, the largest volume increases and the largest apex

curvature decreases. For larger holders, the range of possible drop volumes is larger and

the range of possible curvatures at the drop apex is smaller.

The dimensional analysis shown in Section 4.2.1 (equation 4.11) shows that the di-

mensionless curvature, bd, of the pendant/sessile drop apex depends only on two dimen-

sionless groups: the dimensionless volume, Vd, and the Bond Number, Bo. The predicted

change of the dimensionless curvature, bd, of a pendant drop with the dimensionless drop

volume for different Bond number values (1.22, 2.44, and 4.89) is shown in figure 4.13.


0 10 20 30 40 500

1

2

3

4

5

6

7

8

9

10

Volume, V (µl)

Cu

rva

ture

, b

= 1

/R0 (

cm

−1)

Holder Size: Rh = 1.5 mm

γ = 72 mJ/m2

γ = 36 mJ/m2

γ = 18 mJ/m2

(a)

0 20 40 60 80 100 1200

1

2

3

4

5

6

7

8

Volume, V (µl)

Curv

atu

re, b =

1/R

0 (

cm

−1)


γ = 72 mJ/m2

γ = 36 mJ/m2

γ = 18 mJ/m2

(b)

Figure 4.12: The change of the apex curvature of a pendant drop with surface tensionand drop volume for two different holder sizes: (a) outer radius of 1.5 mm; (b) outerradius of 3 mm.


0 1 2 3 4 50

0.5

1

1.5

2

2.5

Dimensionless Volume, Vd = V/R

h

3

Dim

en

sio

nle

ss C

urv

atu

re,

bd =

Rh/R

0

Bo = 1.22

Bo = 2.44

Bo = 4.89

Figure 4.13: The change of the dimensionless apex curvature, bd, of a pendant dropwith Bond number, Bo, and dimensionless drop volume, Vd. The Bond number, Bo =∆ρgR2

h/γ, is the ratio of body forces (gravitational) to surface tension forces using theholder’s radius as the length scale.


These Bond numbers correspond to the surface tension values of 72, 36, and 18 mJ/m2

using a holder with radius of 3 mm (same cases considered in figure 4.12(b)). Figure 4.13

is considered a general map of the relationship of the three dimensionless groups for the

pendant drop problem (similar to figure 4.4 for the constrained sessile drop case). The

effect of the holder size is integrated inside every one of the dimensionless groups. For

example, a Bond number of 1.22 is equivalent to the two arbitrary chosen cases of: (1)

Rh = 1.5 mm and γ = 18 mJ/m2, shown in figure 4.12(a), and (2) Rh = 3 mm and γ =

72 mJ/m2, shown in figure 4.12(b).

It can be seen from figure 4.13 that there exists a largest dimensionless drop volume,

Vd, and a largest dimensionless curvature, bd, for a given Bond number value. Drop

profiles can not be generated beyond these values. This will be discussed in more detail

below. As the Bond number increases (i.e. a larger holder and/or a liquid with smaller

surface tension value is used), the largest dimensionless volume decreases and the largest

dimensionless apex curvature increases.

Figure 4.14 shows four examples of the predicted drop profile shapes for different

conditions. Figure 4.14(a) shows a pendant drop with γ of 10.0 mJ/m2, Rh of 1.0 mm,

b of 13.2 cm−1, Bo of 1.0, bd of 1.32, and Vd of 5.26. Figure 4.14(b) shows a pendant

drop with γ of 40.0 mJ/m2, Rh of 2.0 mm, and b of 6.6 cm−1, and hence has exactly

the same Bo of 1.0, bd of 1.32, and Vd of 5.26 as figure 4.14(a). The continuous lines

indicate the best fit circle that are fitted to all the drop profile points; this circle is used

in the definition of the shape parameter as shown in equation 4.14. It is apparent that

both drops are well deformed. The only difference is the scaling factor. Therefore, ADSA

should treat them similarly, i.e. ADSA is expected to process these well deformed drops

satisfactorily.

A lower surface tension case is considered in figure 4.14(c). In this case, the pendant

drop shape is considered for the case of γ of 1.0 mJ/m2, Rh of 1.0 mm, b of 25.3 cm−1,

Bo of 10.0, bd of 2.53, and Vd of 0.60. Figure 4.14(d) shows a pendant drop with γ of


−0.2 −0.1 0 0.1 0.2−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

Rh = 1.00 mm, γ = 10 mJ/m

2, Bo = 1.00

x (cm)

z (

cm

)

(a)

−0.5 0 0.5−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

Rh = 2.00 mm, γ = 40 mJ/m

2, Bo = 1.00

x (cm)

z (

cm

)

(b)

−0.2 −0.1 0 0.1 0.2−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

Rh = 1.00 mm, γ = 1 mJ/m

2, Bo = 10.00

x (cm)

z (

cm

)

(c)

−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8

−0.8

−0.6

−0.4

−0.2

0

0.2

Rh = 3.16 mm, γ = 10 mJ/m

2, Bo = 10.00

x (cm)

z (

cm

)

(d)

Figure 4.14: The shape of a pendant drop for different holder sizes and surface tensionvalues. Bond number is indicated on top of every figure. The symbols indicate the dropprofile, and the lines indicate the best circle that fit the profile.


0 1 2 3 4 50

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Dimensionless Volume, Vd = V/R

h

3

Sh

ape

Pa

ram

ete

r, P

c

Bo = 1.22

Bo = 2.44

Bo = 4.89

Figure 4.15: The change of the shape parameter of a pendant drop with Bond numberand dimensionless drop volume.

10.0 mJ/m2, Rh of 3.16 mm, and b of 8.0 cm−1, and hence has exactly the same Bo

of 10.0, bd of 2.53, and Vd of 0.60 as figure 4.14(c). It is clear that both drop can be

fitted to a circle fairly closely and hence will not work accurately with ADSA. It is noted

that constrained sessile drops at high Bond numbers are expected to be well deformed as

shown in figures 4.5(a) and 4.5(b); however, it seems that this is not true for the pendant

drop case as shown in figures 4.14(c) and 4.14(d) where drops at high Bond numbers are

very close to spherical. This point is discussed later in more detail.

Following the similarity between equations 4.11 and 4.15, a map similar – but not

equivalent – to that of figure 4.13 can be readily derived. Figure 4.15 shows the change

of the dimensionless shape parameter with the dimensionless drop volume for different

Bond number values (1.22, 2.44, and 4.89). For the same Bond number value, as the

dimensionless drop volume increases, the value for Pc increases indicating more deformed

drops. There exists a largest dimensionless volume and a largest value for Pc for a given

Bond number value. According to this definition of the shape parameter, the minimum


value for Pc is always zero, similar to the constrained sessile drop case. This indicates

that very small drops, with small dimensionless volumes, are not appropriate for surface

tension measurement even for drops with small surface tension values on large holders.

Figure 4.15 is a general map of the relationship of the three dimensionless groups for the

pendant drop problem.

The fact that there exists a largest dimensionless volume for a given Bond number

value is logical and expected: The pendant drop may be successively increased in size by

adding small amounts of liquid until, at some limiting volume, the drop becomes unstable

and a large portion falls away. The growth and the general conditions that lead to the

instability of a pendant drop were studied before by Padday and Pitt [71]. In that study,

the case of the volume-radius limited pendant drop is equivalent to the case considered

here where the volume of the drop is controlled and the holder used has a fixed radius

that is completely wetted.

