Foam films drawn from dispersions

Citation for published version (APA):Baets, P. J. M. (1993). Foam films drawn from dispersions. Technische Universiteit Eindhoven.https://doi.org/10.6100/IR406827

DOI:10.6100/IR406827

Document status and date:Published: 01/01/1993

Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverne

Take down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.

Download date: 10. Feb. 2022

FOAM FILMS DRA WN · FROM DISPERSlONS .

PJ.M. BAETS

FOAM FILMS DRAWN FROM DISPERSlONS

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de

Technische Universiteit Eindhoven, op gezag van

de Rector Magnificus, prof.dr. J.H. van Lint, voor

een commissie aangewezen door het College

van Dekanen in het openbaar te verdedigen op

vrijdag 17 december 1993 om 16.00 uur

door

PETER JOHANNES MARIE BAETS

geboren te Grathem

Dit proefschrift is goedgekeurrt

door de promotoren

prof.dr. H.N. Stein

en

prof.dr. W.G.M. Agterof

CONTENTS

Chapter 1: Introduetion

Objective of the thesis ...................... 1

Mechanisms of foam destruction ............... 2

Disproportienation of gas bubbles .......... 2

Spreading .................................. 5

Drainage of horizontal faam films .......... 5

Drainage of vertical faam films: ........... 7

marginal regeneratien

Influence of solid particles .............. 12

Film rupture of horizontal films .......... 13

Rheological properties ...................... 14

Foam destructien in practice ............... 18

References .................................. 19

Chapter 2: Drainage of CTAB films containing solid particles

Abstract .................................... 25

Introduetion ................................ 26

Theory ...................................... 27

Experimental methods ........................ 28

The apparatus ............................. 28

Film thickness measurements ............... 30

Light scattering measurements ............. 30

The preparation of the PS particles ....... 31

The characterization of the PS particles .. 32

Results ..................................... 33

Discussion .................................. 38

Conclusion ................................. 40

References .................................. 41

Appendix 2A ................................. 42

Chapter 3: The influence of glass particles on the foam stability

of CTAB solutions

Introduet ion ................................ 44

Experiment al ................................ 44

Method .................................... 44

Materials ................................. 45

Results and discussion ...................... 46

Conclusions ................................. 48

References .................................. 49

Chapter 4: Influence of surfactant type and concentratien

on the drainage of vertical liquid films

Abstract .................................... 51

Introduet ion ................................ 52

Bxperimental section ........................ 53

Materials ................................. 53

Apparatus ................................. 53

Results ..................................... 55

Discussion .................................. 60

Conclusions ................................. 62

Acknowledgement ............................. 62

References .................................. 62

Appendix 4A ................................. 64

Appendix 48 ................................. 71

Chapter 5: Surface rheology of surfactant solutions

close to equilibrium

Abstract .................................... 74

Introduetion ................................ 74

Experimental ................................ 75

The apparatus ............................. 75

Data processing ........................... 77

Experimental errors ....................... 79

Materials ................................. 81

Results ..................................... 82

Discussion .................................. SS

Diffusion of surfactant to the surface .... 87

Electrastatic repulsion between .......... 88

the head groups

Impurities ................................ 89

Micelie/Surface layer interaction; ........ 93

Surface ordering

Conclusions ................................. 94

Acknowledgements ............................ 9S

List of symbols ............................. 96

References .................................. 98

Appendix SA ................................. 10 0

Appendix SB ................................. 101

Chapter 6

Conclusions ................................ 104

Summary .................................... 108

Samenvatting ............................... 112

Curriculum Vitae ........................... 116

Dankwoord .................................. 117

OBJECTIVE OF THE THESIS

The present

dispersions.

theoretica!

investigation

This subject

problems. The

CHAPTER 1

INTRODUCTION

is devoted to the study of foam films in

has connections with both practical and

conneetion with practical problems arises

because foams in dispersions are frequently encountered in a large

nuffiber of situations and applications, such as the preparatien of foamed

concrete, food products and in faam fighting techniques. A closely

related topic is the stability of thin liquid films separating air

bubbles from the surrounding air, e.g. in the manufacture of coatings.

In some cases foam is a problem, in other cases foam is the desired

product. Cantrolling the stability of foam is therefore very important,

and faam stability is determined by the behaviour of the thin liquid

films in them. In theoretica! respect, the study of thin liquid films

containing solid particles is important since it enables us to

differentiate between the influence of bulk rheological and surface

rheological properties on film drainage, as wil! be argued in more

detail in chapter 2.

Foam films break after they reach a critica! thickness as proposed by

Scheludko 1• This thickness has a value between 100 and 500 Á according

to Vrij 2. The time necessary to reach this critica! thickness, is

determined to a large extent by film drainage. Thus drainage of thin

liquid films is important for foam stability.

The aim of this work is to obtain a better understanding of foam

drainage. We are interested in the influence of solid particles wi th

various volume fractions on the drainage ( see chapter 2, 3) . We also

studied the behaviour of solid particles with different partiele

diameters in a faam film (see chapter 2). The drainage rate of various

surfactant solutions (free from particles) at different concentrations

was investigated in chapter 4. With regard to the influence of the type

of surfactant solution, the relation between drainage on the one hand

1

and interfacial and bulk rheological properties on the ether, was

investigated (chapter 5) . The shear stress in a mobile soap film, as can

be calculated according to Mysels' model of marginal regeneration, was

measured and compared to theory (see chapter 4). Calculations on the

persistenee of spots formed by marginal regeneratien are given in

chapter 4.

HECHANISHS OF FOAH DESTRUCTION

A faam is a dispersion of gas in liquid. Th is is a thermodynamically

unstable system. There are two types of foams, depending on the volume

fraction of gas. A low volume fraction of gas will give a dilute faam,

with round gas bubbles. A high volume fraction of gas will give a

polyhedral faam, in which bubbles are pressed against each ether so that

planar films are formed between them. In this stage, Plateau borders

(the liquid canals generated at lines along which three films come

together) play an important rele in the drainage of the films. Examples

of a dilute faam are hair-gel and ice cream, whereas shampoo and coffee

faam (after sufficient drainage has occurred) are polyhedral.

Several mechanisme of faam destruction of polyhedral foams are given

below.

Disproportienation of gas bubbles

Disproportienation is a process, in which large bubbles grow at the

expense of smaller ones. The reasen for this growth is diffusion of gas

through films because of preesure differences between the bubbles. These

pressure differences exist because of differences in bubble size.

Important physical parameters for this process are: the diffusion

coefficient of the gas in the liquid phase, the (dynamic) surface

tension, the solubility of the gas in the liquid, and of course the gas

composition. Apart from that, the film thickness is a very important

geometrical parameter.

For liquid films with a purely elastic surface, Gibbs 3 pointed out that

2

disproportienation can be inhibited by the surface elasticity E if

E>7 /2, where 7=Surface tension. The surface elasticity is defined as

E=d7/dln(A), where A is the total area.

Ronteltap c.s. 4'

5 developed a model which describes the shrinking of a

single bubble floating on a liquid, taking into account the physical

parameters as mentioned above. The model was verified experimentally.

Two dimensional foams are interesting model systems, especially for

investigating the mechanism of coarsening processes. The meaning of a

'two dimensional foam' as used in the work mentioned below, is in fact a

monolayer of foam bubbles between two parallel walls as illustrated in

figure 1.

Fig.l An example of a two dimensional foam between two parallel walls.

Measurements on two dimensional foams were performed by Smith6, and a

linear relation between the average cell area and time was found. From

later work by Aboav7

, can be concluded that the second moment of the

number of sides per cell ~2 increases linearly with time. Here, ~2 is

defined as follows:

~2 = fi (n-6)2*f(n), were f(n) is the fraction of cells having n sides.

3

Recently experimental work on two dimensional foams was reported by

Glazier c.s. 8 • Experimentally hardly realizable parameters like: 't~' and •number of cells~~, can be approximated with computer

simulations~- 13 The influence of the Plateau borders was not introduced

into computer simulations as a physically reliable mechanism of the

influence of Plateau borders on the film drainage is lacking.

It can be shown that bubbles with less than 6 sides shrink and

disappear, and that bubbles with more than 6 sides expand. Six sided

bubbles do not change in area. This rule is called Neumann's law14, and

is aften used in simulations of two dimensional foams. Neumann' s law

prediets a linear increase or decrease of surface area with time, and

only accounts for coarsening due to diffusional processes.

Attempts were made to simulate the topology of a soap froth in two

dimensions~ 13 However, such simulations can give erroneous results, as

can be concluded from Contradietory results obtained about the

development of the second moment of the number of sides per cell ~2 with

increasing time. For example, D.Weaire c.s~ 1 conclude that ~2 increases

linearly with time, whereas Stavans c. s ~ 3 find that ~2 goes to a

constant"'l. 4 as time increases. Monte Carlo simulations 1 0 confirm the

asymptotic behaviour of ~2, being finally 1. 4. Beenakker9 showed that

the average bubble size area increases linearly in time, in agreement

with Neumann's law.

The simulations so far do not account for changes in film thickness or

differences in surface tension due to expanding/shrinking surfaces. The

influence of the Plateau border suction therefore also was neglected. In

spite of that the calculations seem to agree quite well with von

Neumann's law, and with the experiments. It is (as far as we know)

generally accepted that the behaviour of a two dimensional faam with

respect to disproportienation as t~ is : A-t and ~2=Constant. Here A is

the average cell area.

Advanced simulations of two-dimensional networks have been publisbed by

D.Weaire12, in which the influence of the liquid fraction on the

coarsening process was incorporated. Plateau borders appeared to

decrease the amount of film area significantly if the liquid fraction is

high. This reduces the disproportionation-rate.

Experimental research (with three dimensional foams) has been done by

Durian c.s. 15 who used laser light scattering techniques for the

determination of the average bubble si ze. The average bubble size was

found to increase with the square root of time.

Spreading

Another mechanism to destray foams is the spreading mechanism, which was

first discussed by Ross: 6 Oil draplets or particles which contain

surface active material spread over a faam film and destray it by so

doing. A droplet will spread over a film if the sum of the interfacial

surface tensions -r re sul ts in a net force on the oil phase: rr> ( ror +

-rol (see Ross 16). The sub-scripts are defined as r:foam film/air,

or: faam film/oil droplet and o: oil droplet/air. The spreading process

has been described later by Prins~ 7 Kulkarni c.s: 8 propose a mechanism

in which silica particles are dispersed over film surfaces by the

spreading of an oil. The particles deplete the film of surfactant

(locally), and cause rupture.

Drainage of horizontal faam films

Films in polyhedral foams drain, because of the suction of the Plateau

borders, until the film reaches the critica! thickness where it breaks.

This means that a delay in the drainage process, will increase the foam

stability. The driving force for drainage of horizontal films is a

pressure difference between the film and the surrounding Plateau

borders. In the film, the pressure is uniform across the film, and equal

to that in the adjacent gas phases because of the virtual absence of

surface curvature;in the Plateau border, there is a lower pressure than

in the surrounding gas phases because the surface curvature in the

Plateau border is directed that way. This pressure difference is, when

the border is connected with a bulk liquid phase, in final resort due to

gravity. Drainage of horizontal films differs from that of vertical

films, because in the farmer there is no "marginal regeneration". This

5

is a special

{margins) of

drainage phenomenon, which can occur at

vertical films. We will discuss marginal

the borders

regensration

later. The drainage of horizontal films is thus a simplified case of

drainage. We therefore will deal first with drainage of horizontal

films.

Reynolds' equation has been employed to describe film drainage in

cylindrical horizontal films in numerous publications~ 9 21 This equation

reads as follows:

-dh/dt (1)

Equation (1) relates the thinning of the film to the film thickness h,

the bulk viscosity ~. the film radius R and the capillary pressure AP.

Apart from the lubrication assumption three other important assumptions

were used in relation [1] . The film is supposed to have a rigid surface,

and is supposed to be plane parallel. A cylindrical shape was assumed

for the film because this shape is most frequently encountered in

experiments on horizontal films.

However, major discrepancies between theory and experiment were reported

by Radoev c.s: 2 and, Manev c.s~;· 24 especially for films with a large

radius. Manev c.s. found a dependenee of the film thinning rate on the

film radius with a power R-o.e rather than R-~

Radoev c.s~ 5 presented a theory on the drainage of a plane parallel film

with mobile surfaces. They concluded from this theory that the drainage

rate can be considerably higher than the drainage predicted by Reynolds'

equation because of the mobility of the surface.

Sharma and Ruckenstein26 therefore developed a theory in which the

assumption that the film is plane parallel was avoided, by assuming

non-homogeneities to be superimposed on a plane parallel film with rigid

surfaces. An average drainage rate is calculated, and good agreement

with experiment is found, with regard to the drainage times of a

SDS/NaCl salution as a function of the film radius of horizontal films.

However only asymmetrical nonhomogeneities will cause deviations in

thinning rates from Reynolds' law, and at present there is neither a

6

theoretica! basis nor experimental evidence for the asymmetry in the

nonhomogeneities. The agreement with the experimental data of Radoev22

on the film thinning rate dependenee of R does not follow from the

theory rigorously. Experimental data were used (viz. the correlation of

the experimental amplitude of the hydrodynamic nonhomogeneities with R) ,

in order to derive the drainage rate to be proportional to R-o.s.

Nonhomogeneous mobile films were discussed by Sharma and Ruckenstein 27

and Ivanov c.s~ 8

However, the theories mentioned above only describe small fluctuations

in film thickness. Dimple formation was studied by Joye c.s~ 9 Here the

complete drainage process of rigid films is given for horizontal films,

starting with a certain (circular) profile, including the contact angle

with the measuring apparatus. Van der Waals attraction and electrastatic

repulsion are taken into account. Joye c. s~ 9 report good qualitative

agreement between simulation and experiment for bath low and high

electrolyte concentration; the formation of thin annular rings could be

simulated. Finite contact angles were observed, indicating that Van der

Waals attraction and electrastatic repulsion play an important role. The

values of the film thickness in their simulation are in between typical

values of the black film and 1.3 ~m.

Calculations on horizontal films can give only partial information about

the drainage in vertical films. The formation of thin film parts and the

formation of dimples can be predicted. In a gravitational field, these

film parts would move up or down until they reach the height were the

film has the thickness of the rnaving film part, due to surface tension

gradients in the film. This phenomenon is similar to Archimedes' law.

Drainage of vertical faam films : marginal regeneratien

Numerous experimental and theoretica! investigations were performed on

horizontal films: 9-

29 However, the fact that gravity does not cause

differences across a horizontal film, in contrast with the situation in

vertical films, severely reatricts the information which studies of

horizontal drainage can give on drainage of vertical films. The drainage

of mobile vertical films is predominantly determined by the phenomenon

7

of marginal regeneration, which is the turbulent motion visible in the

film along the Plateau borders. Marginal regeneratien ie not obeerved in

horizontal films: 0

The drainage of a vertical rigid film in the absence of Plateau borders

can be described analytically (see Mysels c.s. 30

), and the profile of

the film is then parabol ie. The thickness d is a function of the

distance to the top of the film z, time t, viscosity ~. density p and

gravity.

d2 = (4Z'l'j) I (pgt)

The assumption of absence of the Plateau

justified in view of the great importance

borders.

borders however

of the vertical

(2)

is not

Plateau

In the Plateau borders an underpressure is created by gravity, and

causes the drainage and in some cases marginal regenerat ion. Marginal

regeneratien was already reported by Gibbs 31 (see also Overbeek32). Thin

film parts are created along the sides of the film. These parts rise,

while the central portion becomes thinner. That this mechanism can be

the dominating one for film drainage (see Mysels c.s: 0) was confirmed

much later by Hudales c.s:3

Mysels c. s7° was the first who reported about the different drainage

regimes in vertical soap films. They distinguished rigid, simple mobile,

irregular mobile films, and films with an intermedia te behaviour. We

will restriet here the discuesion to drainage of films in the early

stages of a polyhedral foam, in which the thickness of the film is such

that Van der Waals attraction and electrastatic repulsion in the films

play a minor role. We then can simplify the drainage regimes. We will

distinguish between rigid and mobile films, and films with an

intermediate behaviour. A rigid film shows a large number of

interference fringes after formation. The rather slow drainage process

is found not to be uniform; and the mechanism which in films with mobile

surfaces affects the profile with an orderly increase of film thickness

from top to bottorn apparently is not operative in films with rigid

surfaces. In other words, a rigid film can have various thicknesses at

8

the same height. Mobile films drain relatively fast and nat too close to

the Plateau borders, the film thickness at a given height is uniform as

can be concluded from light interf erenee patterns. Rapid film motion

a long the Plateau borders (marginal regenerat ion) is visible. Mysels

explained the phenomenon of marginal regeneratien in the following way.

Thin film parts (with almast the same surface tension as the bulk

solution) will expand at the Plateau borders because they are nat

exposed to the border suction as much as thick film parts (see figure

2). Thick film parts therefore will disappear into the Plateau border.

An equation was derived with which the film thickness of expanding films

(with constant velocity) can be calculated (Frankel's law). Good

agreement was found between experiment 34 and Frankel's law, with regard

to the film thickness at a certain height near the bottorn film/bulk

salution transition, as a function of velocity of film draw-out.

However, Frankel already mentioned that disagreement with experiment was

found if their theory was applied in order to explain marginal

regeneratien near the vertical borders. The calculated thickness ratio

of film parts entering the film from the border, and film parts leaving

the film and flowing into the border (at the same height) did not agree

with experiment. The thickness ratio was calculated on the assumption

that the inflowing and outflowing film parts have the same surface

tension. Another complication with Mysels' theory is that in the

beginning of the drainage process (up to 60 s.), upward flows along the

Plateau borders are predominantly observed. This direction dependenee

can not be explained by the horizontal flows in fig.2 only.

An analogous theory is proposed by Stein35, where more realistic surface

velocity and liquid flows are assumed. Qualitatively, Stein35explains

the discrepancy between the experimentally observed and calculated

thickness ratio, by doubting the assumed equality in surface tension of

inflowing and outflowing regions. This aspect was already noticed by

Mysels, but no quantitative experimental data on this are available.

/ /

'- ~ r " ""' Fig.2 Marginal regeneratien as proposed by Mysels

Prins c. s ~ 6 showed that marginal regeneratien only occurs when the

surface elasticity does not exceed the value of 25 mN/m (this is an

order of magnitude). No quantitative data on the amount of exchanged

material between the film and the Plateau border could be obtained.

Bousfield37 found that low bulk elasticities (compared to high bulk

elasticities) increase the drainage rate of foam films. The effect of

relative low surface elasticities on the drainage mechanism will be

studied in this work {see chapter SI.

Observations by Hudales c.s~ 8 of particles flowing in the Plateau border

show that the Plateau region near the film flows upwards, and that the

more central part of the Plateau border descends. The reasen for the

upward flow given by Hudales c.s. is a Marangoni flow. This Marangoni

flow is due to an exchange of film parts with a higher surface tension

and liquid of the Plateau border with a lower surface tension. The

preesure drop in a Plateau border conduct was calculated by Leonard

c.s~ 9 as a function of the average velocity and the shape of the Plateau

border. Hudales c. s: 8 measured the shape of the Plateau border at

different heights, from which the preesure inside the borders can be

calculated.