Padday and Pitt [71] studied the criteria of critical stability of axisymmetric menisci

in a gravity field and presented a useful form of the critical volume data of the volume-

radius limited pendant drop in terms of V/X3 and X/k, where V is the drop volume, X

corresponds to the radius of the holder, and k is a form of the capillary constant defined

as (γ/∆ρg)12 . Therefore, V/X3 is equivalent to the dimensionless volume Vd considered

here, and X/k is basically the square root of the Bond number Bo. The relationship

between the largest (i.e. critical [71] or maximum allowable) dimensionless volume and

the Bond number is recalculated here using ALFI and plotted in figure 4.16(a). Each

point in figure 4.16(a) is equivalent to the end point of the appropriate curve in figure 4.13.

The analysis was repeated for a wide range of Bond numbers ranging from 10−4 to 102.

The points are in excellent agreement with those presented by Padday and Pitt [71].

The maximum dimensionless volume as a function of Bond number is shown in fig-

ure 4.16(a). It is clear that as the Bond number increases, the maximum dimensionless

volume decreases. As an aside, it is important to note that the drop volume falling off


10−4

10−2

100

102

100

101

102

103

104

105

Bond Number, Bo

Ma

xim

um

Dim

en

sio

nle

ss V

olu

me

, V

m

(a)

10−4

10−2

100

102

0

20

40

60

80

100

120

Bond Number, Bo

Ap

pa

ren

t C

on

tact

An

gle

, θ (

de

g.)

(b)

Figure 4.16: The change of (a) the maximum dimensionless drop volume, and (b) theapparent contact angle of a pendant drop with Bond number.


is always less than the critical volume, first because experimental vibration promotes

instability at an earlier stage of drop formation, and second because a small part of the

drop remains attached to the needle/holder.

The change of the apparent contact angle of the liquid at the holder with Bond

number, at the maximum dimensionless volume, is shown in figure 4.16(b). This figure

indicates that for small Bond number values (i.e., a small holder and/or a liquid with a

large surface tension value), the apparent contact angle is 90 and the liquid is held just

above the narrowest point of the neck of the profile. As the Bond number becomes larger

(i.e., a larger holder and/or a liquid with a smaller surface tension value), the contact

angle at which critical conditions are reached decreases to zero at a Bond number of

10.338. The zero contact angle is the limit for any pendant drop experiment. Further

increase in Bond number (i.e., a larger holder and/or a liquid with a smaller surface

tension value) results in the shape of the critically stable profile taking a configuration

where the holder is not completely wetted. This is the form of a drop as it breaks away

from a large orifice such as that of a bath tap. This case is outside the scope of this

study.

To further understand the different shapes of critically stable profiles, figure 4.17

shows the pendant drop shapes with the maximum dimensionless volume at different

Bond number (0.01, 0.1, 1, and 10). For very small Bond numbers, the apparent contact

angle is around 90 and the maximum dimensionless volume is very large as expected from

figure 4.16. However, the drop shape is very close to spherical. Therefore, it is expected

that ADSA will not work satisfactorily in this range. As the Bond number increases, the

maximum dimensionless volume and the apparent contact angle decrease as expected

from figure 4.16 and the shape of the drop becomes more deformed. Nevertheless, at the

high end of the Bond number range, the apparent contact angle approaches zero and the

drop shape becomes close to spherical again. Thus, it is expected that ADSA will also

not work satisfactorily in this range.


−1 −0.5 0 0.5 1

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

Bo = 0.01, V/Rh

3 = 530.994, P

c = 0.100

x (cm)

z (

cm

)

(a)

−0.6 −0.4 −0.2 0 0.2 0.4 0.6

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

Bo = 0.10, V/Rh

3 = 47.179, P

c = 0.134

x (cm)

z (

cm

)

(b)

−0.6 −0.4 −0.2 0 0.2 0.4 0.6

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

Bo = 1.00, V/Rh

3 = 5.262, P

c = 0.165

x (cm)

z (

cm

)

(c)

−0.6 −0.4 −0.2 0 0.2 0.4 0.6

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

Bo = 10.00, V/Rh

3 = 0.599, P

c = 0.097

x (cm)

z (

cm

)

(d)

Figure 4.17: The shape of a pendant drop with the maximum dimensionless drop volumefor different Bond numbers. The symbols indicate the drop profile, and the lines indicatethe best circle that fit the profile.


10−4

10−2

100

102

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Bond Number, Bo

Sh

ap

e P

ara

me

ter

of

Ma

xim

um

Vo

lum

e,

P c

Figure 4.18: The change of the shape parameter of pendant drops with the maximumdimensionless drop volume with Bond number.

The shape parameter can be calculated using equation 4.14 for the pendant drop

shapes with the maximum dimensionless volume at different Bond numbers. The shape

parameter for the largest stable pendant drop as a function of Bond number is shown in

figure 4.18. The curve ends at Bond number of 10.338 which is equivalent to zero contact

angle. It is clear that the shape parameter is small for very small values as well as large

values of Bond number for reasons discussed above. This shows that for the pendant

drop case very small values as well as large values of Bond number are not recommended

for accurate surface tension measurements.

At this point, it is clear that at any Bond number, there is a critical shape parameter

above which the drop shape is considered well deformed. To further investigate this point,

experiments were performed to illustrate the change of the critical shape parameter with

the Bond number as illustrated below.


Diffuser

LightSource

Microscope CCD

SteppingMotor

Syringe

Glass Cuvette

Figure 4.19: Schematic diagram of ADSA–PD experimental setup.



For the pendant drop experiments decamethylcyclopentasiloxane (DMCPS) was used

rather than OMCTS, mainly due to availability. DEP and water were used again, and a

fourth liquid (hexadecane) was added to provide more experiments at a different Bond

number. DMCPS [C10H30O5Si5] was purchased from Sigma-Aldrich Co. (cat. 444278)

with purity 97.0% and hexadecane [C16H34] from Sigma-Aldrich Co. (cat. 296317) with

purity ≥99.0%. These four liquids have reasonably low vapour pressure and cover a broad

range of surface tension. DMCPS, hexadecane, DEP, and water have surface tensions of

approximately 18, 27, 36, and 72 mJ/m2, respectively.

Figure 4.19 shows a schematic diagram of the experimental setup for ADSA–PD. A

flat circular holder is used to suspend the pendant drop. Except for the pendant drop

chamber, the setup is exactly the same as that used for the constrained sessile drop

study in Section 4.2.4.1. Three holder sizes were used in this study with outer diameters

of 3.08, 4.24 and 6.25 mm. Two holders were used for all four liquids. The smallest

holder was used only with one liquid, DMCPS. It is noted that holder sizes different from

those used in the constrained sessile drop study were used here. This is mainly due to

availability of the holders. Although the same holder radius can be used for both pendant

and constrained sessile drop setups, the holder length requirement is different for every

setup. Hence, different sets of holders were used in the two types of experiments.



All experiments were performed at room temperature of 24oC. It is important to note

that the temperature was controlled within one degree. More accurate temperature

control requires more sophisticated equipment. Since it is not the purpose of this study

to produce literature values of surface tension, such tight control of temperature is not

needed here. The experimental procedure used here was exactly the same as in the

constrained sessile drop case as shown in Section 4.2.4.2.

In total 9 different experiments were performed to cover a wide range of Bond num-

bers. Every experiment was repeated at least three times (three runs) to confirm the

reproducibility; thus, a total of 27 runs were performed in this study. Each run lasted

approximately 200 seconds, implying that approximately 400 images were acquired in

each run. Hence the study is relying on approximately 10,000 individual experimental

surface tension measurements.

4.3.2 Results and Discussion

The results obtained here are qualitatively similar to the ones obtained for the constrained

sessile drop study. Figure 4.20 shows a typical result of ADSA for a pendant drop

of hexadecane formed at the end of a holder with outer diameter of 6.25 mm. The

figure shows a non-random pattern, and hence lack of consistency with the expectation

of a constant surface tension value. The surface tension values of large drops (at the

beginning and at the end of every run) are constant, i.e. they do not change with drop

size, and they agree with the literature value. However, values calculated from small

drops are not constant and show irregular trends, i.e. not just random errors, as shown

in figure 4.20. All acquired images were analyzed and the the shape parameter values

were calculated according to equation 4.14. To calculate the critical shape parameter for

every experiment, the procedure proposed previously [64] was followed. Briefly, the shape


Figure 4.20: The change of surface tension, drop surface area, drop volume, and thecurvature at drop apex with time of a pendant drop of hexadecane formed using a holderwith outer diameter of 6.25 mm.


0 0.02 0.04 0.06 0.08 0.1 0.12 0.14−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Shape Parameter, Pc

Err

or

in S

urf

ace

Te

nsio

n, ε

(m

J/m

2)

Figure 4.21: The error in surface tension measured by ADSA as a function of the shapeparameter for different drop sizes of a pendant drop of hexadecane formed using a holderwith outer diameter of 6.25 mm. For a maximum error of ±0.1 mJ/m2, the critical shapeparameter is 0.04.

parameter values of every run are plotted against the calculated surface tension for the

run. The critical shape parameter is the value below which the error in the calculated

surface tension value exceeds a specific limit, usually set at ±0.1 mJ/m2.

The error in surface tension measured as a function of the shape parameter is shown

in figure 4.21 for different drop sizes of hexadecane formed with a holder with outer

diameter of 6.25 mm. This case is equivalent to a Bond number of 2.72. For a maximum

error of ±0.1 mJ/m2, the critical shape parameter is 0.04. It is important to note that

this is a conservative value as seen from the figure. It is to be noted that the measured

surface tension is accurate and consistent with an accuracy less than ±0.01 mJ/m2 for

well deformed drops in this run, i.e. for large drop sizes with large shape parameter

values. It is also important to note that the overall error in surface tension for this case

did not exceed ±0.2 mJ/m2 for almost all drops in this run, except for very small values

of shape parameter below 0.01 where the drop is very small and is essentially a spherical


cap.

As in the constrained sessile drop case, it was noted in figure 4.21 that there is a

specific trend for the direction (positive or negative) of the error in the surface tension

measurements in the pendant drop case. Such trend is repeated when decreasing or

increasing the drop volume. Similar trends were also noted in other cases. Figure 4.22(a)

shows the error in surface tension of hexadecane formed on a holder with outer diameter

of 4.24 mm, while figure 4.22(b) shows the error in surface tension of DEP formed on a

holder with outer diameter of 4.24 mm. Both figures show similar – but not exactly the

same – trends to that of figure 4.9. Generally, the errors in the pendant drop cases are

much smaller than in the constrained sessile drop cases shown in Section 4.2.

The same analysis was applied to experiments using the other three liquids, de-

camethylcyclopentasiloxane (DMCPS), diethyl phthalate (DEP) and water, using dif-

ferent holders. Following the same procedure shown above, a critical shape parameter

value was calculated from every run. All the results are summarized in Table 4.2. The

first two columns of the table list the holder size and the liquid used for every experi-

ment. The third column lists the presumably correct surface tension values as found in

the literature and/or previous work [217–219]. The fourth column lists the Bond number

for every experiment; a range of Bond numbers between 0.61 and 5.02 is covered in this

study. The following three columns contain the calculated surface tension value (from

the largest drop sizes) and the accuracy of the calculation; more than 60 drops were used

in the calculation of the average value and the standard deviation in each run. The last

three columns contain the measured critical shape parameter for every experimental run.

These values were measured in a procedure similar to that used in figure 4.21.

Inspection of table 4.2 shows that for all systems, except the two listed first and last,

respectively, there is excellent agreement from run to run, as well as with the standard

values of column 3. It is also noted that the differences from run to run could be due

to ambient temperature changes of the order of 0.1oC. The consistency from run to run


0 0.02 0.04 0.06 0.08 0.1 0.12−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Shape Parameter, Pc

Err

or

in S

urf

ace

Te

nsio

n, ε

(m

J/m

2)

(a)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Shape Parameter, Pc

Err

or

in S

urf

ace

Te

nsio

n, ε

(m

J/m

2)

(b)

Figure 4.22: The error in surface tension measured by ADSA as a function of the shapeparameter for different drop sizes of a pendant drop of: (a) hexadecane formed using aholder with outer diameter of 4.24 mm, and (b) DEP formed using a holder with outerdiameter of 4.24 mm. For a maximum error of ±0.1 mJ/m2, the critical shape parametersare 0.052 and 0.039, respectively.


Tab

le4.

2:Sum

mar

yof

resu

lts

ofp

endan

tdro

pex

per

imen

tsusi

ng

diff

eren

tliquid

san

ddiff

eren

thol

der

size

s.

Hol

der

Liq

uid

γ(m

J/m

2)

Bo

γmeasured

(mJ/m

2)

Pcrit

(mm

)[2

17–2

19]

Run

1R

un

2R

un

3R

un

1R

un

2R

un

3

4.24

Wat

er72

.39

0.61

72.0

33±

0.03

772

.016±

0.02

671

.964±

0.02

7-

--

3.08

DM

CP

S18

.26

1.22

18.2

82±

0.00

418

.287±

0.00

418

.285±

0.00

20.

055

0.04

80.

045

4.24

HE

X27

.17

1.25

27.1

73±

0.01

127

.167±

0.01

227

.152±

0.01

40.

052

0.04

50.

052

6.25

Wat

er72

.39

1.32

72.3

99±

0.01

372

.411±

0.01

072

.391±

0.01

40.

045

0.04

40.

050

4.24

DE

P36

.95

1.33

36.9

62±

0.01

336

.935±

0.00

536

.935±

0.01

10.

043

0.04

60.

039

4.24

DM

CP

S18

.26

2.31

18.3

60±

0.00

518

.302±

0.00

518

.296±

0.01

00.

040

0.04

00.

034

6.25

HE

X27

.17

2.72

27.1

94±

0.00

627

.202±

0.00

427

.201±

0.00

80.

038

0.04

00.

042

6.25

DE

P36

.95

2.90

37.0

35±

0.01

037

.046±

0.00

837

.041±

0.01

40.

035

0.03

70.

037

6.25

DM

CP

S18

.26

5.02

17.8

79±

0.00

218

.060±

0.04

518

.086±

0.03

0-

--


1 1.5 2 2.5 3 3.50.03

0.04

0.05

Bond Number, Bo

Critica

l S

ha

pe

Pa

ram

ete

r, P

crit

Experimental Results

Best Fit (Linear)

Figure 4.23: The critical shape parameter as a function of the Bond number. Theexperimental points were fitted to a linear function (continuous line).

and the accuracy of each run are generally less for the first and last systems, and the

agreement with the standard values is much poorer, out of the stipulated error range of

±0.1 mJ/m2. A critical shape parameter does not exist for these cases. The reason of

this difference in pattern is discussed in detail below.