Recently a new theory on marginal regeneratien was proposed by

Nierstrasz and Frens. Their work is not publ ished at the moment, and

therefore not all details of their theory are known to us. We will

however discues the main idea of their theory as communicated to us

personally. According to their theory, marginal regeneratien along the

10

vertical Plateau border only consists of outflowing film parts. This

assumption was made because mainly outflowing film parts are visible

during the drainage process. The outflowing film part a are exchanged

against inflowing parts only at the bottorn of the film. Qualitatively,

arguments of compression and expansion of film area in relation with

surface tension gradients are used in favour of this model. Nierstrasz

and Frens claim to be able to explain all experiments on the drainage of

mobile soap films performed by Mysels with respect to the dependenee of

film height. However, it is not clear to us how the model explains the

upflowing regions in the Plateau border observed by Hudales c.s.

By just looking at the phenomenon of marginal regeneratien at the bottorn

of the film, one can see some remarkable analogies with conveetien

streams. We will consider film parts which are not in contact with the

Plateau border at the bottorn of the film. The following consideration is

therefore a simplified case of the process of marginal regeneratien

which takes predominantly place at the vertical Plateau borders. The

thin film parts (compared to the average film thickness at the height

concerned) which rise in foam films, can be seen as the two dimensional

analogue of density differences. Low density bodies (in three

dimensions) will rise due to buoyancy forces, or in other words because

of pressure differences acting on the body surfaces. Flat foam films do

not have internal pressure differences, and therefore surface tension

differences will act as buoyancy forces (see tigure 3). The film part

will move up or down until the film part is at a place in the film,

where the weight is just compensated by the surface tension acting on

the circumference.

11

fig.3.The surface tension and gravity, acting on an inhomogeneity.

The circumference can be chosen arbitrarily large from the

center of the inhomogeneity, so that the surface tension

equals the surface tension of a vertical film in equilibrium.

The crigin of the density difference (in three dimensions) eeropared to

the thickness difference (in two dimensions) however is different. In

three dimensions heat/temperature, or concentratien differences will

cause the density difference. The crigin of thicker and thinner film

parts is however determined by surface tension gradients and pressure

gradients in the film, through surface and bulk rheology.

Influence of solid particles

Solid particles can have various effects on foam stability. Kruglyakov

c.s. 40 found a destabilizing effect because of adsorption of surfactant

molecules on particles (silicon dioxide, sulfite cellulose and carbon

black). Hudales c. s~ 1 also found that small particles promate film

rupture to a limited extend at low CTAB concentration, and explained

this effect by lowering of the CTAB concentratien through adsorption on

12

the glass particles. More experimental data on this effect are presented

in this thesis (see chapter 3) .

Most investigations showed that hydrapbobic particles have a

destabilizing effect on faam (Garrett 42), whereas hydrophilic particles

in general have a stahilizing effect, see Hudales c.s~ 1 Fang-Qiong Tang

c.s~ 3 however found that small hydrophobic particles could also have a

stahilizing effect, which was ascribed to the reduction of Ostwald

ripening in foam, by slowing down the diffusion process of gas from

small bubbles into larger bubbles.

A theoretica! discuesion on the destabilizing effect of hydrophobic

particles is given by Frye c.s~ 4 This effect was found to be due to

promotion of film rupture. Aronson 4 5 showed that hydrophobic draplets

stimulate rupture less than hydrapbobic particles, because of lower

surface roughness. Aronson also found that particles can be swept out of

a microscopie foam film into thicker regions of the film. Dippenaar 4 6

used high speed cinematography to study the behaviour of large glass and

silica particles in small horizontal films. These measurements showed

that particles moved in thin films in order to have the right contact

angle with the liquid. In the present thesis, the limited parameter area

as investigated by those authors is extended: experiments are described

with small particles differing in hydrophilic/hydrophobic character in

vertical films (see chapter 2), and it is shown that these particles can

be used to measure the film drainage.

Film rupture of horizontal films

Two reasans for film rupture have already briefly been mentioned, viz.

rupture by spreading, and rupture by hydrophobic particles.

The most common way for films to break, after drainage to the critical

film thickness, is rupture of the film by surface waves (see Vrij 2). We

do not intend to give a review on this subject, since film rupture

itself is a broad subject, we will only outline the major developments

in this area.

13

Repulsive electrastatic farces compensate the Van der Waals attraction

in equilibrium black films exactly. Two types of equilibrium black films

can be distinguished, the first black film (about 600 Ä) and the second

black film (about 50 Ä), see Overbeek~ 7 The electrastatic repulsion and

van der Waals attraction in these black films, or equilibrium films,

become important for film thicknesses of the order of magnitude of 600 Ä or smaller.

De Vries 48 calculated that spontaneous rupture of films due to thermal

motion, becomes highly improbable for films with a thickness higher than

100 Ä. However, the (critical) thickness at which films break is usually

higher.

The fact that a certain type of surface waves, in particular the

"squeezing mode" waves, may become self reinforcing and then lead to

film rupture, is due to the Gibbs free energy decrease when two close

surface parts become still closer because of Van der Waals attraction.

If the amplitude of such surface waves increases above the film

thickness, then rupture occurs. Vrij c.s:' 49 derived an equation for the

critical wavelength above which films rupture due to growing wave

amplitudes. A critical thickness can be calculated from this critica!

wavelength.

RHEOLOGICAL PROPERTIES

The rheological properties of soap solutions can be divided into two

classes, the surface rheological properties and the bulk rheology. We

will (in this chapter) only consider Newtonian liquida (with respect to

the bulk rheology) .

Apart from the bulk viscosity, the surface viscosity and surface

elasticity are thought to play an important role in foam stability. Two

surface viscosities have to be distinguished: the surface shear

viscosity and the surface dilational viscosity.

The surface shear viscosity is the two dimensional analogue of the bulk

viscosity (in three dimensionsJ and has the dimension (Ns/ml, this in

14

contrast with the bulk viscosity {Ns/m2). The order of magnitude of the

surface shear viscosity for surfactant solutions like CTAB, SOS and

Triton X-100 is about Se-8 Ns/m according to Jashnani c.s. 50 Similar

values were reported for Triton X-100 by Shih c.s: 1 and for SDS by

Shah c.s~ 2 Brown c.s: 3 and also Poskanzer c.s: 4 measured substantially

higher values for SDS solutions, being 2e-6 Ns/m. Mysels c.s7° found

surface viscosities of about 1e-8 Ns/m. Lauryl alcohol {which can be

present as an impurity in SDS) increases the surface viscosity of SDS

solutions significantly. This may both explain the large diEferences

between the surface shear viscosities found for SDS solutions, and the

time dependenee of the surface shear viscosity of a SDS salution as

reported by Bul as c. s 7 5 Some methods for measurements of the surface

shear viscosi.ty are summarized in Hühnerfuss 56and Weissberger c. s 7 7 If

we estimate the surface viscosity from the data above, then we obtain

the value se-8 Ns/m. The surface shear viscosity, gives information

about the mobility of complete film parts in the film. It does not give

information on thinning due to liquid flow between the two film

surfaces. In order to estimate the importance of the surface shear

viscosity compared to the bulk viscosity for the movability of complete

film parts, we consider a film with thickness d and shear rate T'=d7/dt,

where T represents the deformation (see figure 4).

15

d

~!'i 7'

fig.4 The role of the surface shear viscosity. The two reetangles repreaent the front and rear side of a .film with thickness d. This film is subject to a time and place dependent deformation as indicated with the arrows. 7' : Shear rate of deformation

The total force F per film height necessary to realize the shear rate 1'as shown in figure 4 will be the sum of the forces necessary to move the bulk liquid between the two surfaces, and the force per unit length along the height of the film,which causes the surface movement:

F (IJ. * d + 2 * IJ.s) * 7' [N/ml (3)

The contribut ion of the surface shear viscosity, compared to the bulk viscosity, can not be neglected for soap films with a thickness of 1 IJ.ffi,

if information is required about the shear stress of film parts rnaving with respect to adjacent film parts.

The importance of the dynamic surface tension for the drainage mechanism of foam films (determining mobile or rigid behaviour) has already been mentioned by Prins c.s: 6 We will discuss two different approaches to characterize these properties.

The surface elasticity and the surface dilational viscosity are both

16

correlated with gradients in surface tension. The dilation process is

drawn in figure 5.

" 1' 1' 1' 1'

"

~ -7

~ -7

~ -7

~ -7

"' -.v -.v -.v -.v "' !___ ..

fig. 5 Surface dilation. The surface tension increases due to

expansion of the surface area.

The system will still be close to equilibrium (and linearl for small

changes in surface area. Large changes in surface area will re sult in

surface properties far from equilibrium, where the surface tension

response on deformation is not linear. There are therefore two different

approaches to measure the surface behaviour, the approach by the

situation close to equilibrium and that by the situation far from

equilibrium. The surface of a situation close to equilibrium resembles

the surface of an already formed faam, and measurements in that case can

give indirectly information about the faam stability. The surface of the

situation far from equilibrium gives information about the surface

tension in the process of faam formation. Since we are interested in the

drainage of an already formed faam, we studied the close to equilibrium

situation in this thesis, with an apparatus similar to the one used

previously by Lucassen c. 8 The ring metbod which can also be used for

surface rheology was developed by Kakelaar c.s: 9

17

FOAH DESTRUCTION IN PRACTICE

A summary of defoaming techniques is given in Ferry c.s~ 0 Techniques which can be used are: thermal methods, mechanica! methods, preesure and acoustic vibrations, electrical methods and chemical defoamers. Here we will relate the more fundamental principles of foam stability/ destructien as described in this chapter to techniques used in practice.

Thermal methods affect the surface composition and surface rheological behaviour; drainage or Ostwald ripening may become faster in this way. Another effect of heating is gas expansion, and accordingly the films in between the gas bubbles will also expand. This results in an increase of surface tension and can destroy the force balance in the foam. Heating also enhances evaporation of liquid from foam films, which will cause thinning and eventually film rupture.

Foam films are deformed and can break by mechanica! action if stationary or rotating breakers are used. The deformation of the liquid/gas surface will result in a surface tension response determined by the surface rheology. The wettability of the foam/stirrer surface (whether moving or stationary) is frequently important.

Ferry c.s~ 0 does notmention any fundamental process responsible for the destructive effects of ultrasonic waves on foams. Experimental results (other than the work mentioned by Ferry c.s~ 0 ) were obtained by Isayev c.s~~ Sun~ 2 Ashley63 and Sandor c.s~ 4 We expect these waves to enhance the marginal regeneratien mechanism.

Foams can be broken by passage through devices similar to electrostatic precipitators for dust. Here the electrostatic double layer and the surface charge at the liquid/gas interface are used for foam destruction.

Chemical defoamers can act according to the spreading mechanism, or by replacement of surface active material by more surface active material

with poor film stability. A special case of chemical defoaming is formed by hydrophobic particles. The antifoaming capacity of FTFE particles, as

described by Garrett: 2 was found to be larger than the antifoaming

18

capacity of hydrophobic liquid particles (Aronson 45). Apart from the

'hydrophobic effect', particles can in principle destabilize the film by

adsorbing surfactant from it, and in this way deplete the film from

surfactant .Another way of chemica! defoaming is decreasing the

surfactant concentratien by reaction. The destabilizing effect by

adsorption is described in this thesis (see chapter 3).

REFERENCES

(1) Scheludko, Proc. K. Akad. Wetensch. B, 65, 87 (1962)

(2) Vrij, A., Disc. Faraday Soc., 42, 23-33 (1966)

(3) Gibbs, J.W., The Scientific Papers, 1, Dover publications, New York,

p. 244 (1961)

(4) Ronteltap, A.D., Damste, B.R., De Gee, M. and Prins, A., Colloids

Surfaces 47, 269-283 (1990)

(5) Ronteltap, A.D. and Prins, A., Colloids Surfaces 47, 285-298

(1990)

(6) Smith, C.S., Metal Interfaces (American Society of Metals,

Cleveland, Ohio, 1952), pp.65-108

(7) Aboav, D.A., Metallography, 13, 43-58 (1980)

(8) Glazier, J.A., Gross, S.P. and Stavans, J, Phys. Rev. A, 36-1,

306-312 (1987)

(9) Beenakker, C.W.J., Phys. Rev. A, 37-1, 1697-1702, (1988)

(10) Wejchert, J., Weaire, D. and Kermode, J.P., Philos. Mag. B, 53-1,

15-24 (1986)

(11) Weaire, D. and Kermode, J.P., Philos. Mag. B, 48-3, 245-259

(1983)

19

(12) weaire, D., Pbysica Scripta., T45, 29-33 (1992)

(13) Stavans, J. and Glazier, J.A., Phys. Rev. Letters, 62-11, 1318-1321

(1989)

(14) Neumann, J. von, Metal Interfaces (American Society of Metals,

Cleveland, Ohio, 1952), pp.108 110

(15) Durian, D.J., Weitz, D.A. and Pine, D.J., Science, 252, 686-688

(1991)

(16) Ross, S., J.Phys. Chem., 54, 429-436 (1950)

(17) Prins, A., Advances In Food Emulsions and Foams, Ed.

E.Dickinson, Elsevier (1988) t p.91

(18) Kulkarni, R.D. I Goddard, E.D. and Kanner, B. I Ind. Eng. Chem.,

Fundam., 16-4, 472-474 (1977)

(19) Dimitrov, D.S. and Ivanov, I. . B., J. Coll. Int. Sci., 64-1,

97-106, (1978)

{20) Scheludko, A., Advan. Colloid. Int. Sci., 1, 391-464 (1967)

(21) Ivanov, I.B., Pure Appl. Chem., 52, 1241-1262 (1980)

(22) Radoev, B.P., Scheludko, A.D. and Manev, E.D., J. Coll. Int. sci., 95-1, 254-265 (1983)

(23) Manev, E.D., Sazdanova, s.v., and Wasan, D.T., J. Coll. Int. Sci.,

97-2, 591-594 (1984)

(24) Manev, E.D., Vassilieff, Chr.St. and Ivanov, I.B., Colloid & Polymer Sci., 254, 99-102 (1976)

(25) Radoev, B.P., Dimitrov, D.S. and Ivanov, I.B., Colloid & Polymer

Sci., 252, 50-55 (1974)

20

(26) Ruckenstein, E. and Sharma, A., J. Coll. Int. Sci.,

(1987)

119-1, 1-13,

(27) Sharma, A. and Ruckenstein, E., Colloid & Polymer Sci, 266, 60-69

(1988)

(28) Ivanov, I.B., Dimitrov, D.S., Somasundaran, P. and Jain, R.K.,

Chem. Eng. Sci., 40-1, 137-150 (1985)

(29) Joye, J., Hirasaki, G.J. and Miller, C.A., Langmuir, 8, 3083-3092

(1992)

(30) Mysels, K.J., Shinoda, K. and Franke!, S., Soap films, studies of

their thinning and a Bibliography, Pergamon Press, London (1959)

(31) Gibbs, J.W., Collected Works, vol I, Thermodynamics, Longmans,

Green and co., New York (1928), p.300-314

(32) Overbeek, J.Th.G., Chemistry, Physics and Application of surface

active substances, Proceedings of the IVth International

Congress on Surface Active Substances, Vol. II-B, Brussels, 7-12

September 1964, Brussels, 19-37, Gordon and Breach Science

Publishers, New York 1967

(33) Hudales, J.B.M. and Stein, H.N., J. Coll. Int. Sci., 138-2, 354-364

(1990)

(34) Mysels, K.J. and Cox, M.C., J. Coll. Int. Sci., 17, 136-145 (1962)

(35) Stein, H.N., Advances in Colloid and Int. Science, 34, 175-190

(1991)

(36) Prins, A., van Voorst Vader, F., Chemie, Physikalische Chemie

und Anwendungstechnik der grenzflachenaktiven Stofte, Berichte

vom VI. Internationalen Kongre~ für grenzflächenaktive Stoffe,

Zürich, vom 11.bis 15. September 1972, earl Hanser Verlag (1973),

München, 441-448

21

(37) Bousfield, o.w., Chem. Eng. Sci., 44-3, 763-767 (1989)

(38) Hudales, J.B.M. and Stein, H.N., J. Colloid Int .. Sci., 137-2,

512-526 (1990)

(39) Leonard, R.A. and Lemlich, R., Chem. Eng. Sci., 20, 790-791 (1965)

{40) Kruglyakov, P.M. and Taube, P.R., Colloid Journal of the USSR, 34,

194-196 (1972)

(41) Hudales, J.B.M. and Stein, H.N., J. Colloid Int. Sci., 140-2,

307-313 (1990)

(42) Garrett, P.R., J. Colloid Int. Sci., 69-1, 107-121 (1979)

(43) Fang-Qiong Tang, Zheng Xiao, Ji-An Tang, Long Jiang, J. Colloid

Int. sci, 131-2, 498-502 (1989)

(44) Frye, G.C. and Berg, J.C., J. Colloid and Int. Sci, 127-1,

222-238 (1989)

(45) Aronson, M.P., Langmuir, 2, 653-659 (1986)

(46) Dippenaar, A., Int. J. Hiner. Process., 9, 1-14 (1982)

(47) Overbeek, J.Th., J. Phys. Chem., 64, 1178-1183 (1960)

(48) de Vries, Rec. trav. Chim., 77, 383-440 (1958)

(49) Vrij, A. and Overbeek, J.Th.G., J. A. c. s., 90-12, 3074-3078

(1968)

(50) Jashnani, I.L. and Lemlich, R., J. Colloid Int. Sci., 46-1,

13-16 (1974)

(51) Shih, F. and Lemlich, R., Ind. Eng. Chem. FUndam., 10-2, 254-259

(1971)

22

(52) Shah, D.O., Djabbarah, N.F. and Wasan, D.T., Colloid & Polymer

Sci., 256, 1002-1008 (1978)

(53) Brown, A.G., Thuman, W.C. and McBain, J.W., J. Colloid Sci., 8,

491-507 (1953)

(54) Poskanzer, A.M. and Goodrich, F.C., The Journal of Physical

Chemistry, 79-20, 2122-2126 (1975)

(55) Bulas, R. and Kumins, C.A., J. Colloid Science, 13, 429-440 (1958)

(56) Hühnerfuss, H., J. Colloid and Int. Sci., 107-1, 84-95 (1985)

(57) Weissberger, A. and Rossiter, B.W., Techniques of Chemistry. Vol I,

Physical Hethods of Chemistry, Part V, Determination of

Thermadynamie and Surface Properties, Wiley-Interscience, New York

1971, pp.569-574

(58) Lucassen, J. and Van den Tempel, M., Chem. Eng. Sci., 27,

(1972)

(59) Kakelaar, J.J., Prins, A. and De Gee, M., J. Colloid

Sci., 146-2, 507-511 (1.991)

(60) Perry, R.H., Green, D.W. and Maloney, J.O., Perry's

Chemical Engineers' Handbook, 6th. ed., McGraw-Hill, New York,

18-86 (1.984)

1283

Int.