The change of the critical shape parameter as a function of the Bond number is

shown in figure 4.23 for all the experiments of this study. In other words, the critical

shape parameter values for every run obtained in a similar fashion to figure 4.21 and

summarized in the last three columns of table 4.2 are used to calculate an average critical

shape parameter value for every Bond number as shown in figure 4.23. As expected,

figure 4.23 shows that the critical shape parameter depends only on Bond number. The

critical shape parameter is equivalent to a critical dimensionless volume (the drop volume

normalized by the cube of the holder’s radius) that the drop has to exceed to allow for

accurate measurement of the surface tension. This can also be understood from figure

4.15 which defines the relationship between the shape parameter, dimensionless volume


and Bond number. The critical shape parameter is one point on every curve below which

the drop shape is indistinguishable from the zero gravity shape (circle in this case).

Similar to the constrained sessile drop case, for Bond numbers below one, the largest

pendant drop that can be formed with a given holder size is not big enough to calculate

an accurate surface tension value. Therefore the critical shape parameters at these con-

ditions, i.e. when the diameter of holder becomes small and approaches zero, cannot be

established. Contrary to the constrained sessile drop case, this is also the case for Bond

numbers above five, i.e. when the diameter of the holder becomes too large or surface

tension becomes too small. This is due to the fact that the largest pendant drop volume

that can be formed is not big enough to produce sufficiently non-spherical drops at high

Bond number in the pendant drop case. This is in agreement with what was expected

from figures 4.16 to 4.18.

The relationship between the critical shape parameter and the Bond number can

be used in the design of a pendant drop experiment. Through the above analysis, we

know that either very low or very high Bond numbers are not suitable and will not allow

accurate surface tension measurement. However, for the constrained sessile drop case,

we know that only very low Bond numbers are not suitable. A low Bond number is

equivalent to a large surface tension value and/or a small holder size, while a high Bond

number is equivalent to a small surface tension value and/or a large holder size. At low

Bond numbers (a liquid with large surface tension value used with a small holder size),

the pendant drop shape is very close to a sphere (low shape parameter). At high Bond

number (a liquid with small surface tension value used with a large holder size), the

maximum pendant drop volume is very small and the shape becomes close to a sphere

again (low shape parameter). If a rough approximation of the surface tension is known,

a suitable holder size can be easily selected to produce accurate measurement. In other

words, designing an ADSA–PD experiment to measure a specific surface tension value

would require a holder diameter between a minimum and a maximum value to ensure a


maximum error below a specified error tolerance. This would also require that the volume

of the pendant drop be large enough so that the calculated shape parameter exceeds the

appropriate critical shape parameter as shown in figure 4.23.

For example, based on the calculations presented here and assuming a density dif-

ference of 1000 kg/m3 and gravity of 9.80 m/s2, holder diameters between 2.5 and 5.5

mm are recommended for a surface tension value of 15 mJ/m2 to ensure a maximum

error of ±0.1 mJ/m2 for large drop sizes. Holder diameters between 4.0 and 8.5 mm are

recommended for a surface tension value of 38 mJ/m2. Holder diameters between 5.5

and 12.0 mm are recommended for a surface tension value of 72 mJ/m2. Generally, it

is advised to make the drop as large as possible so that the calculated shape parameter

exceeds the appropriate critical shape parameter to guarantee accurate results. These

rough examples serve as a guide for selecting the right holder size to produce accurate

measurement, if a rough approximation of the surface tension is known.

It can be concluded that the use of a usually thin needle or capillary for pendant

drop experiments is generally not an optimal choice. No single holder is universally

useable. However, a holder size of 5 to 6 mm diameter would be a good choice for

most common liquids, if ultimate accuracy is not required. But if ultimate accuracy is

required, the choice of the support for a pendant drop experiment for surface tension

measurements is extremely important. The size of a suitable holder depends critically

on the Bond number, specifically the density difference across the drop interface and the

surface tension. Neither holders that are too small or too large are appropriate. It can

be seen from table 4.2 that an accuracy near ±0.01 mJ/m2 can be achieved readily.

4.4 Universality of Results

It is believed that the close-to-spherical limitation does exist for ADSA (independent of

the details of the numerical modules) as well as other drop shape techniques. To further


investigate this, it is important to test the same results using different modules inside

ADSA and other drop shape techniques as well.

The structure of ADSA consists of three main modules. The first module generates

the theoretical profiles by numerical integration of the Laplace equation (Axisymmetric

Liquid Fluid Interface) “ALFI”. The fifth- and sixth-order Runge-Kutta-Verner pair is

used here for the numerical integration [9]. The second module is the image processing,

which extracts the experimental profiles of drops. Here, the Canny edge detector is used

for the image processing followed by image distortion correction (using a grid) and image

enhancement to sub-pixel resolution [8, 220]. The third module is the optimization

procedure to find the best fit of the theoretical Laplacian curves to the experimental

profile. The Levenberg-Marquardt method is used here for the numerical optimization

[7, 9]. In addition to these three modules, there has been one guiding principle: the input

must be the simplest conceptually possible, e.g. there must be no need for identifying

special points on the drop profile, such as the apex.

The three modules are freely exchangeable against other modules designed for the

same purpose. Such a study with different modules was recently performed [218, 219],

for a different drop constellation, a sessile drop with a capillary protruding into the

drop, ADSA – No Apex (ADSA–NA). To ascertain the general validity of the results in

table 4.2, a similar study was performed here for the pendant drop constellation.

The first step is to test the effect of a different image processing technique. The

Canny edge detector was replaced by a robust non-gradient edge detector called SUSAN

[221]. SUSAN is a non-gradient edge detection operator; it does not depend on intensity

gradients in the digitized image. This was followed by the standard ADSA procedure.

The results of this step “ADSASUS” for the case of a pendant drop of hexadecane formed

using a holder with outer diameter of 6.25 mm are shown in figures 4.24(b) and 4.25.

The computation time was less than one second per image on a computer with a 2.66

GHz CPU and 3.00 GB of RAM. This is similar to that of the standard ADSA.


Next, the effect of a different numerical optimization technique is considered. The

Levenberg-Marquardt method was replaced by the non-gradient Nelder-Mead simplex

method [222]. Compared to the gradient methods, Nelder-Mead is computationally eas-

ier to implement since it does not require a derivative of the objective function, but

it consumes more computer time. The results of this step “ADSANM” for the case of

the same pendant drop of hexadecane formed with the same holder are shown in fig-

ures 4.24(c) and 4.25. The computation time was roughly 3 to 4 seconds per image.

The third step is to test a different drop shape technique called theoretical image

fitting analysis “TIFA” [211, 223] that uses a completely different approach from ADSA.

The difference between the strategy of ADSA and TIFA is that, in TIFA, the interfacial

properties are calculated by fitting the whole theoretical image – not the drop profile

only – to the experimental image of the drop. The theoretical image is a black and

white image of the drop generated by numerically solving the Laplace equation. An

error function measures the pixel-by-pixel difference between the gradient of the whole

theoretical and experimental images. The interfacial properties are found by fitting the

gradient of the theoretical image to the gradient of the experimental one by minimizing

the error function. The remarkable feature of TIFA is that it operates without using edge

detection algorithms. In fact, image analysis is tied to the optimization process in TIFA,

and it is not a separate module as in ADSA. The results of this step, using TIFA for

the case of the same pendant drop of hexadecane formed with the same holder are also

shown in figures 4.24(d) and 4.25. The computation time was approximately 72 seconds

per image (approximately 8 hours for this run).

Figure 4.24 shows the comparison between the surface tension values of a pendant

drop of hexadecane formed using a holder with outer diameter of 6.25 mm calculated using

the standard ADSA algorithm, the modified algorithms (ADSASUS and ADSANM), and

the TIFA algorithm. The calculated surface tension values for the large drops are very

consistent for all four algorithms, with values of 27.202±0.004 mJ/m2, 27.208±0.004


26

27

28

29

γ (m

J/m

2)

γ = 27.202±0.004 mJ/m2

(a)

26

27

28

29

γ (m

J/m

2)

γ = 27.208±0.004 mJ/m2

(b)

26

27

28

29

γ (m

J/m

2)

γ = 27.201±0.004 mJ/m2

(c)

0 50 100 150 20024

26

28

30

γ (m

J/m

2)

Time, t (s)

γ = 27.194±0.005 mJ/m2

(d)

ADSA

ADSASUS

ADSANM

TIFA

Figure 4.24: The change of surface tension with time of a pendant drop of hexadecaneformed using a holder with outer diameter of 6.25 mm. The calculations are repeatedusing different software options; ADSA: the default options using Canny for edge detec-tion and Levenberg-Marquardt for optimization; ADSASUS: SUSAN is used instead ofCanny; ADSANM : Nelder-Mead is used instead of Levenberg-Marquardt; TIFA: theoret-ical image fitting analysis.


0 0.02 0.04 0.06 0.08 0.1 0.12 0.14−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Shape Parameter, Pc

Err

or

in S

urf

ace

Te

nsio

n, ε

(m

J/m

2)

ADSA

ADSASUS

ADSANM

TIFA

Figure 4.25: The error in measured surface tension as a function of the shape parameterfor different drop sizes of a pendant drop of hexadecane formed using a holder with outerdiameter of 6.25 mm. The calculations are repeated using different software options;ADSA: the default options using Canny for edge detection and Levenberg-Marquardt foroptimization; ADSASUS: SUSAN is used instead of Canny; ADSANM : Nelder-Mead isused instead of Levenberg-Marquardt; TIFA: theoretical image fitting analysis.

mJ/m2, 27.201±0.004 mJ/m2, and 27.194±0.005 mJ/m2, respectively. For the small

drops, all algorithms fail to predict the correct value for the surface tension. Interestingly,

the ADSA algorithms are very consistent from one ADSA version to the next, even for

small drops. However, the TIFA algorithms show larger deviation from the correct surface

tension value in the case of small drops.

The error in surface tension measured by these four different algorithms as a function

of the shape parameter is shown in figure 4.25 for the same run. The original and modified

ADSA algorithms are very consistent and show very similar trends. It is important to

note that the overall error in surface tension for this case did not exceed ±0.2 mJ/m2 for

almost all drops in this run, except for very small values of shape parameter below 0.01

where the drop is very small and is essentially a spherical cap. The TIFA algorithm shows


similar results for large drops (large shape parameter) but deviates dramatically for small

drops (small shape parameter). For a maximum error of ±0.1 mJ/m2, a conservative

critical shape parameter value is 0.04 in this case.

Stepping well back, it is apparent that, for drops of a reasonable size, high quality

surface tension results are readily obtainable from drop shape techniques. While the

choice of optimization method has a considerable effect on computation time and neces-

sary accuracy of the initial guess, it does not have an appreciable effect on the surface

tension result, see specifically figures 4.24(a) and 4.24(c). Less expected is the finding

that edge detection also does not have a significant effect; the standard ADSA using

Levenberg-Marquardt and Canny (figure 4.24(a)) or alternatively Levenberg-Marquardt

and SUSAN, i.e. a non-gradient edge detection strategy (figure 4.24(b)), agree well. A

method totally outside the ADSA scheme, TIFA, also yields the same results, for large

enough drops.

Finally, the results show that all techniques are outside the stipulated error range of

±0.1 mJ/m2 when the drop or bubble approaches spherical shapes. Using non-gradient

edge detection or non-gradient optimization modules did not change the results. It was

noted that TIFA techniques work well for well deformed drops but yield erroneous results

(worse than ADSA) for close-to-spherical drops. This is in agreement with other studies

in the literature [219].

Chapter 5

Summary of Progress and Outlook

The ADSA–CSD configuration has been further developed to produce a highly versa-

tile methodology for surface tension measurements. ADSA–CSD was used to probe the

behaviour of films adsorbed or spread at air-water interfaces. During these studies it

became clear that the accuracy of the data needed to be quantified and measured. In

Chapter 4, a derivation of a versatile assessment of the accuracy of surface tension mea-

surement is described. This represents a fundamental improvement which can be applied

to other shape dependant configurations.

The accuracy of any drop shape technique will depend on the deviation of an exper-

imental drop shape from the zero gravity shape, i.e. the spherical shape in the case of

sessile/pendant drops considered here. This difference between the two shapes can be

expressed quantitatively as a shape parameter. By comparing shape parameters with

the deviations of calculated surface tensions for different drop sizes of liquids of known

surface tension, a critical shape parameter was established, below which surface tension

measurements will exceed a specified error tolerance. The key element of this proce-

dure is a dimensional analysis used to describe similarity in constrained sessile drop and

pendant drop shapes. The shape parameter concept was used in Chapter 4 to quantify

the accuracy of both the constrained sessile drop (ADSA–CSD) and the pendant drop

185

Chapter 5. Summary of Progress and Outlook 186

(ADSA–PD) constellations. It was shown that an accuracy near ±0.01 mJ/m2 can be

achieved readily for well deformed drops.

It is known that the pendant drop constellation yields the most accurate results among

the drop shape methods. However, in the case of low surface tension values, gravity tends

to detach the drop from the capillary holder before it is large enough [71], making surface

tension measurement impossible. For such low surface tensions, the constrained sessile

drop constellation is more suitable. Such low surface tension values (near 1 mJ/m2) are

very common in lung surfactant studies. The analysis presented in Chapter 4 can be

used in the design of constrained sessile drop and pendant drop experiments for surface

tension measurement. If a rough approximation of the surface tension is known, a holder

of suitable size for a specified accuracy can be easily selected. The size of a suitable

holder depends critically on the Bond number, which in turn depends on the density

difference across the drop interface and the surface tension.

It was shown in Chapter 4 that the use of different edge detectors or optimization

techniques is not expected to improve the accuracy of the surface tension measurements.

If further progress on accuracy is needed, it is recommended to look further into the

quality of the images obtained. Specifically the optics of the whole system, lighting

and refraction, and possibly image magnification are to be considered. It is doubtful if

accuracy can be enhanced much but possibly the range of critical shape parameter and

the working range of Bond numbers for different constellations might be improved (cf.

tables 4.1 and 4.2). A suggested strategy would be to repeat the pure liquids experiments

and shape parameter analysis done in Chapter 4 with different optics. Any such work

would need extreme temperature control.

Using the high accuracy now obtained, the pendant drop method can be used for

many applications. Thus, more accurate temperature dependant surface tension mea-

surement data could be produced. For example, as temperature coefficients of surface

tension are generally in the order of 0.1 mJ/m2·K, using a method with accuracy of ±0.1


mJ/m2 requires measurements at a much wider temperature range than is needed in a

method with accuracy of ±0.01 mJ/m2. The pendant drop technique has the potential

of being used to determine the effect of temperature on surface tension with very high

accuracy. Most of the present literature data for temperature dependant surface tension

measurement were produced a long time ago with methods such as the capillary rise,

the maximum bubble pressure, or the drop weight [224]. These methods have limita-

tions of which ADSA–PD is free [93, 225]. The capillary rise method requires a very

sophisticated setup, the maximum bubble pressure method assumes a spherical bubble,

and the drop weight method relies heavily on an empirically determined correction fac-

tor [93, 225]. Therefore, there is considerable potential in drop shape techniques due

to the compactness and complete isolation of the experimental setup, allowing for var-

ious experimental conditions ranging from high pressure and high temperature to high

and ultra-high vacuum. The only problem was uncertainty about accuracy which was

removed in Chapter 4.