(61) Isayev, A.I. and Mandelbaum, S., Polymer Eng. Sci., 31-14,

1051-1056 (1.991)

(62} Sun, S.C., Hining Engineering, Transactions aime, 865-867 (1951)

(63) Ashley, M.J., The Chemical Engineer, 368-371 (1974)

(64) Sandor, N. and Stein, H.N., submitted for publication, J. Colloid

Int. Sc i.

23

CHAPTER 2 • DRAINAGE OF CTAB FILMS CONTAINING SOLID PARTICLES

ABSTRACT

In this chapter, marginal regeneratien in films drawn from CTAB

(=cetyltrimethylarnrnoniumbromide} solutions in a frame will be

discussed. The film thickness was measured as a function of time and

height, using interterenee colours which were evaluated by a computer

program, and a film thinning relation was derived for this type of

films. The program used for calculating film thicknesses is briefly

discussed.

Film thickness measurements were performed on polystyrene (PS)

dispersions in CTAB solutions up to 25 vol% PS. The thinning velocity

of the film was related to the viscosity of the dispersion.

PS particles in the film could be observed through their light

scattering. The particles were present in a film from the bottorn up to

a height where the film had a certain thickness. This thickness could

be correlated with the partiele diameter and the contact angle of the

PS particles with the CTAB film.

We also studied the influence of low volume fractions of glass

particles on the drainage of CTAB films. No partiele borderline could

be observed because of the polydispersity of the glass. Low volume

fractions of glass did not affect the drainage rate of the films. The

experiments performed with the glass particles confirm that the

drainage of the particles is determined by the hydrophobicity and the

film thickness.

•This chapter has been publisbed in Chem. Eng. Sci., 48-2, 351-365

(1993)

25

INTRODUCTION

Three phase systems are of ten used in industrial processes. In the

flotation process for example, particles are separated from the liquid

by creating a foam in which the particles disperse preferably. The

present investigation deals with the influence of solid particles on

foam.

Some particles lower the surfactant concentratien and therefore act as

a destabilizer (Kruglyakov1).

Most investigations showed that hydrophobic particles have a

destabilizing effect on foam (Garret 2), whereas hydrophilic particles

in general have a stahilizing effect (Hudales and Stein3). Fang-Qiong

Tang et al~, however found that small hydrophobic particles could also

have a stahilizing effect which was ascribed to the reduction of

Ostwald ripening in foam.

The destabilizing effect of hydrophobic particles has been

theoretically discussed (Frye and Berg5) and was found to be due to

promotion of film rupture. Aronson 6 showed that hydrophobic ( solid)

particles stimulate rupture more strongly than hydrophobic dropiets

because of higher surface roughness. Aronson also found that particles

can be swept out of a microscopie foam film into thicker regions of

the film. Dippenaar7 used high-speed cinematography to study the

behavior of large glass and silica particles (>160 ~m) in small films.

These measurements showed that particles moved in thin films in order

to have the right contact angle with the liquid.

The drainage of the type of films studied, is determined by marginal

regeneratien (Mysels 8, Hudales et al~).

In this work we used monodisperse PS particles (1900 nm, 1007 nm and

300 nm) in 20mmx15mm films drawn from CTAB (=cetyltrimethyl­

ammoniumbromide) solutions. The maximum height that the particles

reach in the film is correlated with the film thickness measured with

a Fizeau interferometer. The influence of higher volume fractions of

PS on the drainage rate is studied.

26

THEORY

A film of thickness d reflects in normal direction an amount of light

I:

I=I sin2 (2nnd/A) 0

(1)

In this equation n is the refractive index of the liquid film (1.33),

and A is the wavelength of the light (546 nm). The absolute value of

the film thickness can be calculated at the top of the film as soon as

a black film bacomes visible. Equation (1) can be used for a film

region with no or only minor quantities of solid particles, because in

films containing solid particles the scattering of light makes

observation of interterenee fringes difficult, so that equation (1)

cannot be used for evaluating their thickness.

We observed a partiele borderline (above which there are no particles

in the film) as the films were draining. We will first show that this

effect is not directly caused by diffusion nor gravity (the particles

did nat fall down), but indirectly.

Ditfusion cannot cause the downward motion of the particles, because

this is in one direction only. Diffusion might counteract this

downward motion. However no distinct blurring of the transition

(part iele containing film) I (part iele free film) was observed.

Diffusion translates particles over a distance S:

S=v(2 (kT/(6rr~dll * t) (2)

The particles used can be displaced by diffusion in the drainage time

applied, here we see that this process can be neglected for the two PS

samples:

d=2 ~m;t=20 s; S=2 ~m

d=0.3~m;t=250s; S=20~m

The observed displacement of the partiele borderline was about 13 mm.

The effect of gravity on the partiele velocity in an infinite amount

of liquid or gas can be calculated with equation (3) (a balance

27

between gravity and viscous forces on a single particlel :

V= ~®~ *d2

(3)

The velocity in water and air according to this equation : Air :~=l.8x10- 5 Pas, àp=1000 kg/m3

, g=9.8l m/s 2, d=2x10- 6 m

Water:~=1.0xl0- 3 Pas, àp=70 kg/m3, 9=9.81 m/s 2

, d=2x10- 6 m The Reynolds number (Air) :p vd/~ = 1.2(kg/m3

) x 1.3e-5 = 1.6e-5

Calculated velocities:Vatr=0.12 nun/s;Vwater=0.00015 nun/s. The Reynolds number is small enough for neglecting turbulence (Cl i ft et al~ 0 l, equation 3 can be applied.

We can conclude from the fact that the particles would fall slower in air than they do in the foam film (measurements : 0.56 nun/s), that gravity indeed does play a minor role, and that there must be another reason for the separation of the particles from the liquid. This is

the contact angle phenomenon.

EXPERIHENTAL HETHODS

The apparatus

A film was drawn in a vertical brass frame (see figure 1), which was

held at a fixed position. The four legs of the frame formed four identical films. A fifth film in the middle of the former four mentioned, was a film with completely free Plateau-zones. The frame was positioned in a thermostatted tank in order to avoid evaporation of the liquid. The film could be observed from both the front as well as the back through two windows in the tank. From the front the film was illuminated by a 50 W super pressure mercury lamp (Osram HBO 50 Wl

(see figure 2) . Through the front window, the interterenee pattern of light reflected from the front and rear surfaces of the film was observed; through the rear window, light scattering information was obtained.

28

ALL ANGLES 120 DEOREES

,. .. ,."""'

;

' ,.)·----

20MM

Fig.l.The brass frame in which the films were drawn

Hg lamp Lens Semi reflecting Mirror

Filter

I

Thermostatted tank

Fig.2.The Fizeau interferometer

29

Frame

We placed a light filter (SFK21 Schott, 546 nml in the beam in order

to separate the (green) light from the other wavelengths.

Film thickness measurements

The film was observed with a Panasonic CCTV camera through the

semi-reflecting mirror (figure 2), and the pictures were analyzed

on-line with a computer. The program which calculated the film

thickness from the int erferenee pattern was as follows. First we

determined the exact position of a film in the picture and the

magnification (mm/byte) . After forming a new film in the frame,

pictures (384*288 byte, 256 grey levels) were taken with a variable

interval (0.5 s to 10 s). We masked every picture so that only film

information was visible. We added all bytes in horizontal direction

and put the result in a word (16 bit information) . It appeared that

the value (so calculated) never exceeded the maximum value of a word.

This array of words was stared in a file and processed afterwards. The

film thickness was determined by using equation (1). All films were

measured until the black or silver-black film was visible.

Light scattering measurements

The presence of the PS particles could be easily detected by their

light scattering causing a hazy aspect of the film (see figure 3).

30

Fig.3.The partiele borderline and marginal regeneratien

a 10 vol% dispersion of PS (sample 1, 1900 nm)

Therefore we measured the decrease of the height with time . For these

measurements we again reduced the pictures to an array of words. This

array was processed afterwards in order to calculate the height of the

partiele borderline.

The preparatien of the PS particles

We used for our experiments three PS samples. The preparatien of the

first sample is described below. The secend and the third samples were

kindly donated by H.Leendertse, and B.Krutzer respectively. The secend

and third samples were prepared surfactant-free.

We used a recipe similar to the one described by Almog et al~ 1 We used

PVP, ACPA and CTAB >99% (the recipe gives also good mono-disperse

particles if SOS is used instead of CTAB) The PVP

31

(polyvinylpyrrolidone, average MW 40000) was used for steric stabilization, and the ACPA (4,4'-Azo-bis(4-cyanopentanoic acid),

>98%) is the initiator for the emulsion polymerization. The styrene

{99%) was stabilized with 10-15 ppm p-tert-butyl-cathochol.

We prepared the particles in a batch reaction at 7o"c in 1000ml.

ethanol. The PVP (40 gram in 150 ml ethanol) was added with the CTAB

(12 gram in 50 ml ethanol) . We mixed 2. 8 gram of ACPA in 100 ml.

ethanol and after stirring (the ACPA did not dissolve completely), 300

ml of styrene was added to the ACPA. This was stirred for 5 seconds

and added to the reactor. The emulsion was slightly turbid after 10

minutes. The reaction stopped after 24 hours. The PS was centrifuged 4

times with water.

The characterization of the PS particles

The partiele diameter was determined both with the Coulter counter ZM and with the Coulter LS 130 (see table I). The (-potential of the

particles was determined with the Malvern (-sizer 3 (see table I) in a

0.002 M CTAB solution.

Table I. The partiele size and (-potential of the particles

Sample 1 diameter(f.,!m) stand.dev(f.,!m) (-pot. (mV) Coulter LS130 1.895 0.281 +15 Coulter Counter ZM 2.032 0.187

Sample 2 (-pot. (mV) Coulter LS130 0.270 +64 Electron microscopy 0.300

Sample 3 (-pot. (mV) Coulter LS130 0.980 0.050 +72 Coulter Counter ZM 1. 034 0.125

32

RESULTS

The film is essentially free from particles above a certain height.

This is what we can see in figure 3, a picture taken through the rear

window. We can also see that marginal regenerat ion causes thin film

elements, near the Plateau-border, which rise in the film.

We will first campare the height at which the partiele borderline is

visible to the height at which the film has the thickness of the

particles for all the PS samples (see figures 4,5) The volume

fraction of PS in the bulk was lower than 0.5\.

Both the 300 nm and the 1007 nm particles have almast the same

diameter as the thickness of the film, therefore their contact angle

with the film is arccos(1)=0 degrees. The 1900 nm particles can be

incorporated in a significantly thinner film. This indicates that the

hairy stabUizer present at the 1900 nm particles, decreases the

amount of CTAB at the surface. This is supported by the fact that

sample 1 has surfaces which are only partially covered by CTAB (as

shown by the (-potential) whereas samples 2 and 3 have surfaces which

are covered by an adsorbed layer of CTAB. Our results suggest that the

smaller amount of CTAB adsorbed at the PS surfaces in the presence of

polyvinylpyrolidone (sample 1) result in a hydrophobicity, and that

this sample has a finite contact angle. From table 2 we calculate this

angle to be arccos(1310/1900)=46 degrees.

Figures 4 and 5 show the difference

hydrophobic/hydrophilic particles. We verified

particles give a similar behaviour.

33

in behaviour of

if hydrophilic glass

14

12 ,.....,

10 ~ ~ -+- PS 1900 NM ........ 8 E-4 ::z::

6 - 1900 NM FILM 0

\ ...... l.t:.1 ::z:: 4

2

0 0 5 10 15 20 25

TIME [S]

Fig.4.Drainage of hydrophobic polystyrene (samplel)

14

12 ~-. • PS

,....., 10 • oo• ::s \ o•

~ e o• 0 FILM ......... 8 • Dj!! E-4 ' ~. ::z:: 0 6

\ o•i • PS ...... l.t:.1 ::z:: 4 • iiiliilo

0 FILM 2

1007 NM 300 NM

0 0 50 100 150 200

TIME (S]

Fig.S.Drainage of hydrophilic polystyrene {samples 2 and 3)

34

First, the influence of low volume fractions of glass particles on the

film drainage was studied (fig.6). No significant effect was observed.

Then, we checked the existence of the partiele borderline for glass

particles 1.61 11m, s.d.~0.44 ~-tm. The film wasaftera while free of

particles as far as detection by light scattering is concerned. The

glass particles were not as monodisperse as the PS particles,

therefore a sharp partiele borderline was not observed. This is to be

distinguished from the microscopie measurements (Hudales and Stein3)

in which they observed glass particles which became visible after a

while, when the film was much thinner al ready. The explanation for

this might be that they looked at reflected light, while our

measurements are based on through falling scattered light.

If the logarithm of the film thickness is plotted against the

logarithm of time at a fixed height, then a straight line results in

agreement with measurements by Hudales and Stein 9 (see figure 6).

Equation (1) in their paper Q=kdn, where Q is the volume flow out of

or into the film per unit length (in height) can be rewritten to ,

(4)

Here d represents the film thickness, t time, and A and b are

constants (see Appendix 2A) .

We made double logarithmic plots for the glass dispersion {VOL%

glass<0.5%), and for a 0.002 M CTAB film at two temperatures. At this

vol%, the presence of glass particles did not have any effect on the

film drainage, and a temperature increment of 6.s·c increased the

thinning velocity slightly.

Secondly we investigated whether the partiele concentratien (PS) has

any effect on the film thickness at the partiele borderline. Therefore

we calculated for all films (volume fractions <0.5\, 11.1%, 17.4\ and

25.0%) the film thickness at the partiele borderline for all pictures.

The average value and standard deviation is given in table II. From

this we can see that the particles can be incorporated into the film

at a rather well defined thickenss (1310 nm).

35

8

,.-.. ,......, 7 e -e- T=29C = ...... <ll 6 <ll 4.1 -a- T=22.5C = ..lil 0

:a 5 !-< --- T=22.5C '-' Glass <lww% z ...:l 4

3 2 3 4 5 6 7

LN(Time [s])

Pig.6.The influence of temperature and glass particles

Table II. The Film thickness at the partiele borderline

Vol % PS Thickness average Thickness 0" Number [nm] [nm] of points

<0.5 1371 79 37 11.1 1500 156 17 17.4 1384 127 32 25.0 1109 75 49 25.0 1201 210 46

The influence of the particles on film thinning can be seen in figure

7, if the amount of PS (sample 1, 1900 nml increases, the film

thinning process becomes slower.

There may be a difference between the height down to which the film

thickness can be measured by interference, and the height of the

highest particles, because near the partiele the film may nat be

exactly plane parallel. However in films containing small amounts of

particles, interference fringes could be observed bath in the film

region containing particles as well as in film regions free of

36

particles. In these cases no discontinuity at this transition was

observed. These facts give us confidence that there is no substantial

difference between the film thickness measured by interterenee just

above the highest particles, and the film thiekness at the height of

the highest particles.

14 •

12 .. ~ • <0.5

....... 10 VV%PS

~ 0 0

6 Hoo • 11.1 8 .aoCb

E-< ~0, VV%PS

:::z:: 6 0 17.4 0 .. 0 DO -~ ..

00 DO VV%PS

:::z:: 4 .. 0 0

• 00 ~ 0 25.0 2 •• 0 0 VV%PS .o ~

000

0 0 10 20 30 40 50 60 70

TIME [S]

Fig.7.The drainage of the partiele borderline as a

function of vol% PS(sample 1, 1900 nm)

The lines in the figure can be extrapolated to zero-height, and the

eorresponding time can be used as a measure for the film thinning

velocity. In order to check the influence of flow by the particles on

the flows in the film, we measured the bulk viscosity of suspensions

of latex particles. Although in principle there may be a difference

between the viscosity of a 3-dimensional bulk suspension and the

suspension in the film containing a 2-dimensional array of particles,

this differenee is neglected here as a first order approximation (no

data on the viscosity of two-dimensional thin arrays being available) .

We measured the viscosity of the dispersions with an Ostwald

viscosimeter. The data fitted reasonably well with the Mooney

37

equation, with ~;70.0 vol\. Although this is not a realistic value

for the constant 1/lmax, we wil! use it for interpolation since it fits

the measurements satisfactorily. Table III gives the film thinning

velocity in relation with the viscosity of the dispersion. It appears

that the drainage retardation on increase of the partiele volume

fraction, is a consequence of the increased viscosity of the bulk

solution.

Table III. Film thinning velocity as a function of the bulk viscosity

Vol % PS Tot al film Bxtrapolated Velocity Vx11/110

CTAB

Hei~ht [mrn] Time [s] V[mrn/s] (mrn/s] [mol/11

<0.5 l3 .4 24 0.56 0.56 2.0e-3 11.1 13.5 30 0.45 0.63 5.1e-3 17.4 13.0 42 0.31 0.55 5.1e-3 25.0 12.5 65 0.19 0.50 6.7e-3

DISCUSSION

In figure 3 we can see an interesting phenomenon. The process of

marginal regeneratien has been made visible by means of the PS

particles. Marginal regenerat ion creates thin film parts which rise

(rapidly) in the film. These parts again are essentially free of PS

particles. This indicates that neither gravity nor ditfusion is the

reason for the fact that the particles used can nat be present in a

film which is much thinner than the partiele diameter itself.

The place of the partiele borderline (above which there are no

particles in the film), can be explained similarly to the reasoning by

Dippenaar7 on the contact angle between glass particles in a film.

The film is expected to thin until it has reached a slightly smaller

thickness than the partiele diameter (see figure 8) . The particles

will create a contact angle and fall dry for a part. The film

continues thinning until it has no radius of curvature near the

particle. The partiele will be pushed downward in a thicker region. In

our case it is not clear whether the last drawing of figure 8 will be

reached in the thinning process, since the film is very large compared

38

to the particle. The film therefore has no significant radius of

curvature in all directions.

Fig.B.A partiele in a film,the drainageprocessof the partiele

in the film.

The hydrophilic particles (both 300 nm and 1007 nm) were pushed out of

the film when the film reached their own thickness. Hydrapbobic

particles could be present in a film which is thinner than the

partiele diameter. This can be explained by the larger contact angle

of the hydrapbobic particles, we calculated this angle to be 46

degrees. The small particles act the same as large particles (>160 ~m)

with which Dippenaar7 performed experiments. The contact angle causes

drainage of the particles which follow the drainage of the film

completely. If the particles stick to the surface, their Brownian

motion will be suppressed by the Marangoni effect and by contact angle

hysteresis. They will thus tend to follow the motion of the film. This

phenomenon appears to be strong enough to suppress even the Brownian

motion of the 300 nm spheres. We found a similar behaviour for glass

particles (1-2~.tm) which did not have a distinct effect on the film

thinning process of films drawn from CTAB solutions unless they lower

39

the CTAB concentratien by adsorption. Tbis bowever could not happen at

the volume fractions used ( <0. 5%) . The hydrophilic glass particles were not monodisperse, and the partiele borderline therefore was not

very sharp.

In table III we find within experimental accuracy a linear correlation between the thinning velocity (V) and the viscosity of the liquid:

(5)

The result of the present investigation indicates that marginal regeneratien is inversely proportional to the viscosity of the solution, since marginal regeneratien is the major mechanism of film drainage.

CONCWSIONS

The actual thickness of the film at the partiele borderline is determined by the hydrophobicity of the particles. This is in agreement with other investigations (Dippenaar 7

). The particles do not flow down because of gravity directly. Diffusion can be neglected.

The thinning rate from foam films of PS dispersions in CTAB (up to 25

vol% PS) is more or less linearly correlated with the viscosity. This suggests that marginal regeneratien is also linearly correlated with the viscosity, because marginal regeneratien is the major mechanism of film thinning in this type of films.

Low volume fractions of glass particles did not affect the drainage rate of CTAB films. The particles did not give a partiele borderline because of their polydispersity. The experiments with the glass particles confirm that the drainage of the particles is determined by the hydrophobicity and the film thickness.

40

REFERENCES

(1) Kruglyakov, P.M. and Taube, P.R., Colloid Journalof the USSR,

34, 194-196 (1972)

(2) Garret, P.R., J. Colloid Interface Sci., 69-1, 107-121 (1979)

(3) Hudales, J.B.M. and Stein, H.N., Colloid Interface Sci., 140-2,

307-313 (1990)

(4) Fang-Qiong Tang, Zheng Xiao, Ji-An Tang and Long Jiang, J. Colloid

Interface Sci., 131-2, 498-502 (1989)

(5) Frye, G.C. and Berg, J.C., J. Colloid Interface Sci., 127-1,

222-238 ( 1989)

(6) Aronson, M.P., Langmuir, 2, 653 659 (1986)

(7) Dippenaar, A., Int. J. Hiner. Process., 9, 1-14 (1982)

(8) Mysels, K.J., Soap films studies of their thinning and a

Bibliography, Pergamon Press, London (1959)

(9) Hudales, J.B.M. and Stein, H.N., J. Colloid Interface Sci., 138-2,

354-364 (1990)

(10) Clift, R., Grace, J.R. and Weber, M.E., Bubbles, Drops and

Particles, Academie Press (1978).

(11) Almog, Y., Reich, S. and Levy, M.,

(1982)

41

Polym. J., 14-4, 131-136

APPENDIX .ZA

We consider a film element with height Ah, width b and thickness d.

The volume V will therefore be V=b*d*Ah. The flow per unit of

height out of such an element will be:

Q = * v· =b*d' n

Hudales found Q to be equal to Q=k*d were k and n are arbitrary

constante. Separating thickness d from time t, and integration in time

leads to:

( 1-n) kt/b=d1-n

Here we assumed the film to be infinite thick at t=O, and n>1. A

double logarithmic plot gives information about k/b and n

lnld)=1/(1-n) * ln(t) + 1/(1-n) * ln(k(l-n)/b)

42

CHAPTER 3

THE INFLUENCE OF GLASS PARTICLES ON THE FOAM STABILITY

OF CTAB SOLUTIONS

INTRODUeTION

Solid particles can have many effects on the foam stability of

surfactant solutions. Both stahilizing and destabilizing effects have

been reported in literature~ 5 The stahilizing effect can be explained

by an increase in bulk viscosity (see chapters 2,4).

In this chapter, the destabilizing effect by adsorption of surfactant

on solid particles is investigated. The adsorption not only decreases

the surfactant concentration, but can also make the partiele surface

hydrophobic.

EXPERIMENT AL

Two kinds of experiments are described

experiment concerns the faam stability

in this chapter. The first

of a CTAB-solution/glass

mixture, and the second experiment is a direct adsorption maasurement

of CTAB on glass.

The foam stability was measured in a closed measuring cylinder. An

amount of surfactant salution to which glass was added, was mixed

rigorously in the measuring cylinder by shaking by hand for 10 s. A

foam was formed in the measuring cylinder. Af ter a certain time, a

rather well defined faam/pure liquid interface became visible. The

height in the measuring cylinder of this interface increased due to

drainage. It appeared that the foam/pure liquid interface was sharp

enough af ter 40% drainage of all liquid present. Two drainage times

were measured, going from 40% liquid drainage to 60% drainage (initial

drainage ra te), and from 60% to 80% drainage ( final drainage ra te) .

The experiments were performed in two measuring cylinders, 100 ml.

44

(filled with 25 ml. glass/surfactant solutionl and 250 ml. (filled with 50 ml. glass/surfactant solution) respectively. In this way, the drainage velocity {ml/s) could be calculated. Although this metbod cernprises shaking by hand and thus is subject to differences between different investigators, it is found that results obtained by one investigator aiming at reproducability of shaking, show a reasonable degree of reproducability.

The adsorption of CTAB on glass was measured directly by means of a potentiometric titration with the Orion 940/960 Autochemietry System, with an ion-selective electrode developed by Holten c.s~ Glass was added to a 0.01 M CTAB solution and stirred for 30 min. The glass was then separated by means of a centrifuge, and the CTAB concentratien was measured with the potentiometric titration. The separation of the glass was relatively easy because of the large density difference with the soap solution.

Materials

The adsorption and foam stability were measured with the following substances: CTAB (~ Sigma Chemica! Co.) and glass particles (<10 ~m Lauwers Glass, Hapert, The Netherlands). Twice distilled water was used toprepare the surfactant solutions. The particles were separated into fractions with different sizes by sedimentation~ The density of the glass particles was determined in a Quantachrome stereo-pycnometer SPY-3, and the partiele size distribution was measured with a Coulter Counter ZM (see table I).

Table I, The characterization of the glass particles Mean values and standard deviation

Glass 2-3 ~m Glass 4-5 ~m Glass 5-10 ~m Density [kg/m3

] 2422 ± 1 2559 ± 3 2424 ± 8

Diameter [j.tm] 2.7 ± 0.8 4.6 ± 1.2

45

RESULTS AND DISCUSSION

Two CTAB Concentratiens were used (0.02 M CTAB and 0.001 M CTAB). Bath

concentrations are above the cmc (9e-4 M). The results are presented

in figure 1 (0.02 M CTAB) and figure 2 (0.001 M CTAB).

We can only see an increase in foam stability, on the addition of

glass particles for the 0.02 M CTAB solution. The CTAB concentratien

will decrease due to the addition of the glass, but will not drop

under the cmc. For the 0.001 M salution (which is just above the cmc),

we see a decrease in foam stability due to adsorption of the CTAB on

the particles. In figure 2, the data for the 10 ww% 4-5 ~m glass and

20 ww% 5-10 ~m glass are not presented, because almast no foam was

formed after shaking.

The increase in foam stability of the 0. 02 M CTAB salution on the

addition of glass particles does not scale linearly with the increase

in bulk viscosity of the homogeneaus dispersion. The foam in

dispersion is however not a homogeneaus one, since the particles are

preferably present in the thicker Plateau borders. This gives rise to

an additional increase in bulk viscosity, and might explain the

apparent discrepancy with the results of chapter 2.

The very st rong decrease in foam stability of the 0. 001 M CTAB

salution on the actdition of glass particles can be explained by the

hydrophobic character of the glass in a CTAB salution with a

concentrat ion lower than the cmc. Hydrophobic surfaces destabilize

foam according to Garrett 4 and Frye c ..

From the adsorption measurements performed with the potentiometric

titration, we plotted the concentratien after the actdition of the

glass toa 0.01 M CTAB salution in figure 3. We can clearly see that

the glass decreases the CTAB concentratien in salution strongly.

46

1.00

0.80 .!e. :g til

0.60 I- -11- INITIAL RATE < ~ til 0 < 0.40

_._ FINAL RATE

z < ~ Q

0.20

0.00 0 10 20 30 40

WW% GLASS

Fig.1 The drainage rate [ml/sl - ww% Glass 4-5 ~m in a 0.02 M CTAB solution.

1.50 r-----.--r----..,...------.. I I ..

1.00

'I .. I' .I

'I .. I' •' I I •' '. .. 'I .. I' •' -11- INITIAL RATE I I ..

I .. .. 4-5 11m GLASS I • .. ,I

•' --- FINAL RATE .. .. •' Jl

4-Spm GLASS

•' •' •' -e- INITIAL RATE ,. 5-IOpm GLASS •: 0.50

-e- FINAL RATE 5-IOpm GLASS

0.00 ...._ _____ ......_ _____ __J

0 10 20

WW% GLASS

Fig.2 The drainage rate [ml/sl - ww\ Glass 4-5 ~m and 5-10 ~m

in a 0.001 M CTAB solution.

47

10

9

~ 8 0 ); 7 • ! :z 6 0 1= 5 < a: 4 .... z Q;l u 3

z 2 0

u

0 0 2 3 4 5 6 7 8 9 10

WW% GLASS 2-3 [f.lm)

Fig.3 The adsorption of CTAB on 2-3 ~m glass particles. Concentratien [rnMol/11 wwt glass.

CONCWSIONS

The results indicate that glass particles increase the faam stability if they do not decrease the surfactant concentratien to values below the cmc. Hudales c. s ~ found an increase in foam stability af ter addition of large glass particles, and a decrease in foam stability after actdition of small glass particles. This is in agreement with our work, since small particles have a much higher specific area. They will therefore decrease the CTAB concentratien and foam stability much more.

48

REFERENCES

(1) Schellinx, J., De Invloed van Vaste Deeltjes op de

Schuimstabiliteit van CTAB-oplossingen, afstudeerverslag T.U.E.,

Eindhoven ( 1990 l

(2) Hudales, J.B.M. and Stein, H.N., J.Colloid Interface Sci., 140-2,

307-313 (1990)

(3) Kruglyakov, P.M. and Taube, P.R., Colloid Journalof the USSR, 34,

194-196 (1972)

(4) Garrett, P.R., J.Colloid Interface Sci., 69-1, 107-121 (1979)

(5) Frye, G.C. and Berg, J.C., J.Colloid Interface Sci., 127-1,

222-238 (1989)

(6) Holten, C.L.M. and Stein, H.N., Analyst, 115, 1211-1214 (1990)

49

ABSTRACT

CHAPTER 4

INFLUENCE OF SURFACTART TYPE AND CONCERTRATION

ON THE DRAINAGE OF VERTICAL LIQUID FILMS•

For a better understanding of marginal regeneratien in mobile faam

films, two experimentally accessible parameters were measured, viz.

the drainage and the wavelength of marginal regeneratien at the bottorn

of the film.

The drainage was measured either by interference or by the downward

velocity of polystyrene particles. The latter could be observed by

means of light extinction. The drainage time of films of 1. 5 11m

thickness (measured with polystyrene particles) was found to be

independent of the film height within the investigated range (13

mm .. 17 mm) and was proportional to the bulk viscosity for solutions

containing water/glycerol and CTAB. Xhe drainage rate is independent

of concentratien above the critica! micelle concentratien (cmc), and

films drain faster below the cmc. Liquid films drawn from CTAB

solutions are mobile below the cmc.

Thick:.er and thinner regions at the film/Plateau border transition

alternate; the corresponding wavelength does not vary strongly with

the bulk viscosity.

From the drainage time of films drawn from solutions with a

complicated rheological behaviour, the effective shear stress and

shear rate in the dominant process of film thinning can be estimated.

Reasonable agreement was found with calculated values based on Mysels'

theory on marginal regeneration.

• This chapter has partially been published in Langmuir, 8, 3099-3101

(1992)

51

INTRODUeTION

The drainage of liquid films is important for processas invalving

foams and emulsions.

There are several methode to atudy the drainage of, for example, a

foam~-J We used in our

conatructed analogoualy to

foam film. Mysels et al7

inveatigations a Fizeau interferometer

the one Mysels used, thus for a vertical

already showed that there are aeveral

drainage types for foam films. Most of the films studied in our work ~­

were mobile films (except for the CTAB/SA combinationl . Later

work4 confirmed Mysels' view that marginal regeneratien is the major

mechanism of film thinning in this type of film.

Therefore we focused our attention on marginal regeneratien and

measured two characteristics thereof. The drainage time of 1500 nm

film thickness was determined for several surfactant solutions. We

also meaaured the wavelength of the "peacock feathers" in the

int erferenee fringes caused by alternating thick/thin reg i ons at the

film/Plateau border transition as a function of the bulk viscosity and

film thickness.

The "peacock feathera" only occur in vertical films. Nonhomogeneities

have been observed in horizontal films': These nonhomogeneities are

supposed to act as surface waves pumping liquid out of the film,

increasing the drainage ra te. Sharma and Ruckenstein6' 7 gave a

mathematica! description .for this process in which, however, no a

priori reason could be given for an asymmetrie character of the

surface waves as required for a pumping action. There are in addition

some problema in applying the equations (derived for horizontal films)

to vertical ones, since the equations do not account for surface

tension gradients. Another complication is that gravity acts in

vertical films directly on the nonhomogeneities, which causes the thin

parts to flow upward (similar to Archimedes' law).

52

EXPERTMENTAL SECTION

Materials

The following chemieals were used without further purification:

SDBS (Nansa 1260 >99.2% ex Albright+Wilson);

sodium p-(3-dodecyl)benzenesulphonate (>99%, KSLA);

sodium 3-(3-dodecyl)-6-methylbenzenesulphonate {KSLA);

sodium 2 (3-dodecyl)-4,5-dimethylbenzenesulphonate (KSLA);

CTAB (>99% ex Janssen Chimica);

Octanol (>99% ex Merck);

Pentanol (>99% ~ Merck);

Salicylic Acid (p.a. ~ U.C.B);

Glycerol (>98% ex Merck);

Polystyrene particles (d=1500 nm, ~=240 nm) ;

Distilled water (twice);

~paratus

Most solutions were measured in a Fizeau interferometer constructed

analogously to the apparatus used by Mysels et al~ . In addition to

the observation metbod by reflected light, our apparatus has the

possibility of observing transmitted light. This is useful in the case

of surfactant solutions with a complex rheological behaviour, such as

the CTAB/SA solutions (Strivens 8) . This gives rise to nonuniform film

thicknesses, the (rigid) film can have different thicknesses at a

certain time and height, this in contrast with a mobile film. The

interterenee pattern is then too complicated to be analyzed. In such

cases, measurements of the drainage rate can be performed by following

the downward motion of monodisperse hydrophilic polystyrene particles

(1500 nm) which cannot be present in a film which is thinner than the

partiele diameter9• The particles therefore mark the places in the

film above which the film is thinner than 1500 nm. By estimation of an

average height of the (particle free film)/(particle containing film)

transition at different times, a drainage rate can be measured, which

represents the drainage rate for the film thickness equal to the

partiele diameter.

53

Figure la. The metal frame

I r

~ ' -

Figure lb. The glass frame

54

We used for our experiment two frames {see figure 1). A roetal frame

with four sharp-angled legs was constructed to form four soap films,

with a fifth film in the middle. The fifth film (the film we are

measuring) has two free Plateau borders. A glass frame (two legs) was

used for the branched SDBS solutions which did not farm soap films in

the roetal frame. The length of the legs (in both frames) is 2.0 cm.

Forthesodium p-(3-dodecyl)benzenesulphonate it was even necessary to

bring the pH under the IEP of the glass (with HCl), probably in order

to increase the wetting of the salution on the frame.

RESULTS

In figure 2, the height at which the film has a thickness of 1500 nm

is shown as a function of time. Polystyrene particles were used for

the measurements of the CTAB/SA solution; the other two lines were

obtained by means of interferometry. Extrapolation of the straight

upper part of the drainage lines in figure 2 gives a time (seconds) at

zero height, which can be taken as a measure for the drainage rate. Of

the solutions measured the only one which does not give a straight

part in the drainage line was the CTAB/SA combination. This is

ascribed to its complicated rheological behavior~' 10

15

,....... E 10 E

E-< :I: 0 ..... ~ 5 :I:

0 0

EXTRAPOLATED TIME

-+- 50 ww% glyc. 0.004M CTAB

---- 0.001 M SA 0.001 M CTAB

-e- CTAB 0.002 M

300

TIME [s]

Fig. 2. Drainage of several soap solutions (height-time).

55

We found that this drainage time does not depend on the initial film

height for heights in the interval 13-17 mm (see Table I). We verified

this for two surfactante CTAB (0. 002 M) and sodium p- (3

dodecyl}benzenesulphonate (0.003 M} in a glass frame, with traces of

PS particles 1500 nm. The drainage time listed is the time after film

formation when the film is free of solid particles.

Table II lists both the extrapolated times and the bulk viscosity- of

the solutions. The temperature is the temperature of the drainage

experiment. The viscosity was calculated from a viscosity maasurement

at that temperature (±1.C}. Most solutions were measured with a

Ubbelohde viscosimeter, except for the CTAB/SA solution. The viscosity

of the CTAB/water/glycerol salution was measured with the Rheometrics

RFS II system and found to be Newtonian (see figure 3). The rheology

of the CTAB/SA system bas been investigated by Strivens 8 and by

Wunderlich and Brunn: 0 The data of Wunderlich however could not be

used, since the concentrations were different from those employed in

the present work. Figure 4 gives the measurements performed on a

O.OOlM CTAB/SA solution, with regard to the steady flow viscosity. A

double gap 40/50 was used with the Bohlin measurements. Measurements

were performed both with increasing shear rate (L-H measurements) and

with decreasing shear rate (H-L measurements) . We used single

concentric cylinders in the Deer viscosimeter (2.00-1.80 cm* 6.50 cm)

and applied at least 15 min shear befare every measurement.

56

-2.00

~

rJJ -2.20 "' e::. >< • • • f-< -2.40 • • • • • ...... U)

0 u U) -2.60 ...... > '-' C)

-2 .80 0 ....l

-3.00 0.00 0.40 0.80 1.20 1.60 2 .00

LOG(SHEAR-RATE [/s])

Fig.3 . Rheology of a CTAB (0.004M) in water/glycerol 50%

solution at 30 oe. (log(shear-rate] - log [viscosity] )

0.00

~

rJJ

"' p... -0.75 ~ - DEER

>< 22 c f-< ...... U)

0 -1.50 u

-a- BOHLIN CS (L-H) 20 C

U) ..... > '-' -2.25 C)

~ BOHLIN CS (H-L) 20 C

0 ....l

-3.00 -2.00 0.50 3.00

LOG(SHEAR-RATE [/s]) Fig.4. Rheology of CTAB/SA (0 . 001 M) in wa t er

(log[shear - rate ] - log[viscosi t y])

57

Fig . Sa. An example of a picture used for wavelength cal culation.

THE WAVELENGTH ,( ), I

Fig.Sb. A schematic representation of the bottorn of the f ilm.