The shape parameter analysis presented here is also applicable – in principle – to other

configurations such as unconstrained sessile drops, captive bubbles, liquid bridges, and

liquid lenses. However, the comparison with a circle will only apply to sessile/pendant

drops and bubbles. For other configurations, the drop shape must be compared to the

respective zero gravity shape for each case. These drops at zero gravity may assume

different shapes including cylindrical, nodoidal, unduloidal and catenoidal. The radius

of the drop holder can still be used for normalization in the case of a liquid bridge. It

can be replaced by the radius of the capillary in the case of pendant drop or the contact

radius in the cases of unconstrained sessile drop or liquid lens. For the liquid bridge

case, the radius of the upper holder will be a new parameter that has to be considered in

defining the shape. For the unconstrained sessile drop and liquid lens cases, the diameter

of the pedestal (holder) does not exist. The contact angle and contact radius will play

an important role in defining the shape of the drop for these cases.


In the lung surfactant context, the performance of surfactant preparations were as-

sessed using the dynamic surface tension response to film compression and expansion.

Prior to this work, typically only the minimum surface tension values at the end of com-

pression were reported. Several distinctive physical surface effects are expected to play a

role in the process of film compression and expansion: elasticity, adsorption and desorp-

tion. So far only the elasticity during compression had been considered by determining

the slope of the surface tension versus surface area plot. There are two concerns with

this procedure. First, as seen in Chapter 4, the accuracy of the surface tension and

indeed the surface tension value itself determined by ADSA can depend on drop size,

unless all drop sizes are associated with a sufficiently large shape parameter. If such a

trend of erroneous surface tension occurs, the error in the elasticity as a slope of surface

tension versus area can be quite large. The results of Chapter 4 show how to avoid

these errors. Second, relying on the slope of the surface tension response to the surface

area changes as a strategy to determine elasticity assumes that there is no simultaneous

change of surface concentration, say during compression. This assumption is at variance

with known experimental facts of squeeze out, relaxation and spreading. This difficulty is

removed by the model described in Chapter 3 by allowing the surface tension to change

due to simultaneous effects of one or more of these dynamic phenomena. A dynamic

compression-relaxation model (CRM) was developed and used to describe the mechan-

ical dynamic properties (elasticity, relaxation and adsorption) of insoluble pulmonary

surfactant films by investigating the response of surface tension to changes in surface

area. Multi-variable optimization was introduced here to calculate the dynamic param-

eters from experimental results of dynamic surface tension measurements. A detailed

sensitivity study for CRM was also performed in Chapter 3.

Combined with the unique capabilities of ADSA–CSD, CRM was used to study the

effect of humidity, concentration, compression ratio and frequency of a lung surfactant

preparation, BLES. The highest concentration used was 27 mg/ml, similar to that used


clinically. Low surface tension at such high concentrations are very difficult to measure

using other methods as discussed in Chapter 1. While the dynamic properties of BLES-

only preparations do not improve significantly with increasing BLES concentration, the

same might not be true in the presence of inhibitors. Using ADSA–CSD, CRM studies of

the dynamic properties of lung surfactant preparations can be extended to more complex

systems containing inhibitors.

There is an urgent need to be able to access the air/liquid interface from both sides.

This need arises from clinical reality: contaminations (pollution) affect the surfactant

interface from the air side and therapeutical surfactant preparations are instilled to the

lungs from the air side, while leakage of plasma and blood proteins can occur from the

liquid side causing severe lung injury. Therefore, accessing the lung surfactant interface

from both sides is a desirable feature in any in vitro technique. The ADSA–CSD setup

was further developed in Chapter 2 to allow for such studies.

Two main capabilities were added to the ADSA–CSD setup. The first one was the

deposition capability which allows spreading of material onto the air/liquid interface from

the air side. This permits the study of the collapse of deposited films through the study of

pure monolayers as well as mixed monolayers. DPPC and DPPG monolayers, which are

the main components of most commercial lung surfactant preparations (Appendix A),

were studied to characterize the role of such molecules in maintaining stable film prop-

erties and surface activity of lung surfactant preparations. The second capability added

was the double injection which facilitates the complete exchange of the subphase of a

spread or adsorbed film from the liquid side. The development was illustrated through

inhibition studies using serum, albumin, fibrinogen, and cholesterol. Evaluation of lung

surfactant inhibition, resistance and reversal under completely controlled physiological

conditions is illustrated in Chapter 2. It is noted that the redesigned ADSA–CSD is

a versatile tool for surface tension measurements that has a wide range of applications

outside the scope of the lung surfactant research area as well.


Clinical lung surfactant therapies currently use mechanical ventilation, and more

recently High Frequency (more than 1 Hz) Ventilation (HFV). However, little is known

about the role of surfactants in high frequency ventilation. The present ADSA–CSD

setup is not capable of simulating the high frequency cycling of more than 1 Hz due to

mechanical limitations of the servo-mechanism controlling the syringe. However, high

frequency studies can be readily facilitated in ADSA–CSD by straightforward hardware

upgrades. Two main items are needed: a piezo-actuator with a dedicated computer-

programmable controller to facilitate the low amplitude high frequency oscillations of

the drop volume, and a high speed camera. Both are readily available commercially.

The future high frequency ADSA–CSD can be used in conjunction with CRM to char-

acterize the surface activity of relevant lung surfactant preparations at higher frequency,

and to study the changes of the dynamic properties (elasticity, relaxation, and adsorp-

tion) at high rates of film compression and expansion. A high frequency ADSA–CSD

methodology and the ability to characterize dynamic interfacial properties using CRM

at high frequency will have great potential for a wide range of colloid and interfacial

applications, beyond lung surfactants.

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[300] A. Anzueto, R. P. Baughman, K. K. Guntupalli, J. G. Weg, H. P. Wiedemann, A. A.Raventos, F. Lemaire, W. Long, D. S. Zaccardelli, E. N. Pattishall, Aerosolizedsurfactant in adults with sepsis-induced acute respiratory distress syndrome, NewEngland Journal of Medicine 334 (22) (1996) 1417–1421.

[301] I. W. Levin, Interactions of model human pulmonary surfactants with a mixedphospholipid bilayer assembly: Raman spectroscopic studies, Biochemistry 32 (32)(1993) 8228–8238.

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[304] C. G. Cochrane, S. D. Revak, T. A. Merritt, G. P. Heldt, M. Hallman, M. D.Cunningham, D. Easa, A. Pramanik, D. K. Edwards, M. S. Alberts, The efficacyand safety of KL4-surfactant in preterm infants with respiratory distress syndrome,American Journal of Respiratory and Critical Care Medicine 153 (1) (1996) 404–410.

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[315] S. Hawgood, A. Ogawa, K. Yukitake, M. A. Schlueter, C. Brown, T. White,D. Buckley, D. Lesikar, B. J. Benson, Lung function in premature rabbits treatedwith recombinant human surfactant protein-C, American Journal of Respiratoryand Critical Care Medicine 154 (2) (1996) 484–490.