58

Table I, The drainage time as a function of film-height

Time measured until the film is free of PS

CTAB Na-p-(3-dodecyl) benzene sulphonate

0.002 M 0.003 M;pH=2 with HCl

Height [mm] time[s] <T [ s] n Height[mm] time [s] <T [s] n

6.57 27.0 1.0 2 8.46 6.2 0.4 6

10.37 25.6 2.1 7 9.66 6.4 0.3 6

12.37 23.6 0.4 5 12.58 7.2 0.2 4

13.07 22.3 0.5 3 14.23 8.7 0.1 4

17.3 22.8 0.3 2 15.13 8.2 0.2 5

17.08 8.6 0.3 6

Table II, The drainage of the surfactant solutions

measured in a metal frame

Salution Conc. Drainage Height Viscosity Temp time vel.

[mol/1] [s] [mm/s] [mm] [mPas] [C]

CTAB 0.0006 29.9 0.361 11.9 0.91 24.3

CTAB 0.0008 30.6 0.392 12.4 0.90 24.5

CTAB 0.002 32.7 0.440 14.3 0.91 24.3

CTAB 0.02 34.1 0.413 13.8 0.96 25.2

CTAB 0.004 184 0.101 12.8 4.5 28.4 50 ww%glycerol

CTAB 0.002 33.3 0.430 14.7 0.90 24.9 pentanol 0.002

CTAB 0.002 36.8 0.407 14.3 0.90 24.9 actanol 0.002

CTAB 0.001 see

Salicylic acid 0.001 231 0.063 14.9 fig.4 24.0

SDBS 0.003 28.4 0.505 13.9 0.89 25.1

59

Table II, The drainage of the surfactant solutions measured in a glass frame

Salution Conc. Drainage Height Viscosity Temp time vel.

[mol/11 {s] [mm/s] [mmJ [mPasJ [Cl

* Na-p-(3-dodec) 0.003 8.7 1.63 14.2 25.4 BS pH=2 (HCl)

Na-3- (3-dodec) 0.0054 28.8 0.47 14.1 0.94 24.0 6 methyl BS Na-2-(3-dodec) 0.0078 24.3 0.53 14.0 0.83 29.7 4,5dimethyl BS ..

Time when the film was free of PS particles

Additional to the drainage times, information on marginal regeneration can be obtained by measuring the wavelength of the thin film spots at the bottorn of the film. The wavelength of these spots in the CTAB/water and the CTAB/water/50% (w/w) glycerol mixtures was measured near the horizontal film/bulk liquid transition at the lower side of the film. The results are given in Table III. Figure 5 is an example of an analyzed picture.

Table III, The wavelenght of marginal regeneration at the bottorn of a film

Water/CTAB 0.002 M glycerol/wateriCTAB 0.005 M

thickness wavelength thickness wavelength d[nm] À [mm] d[nml À [mmJ

1539 0.86 781 0.47 1232 0.79 391 0.35

513 0.62 293 0.31 410 0.62 195 0.32

DISCUSSION

The CTAB solutions below the critica! micelle concentration (cmc=9e-4 M) did not give rigid films and drained faster than solutions above

the cmc. The drainage time above the cmc was no langer a function of

60

the concentratien (except for a slight increase which can be ascribed

to the increase in viscosity} . The measurements below the cmc however

were very tedious and were performed with great care in order to

prevent dust from entering the solution. We found that sametimes rigid

films were formed below the cmc if this preeautien was not taken. This

gave rise to poor reproducibility. Rigidity was found to be due to

impurities by other researchers as well ':' 11

There is (as far as we know) no theory which describes the drainage of

mobile vertical films quantitatively. Seeking an easy way to campare

the measurements, we considered two possibilities: the drainage

velocity and the (extrapolated) drainage time. Although both options

are characteristic for the drainage process, we pref er to use the

drainage time because it is independent of height.

A significant effect but not a very strong

film thickness was found on the wavelength of

the bottorn film/Plateau border boundary.

horizontal (SDS + NaCl) film was measured

effect of viscosity and

marginal regeneratien at

The wavelength in a

by Radoev et al: The

diameter of the nonhomogenities was slightly larger than 0. 005 cm.

This is 1 order of magnitude smaller than the wavelength found in our

systems (about 0.07 cm). The influence of surface rheological

parameters on the decay of the amplitude of transveraal surface waves

is investigated in appendix 4A. The amplitude decay of the surface

waves was found to be negligible within the time scale of measurement

of the wavelength (see ref.2 appendix 4A).

The measurement of the glycerol/wateriCTAB mixture indicates that the

drainage-time scales (almost) proportional to the bulk viscosity, in

agreement with the theory of Ruckenstein and Sharma~' 7 The

proportionality can be used to estimate the effective shear rate and

shear stress, in the dominant process of film thinning as fellows. We

measured the CTAB/SA system in a Deer and a Bohlin viscosimeter and

found our results to be in agreement with the measurements of

Strivens~ At low shear rates, hysteresis was observed with the Bohlin

viscosimeter. For the CTAB/SA sample we found a drainage time of 231

s. This indicates that the viscosity of the salution is about 6. 4

mPas. The shear rate in this process therefore is (see figure 4) 100

61

/s. The shear stress therefore is 0.64 N/m2. This value is compared to

the shear stress as can be calculated with Mysels' theory on marginal

regeneration. Reasonable agreement was found (see Appendix 4B).

CONCLUSIONS

The drainage of thin liquid CTAB films does not depend on the film

height within the range 13 -17 mm. The drainage of a CTAB film above

the cmc is not a function of the concentratien (0. 001M-0.02Ml. The

drainage below the cmc shows a slight increase with a decrease of

concentration.

The drainage rate was found to be inversely proportional to the

viscosity. The shear stress causing the drainage was estimated to be

0. 64 N/m2• Reasonable agreement was found with calculated values on

the basis of Mysels' theory on marginal regeneration.

The wavelength of the film spots in marginal regeneratien was one

order of magnitude larger than the wavelength found in horizontal

films.

ACKNOiiLEDGEHENT

This work was made possible by financial support from Stichting

Technische Wetenschappen and Voorbij Beton b.v. We thank dr. N. van Os

for the donation of 3 SDBS samples, and A.J.G. van Diemen for placing

polystyrene particles at our proposal.

REFERENCES

(1) Brady, A.P. and Ross, S. J.Am.Chem.Soc. 66, 1348-1356, (1944)

(2) Rácz, Gy. Erdös, E. and Kocz6, K. Coll. Polym. Sci. 260,

720-725, (1982)

62

(3) Mysels, K.J. Shinoda, K. and Frankel, S., Soap films studies of

their thinning and a bibliography; Pergamon Press:London, 1959;

Chapter 2-1

(4) Hudales, J.B.M. and Stein, H.N. J. Colloid Interface Sci. 138,2,

354-364, (1990)

(5) Radoev, B.P. Scheludko, A.D. and Manev, E.D. Journal Colloid

Interface Sci. 95,1, 254-265, (1983)

(6) Ruckenstein, E. and Sharma, A.J., J.Colloid Interface Sci., 119,

1-13, {1987)

(7) Sharma, A. and Ruckenstein, E., Colloid Polym. Sci., 266, 60-69,

(1988)

(8) Strivens, T.A. Coll. Polym. Sci. 267, 269-280, (1989)

(9) Baets, P.J.M. and Stein, H.N., Chem. Eng. Sci., 48-2, 351-365

(1993)

(10) Wunderlich, A.M. and Brunn, P.O. Coll. Polym. Sci. 267, 627-636,

(1989)

(11) Prins, A. Arcuri, C. and Van den Tempel, M. J. Colloid Interface

Sci. 24, 84-90, (1967)

63

APPENDIX 4A

TUE INFLUI!!HCI!! OP' SUltFACE RHEOLOGICAL PARAMETERS ON

TRANSVERSAL SURFACE WAVES IN HORIZONTAL FILMS

In this appendix we will investigate the role of surface rheology on

the drainage process in horizontal films. This is useful in order to

determine the time scale over which (small amplitude) ripples are

restored by Marangoni flow. In order to sol ve the film drainage

problem, we will make some assumptions. In the following we will study

the film flow for the case of two deformable interfaces, with a

certain elasticity and surface tension, in one dimeosion only (see

figure 1). The drainage process calculated in this Appendix will be

part of the much more complicated drainage process of vertical films.

FORHULATION AND SOLUTION OF THE FLOW PROBLEH FOR A HORIZONTAL FILH

In our problem only viscous farces will be considered (the lubrication

approximation), and we will assume that the pressure is a function of

x only. The curvature of the film determines the preesure (see

equation [1]), if the assumption is introduced that BH/Bx"*O. This

assumption is valid for small amplitude ripples.

[1]

In equation [1], H(x, t) is the film thickness, Ho the average of

H(x,t), <T(X,t)

flow velocity

the surface tension, ~ the viscosity and u(x,z,t) the

in horizontal direction (see figure 1) . A small

amplitude wave is superimposed on the film with an average thickness

Ho and width b. We restriet the calculation to one Fourier-component

of the "squeezing-mode" only. The influence of the bending mode on the

drainage is not considered here, since there are no thickness

fluctuations involved in that type of waves.

64

Ho

z=O

-Ho

z

y ~x u(x,z,t)

Fig.l, The dimensions of the drainage problem. The dimension in the

z-direction is strongly exaggerated.

For the right hand part of equation [1) we write:

[2] 8P/8x = -1/2 <ro

neglected term

We will neglect the second term in the right hand expression of

equation [2] , and prove later on that this is correct for small

amplitude ripples. Tagether with our first formula we obtain after

integration:

[3] 3

~- = - CTo ( .il..._!!3) Z az 2TJ ax

The boundary condition Bu/Bz=O at z=O was used. The complete velocity

profile of the liquid in the film can be calculated by integration of

equation [3], when boundary condition at the surface is known (or

assumed). The velocity at the surface us(x,tl is assumed and we obtain

the following result:

65

(4] u(x,z,t) = -f(x,t) * (z 2 - H(x,t) 2 /4) + us(x,t)

Here f (x, tl is defined as:

[5] f(x,t) = Cfo 03

* Tx3 H(x, t) /411

These equations are similar to the ones which were derived by Sharma and Ruckenstein 1 earlier. The change in film thickness is determined by this velocity profile, the mass balance [6], and the average

velocity u (formula [8]).

[61 a (HU)

+ ~- 0 ----ex- at -

The average velocity U can be calculated from:

Ho/2 [7] HoU= J u(x,z,t)dz

-Ho/2

[8] U(x,tl f(x,t) * ~/6 + Us(x,t)

A force balance at the film surface gives information about the surface tension gradient. This surface tension gradient is small, as can be verified with equation [13], but has to be calculated since it determines the surface velocity in time through the elasticity. The surface tension gradient is assumed to compensate the pressure gradient exactly.

[9) au au I ax = 11 az

Ho/2

Ho*f (x, t) *ll

The surface elasticity of the film relates the surface velocity with the surface tension behaviour in time, according to equation [10):

au aln A [10] at = c ---at c &A A at

c ( a (bus) A ) bAx ax x

au. c-­ox

In this relation, c is considered to be a constant (c*f(t)), because the film is close to equilibrium. Now we have a set of 5 equations, which can be reduced to one differential equation. Formula [12] was

obtained from equation [6] were the assumption 8H/ax~O was used.

66

[ll] u (x, t) f(x,t) H~/6 + Us(x,t)

[12] Ho~ a x + BH 0 --at=

[13} 8f1' f (x, t) Ho 0 ax + 'Ij

[14] 8f1' aus(x,t) 0 at - e a x =

[15] f(x,t)

Differentiat:ion of [13] to t and [14] to x eliminatea the surface

tension as variable:

[16] = 0

Single integration of [16] gives (taking into consideration that the

derivatives for t~ go to zero):

[17] 0

Introducing forrnula [11] and [15] into [12] :

[18] 3 4

~f!o _2_!!4 + Ho 241J ax

BH + at 0

The surface velocity us can be eliminated with equation [17]. We then

obtain one differential equation [19] , which describes the drainage

behaviour in time.

[19] HofJ'o ~

1 BH +~at 0

It is useful to make this relation nondimensionless. We therefore

introduce the following parameters [20] into equation [19] and obtain

the dimensionless differential equation [21] :

[20) H=.lf*Ho X=~*Ho ; t= t*to where to 241JHo/fJ'o

[21]

67

I

We try the following solution, with the dimensionless parameters A, w ~ (W;W•* tol and k (k;k*Ho=2rrHo/À), for this equation:

[22] U = 1 + A*ei (wt-k)

and obtain the dispersion equation [231 for this problem.

Or, rewriting [23]:

[24] w

After resubstitution of the dimensionless parameters k,w as used in this Appendix, we obtain equation [25) . This relation has previously been derived by Vrij c.s~ as a special case of equation (5) in their paper, for the limiting case p~O and ~0.

1251 w• ( 24;Ho J = i (k Ho) 4

The assumption 8H/8x~o (which implies aujax~O according to equation [13]) is indeed valid for small amplitudes (A) as can be seen in formula [22). The neglected term in equation (2] contains A2

, and is smal! compared to the ether term which scales with A.

What we originally wanted to know is how fast ripples on a film surface fade away. If we start with the following film profile:

H(oc,O) = 1 +A cos (koc)

Then the evolution of the thickness u (a:, t) in time will be according to [221 :

The characteristic time (in [s]) for fade away of a ripple with wavelength À=2rr/k (m] on a film surface is therefore:

68

to * (1 + CTo(Hok) 2 /4c)/(Hok) 4 [s]

The wavelength of the waves in marginal regeneratien is for wateriCTAB

films 0.7 mm (see chapter 4). We take the following values:

Ho=1e-6 m, cro=37e-3 N/m, c=le-3 N/m, k=9e+3 /m, and l)=le-3 Pas. The

calculated characteristic time is r=100 s. This time will not decrease

significantly if the film elasticity is increased, because the term

cro(Hok) 2 /4c is small compared to unity already.

In the foregoing data obtained from measurements on vertical films has

been used (viz. the wavelengthof marginal regeneratien at the bottorn

film boundary) . It is not a priori clear on what bases these data can

be applied for calculations on the drainage of horizontal films. In

fact in the case of horizontal films as discussed here, Maraugani

flows are calculated which are formed spontaneously in order to

compensate for the pressure differences due to curvature of the film

surface. There are in this case no external influences on the film or

the film surface, since the contact with the Plateau border is

supposed to be absent in this calculation. It is reasonable to expect

that drainage by curvature also takes place in vertical films, as a

part of a much more complicated drainage process. It is therefore

useful to estimate the contribution of spontaueaus Marangoni flows in

combination with the Poiseuille flows on the drainage process.

If we look at the spots, formed at the bottorn of a vertical CTAB film,

we see that these spots rise in the film until they reach the height

were they have the same thickness as the film. The time necessary for

this process is much smaller than 100 s (the order of magnitude is 1

s). Therefore, spontaueaus Marangoni flows in the film do not have

enough time to affect the amplitude or the wavelength of the wave. The

wavelength will be the same at all times, according to equation [25].

We can therefore conclude that the wavelength measurements as

presented in Chapter 4, are not subject to significant errors due to

the process mentioned above. The large characteristic fade away time

also gives an explanation for the persistenee of the marginal

regeneratien spots in vertical films.

69

REFERENCES

(1) Ruckenstein, E. and Sharma, A., J. Colloid Interface Sci., 119-1

1-13 (1987)

(2) Vrij, A., Hesselink, F.Th., Lucassen, J. and Van Den Tempel, M.,

Proc. Kon. Ned. Akad. Wetensch., 873, 124-135 (1970)

70

APPENDIX 48

COHPARISON WITH HYSELS' THEORY OF MARGINAL REGENERATION

The shear stress far the process determining film thinning in a

CTAB/SA salution (0.001M) as calculated in the present work fram the

drainage time is 0. 64 N/m". We will naw calculate the shear stress

according to the theory of marginal regeneratien of Mysels et al~

The shear stress ~ will be equal to the gradient in surface tension,

and thatwill compensate the pressure gradient exactly, because there

is no net force acting on film elements. The symbols used are defined

as in Mysels' work, were r is the shear stress, ~ the viscasity, 7 the

surface tension, x the direction of flow, T the film thickness, P the

pressure, and y the direction perpendicular to the direction of flow.

[1] ~ = -dT/dx = -(T/2) dP/dx = (T/2) r d3y/dx3 [N/m2]

The shear stress in [1] scales linearly with the pressure gradient and

the film thickness. We now replace for the parameters y and x the

dimensionless parameters Y=2y/T and X=(24v~/r) 1/

3 x/T respectively.

In this equation, v is an unknawn parameter. A maximum value for the

velocity v with which film elements are produced can be estimated by

using the equation derived by Mysels [3] for film draw-out. The value

abtained is a maximum value, since the films of the elements produced

during draw-out are thinner than the film at the height concerned.

[3] T ao(h~/h) (v/vo)2/3 [m]

In this relation, ao is a constant calculated by Mysels c.s:

(ao=O. 64), vo is a velocity related to the speed of retraction of a

braken film (vo = r/3~) and ho is defined as ho=v(2r/pg)

Substituting [3] into [2] will give:

71

[N/m]

The shear stress scales linearly with the nondimensionless preesure

gradient, and the nondimensionless velocity of film draw-out according

to equation [4]. The parameter d3Y/dX3 will have a maximum value in

the region of the film which determines the film thinning. This

maximum value is 4/27 according to Mysels et al~ We can now determine

what the shear stress for the film thickness 1500 nm should be at an

average height of 0.01m.

[ 5 J 't (2*36e-3/1.5e-6)*(4/27)*(1.5e-6*0.01/2.5e-32 *0.64) 312 [N/m]

1.6 N/m2

The value of the shear stress calculated from this relation is a

maximum value, since both the parameters v and d 3Y/dX 3 were given

their maximum value. The order of magnitude of the measured shear

stress in the CTAB/SA system is in agreement with the theory of Mysels

on marginal regeneration, and Hudales, who fellows this theory in this

respect. The shear stress is calculated for the out-flow of the

Plateau border. The experimental agreement indicates that out-flow is

the rate determining step.

REFERENCES

(1) Mysels, K.J., Shinoda, K. and Franke!, S., Soap films studies of

their thinning and a bibliography; Pergamon Press: Londen, 1959;

Chapter 5

72

CHAPTER 5

SURFACE RHEOLOGY OF SURFACTANT SOLUTIONS CLOSE TO EQUILIBRIUM

ABSTRACT

In this chapter we present surface rheological measurements of various

surfactant solutions close to equilibrium in a Langmuir trough. We

found that the starage modulus is, in the systems investigated, higher

than the loss modulus. The rheological behaviour depends strongly on

the surfactant concentration, even at concentrations exceeding the

cmc. Films with quite different surface rheological properties were

found to show similar drainage rates. This supports earlier work! in

which the velocity of film drainage was found to be determined by bulk

viscosity effects.

A number of possible explanations are examined for the cause of the

surface rheological effects found in our solutions. The rheological

effects at concentrations exceeding the cmc can best be ascribed to

2-dimensional ordering of surfactant molecules at the surface combined

with interaction of these molecules with micelles in the nearby

solution.

INTRODUCTION

It is generally accepted that knowledge of surface rheology is

indispensable for a good understanding of foam production and faam

stabilization or destruction. Two major types of surface rheology for

liquid surfaces can be distinguished: the surface rheology far from

equilibrium and the surface rheology close to equilibrium. Each type

has its own field of interest. The situation far from equilibrium is

interesting to obtain information about foam production, since this

process is usually accompanied with expanding liquid surfaces due to

bubble formation. The situation close to equilibrium resembles an

already formed foam during drainage. The latter gives therefore

74

information about the foam stability once it is formed.

Measurements at the situation far from equilibrium give information about the diffusion coefficient of soluble surfactants, as reported by Rillaerts c.s~ and Fang c.s: Measurements in the situation close to equilibrium can give information about the diEfusion coefficient and can also be used to determine the surface elasticity and surface dilational viscosity due to other processas than diffusion.

Our research was focused on the situation close to equilibrium. There are a number of ways to create such a situation, a.o. the methad used by Kakelaar c.s~ In our experiments, a Langmuir trough was used to measure the surface dilational and elastic behaviour, similar to its use in measuring monolayers (see Lucassen c.s~l.

The foams in which we are interested, are foams made from solutions with a surfactant concentratien exceeding the cmc. Recent experimental and theoretica! work on surface rheology of surfactant solutions above the cmc has been done by Dushkin c. s ~, Fainerman 7 and Fang c. s ~ Lucassen 8 investigated the surface rheology of surfactant solutions above the cmc, subject to periodical oscillations. This theory was generalized by taking into account the effect of polydispersity of diffusing micelles by Dushkin c.s:

EXPERIMENT AL

The apparatus

The experiments were performed in a PTFE trough (see fig.1), with PTFE barriers. The effective length of the trough (L) could be varied in between 76 and 510 mm. The width (160 mml was fixed, and the trough was filled up with liquid to the rim (depth 12 mm) . Overflow was prevented by the finite value of the contact angle. The solutions were measured within one hour. One of the barriers was driven by an excentric (angular frequency varying from 0.003 to 1 s- 1

), the other barrier was fixed. The displacement of the harriers was measured with

75

a Sangamo Schlumberger DFS displacement transducer. The signal

produced by the displacement transducer had a sinusoidal character

with a r.m.s. deviation of 0.006 mm (for an amplitude of 2.96 mml.

Deviations Erom sinusoidal deformation were about 0.2% of the

deformation at the time concerned. The surface tension was measured as

close to the stationary barrier as possible, with the maximum distance

between the edge of the plate and the barrier being 5 mm. This was

done in order to minimize the disturbing influence of the oscillating

bulk liquid on the Wilhelmy plate, by means of drag forces. These

farces might be important for solutions with low elasticities.

Solutions with higher elastic moduli can best be measured at a

di stance of 0. 423*L from the moving barrier as reported by

Lucassen:'· 10 The surface tension was measured as a function of time

with a Cahn 2000 balance and a Pt Wilhelmy plate with a circumference

of 40.0 mm (see fig 1).

STATIONARY BARRIER

MOVING BARRIER

~ I

·;;- 160 MM

j L

WILHELMY PLATE fig.l The Langmuir trough.

Two signals in time were obtained from the trough measurements, one

from the Cahn balance (the surface tension), and one from the

76

displacement transducer {the barrier movementl . Bath signals were

stared and processed in a computer. The phase angle and the amplitude

or the signals were calculated from these data.

Data processing

The methad of data processing, as reported below, is an easy to use

and fast algorithm to calculate the relative phase angle and amplitude

of the surface tension response on deformation. Attention is paid to

this process, in order to eliminate the disturbing influence of signal

noise as much as possible.

For a calculation of surface rheological properties, we need

values of the surface tension amplitude, the barrier position

amplitude, the angular frequency and the relative phase angle.

The angular frequency {w) of bath signals is the same. Bath the

angular frequency and the barrier position amplitude are well known

(determined by the excentric) . The phase angle ~ {compared to a pure

sinus with arbitrarily chosen time of passage through zero

displacement) was calculated for bath signals; and the angles were

subtracted from each other in order to calculate the relative phase

angle e (8=~1-~2) . The average value of the surface tension was

estimated manually, from a plot of the surface tension against time,

because a numerical summatien of the data might introduce errors due

to 'incomplete' waves. A sample timeT was chosen for bath the surface

tension signal (consisting of N points at times [O,T,2T, .. , (N-l)T])

and the signal from the barrier movement (consisting of N points

measured at the same times) . The constant sample time T was chosen

arbitrarily but subject to the condition that T<O .ln/w. This means

that during one barrier movement at least 20 measurements were

performed. The total nuffiber of measurements N was chosen as N>60.

The surface tension signal for example was treated as fellows.

The average surface tension value was subtracted from every point,

77

g1v1ng N points y1

• The obtained values were then used for calculating

the following two summations ( [1], [2]) which are regarded as the

numerical approximations of the integrals ( [3], [4]), for which also

analytica! expressions are available.

N-1 L y1sin (wiT) * T M [1]

1=0

N-1 L y1cos (wiT) * T Q [2]

l=O

Two equations ([3), [4)) with two unknown parameters, ~ and A

(amplitude) are obtained.

NT-T/2

Afsin(wt+~)*sin(wt)dt= -T~ 2 [

NT-T/2

0.25*A* 1- sin(2Wt+4>l/w -T /2

+ 2 co'(•lt] [3]

[

NT-T/2 NT-T/2

Afsin(wt+~)*cos(wt)dt= 0.25*A* 1- cos(2wt+4>)/w + -T7 2

-T /2 2 ''"'·"] (4]

The unknowns A and 4> in the analytica! salution of the integrals

( [3], [4]) can be calculated when the approximation of the equations

([3], (4]) is known numerically by means of formulas ([1], [2)).

The Gibbs elasticity (Ect) and the dilational surface viscosity (1!d)

can be calculated from the relative phase angle e (or loss modulus)

and the amplitude A, using the following two equations (Lucassen

c. s:).

E' '= l}d w IEl cos e (N/m)

IEl sin e (N/ml

[5]

[6]

Here IE I indicates the amplitude ratio between the surface tension

signal and the strain signal.

78

Experimental errors

There are several sourees of errors which ean influenee the results.

The Cahn balance used can measure very small

(about 2 .5e-4 mN/m with our Wilhelmy plate)

farces, down to 1 JJ.g

and is unlikely as a

souree of experimental error with respect to the accuracy of the

absolute value of the surface tension. There is however a time delay

in the Cahn balance: This time delay was measured by connecting a

rubber band to the rnaving harrier and the Cahn balance. The rubber

band was stretched slightly at the initia! position of the harrier

(smallest trough length), and was assumed to give a completely elastic

response.

In agreement with this assumption is that the Cahn balance response on

such a movement was very close to a sinuscictal response, with a r.m.s.

deviation of 0.4%. The phase angle reported in this paper was

corrected on the basis of these measurements. The effect of the time

delay on the amplitude of the signal could be neglected for angular

frequencies smaller than 0. 8 /s. The question whether the trough

length is too large to use the equations developed by Lucassen c.s.

(where it is assumed that the whole surface moves in phase), can be

checked independently with equation [10] . The major sourees of

experimental errors are signa! noise and evaparatien or condensation

of liquid at the Wilhelmy plate during the measurements. Impurities of

surfactant are nat considered here as an experimental error, although

they may have a large influence on the measurements.

Making use of equations (5] and [6) introduces the assumption of a

small trough length compared to the wavelength of the experiment. At

higher frequencies however, this assumption is net valid. Lucassen

c. s ~ 0 der i ved a set of equations which can be used in order to

estimate the experimental error. Equations [7,8,9) will be used in

formula [10} to estimate the error due to the assumption mentioned

above.

·The authors thank Dr. J.Lucassen (Oegstgeest, The Netherlands) for

drawing their attention to this point.

79

w 1/(13 L)

B cot (n/8 + 8/2) - i

[7]

[8]

[9]

First, uniform deformation is assumed, and a surface elasticity is

calculated. Then we verify if a surface with such an elasticity would

give a uniform deformation. If that is the case, then we see no reason

to reject the measurement.

A correction for small wavelengths in the trough was made on the

moduli with equation [10], after a slight modification of the

derivation given by Lucassen:

(E' + i E' 1) correct.ed

(E' + l. E'')unlform H

S e [10]

In this equation, S represents the ratio of IEicorrected/IEiun!form,

and <I represents the correction on the phase angle. The data was

rejected if the correction on IEl was larger than 20\, or if the phase

angle changed more than 9 degrees af ter correction. The points in

figures 3,4,5 and 6 repreaent the average of the modulus IEl and phase

angle e befare and after correction.

A frequency spectrum of the surface tension data can be plotted using

equation [11] in order to verify the presence or absence of higher or

lower order harmonies, making use of Fourier transfarm equations~ 1

t=tend

I(w) 2 IJ elwt y(t)dt I [11]

t =0

From fig. 2 it can be concluded that harmonies other than that with

frequency w/2n do not play an important role for the CTAB 0. 002M

solution. The higher and lower order harmonies in that figure are due

to the finite time of measurement, since these peaks in the spectrum

increase with decreasing integration time interval.

80

5 OOE-05

4.37E-05

3 75E-05

3.12E-05

I .!.., 2 50E-05

>-::;1.87E-05 IJ) z w ~ 1 25E-OS H

6.25E-06

0. OOE+OO

0 0 10 20 3.0 4.0 FREIJUENCY [s] * 100

fig.2 The frequency spectrum of a 0.002M CTAB measurement.

One set of measurements (0.002 M CTAB) was compared to results

obtained by measurements wi th the ring method by J. J. Kokelaar c. s ~ Good agreement between these measurements and our results was found

for the elastic modulus IEl.

Materials

The elasticity and viscosity were measured with the following

substances at the concentrations (mostly 2* cmc) as listed below:

CTAB 0.002 M and 0.02 M (>99% ex Janssen Chimica); CTAB/octanol 0.002M

( >99% ex Merck) ; CTAB/pentanol 0. 002M ( >99% ex Merck) ; CTAB

glycerol/water 0. 004 M/50 ww% ( >98% ex Merck) ; SDBS 0. 003 M (Nansa

1260>99.2% ex Albright+Wilson); DTAB 24.4 gr/1 (ex Kodak Bastman Fine

Chemicals, 99%).

Twice distilled water was used to make the surfactant solutions.

The following chemieals were placed at our disposal by Dr. N. van Os

(Koninklijke Shell laboratorium Amsterdam) on our request for pure

surfactants:

Sodium p- (3-dodecyl)benzenesulfonate 0.0031 M (>99%); Sodium 3- (3-

81

dodecyl) -6-methylbenzenesulfonate 0.0054 M; Sodium 2-(3-dodecyl)-4,5

-dimethylbenzenesulfonate 0.0078 M; TRITON X-100 0.3 gr/1 and 3 gr/1

The parameters r"'and a as used in the Szyszkowski equation (see Prins

c.s: 2) were obtained from surface tension measurements of CTAB:

r"' (mol/m2) =9. 7e- 6 and a=O. 35 mol/m3

. The value for r"' was' 20\ smaller

than the one f ound by Prins c. s: 2 earlier. This difference is not

very large if we take into account the sensitiveness of the parameters

100

and a to the input data (c.~).

RESULTS

The parameters IEl and e are plotted in fig.3,4,5 and 6. The

experimental errors due to small wavelengtbs are estimated according

to equation [10] . The data was rejected if the experimental error in

IEl was larger than 20%, or if the phase angle changed more than 9

degrees af ter correction. Negati ve phase angles we re a lso rej ected,

since this was considered to indicate that the wavelength was too

small compared to the length of the trough. At low frequencies, the

surface tension signal of a 0. 002M CTAB solution, measured in the

vicinity of the moving harrier, was the same as the surface tension

signal measured near the stationary harrier. This proves uniform

dilation. The elastic modulus was in general larger than the loss

modulus of the solutions. Measurements on a 0.002M CTAB solution were

compared to measurements obtained in a ring trough.

82

• PENTANOL 0.002 M;22.8

-2

• OCTANOL 0.002 M;22.4

,. O.G2 M;24.9

-3 0 0.002 M;22.0

+ 0.002 M RING TROUGH

-4 • GLYCEROL -3 -2 -l 0 0.004 M;32.0

LOG(ANGULAR F.[/s])

fig.3 The modulus IEl of the CTAB solutions.

...-.. ....... E --z ........

U.l '-' 0 0 ....1

The curve is calculated for a CTAB solution at the cmc from the parameters V, r~ and a (see text) .

-2 ,---------.....,

~ -3

~ -4

-3 -2 -l 0

LOG(ANGULAR F.[/s])

• SDBS 0.003M;21.0

• TRITON XIOO 0.3gr/l;22.8

,. DTAB 24.4gr/l;24.

0 p-3-SDBS 0.0031 M;25.0

+ 336-SDBS 0.0054M;25.5

fig.4 Modulus IEl of the surfactant solutions.

83

• PENTANO 0.002 M;22.8

""' 45

rn p:,l 40 " 0.02 M;24.9 p:,l ~ 35 C) p:,l 30 0 .._, 0 0.002 M;22.0 p:,l 25 ~ 20 C) z 15 < + 0.002 M RING

p:,l 10 rn < 5 :I: jl.,

0 • GLYCERO 0.004 M;32.0

-3 -2 -1 0

LOG(ANGULAR F.[/s])

fig.S Phase angle of the CTAB solutions.

• SDBS 0.003M;21.0

""' 45 rn p:,l 40 • TRITON XIOO p:,l ~ 35 O.Jgr/1;22.8 C) p:,l 30 0 .._,

" DTAB ~ 25

24.4gr/l;24. ~ C) 20 z 15 < 0 p-3-SDBS ~ 10 0.0031 M;25.0 rn < 5 :I: jl.,

0 + 336-SDBS

-3 -2 -1 0 0.0054M;25 .5

LOG(ANGULAR F.[/s])

fig.6 Phase angle of the surfactant solutions.

84

DISCUSSION

We found for all solutions investigated, with increasing frequency, an

increase in IEl and a decrease in phase angle. Another trend is that

all phase angles (for the pure surfactants) were lower than 35

degrees, causing the values for E' to be much larger than the ones for

E' '. A large difference was found between the O. 02M CTAB and the

O.002M CTAB solution. This is remarkable, since the concentration is

in both cases above the cmc, and the surface excess is expected to be

almost the same in both systems. Diffusional exchange of micelles,

accompanied with a slow micellization process, might in principle

explain these differences. However, we will show later on that this

model can not explain the experiments.

IE we compare the large relative changes in IEl (for the two CTAB

solutions) to the differences in film drainage~ then we see that there

is, within the IEl detectable effect

drainage times.

range observed

of the surf ace

in the present investigation,

rheological properties on

no

the

Marginal

mechanism

regeneration is, for mobile films, the

of film drainage. Marginal regeneration

most important

occurs at the

borders of the film. The Plateau borders are very thick and will

always be able to provide a sufficient amount of surfactant. The most

important part of the film is therefore expected to show a surface

rheological behaviour equal to that measured in the Langmuir trough.

The surf ace elasticity apparently has no effect on marginal

that the regeneration in the solutions investigated. It is known

marginal regeneration process can be inhibited completely

surface elasticity is much higher (see Prins l3) than found

present work, although the relative differences between the IEl

if

in

the

the

values

reported here may be large. In table I, some relevant data for O.002M

and O.02M CTAB solutions at 24.5 Care compared.

The measurements of the O. 002M CTAB solut ion in the Langmuir trough

are compared to measurements in a ring trough. Good agreement was

85

found for the elastic modulus I EI. The phase angle could not be

measured accurately enough in the ring trough, but estimated values

are given in figure 5.

TABLE I

Drainage time of CTAB solutions

Concentration CTAB 0.002M 0.02M 0.004M glycerol 50ww\

Drainage time (ref 1) [5] 32.7 34.1 184

Bulk viscosity (ref 1) [mPas] 0.91 0.96 4.5

IEl [N/m] at w=0.1 /5 1. 6e - 3 ge-4 2.1e-3

e [deg] at w=0 . 1 /5 30 5 12

The measurements reported in this chapter exclude the possibility that

differences in surface elasticity affect the drainage of the soap

films investigated previously! since a relatively large difference in

surface elasticity does not significantly affect the drainage of the

films concerned. The drainage time is related much more closely to the

bulk viscosi ty, as suggested in chapter 4. We also see (fig . 3) that

the elastici ty increases when glycerol is added i however we do not

expect a large effect on film drainage by this increase of elasticity,

since similar surface rheological differences were found to have only

a small effect on the drainage time in the case of CTAB solutions

(0.002M and 0 . 02M).

Both octanol as weIl as pentanol were added to the CTAB solution. In

the case of pentanol we found very different values for the phase

angle. Addition of oetanol results in sueh low IEl values as to make

them very diffieult to measure preeisely by our apparatus. However,

the drainage times of the CTAB solutions with or without the added

aleohols were almost the same (32.7, 33.3 and 36.8 5) .

A number of SDBS solutions differing in the place of attaehment of the

benzene ring to the alkyl ehain were measured, and all of them gave

low IEl moduli and low phase angles. The Na 2-(3-dodecyl)-4,5 dimethyl

benzenesulfonate gave moduli with too much signal

interpretation.

86

noise for

An attempt to explain the surface rheological behaviour in terms of molecular struct\.lr& (see Appendix 5A) was ba.mp&red by Uw high dependenee of the data on concentration, even at concentrations exceeding the cmc. In the case of CTAB, which was investigated at concentrations 2*cmc and 20*cmc, the solutions showed only minor differences in bulk viscosity (see table I). This excludes the formation of liquid crystals.

The observed surface rheological behaviour can not be explained by diffusional exchange of surfactant molecules to the surface. Arguments for this are given below. In order to explain the surface rheological behaviour and the influence of concentratien on this, we consider apart from the diffusional exchange mechanism three other possibilities.

A) Diffusion of surfactant to the surface

It is interesting to know whether diffusion plays a role in the measurements close to equilibrium. A model which describes the surface rheology determined by diffusion, was presented by Lucassen c.s: This theory is valid for solutions with a concentratien up to the cmc. We apply the theory for a salution at the cmc, starting with the calculation of the parameter ( = {F v (ID/2w) for a CTAB sol ut ion. In this relation, c is the concentratien of surfactant, r the surface excess, ID the diffusion coefficient and w the angular frequency. For the diffusion coefficient, a value of 5.6e-10 m2 /s (Rillaerts and Joos 2

) was employed.