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[316] A. J. Davis, A. H. Jobe, D. Hafner, M. Ikegami, Lung function in premature lambsand rabbits treated with a recombinant SP-C surfactant, American Journal ofRespiratory and Critical Care Medicine 157 (2) (1998) 553–559.

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[318] D. Hafner, P. G. Germann, D. Hauschke, Effects of rSP-C surfactant on oxygenationand histology in a rat-lung- lavage model of acute lung injury, American Journalof Respiratory and Critical Care Medicine 158 (1) (1998) 270–278.

[319] M. Ikegami, A. H. Jobe, Surfactant protein-C in ventilated premature lamb lung,Pediatric Research 44 (6) (1998) 860–864.

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Note: All references starting with Ref. 226 are only used in Appendix A.

Appendix A

Commercial Lung Surfactants∗

Several classification systems are used for commercial exogenous lung extracts [1, 174,

175, 226]. Figure A.1 divide different commercial lung extracts into two main categories

according to the source of the preparation. The first category is natural lung surfactants

which contains endogenous lung extracts from animals. The second category is synthetic

lung surfactants which does not contain any natural extracts. Generally, preclinical an-

imal testing and clinical trials suggest that the performance of natural animal-derived

preparations is much better than synthetic preparations [227–229]. However, batch to

batch variations, low content of surfactant proteins and high cost are among the limita-

tions of natural animal-derived preparations [230, 231].

A.1 Natural Surfactant Extracts

Natural surfactants [230–234] can also be classified into three categories. The first con-

tains exogenous surfactants extracted by animal lung lavage (Alveofact, BLES, Infasurf).

The general extraction procedure is summarized in figure A.2. The second group contains

exogenous surfactants processed from animal lung tissue (Curosurf). The third group is

∗References used here are contained in the bibliography list at the end of the body of the thesis.

219

Appendix A. Commercial Lung Surfactants 220

Commercial Lung Extracts

Ani

mal

Lung

La

vage

BLES

Alveofact

Infasurf

Natural Synthetic

Surfacten

Curosurf

Survanta

Exosurf

ALEC

Surfaxin

Venticute

Ani

mal

Lung

Ti

ssue

Supp

lem

ente

d Lu

ng T

issue

Prot

ein

Free

Sim

plifi

ed

Pept

ides

Prot

ein

Ana

logs

Figure A.1: General classification of commercial lung extracts.


Intact Bovine LungsIntact Cow Lungs Intact Calf Lungs

BLESAlveofact Infasurf

BLSE CLSE

Endogenous Lung Surfactant



Bronchoalveolar Lavage (with 0.15 M NaCl)

cells removed by low-speed centrifugation (150 - 200 g)

pelleted by high-speed centrifugation (10000 - 12000 g)

extract with Chloroform-Methanol (remove SP-A)

extract with Acetone (deplete Cholesterol and NL)









Figure A.2: Extraction procedure for surfactants extract of lung lavage.

similar to the second one; however, these surfactants are supplemented with synthetic

additives (Surfacten, Survanta). The general extraction procedure of second and third

categories is summarized in figure A.3. A comparison of the composition of the six nat-

ural surfactant extracts is shown in figure A.4. More details about natural surfactants

can be found in a recent review [235].

A.1.1 Alveofact

Alveofact (SF-RI 1 or bovactant) is a clinical exogenous lung surfactant obtained from

bronchoalveolar lavage of bovine lung surfactant [236–240]. The lavage is pelleted by

centrifugation, followed by extraction with chloroform methanol to remove hydrophillic

surfactant protein (see figure A.2). It contains weight distribution of 99% phospholipids


Bovine Lung TissuePorcine Lung Tissue Bovine Lung Tissue

SurfactenCurosurf Survanta

Lung Tissue Extract Lung Tissue Extract Lung Tissue Extract

homogenize or mince (in 0.15 M NaCl)

differential centrifugation and flotation steps

extract with ethyl acetate (reduce neutral lipids)

extract with Chloroform-Methanol (remove ethyl actetate)

supplement with synthetic DPPC,

Palmitic Acid, and Tripalmitin


wash and centrifuge (1,000 - 3,000 g)

extract with Chloroform-Methanol (2:1)

supplement with synthetic DPPC,

Palmitic Acid, and Tripalmitin

liquid-gel affinity chromatography


differential centrifugation and flotation steps

extract with ethyl acetate (reduce neutral lipids)

extract with Chloroform-Methanol (remove ethyl actetate)

Figure A.3: Extraction procedure for surfactants extract of lung tissue.


PL/NL: 95%

Cholesterol: 4%SP−B/SP−C: 1%

(a) Alveofact

PC: 78%

Other PL: 21%

SP−B/SP−C: 1%

(b) BLES

PC: 77%

PG: 6%

PI/PS: 4%

PE/SPH: 5%

Other PL: 2%Cholesterol/NL: 5%SP−B/SP−C: 1%

(c) Infasurf

PC: 70%

PE/SPH: 17%

Other PL: 12%SP−B/SP−C: 1%

(d) Curosurf

PL: 84%

Palmitic Acid: 8%

Tripalmitin: 7%SP−B/SP−C: 1%

(e) Surfacten

PL: 84%

Palmitic Acid: 8%

Tripalmitin: 7%SP−B/SP−C: 1%

(f) Survanta

Figure A.4: Composition of natural surfactants extracts.


(PL) and neutral lipids (NL) [that include 4% cholesterol], and 1% hydrophobic surfactant

proteins SP-B and SP-C as shown in figure A.4(a). It is formed clinically as a sterile

suspension in 0.15 M NaCl at 45 mg/ml with dosing amount of 1.2 ml/kg. Alveofact

is produced by Thomae GmbH, Biberach, Germany; and Boehringer Ingelheim Co.,

Ingelheim, Germany.

A.1.2 BLES

BLES (bovine lipid extract surfactant) is a clinical exogenous lung surfactant made from

of lung surfactant lavaged from cows [241–244]. The lavage is pelleted by centrifugation,

followed by extraction with chloroform methanol to give BLSE (bovine lung surfactant

extract). Additional extraction with acetone is used to remove cholesterol and other

neutral lipids (see figure A.2). It contains weight distribution of 98-99% phospholipids

(PL) [that include 79% phophophatidyl-choline (PC)], and 1% hydrophobic surfactant

proteins SP-B and SP-C as shown in figure A.4(b). It is formed clinically as a sterile

suspension in 0.15 M NaCl and 1.5 mM CaCl2 at 25 mg/ml with dosing amount of 5

ml/kg (135 mg/kg), 1-2 doses every 8 h. BLES is produced by BLES Biochemicals Inc.,

London, Ontario, Canada.

A.1.3 Infasurf

Infasurf (CLSE or calfactant) is a clinical exogenous lung surfactant obtained from calves

lung lavage (CLSE) [245–257]. The lavage is pelleted by centrifugation at 10,000 - 12,000

×g, followed by extraction with 2:1 chloroform methanol to give CLSE or calf lung

surfactant extract (see figure A.2). It contains weight distribution of 93% phospholipids

(PL) [that include 83% phophophatidyl-choline (PC), 6% phosphatidyl-glycerol (PG), 4%

phosphatidyl-inositol (PI) and phosphatidyl-serine (PS), 3% phosphatidyl-ethanolamine

(PE), and 2% sphinogomyelin (SPH)], 5% cholesterol and neutral lipids (NL), and 1.5%

hydrophobic surfactant proteins SP-B and SP-C as shown in figure A.4(c). Desaturated


PC is approximately 50% of the total phopholipids. It is formed clinically as a heat-

sterilized suspension in 0.15 M NaCl at 35 mg/ml with dosing amount of 3 ml/kg (105

mg/kg), 1-4 doses every 6-12 h. Infasurf is produced by ONY Inc., Amherst, New York,

USA (for Forest Pharmaceuticals Inc., St. Louis, Missouri, USA).

A.1.4 Curosurf

Curosurf (poractant alpha) is a clinical exogenous lung surfactant obtained from minced

porcine lung tissue [258–264]. The process include washing, centrifugation at 1,000 - 3,000

×g, followed by extraction with 2:1 chloroform methanol, and liquid-gel affinity chro-

matography (see figure A.3). It contains weight distribution of 93% phospholipids (PL)

[that include 67-75% phophophatidyl-choline (PC), 12-22% phosphatidyl-ethanolamine

(PE) and sphinogomyelin (SPH)], and 1% hydrophobic surfactant proteins SP-B and

SP-C as shown in figure A.4(d). It is formed clinically as a suspension sterilized by high

pressure filter system (0.45 and 0.2 µm filters), dried or lypohilized and stored in vials

then suspended in saline by sonication at 80 mg/ml prior to use with dosing amount

of 2.5 ml/kg (200 mg/kg) to 1.25 ml/kg (100 mg/kg). Curosurf is produced by Chiesi

Farmaceutici, Parma, Italy.

A.1.5 Surfacten

Surfacten (Surfactant TA) is a clinical exogenous lung surfactant made by organic sol-

vent extraction of finely ground bovine lung tissue supplemented with synthetic DPPC,

palmitic acid, and tripalmitin [265–270]. The lung tissue goes through several centrifuga-

tion and floatation processes, extraction with ethyl acetate to reduce neutral lipids, and

additional extraction with chloroform methanol to remove ethyl acetate. The extract

is then supplemented with the aforementioned synthetic additives (see figure A.3). The

final product contains weight distribution of 84% phospholipids (PL), 8% palmitic acid,

7% tripalmitin, and 1% hydrophobic surfactant proteins SP-B and SP-C as shown in


figure A.4(e). It is formed clinically as a suspension sterilized by high pressure filter,

lypohilized and stored in vials then suspended in sterile 0.15 M NaCl at 30 mg/ml prior

to use with dosing amount of 4 ml/kg (100 mg/kg), 1-4 doses every 6 h. Surfacten is

produced by Mitsubishi Tanabe Pharma Corporation (formerly Tokyo Tanabe Co. Ltd.),

Tokyo, Japan.

A.1.6 Survanta

Survanata (beractant) is a clinical exogenous lung surfactant made by organic solvent

extraction of processed and supplemented bovine lung tissue [230, 255, 263, 271–279]. It

is prepared by similar methods and identical synthetic additives as in Surfactant TA (see

figure A.3). The final product contains hydrophobic surfactant proteins slightly less than

1% (include a small amount of SP-B) as shown in figure A.4(f). It is formed clinically as

an autoclave-sterilized suspension in 0.15 M NaCl at 25 mg/ml with dosing amount of 4

ml/kg (100 mg/kg), 1-4 doses every 6 h. Survanta is produced by Abbott Laboratories,

Abbott Park, Illinois, USA.

A.2 Synthetic Surfactants

Synthetic Surfactants [280–282] can also be classified into three categories. The first

contains synthetic exogenous surfactants with no proteins (ALEC, Exosurf). The sec-

ond group contains synthetic exogenous surfactants with synthetic simplified peptides

(Surfaxin). The third group contains synthetic exogenous surfactants with recombinant

human apoproteins (Venticute). A comparison of the composition of the four synthetic

surfactants is shown in figure A.5. More details about synthetic surfactants can be found

in recent reviews [280, 283–288].


DPPC: 70%

egg PG: 30%

(a) ALEC

DPPC: 85%

Hexadecanol: 9%

Tyloxapol: 6%

(b) Exosurf

DPPC: 64%

POPG: 21%

Palmitic Acid: 13%

Sinapultide (KL4): 2%

(c) Surfaxin

DPPC: 65%

POPG: 28%

Palmitic Acid: 5%rSP−C: 2%

(d) Venticute

Figure A.5: Composition of synthetic surfactants.


A.2.1 ALEC

ALEC (artificial lung expanding compound) is a clinical exogenous lung surfactant con-

taining synthetic dipalmitoyl-phosphatidyl-choline (DPPC) and egg phosphatidyl-glycerol

(PG) in a 7:3 molar ratio [79–81, 289, 290] as shown in figure A.5(a). DPPC is the main

component for lowering surface tension, while egg PG is to improve adsorption and

spreading. It is formed clinically as a fine white powder mixed (below 30C) with sterile

0.15 M NaCl. It is produced by Britannia Pharmaceuticals Ltd., Redhill, Surry, United

Kingdom. ALEC was withdrawn from the market few years ago.

A.2.2 Exosurf

Exosurf (colfosceril palmitate) is a clinical exogenous lung surfactant containing synthetic

dipalmitoyl-phosphatidyl-choline (DPPC), hexadecanol, and tyloxapol in a 1:0.111:0.075

weight ratio [252, 254, 279, 291–300] as shown in figure A.5(b). DPPC is the main

component for lowering surface tension, while the nonionic detergent and the C16:0

alchohol hexadeconal are to improve adsorption and spreading. It is formed clinically

as a sterile lyophilized powder in vaccum-sealed vials with 0.1 M NaCl then suspended

in 8 ml of distilled water prior to use with dosing amount of 5 ml/kg (67.5 mg/kg), 1-4

doses every 12 h. It is produced by GlaxoSmithKline (formerly Burroughs Wellcome),

Research Triangle Park, North Carolina, USA. Exosurf is no longer available in USA and

Canada.

A.2.3 Surfaxin

Surfaxin (KL4 or lucinactant) is a clinical exogenous lung surfactant containing syn-

thetic dipalmitoyl-phosphatidyl-choline (DPPC), palmitoyl-oleoyl-phosphatidyl-glycerol

(POPG), palmitic acid, and a 21 amino acid synthetic hydrophobic peptide with repeated

sequences of one lysine (K) and four leucine (L) residues [82–84, 301–314]. DPPC and


POPG are present in 3:1 weight ratio. Palmitic acid is present at 15% by weight relative

to phospholipids, while the hydrophobic peptide (known as KL4 or sinapultide) is present

at 3% by weight as shown in figure A.5(c). It is produced by Discovery Laboratories Inc.,

Warrington, Pennsylvania, USA. Recently, an aerosolized version of Surfaxin was devel-

oped by the same producer called Aerosurf. Surfaxin and Aerosurf are investigational

drug products, and are not approved for use yet.

A.2.4 Venticute

Venticute (Recombinant SP-C or lusupultide) is a clinical exogenous lung surfactant con-

taining synthetic dipalmitoyl-phosphatidyl-choline (DPPC), palmitoyl-oleoyl-phosphatidyl-

glycerol (POPG), palmitic acid, and human sequence or modified human sequence recom-

binant surfactant apoprotein (rSP-C) [85–87, 184, 198, 315–320]. DPPC and POPG are

present in 7:3 weight ratio. Palmitic acid is present at 5% by weight relative to phospho-

lipids, while the rSP-C protein is present at 2% by weight as shown in figure A.5(d). It is

produced by Altana Pharma AG (formerly Byk Gulden), Konstanz, Germany. Venticute

is an investigational drug product, and is not approved for use yet.

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