For dc/dï we derive from the Langmuir equation, dc/dr=(2a/rool (c/a+ll~

Using the experimentally obtained rro and a values, we obtain for ((w),

((w) 15.4/vw. If diffusion is rate determining, then the phase angle e and modulus IEl will be:

B = atn((/(1+())

-(d~/dlnï)/v(1+2(+2(2)=RTÏ00 (c/a)/v(l+2Ç+2Ç2 )

0.0618/11'(1+2(+2( 2)

87

[12]

[13)

[14)

From this result it is clear that values calculated for the phase

angle e are in between 44.8 and 43 . 2 degrees for w=O.Ol/s to 1/5. The

curve plotted in Eig.3 , represents the modulus IEl calculated with

equation [14).

A more sophisticated model was described by Lucassen~ taking into

account micellization . Both the phase angle and the slopes of the

log I EI-log w plot were expected to increase due to the presence of

micelles. Lucassen 8 also concluded that the elasticity IEl decreases

for solutions exceeding the cmc . However, we found substantially lower

phase angles than 43 degrees and the slopes of the log/EI-log w plot

were lower than 0.5. Moreover, the measured elasticities IEl were

higher than the values calculated according to the diffusion mechanism

at the cmc, whereas lower elasticities were expected.

These observations exclude an explanation of the difference between

surf ace rheological data at concentrations 2*cmc and 20*cmc by

diffusion .

B) Electrostatic repuls ion between the head groups

An explanation for the large differences in surf ace rheological

properties found between the two CTAB solutions above the cmc might be

a difference in electrostatic repulsion between the he ad groups. The

effective free ion concentration however, is not expected to change

above the cmc for a surfactant solution.

The double layer (l/k) calculated on the basis of surEactant molecules

not bound in micelles is in both cases (0.002M and 0 . 02M CTAB) 10 nm .

This is much larger than the average di stance between adjacent

adsorbed CTA' ions, calculated Erom r oo and a (0 . 70 nm, on the

assumption oE cubic close packing) .

The electrostatic repulsion between micel les may be important iE the

average distance bet ween micelles becomes smaller than twice the

electrical double layer, al though we expect also a more pronounced

diEEerence in viscosity tor the two samples it this interaction would

88

be important. The number of surfactant molecules per micelle as given

by Roelants C.S~4 for CTAB is 104. This means that the average

distance bet ween micelles varies from 55 nm in the 0.002M solution to

20 nm in the 0.0 2M solut ion . lntermicellar interact ion can only j ust

explain the differences bet ween the two concentrations (since the

intermicellar distance equals twice the double layer), but not the

existence of the surface rheology of the systems.

This conclusion was corroborated by data for Triton X-IOO solutions .

In this case, the cmc as determined by the break point of the surf ace

tension curve with log (concentration) is 0 . 16 gr i l. Solutions of

Triton X-IOO were measured at two concentrations above the cmc (0.3

gril and 3 gril). The signal noise was too large in the lat ter case.

This confirms our view that electrostatic repulsion does not dominate

the rheological behaviour of the surface, since Triton is a nonionic

surfactant. Moreover we would not have had any response in surf ace

tension from the Triton sample if electrostatic interactions would

determine the surface rheology.

Cl Impurities

A common way for testing the purity of a surfactant is measuring the

1/log(cl curve . The 1/log(c) curve for CTAB does not show a minimum

(see fig.7).

89

80

a 70 Z-a z S2 60 Vl Z IJ.! i- SO IJ.! U « u.

'" 40 ::> Vl

30 -5 -4 -3 -2

LOG(CONCENTRATION (gr CTAB/gr WATER]

fig.7 Surface tension CTAB - log(concentration)

The absence of a minimum is astrong indication that the surfactant is

pure, but does not prove that the surfactant is pure enough . Only

surface a c tive impurities are expected to be able to influence the

measurements significantly.

Another indication of the purity of the CTAB can be found by comparing

the parameters of the Szyszkowski equation to the ones obtained by

Prins C.S~2 earlier. The value obtained for r W was 20% lower than the

one calculated by Prins c. s ~ 2 The presence of impurity reported by

Prins, as could be concluded from the rigidity of the surface af ter

standing for hours, was not observed in our experiments.

The concentration dependenee of the surf ace rheological properties of

CTAB solutions above the cmc might be explained through impurities

which are adsorbed into micelles to a larger extent in 0 . 02M than in

0.002M CTAB solutions, and are not readily released from the micelles

on deformation of the surface.

A theory is presented (see appendix 5B), in which the influence of a

90

single surface active impurity on the surface rheology of a surfactant salution below the cmc was derived, analogous to the theory of Lucassen c.s~ However, large amounts of data (relations between r,7

and cl are required if the theory is to be applied. Unfortunately, these data are only available (as far as we know) for the system

SDS/dodecanol.

We will now investigate the influence of dodecanol on the surface rheology of SOS, making use of the equations derived in Appendix SB. Data for the BOS/Dodecanol mixture can be obtained from Fang c.s7; 15

were the following 5 relations are applied: Csds

Cd oh

rsds

asds rsas/(rm rsds rdoh)

adoh rdoh/(r~ rsds - rdoh)

rm (Csds/asds)/(1 + Cdoh/adoh + Csds/asds)

rdob rm (Cdoh/adoh)/(1 + Cdoh/adoh + Csds/asds)

n = -RTr00 ln (1 - rsds/r

00- rdoh/r

00)

[15] [16] [17] [18]

[19] The partial derivatives of equation [15] and [16] are order to calculate (J:

required in

ac,;arJ = aJ * (r00

- rk)/(r00

r, - rk)2

[20]

The partial derivatives of equation [19] are equal to: EJ =- 87/olnrJ - RTr"" rJ/{r~ rsds rdoh) [21]

Figures · 8 and 9 were constructed, using the following parameters as reported by Fang c.s~ 5 :

101 = 102 Se-10 m2/s; adob 3.7e-3 mol/m3; asds 1.6 mol/m3

r"" = 6e-6 mol/m2

CONCENTRATIONS IN MOL/m3

1 0

- -2 5e-5 s -z ......... "'-"~ -3 1.25e-3 '-' 0 0 .....l

-4 3.13e-2

0.781

-5 -3 -2 -1 0

LOG(ANGULAR F. [/S])

fig.8 Modulus IEl of SDS-dodecanol mixtures with 8 mol/m3

SDS.

45

---- 40 til ~ ~ ... 35 co ~

'"0 30 '-'

"'-"~ 25 .....l 0 20 z < 15 "'-"~ en

10 < ::c 5 p...

0 -7 -6 -5 -4 -3 -2 -1 0

LOG( CONCENTRA TION DOH [moljm 3])

fig.9 The phase angle of SDS-dodecanol mixtures with 8 mol/m3 SDS.

92

The phase angle which we expect according

minimum value and goes to 45 degrees for

to this t heory, shows a

very high and very low

impurity concentration. At a very low concentration, we have a pure

component with a dominant diffusional exchange process. The

contribution of the impure component to the phase angle of the mixture

is low because of the very low partial surface elasticity. At a

moderate concentration of impurity, the relative phase angle of the

mixture is low because of the sufficiently high partial surface

elasticity and the low phase angle of the impure component. At a

relatively high concentration of the impure component, both phase

angles are 45 degrees.

The phase angle of such a mixture can indeed decrease, but this

decrease can only be expected for a limited concentration range of the

impurity.

It is therefore very unlikely (though strictly speaking not

impossible) that di f fus ion of impuri ty can explain all our

measurements. Moreover, the decrease in phase angle due to the

impurity should at least partially be compensated due to the fact that

our measurements were performed with solutions at concentrations

exceeding the cmc. This was not observed.

If impurities would be responsible for the low values of the phase

angle found quite generally for the solutions investigated here, then

all surfactants employed by us should have impurities in a certain

concentration range. This appears to be unlikely.

0) MicellejSurface layer interaction; Surface ordering

The dit ference in surface rheology bet ween O. 002M and O. 02M CTAB

solutions might be due to interaction of micelles with surfactant

molecules adsorbed at the surface. On this basis, our observations can

be understood if it is assumed that the distinct IEl values measured

in O. 002M CTAB solutions are due to a 2 -dimensional ordering of

surfactant molecules at the surf ace when at rest. The existence of

93

surface ordering, in the case of DTAB, has been shown by neutron

reflection l6•

17 In such a situation, every surfactant molecule at the

surface is in a position of low potential energy, and reshuffling of

such molecules requires that a number of them be removed from such a

low-energy position. Micelles, on approaching the surfactant layer at

the LG surface, might disturb this order, e . g . by influencing local

potentials at the positions of the CTA+ head groups . By so doing they

facilitate motion of the surfactant layer molecules .

This explanation is compatible with a similar role of micelles in the

case of a non-ionic (Triton X-IOO), with the proviso that the low

energy positions of the surfactant molecules in the surface at rest

are deterrnined here by attraction between the hydrophilic head groups

of the surfactant and the hydrophilically bound water molecules . The

ensuing order is then supposed to be disturbed by approaching micel les

because the lat ter entrain another hydrophilically hydrated region

into the vicinity of the surfactant layer at the LG surface.

The explanation mentioned sub D, though remaining hypothetical at the

moment, appears to be the most acceptable one to the present authors .

CONCLUSIONS

Surface rheological properties in the surfactant solutions

investigated, do not play a major role in deterrnining drainage rates

of free films. The film elasticity in these solutions apparently does

not af fect the process of marginal regenerat ion. Surf ace rheology

changes at concentrations exceeding the cmc, both for an ionic

surfactant (CTAB) and for a non-ionic one (Triton X-IOO) In both

cases, E' has values at 2*cmc which are at least 40% higher than the

values at 20*cmc. Similar differences are found for E". This can be

explained best by assuming a 2 -dimensional ordering of surfactant

molecules at the LG surface, which is disturbed by the nearby presence

of micelles. The diffusion model can not explain the surface

rheological behaviour because of the low phase angles measured in our systems .

94

The addition of alcohols affects the surface elasticity IEl and phase

angle a of CTAB solutions significantly.

ACKNOWLEDGEHENTS

This work was made possible by financial support from Voorbij Beton

b.v. and Stichting Technische wetenschappen. Parts of the Langmuir

trough were kindly donated by prof. dr. ir. Massen from the Physics

department of the Eindhoven University of Technology. We wish to thank

J.J. Kakelaar from the Agricultural University of Wageningen for

measuring our CTAB salution in their ring-trough, and dr. N. van Os

(KSLA) for the donation of the Triton X-100 and the branched SDBS

samples. We thank especially Dr. J. Lucassen (Oegstgeest, The

Netherlands) for his very helpful remarks on this paper.

95

LIST OF SYHBOLS

a

A

B

: [mol/m3]: Parameter in the Szyszkowski equation

: [N/m]

: [ -]

Amplitude of the surface tension

Dimensionless parameter

c : [mol/m3] : Concentratien of surfactant

E' : [N/ml

E', : [N/m]

Ed : [N/m1

IEl : [N/m]

L : [m]

M : [Ns/ml

N : [ l

Q : [Ns/ml

s : [- -]

T : [s]

w : [ l

e :[rad]

{3 : [/m]

0 : [rad]

<P :[rad]

Starage modulus

Loss modulus

Elasticity of the surface

The amplitude ratio between surface stress and strain

Length of trough

value obtained by numerical integration

Number of measurement points

Value obtained by numerical integration

The ratio of IEl, befere and after correction

Sample time

Dimensionless parameter

Loss angle

The damping coefficient of surface waves

The difference in phase angle

befere and after correction

Phase difference of surface ~ension (or displacement

transducer signal) with pure sinus

96

rm : [mol/m2]: Parameter in the Szyszkowski equation

r :(mol/m2]: Excessof surfactant

~ : [N/m] Surface tension

~ : [Pas] Bulk viscosity of surfactant salution

~d : [Ns/m] Dilational viscosity of the surface

w : [rad/s] Angular frequency of harrier in trough

p : [kg/m3] Density

(J : [--] : ~~J v(IDJ/2w) parameter for component j

IDJ : [m 2 /s) : diffusion coefficient of component j

97

REFERENCES

1. Baets, P.J.M., and Stein, H.N., Langmuir, 8, 3099-3101 (1992).

2. Rillaerts, E., and Joos, P., J.Phys Chem., 86, 3471-3478, (1982)

3. Fang, J.P. and Joos, P., Coll. Surf., 65, 121-129 (1992)

4. Kakelaar, J.J., Prins, A., and De Gee, M., J.Colloid Interface

sci., 146, 507-511, (1991)

5. Lucassen, J., and Van den Tempel, M., Chem. Eng. Sci. 27, 1283

(1972).

6. Dushkin, C.D., Ivanov, I.B. and Kralchevsky,

surfaces, 60, 235-261 (1991)

P.A., Colloids and

7. Fainerman, V.B., Colloids and Surfaces, 62, 333-347 (1992)

8. Lucassen J., Faraday Discuss. Chem. Soc., 59, 76-87 (1976)

9. Dushkin, C.D. and Ivanov, I.B., Colloids and Surfaces, 60, 213-233

(1991)

10. Lucassen, J., Barnes, G.T., J.Chem.Soc., Faraday Trans.l, 68, 2129

(1972)

11. Press, William H., Flannery, Brian P., Tenkolsky, Saul A.,

Vetterling, William T., 'Numerical recipes the art of Scientific

computing', Cambridge University Press, New York (1988), 381

12. Prins, A., Arcuri, C. and Van den Tempel, M., J.Colloid Interface

Sci., 24, 84-90 (1967)

13. Prins, A., van Voorst Vader, F., Chemie, Physikalische Chemie und

Anvendungstechnik der grenzflachenaktiven Stoffe, Berichte vom VI.

Internationalen Kongreg für grenzflächenaktive Stoffe, Zürich, vom

98

11.bis 15. September 1972, Carl Hanser Verlag (1973) München, 441-

448

14. Roelants, E., and De Schrijver, F.C. Langmuir 1987, 3, 209

15. Fang, J.P. and Joos, P., Colloids and Surfaces, 65, 113-120 (1992)

16. Lee, E.M. and Thomas, R.K. J.Phys.Chem., 93, 381-388, (1989)

17. Lee, E.M., Simister, E.A., Thomas, R.K., and Penfold, J.,

Progr. Colloid Polym. Sci., 103, 82-99, (1990)

99

APPENDIX SA, THE STRUCTURAL FORMULAS

Aj::::· Naso;'V bH

3

Na p-3-dodecylbenienesulphonole

No S03 CH CH

Aj::)8

3

H3C""v bH I 3

CH3

Na 2-13-dodecyl l 4-5 dimelhylbenzenesulphonate

A....-ICH2 l11 CH 3

Naso3 ...... V Na dodecylbenlenesulphonale

CTAB DTAB

100

APPENDIX 5B, THE INFLUENCE OF IHPURITIES ON THE PHASE ANGLE

The following theory is derived making use of the formulas presented

by Lucassen c.S S The following equations will hold tor a surfactant

solution with one impure compound below the cmc. The same assumptions

as made by Lucassen c.s~ are applied in this theory, e.g. convection

terms are neglected, reorientation effects in the surface are

neglected, the diffusion coefficient is constant right up to the

surface. and the surface excess is expected to be always in

equilibr ium with the subsurface concentration.

The solution of the diffusion equation for component J reads:

[BI) CJ = cJ+ QJ e nJY eiwt

In this relation, nJ was defined as: nJ=(1 + i)~(w/2~J).

For the surface elasticity of a two component system we write:

d, a, dlnr, a, dlnr 2 [B2] c = dlnA = alnr, dlnA + al nr2 dlnA

The following relation (which

applied for both components

dlnrJ ( dCJ [B3) dlnA 1 + ~J drJ

was derived by Lucassen c.S S) can be

We now find af ter substitution of [BI) in [B3):

[B4) = - (1 + (J(l-i) rl

with (J = ~~J ~(~J!2w) The surf ace elasticity of the two component system will therefore be:

[BS] c = al-nar', 1+(' +i(' 2 + -a, 1 +(2 +i(22 1+2(1+2(, alnr2 1+2( 2+2 (2

Or introducing EJ = -( al /a lnrJ) /~(1 +2(J +2d) and the phase angles eJ:

[B6] c = E, cos el + E2 cos e2 + i (EI sin e, + E2 sin e2)

The mixture of the surfactant with impurity will have an effective

phase angle e, 50 that c = d, / dlnA = I E I (cos e + i sin e) In this

relation IEl has the value:

[B7] IEI=~( [EI (cos et) + E2(cos e2) ]2+ [EI (sin et) + E2 (sin e2) ]2) .

The influence of the impure component on the phase angle can be

calculated if EJ and (J are known.

A pure solution will have a phase angle smaller than 45 degrees,

therefore e, and e2 are both <45 degrees. We will now show that an

101

impure compound can only decrease the phase angle of surfactant

solutions as employed in this work . We assume that the pure solution

has a phase angle of 45 degrees . very close to the value calculated in

this paper .

The phase angle of the mixture can be calculated from [B8)

[B8) tan e = El sin el + E2 sin e 2 El cos el + E 2 cos e2

The difference in phase angle with the pure compound will be (using

el=45 degrees)

[B9J ll tan e = o . 5,12 + E2/ El sin e 2 0.5/2 + E2/El cos e2

- 1 = E2 sin e2 - cos e 2 0 . 5/2 E1+ E 2 cos e2

The difference in phase angle will therefore always be negative. since

e 2< 45 degrees ,

102

CHAPTER 6

CONCLUSIONS

In this work, film drainage of mobile vertical faam films was

investigated with a view to better understand the behaviour of foams

in dispersions, such as foamed concrete. The film drainage was related

to the surface rheological properties and the bulk viscosity of the

soap solutions. The influence of solid particles on the drainage of a

single foam film was studied. We also studied the behaviour of solid

particles in a foam film.

There are several ways to measure the drainage velocity of a vertical

foam film. We measured the drainage rate a) by following the thickness

of a film at various heights by means of interferometryi b) by

measuring the drainage time for 1500 nm: the time after which the film

is thinner than 1500 nm at all heights, because this time was shown to

be independent of the total film height within the investigated range

of film heights. The latter methad has the advantage that it can be

applied to films with high volume fractions of monodisperse solid

particles, and to films with rigid surfaces.

The drainage time was found to be (almost) independent of the type of

surfactant used. The drainage time scaled linearly with the bulk

viscosity.

The surfactant solutions appeared to have pronounced

diEferences in surface rheological behaviour although the surface

elasticity did not exceed values of 4 mN/m. This did not affect the

drainage rates.

Solid particles can have two different types of effects on the foam

stability as observed in this work. Adsorption of surfactant on the

particles can decrease the surfactant concentratien considerably, and

can also make the partiele surface hydrophobic. These effects are

destabilizing. The addition of solid particles on the other hand does

increase the bulk viscosity. The drainage time of vertical foam films

with different fractions of solid particles was found to scale

linearly with the bulk viscosity.

104

The contact angle of the particle / film / air transition region

determines the place of the particles in a film, if the film has a

thickness lower than or equal to the particle diameter. Solutions of

monodisperse polystyrene particles gave a sharp particle-borderline in

a vertical foam film . Above this line the film was found to be free of

particles .

It was shown theoretically that the film elasticity can not restore

the ripples (within an acceptable time scale) caused by marginal

regeneration. This explains the persistence of film spots formed by

marginal regeneration.

The measured shear stress

predicted shear

regeneration.

stress

in

by

foam

the

films

theory

is

of

in agreement

Mysels on

with the

marginal

with regard to the problems related to foam stabilities of dispersions

which we re mentioned in chapter 1, the following conclusions can be

drawn :

1.)

Dispersed particles may destabilize foam by removing the foam

stabilizing surfactant through adsorption . This is especially

pronounced with dispersed particles with a large specific surface (as,

e .g., hydration products of cement) in the presence of quantities of

surface active material only slightly exceeding the cmc.

2 . )

For formation of a stabIe foamed product, it is essential to avoid the

expulsion of solid particles from the top of the foam lamellae. A foam

lamelIa free of solid particles drains more rapidly, and if the

lamelIa does not contain enough material which will eventually lead to

stiffening of the liquid (as, e.g . hydrating cement particles) , the

lamelIa will sooner or later break .

3. )

A complex dispersion as used in foamed concrete product ion, frequently

contains in addi tion to Port land cement, other hydrat ing components

105

such as Dy ash. Fly ash will only form hydrat ion products in the

presenc e of Port land cement . The effect of expulsion of larger

particles from the film may lead to separation of Port land cement and

fly ash with unfavourable consequences for the hydration process.

4. )

The use of surfactants with increased surface elasticities will only

slow down the film drainage if the surface elasticities are high

enough to suppress the marginal regeneration.

5. )

The use of aqueous solutions with increased bulk viscosities will

decrease the drainage rate of thin films. However, the additives

concerned must be chosen with care in order to avoid disturbance of

the hydration reactions.

106

SUMMARY

The stability of foam in dispersiena is important both from a

practical and a theoretica! point of view. The practical importance

arises because of the large number of systems in which foamed

dispersiena are involved (e.g. foamed concrete and nutritions). Faam

films drawn from dispersions offer a new way to measure the drainage

of faam films, which is of theoretica! importance. The objective of

this project was the development of a procedure for the reproducible

production of a foam in dispersions. Such a faam is desired for the

production of foamed concrete.

A faam is a geometrically very complex system. The lifetime of foam is

determined by disproportienation and by the lifetime of the faam films

in it; the latter is determined by two successive processes in each

film: drainage and rupture. Rupture occurs by the influence of a third

phase (oil or solid particles), or when a faam film reaches the

critica! thickness after drainage; therefore the lifetime is mainly

determined by drainage. A common simplification used in literature for

studying foams is to consicter one single horizontal film. The

measurements described in this thesis are measurements performed on

similar vertical films and experiments on real foams. This provides

information on real complex foams.

In order to obtain a better understanding of such systems, we

investigated the following on the drainage of single vertical films.

* The relation between film drainage and bulk rheology

* The relation between film drainage and surface rheology

* The influence of solid particles on film drainage

* The behaviour of solid particles in a soap film

* A theoretica! consideration of the persistenee of thin film parts

formed by marginal regeneratien

The following techniques were used. The drainage time was measured in

a Fizeau interf erometer. This apparatus offers the possibility to

measure the film thickness as a function of height and time by means

of interferometry. Pictures of the faam film were taken, processed and

108

stored in a computer . The surface rheological behaviour of the

solutions concerned was measured in a Langmuir trough . Special

attent ion was paid to the problem of signal noise. The surf ace

elasticity and surf ace viscosity could be calculated from these

measurements. Adsorption of surfactant on solid particles is one of

the influences of solid particles on a foam. This adsorption was

measured with a surfactant selective electrode.

As the continuous phase of the foam solutions of sodium

dodecylbenzenesulphonates, cetyltrimethylammonium bromide, dodecyl­

trimethylammonium bromide and triton X-IOO (polyethylene glycol

tert-octylphenyl ether) were used in the absence or presence of

alcohols (pentanol, octanol) The disperse phase consisted of both

hydrophilic particles (glass) and hydrophobic particles (polystyrene).

No relation could be found between the surf ace rheological behaviour

of the surfactant solutions and the drainage times. The drainage times

were found to be linearly correlated to the bulk viscosity of the

solutions. Marginal regeneration, the most important drainage

mechanism in mobile foam films, does therefore only depend on the bulk

viscosity and does not depend on surface rheology for low values of

the elastic modulus.

The influence of solid particles on the film drainage was found to be

determined by the increase of the bulk viscosity due to the presence

of the solid particles. A destabilizing effect of solid particles is

obtained when the surfactant concentration is decreased (to values

below the cmc) by adsorption of surfactant on the particles.

From experiment s wi th monodisperse part icles, a new phenomenon was

observed, which made it possible to examine the drainage rates of

rigid foam films. It appeared that hydrophilic particles could not be

present in foam films which had a thickness smaller than the particle

diameter . In general we found that the particles can not be present in

foam films from which a too high contact angle would result. This

means that a very sharp particle borderline becomes visible in foam

films drawn from a suspension of monodisperse particles. No particles

are present above that line, because the film is too thin to contain

any particles. The drainage of foam films can be measured by following

109

that particle borderline.

The shear stress in a soap solution was measured indirectly. The value

obtained agrees quite weIl with calculations on marginal regeneration

according to the theory of Mysels. This supports both the theory

proposed by Mysels as weIl as the theory of Hudales, where more

realistic surface velocities can be introduced.

A straightforward theory on the decay of small amplitude ripples due

to film elasticities is presented . It is shown that the time scale

over which this decay takes place, for waves with a wavelength as

observed in our films, is large compared to the drainage effects . This

can explain the persistence of spots formed by marginal regeneration .

The relation bet ween the conclusions presented in this thesis and real

complex practical systems can be illustrated by the example 'foamed

concrete' . This material consists of a cured mixture of cement and fly

ash in foam . When producing foamed concrete, one is of ten confronted

with a foam which does not remain stabIe during this process.

Undesired nonhomogeneities appear in the product. We concluded al ready

that particles can not be present in a too thin foam film. From this

we conclude that the used cement and fly ash particles should not

differ too much in size, because otherwise they would separate from

each other by drainage, so that the curing will not occur

homogeneously . We can also conclude that the bulk viscosity will

decrease due to drainage of large particles out of the film , and that

this will increase the drainage rate. Moreover, films with few cement

particles in it will cure more slowly and remain weak. We can however

not recommend the use of glycerol / polymer for the i ncrease in bulk

v iscosity, because this might affect the curing process . Affecting the

surface rheological behaviour by choosing another surfactant will only

be useful wh en the surface elasticity (E) rises above a critical

value, 50 that marginal regeneration will not occur . The surfactant

solutions used in this investigation had a surface elasticity which

was too low to inhibit marginal regeneration.

110

SAMENVATTING

De stabiliteit van schuim in dispersies is belangrijk zowel in

praktisch als in theoretisch opzicht. Het praktische belang komt voort

uit het groot aantal systemen dat is opgebouwd uit schuim in

dispersies (zoals schuimbeton en voedingsmiddelen). Zeepfilms

getrokken uit een dispersie bieden een nieuwe mogelijkheid om de

drainage te meten, dit is theoretisch belangrijk . De doelstelling van

dit project was het ontwikkelen van een basis voor het reproduceerbaar

vervaardigen van een stabiel schuim in dispersies . Een dergelijk

schuim is vereist voor de fabricage van schuimbeton .

Een schuim is geometrisch gezien een zeer complex systeem. De

levensduur van schuim wordt bepaald door disproportionering en door de

levensduur van afzonderlijke schuimfilms; deze levensduur wordt

beperkt door twee processen die voor iedere film na elkaar optreden :

drainage en breuk. Breuk treedt op door de invloed van een derde fase

(olie, vaste stof), of zodra de schuimfilm door drainage een kritische

dikte bereikt heeft; de levensduur wordt dus voornamelijk door de

drainagesnelheid bepaald. Een in de literatuur vaak gebruikte

vereenvoudiging bij het bestuderen van schuimen is het meten aan één

geisoleerde horizontale film. De metingen beschreven in dit

proefschrift zijn verricht aan dergelijke geisoleerde vertikale films.

Daarnaast werden ook metingen verricht aan schuimen. Hierdoor

verkrijgen we inzicht in systemen zoals die in de praktijk voorkomen.

Om meer van dergelijke systemen te begrijpen werden de hieronder

genoemde punten onderzocht aan de drainage van geisoleerde vertikale

films.

* Het verband tussen filmdrainage en bulkreologie

* Het verband tussen filmdrainage en oppervlaktereologie

* De invloed van vaste deeltjes op filmdrainage

* Het gedrag van vaste deeltjes in een zeepfilm

* Theoretische beschouwing over de persistentie van

dunne filmdelen gevormd door marginale regeneratie

Hierbij werden de volgende technieken gebruikt . De drainagetijd kan

112

interferometrisch worden gemeten en de oppervlaktereologie werd in een

Langmuir trog bepaald. Bij het meten van de drainagetijden kan de

filmdikte als functie van de hoogte en tijd worden berekend. In dit

onderzoek werd dit gedaan door beelden van een zeepfilm te analyseren

en op te slaan in een computer. Bij de metingen in de Langmuir trog

werd speciale aandacht besteed aan het verwijderen van ruis op de

gemeten signalen. De oppervlakte-elasticiteit en oppervlakte­

viscositeit kon uit deze metingen worden berekend. Een van de

invloeden van vaste deeltjes op schuim is de adsorptie van surfactant

op deze deeltjes . Deze adsorptie werd gemeten met een

surfactant-selectieve electrode .

Als continue fase in schuim fungeerden oplossingen van surfactants

(Na-dodecylbenzeensulfonaten; cetyltrimethylammonium bromide,

dodecyltrimethylammonium bromide en triton X-100), al dan niet in

aanwezigheid van alcoholen (pentanol, octanol). Als gedispergeerde

deeltjes werden zowel hydrofiele (glas), als hydrofobe (polystyreen)

deeltjes toegepast.

Er kon geen verband worden gelegd tussen de oppervlakte reologie en de

drainagetijden van de surfactant oplossingen . Wel bleken de

drainagetijden lineair te schalen met de bulkviscositeit . Marginale

regeneratie, het meest belangrijke drainage mechanisme in mobile

zeepfilms, hangt daarom alleen af van de bulkviscositeit en hangt niet

af van de oppervlaktereologie voor oplossingen met een lage elastische

modulus.

De invloed van vaste deeltjes op de filmdrainage werd bepaald door de

toename in bulkviscositeit door de aanwezigheid van de vaste deeltjes.

Een destabiliserend effect van vaste deeltjes werd waargenomen wanneer

de surfactant concentratie tot onder de cmc daalt, door adsorptie van

surfactant op de deeltjes.

Uit experimenten met monodisperse deeltjes werd een nieuw fenomeen

waargenomen, waardoor het ook mogelijk werd drainagesnelheden in niet

mobiele zeepfilms te bepalen. Het bleek dat hydrofiele deeltjes niet

in zeepfilms aanwezig waren die een dikte kleiner dan de

deeltjesdiameter hebben. In zijn algemeenheid geldt dat deeltjes niet

in een film kunnen zitten op plaatsen waar de contacthoek tussen

113

film/deelt je/ lucht te hoog zou zijn . Dit heeft tot gevolg dat een

zeer scherpe grens zichtbaar wordt in zeepfilms getrokken van

suspensies die monodisperse deeltjes bevatten. Boven die grens zullen

zich geen deeltjes in de film meer bevinden, omdat de film daar te dun

is geworden om deeltjes te bevatten. De drainage kan daarom gemeten

worden door de plaats van die grens te volgen.

De shear stress in een drainerende zeepfilm werd indirect gemeten . De

verkregen waarde komt goed overeen met berekeningen aan filmdrainage

volgens de theorie van Mysels . Dit ondersteunt zowel de theorie van

Mysels als de theorie van Hudales, waarbij meer realistische

oppervlakte snelheden kunnen worden geintroduceerd.

De mate waarin de oppervlakte - elasticiteit het herstel van opperv lakte

golven bepaalt werd theoretisch afgeleid. De tijdschaal waarover dit

proces plaatsvindt voor typische golflengtes van marginale

regeneratie, bleek veel groter te zijn dan de tijdschaal van het

drainageproces in zijn geheel. Dit kan de persistentie van eenmaal

gevormde dikteverschillen in zeepfilms verklaren.

Het verband tussen de in dit proefschrift getrokken conclusies en

praktijksystemen kan wellicht het best worden geilustreerd met

'schuimbeton' als voorbeeld. Dit materiaal bestaat uit een uitgehard

mengsel van cement en vliegas in schuim. Bij de produktie van

schuimbeton kan men worden geconfronteerd met een schuim dat tijdens

het uitharden niet voldoende stabiel blijft . Hierdoor treden er in het

materiaal ongewenste inhomogeniteiten op . We concludeerden reeds dat

deeltjes niet in een te dunne zeepfilm aanwezig kunnen zijn. Hieruit

volgt dat de gebruikte vliegas - en cementdeeltjes niet te veel mogen

verschillen in grootte, omdat anders scheiding door drainage optreedt

en homogeen uitharden onmogelijk wordt. Verder zal door verdwijnen van

te grote deeltjes uit de films de bulkviscositeit dalen, en het

drainage proces versnellen. Bovendien zullen films die slechts weinig

cement bevatten langzamer en slechter uitharden. Het is echter niet a

priori aan te bevelen de bulkviscositeit te verhogen met bijvoorbeeld

glycerol / polymeer, omdat di t het uithardingsproces zou kunnen

beinvloeden. Veranderen van de oppervlaktereologie door een goede

keu ze van surfactant is alleen nuttig, indien men de

oppervlakte-elasticeit (E) boven een bepaalde waarde weet te brengen

114

zodat marginale regeneratie niet meer optreedt. De surfactant­

e>plossing~I1 die in c:l~t onder2;()ek werden betrokk(;!n __ h~dden~J:Vla~te­elasticiteitswaarden.die daarvoor te laag waren.

115

CURRICULUM VITAE

Peter Baets werd geboren op 6 juli 1965 te Grathem. In 1984 slaagde

hij voor het eindexamen VWO aan de scholengemeenschap St. Ursula te

Horn. In datzelfde jaar begon hij met de studie scheikundige

technologie aan de Technische Universiteit Eindhoven. Het

propaedeutisch examen werd in 1985 behaald. Het afstudeeronderzoek

betrof een studie naar de reologie van geconcentreerde dispersies en

vond plaats in de vakgroep colleidchemie van prof. H.N. Stein. In 1989

slaagde hij cum laude voor het ingenieursexamen. Aansluitend begon hij

in de vakgroep colleidchemie aan een promotieonderzoek naar de

stabiliteit van schuim in . In oktober 1993 treedt hij in

dienst bij Procter&Gamble, te Strambeek-Bever (Belgiê) .

116

DANKllOORD

Op deze plaats wil ik eenieder bedanken die op kleine of grote

wijze heeft bijgedragen aan het tot stand komen van dit

proefschrift. Ik heb daarbij van velen hulp gehad op

wetenschappelijk en technisch vlak, of op andere wijze steun

ondervonden. Het is vrijwel onmogelijk iedereen persoonlijk te

noemen, maar een aantal van hen wil ik toch in het bijzonder

bedanken.

Ten eerste ben ik prof.dr. H.N. Stein zeer erkentelijk voor de

plezierige begeleiding en de vrijheid die hij gaf bij het

uitvoeren van het onderzoek.

Veel dank ben ik verschuldigd aan de leden van de vakgroep

colloidchemie en aan studenten die er practicum deden, voor de

plezierige samenwerking. Daarbij wil ik John Schellinx noemen

voor het werk dat hij tijdens zijn afstuderen heeft verricht, en

Wim Drost voor de bijdrage die hij tijdens zijn stage heeft

geleverd. Hierbij dank ik natuurlijk ook Jacques van der Donck,

Jan Vaessen en Gert Tuin voor de vriendschap en voor de

weerstand die ze boden tijdens het bridgen.

Tot slot gaat een bijzonder woord van dank uit naar mijn ouders

voor de geboden opvoeding en steun, die het ontstaan van dit

proefschrift mogelijk maakten.

117

Stellingen Behorende Bij Het Proefschrift

Foam Films Drawn From Dispersions

Van P.J.M. Baets

(1)

Bij de drainage van verticale mobiele bepalend voor de drainagesnelheid en

geen belangrijke rol.

Dit proefschrift, hoofdstukken 2,4,5

(2)

zeepfilms is de bulkviscositeit speelt de oppervlaktereologie

Het aanwezig kunnen zijn van ronde deeltjes in zeepfilms wordt bepaald door de deeltjesdiameter, de filmdikte en de contacthoek.

Dit proefschrift, hoofdstuk 2

(3)

Glasdeeltjes kunnen zowel stabiliserend als destabiliserend werken op

schuim.

Hudales, J.B.M and Stein, H.N., J.Colloid Interface Sci., 140-2, 307-313 {1990)

(4)

De door Kale et al. gerapporteerde oplosbaarheden van CTAB en de verklaringen voor de gevonden lage hellingen in de E(mV)-log(c) curve zijn ongeloofwaardig.

Kale, K.M., CUssler, E.L. and Evans, D.F., J.Sol.Chem., 11-8, 581-592 (1982)

(5)

Bij het construeren van een adsorptie-isotherm uit adsorptiemetingen van ionogene surfactants aan vaste stoffen dient rekening te worden gehouden met de mogelijkheid dat er ionen worden afgegeven door de vaste stoffen.

(6)

De conclusies van Hühnerfuss omtrent de oppervlakte shear viscositeit

van surfactant oplossingen zijn onvoldoende gefundeerd.

Hühnerfuss, H., J.Colloid Interface Sci., 126-1, 384 385 (1988)

(7)

Blokkeringaverschijnselen bij afschuifstroming van geconcentreerde

suspensies van monodisperse deeltjes kunnen worden verklaard door

orde/wanorde overgangen.

Schreuder, F.W.A.M., van Diemen, A.J.G. and Stein, H.N., J.Colloid

Interface Sci., 111, 35 (1986)

(8)

De experimentele overeenkomst met de theorie over filmdrainage van

Ruckenstein en Sharma bewijst niet de juistheid ervan, omdat

experimentele gegevens in die theorie zijn verwerkt.

Ruckenstein, E. and Sharma, A., J.Colloid Interface Sci., 119-1, 1-13

(1987)

(9)

Euwe heeft bij het uitspreken van zijn verwachting betreffende de

ontwikkeling van de speelsterkte van schaakprogramma's (10 juni 1980)

in onvoldoende mate rekening gehouden met het feit dat een

schaakprogramma mogelijk beter speelt dan de programmeur.

H.J. van den Herik, Computerschaak, schaakwereld en kunstmatige

intelligentie, Academie Service (1983), p.419

(10)

Waarschuwingen voor de volksgezondheid op verpakkingen van

rookartikelen suggereren ten onrechte dat producten die geen

waarschuwing dragen onschadelijk zijn.