Effect of Surfactants and Hydrodynamic Factors on the Drop
Transcript of Effect of Surfactants and Hydrodynamic Factors on the Drop
Effect of Surfactants andHydrodynamic Factors on
the Drop-Size Distribution inMembrane Emulsification
Peter A. Kralchevsky, K. D. Danov, N. C. Christov, D. N. Ganchev
Laboratory of Chemical Physics & Engineering
Faculty of Chemistry, University of Sofia, BULGARIA
Scheme of a typical membrane emulsification modulus �
dispersedliquid
continuousliquid
flow
pressure
membrane
Tubular membrane of porous glass (Shirazu, Miyazaki, Japan)
Observation of the forming drops at the outer membrane surface
Surface of membrane with 2 µm pore size
Produced monodisperse emulsion (pore diameter 3.2 �m) �
Oil-in Water Emulsions Obtained by Hydrophilic Membranes
Typically ddrop/dpore � 3
ddrop/dpore is independent of theinterfacial tension
ddrop/dpore is independent of thepore size
�
Droplet diameter, �m0 10 20 30
Num
ber o
f dro
plet
s
0
20
40
60
80
100
120
2 wt % Tween 20oil: hexadecanedpore = 3.2 �m
5 mM AOT at various NaCl concentrationshexadecane drops; pore diameter = 1 �m
Interfacial tension oil-water, � (mN/m)0 1 2 3 4 5
Mea
n dr
op d
iam
eter
, ddr
op (�
m)
0
2
4
6
8
105 mM AOT + 20 mM NaCl;� = 0.44 mN/m
Mean pore diameter, dpore (�m)0 1 2 3 4
Mea
n dr
op d
iam
eter
, ddr
op (�
m)
0
2
4
6
8
10
ddrop/dpore � 3
Basic Question:
Why ddrop/dpore � 3 ?
(irrespective of pore size, interfacial tension andviscosity of the liquid phases?)
Theoretical Analysis:
Condition for Detachment of aGrowing Drop from a Pore
KEY:Analogy: detachment of a pendantdrop� Steady state growth: Ftot = 0;� At a given size the drop profile
becomes unstable;� The critical value of the body
(gravitational) force is:
Fcr = � ddrop �(x); x = ddrop/dpore
�(x) � known universal function
�
�(x) � (Vmax)2/3; Vmax – dimensionless maximum drop volume [2]
In the case of membrane emulsification the deformation of dropprofile is due to the hydrodynamic force (rather than to gravity)
At the moment of detachment:
{hydrodynamic force} = {critical body force}
� fd � Rdrop vav(�P) = � ddrop �(x)
fd – hydrodynamic drag coefficient;
� – viscosity of the drop (oil) phase;
vav(�P) = ���
����
���
d
2pore 2
8 RP
LR �
� – average velocity of oil supply
�P – pressure difference between the oil and water phases.
0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Vertical velocity component (domains A and B)
x1 - coordinate
x 2 - c
oord
inat
e
membrane pore
O r
z
x = const 1
x = const 2
x = � 2
x = 0 2 x = � 2
c
x =
1
1x =
0
1x
= 0
1
x = -1 2
Determination of the hydrodynamic drag coefficient fd
� The Navier-Stokes equation isintegrated numerically
�c
� The fields of velocity andpressure are computed for theinterior and exterior of an oildrop growing at the orifice of amembrane pore
Contour plot of the vertical velocity component for �c = 160�.
�c – central angle of a spherical drop
Distribution of the velocity field in the drop at different values ofthe ratio Rd/Rpore: а) 1.1 and b) 1.3. (No vortices!)
�P = 0.02 kgf/cm2; 0.25 M SDS + 12 mM NaCl, Pore diameter 10.4 �m; Oil: hexadecane
(a) Drop diameter, �m10 20 30 40 50 60
Num
ber o
f dro
ps
0
50
100
150
200
250
�P = 0.05 kgf/cm2; 0.25 M SDS + 12 mM NaCl,Pore diameter 10.4 �m; Oil: hexadecane
(b) Drop diameter, �m
0 10 20 30 40 50 60
Num
ber o
f dro
ps
0
20
40
60
80
100
120
Point C:
�P = �Pcr
�P � �Pcr �P > �Pcr
� For �P < �Pcr emulsion drops are not released from the membrane.
� For �P > �Pcr drops with two different sizes, corresponding to thepoints A1 and A2, � two-peak drop-size distribution;
� For �P = �Pcr (point C) monodisperse drops are produced withddrop/dpore � 3.
This explains why if monodisperse drops are produced by means of amicroporous membrane, one has ddrop/dpore � 3, irrespective of the type ofthe oily and aqueous phases, of the interfacial tension, bulk viscosities,surfactant adsorption kinetics, etc.
ddrop/dpore
1 2 3 4 5 6 7 8 9 10
�P
/ �P c
r
0
1
2
3
4
5
6
7
8
9
10
A1 A2
C
Role of the Membrane Wettability
cos� = (�so � �sw)/�ow
(a) Small dynamic contact angle �: the contact line solid-water-oil isfixed at the pore diameter: � ddrop/dpore � 3.
(b) Larger angle � facilitates contact-line expansion; the latter may spantwo or more pores: ddrop/dpore > 3 (exclusions from the rule) [3].
0.02 wt. % Tween 20
1 10 100
Num
ber o
f dro
plet
s in
cla
ss
0
10
20
30
40
50
0.2 wt. % Tween 20
1 10 100
Num
ber o
f dro
plet
s in
cla
ss
0
10
20
30
40
50
2 wt. % Tween 20
Droplet diameter, �m
1 10 100
Num
ber o
f dro
plet
s in
cla
ss
0
20
40
60
80
100
120Gaussian fit
Exclusions from the Rule ddrop/dpore � 3
{Lowering of surfactant concentration} � {Slowdown of adsorption}
� {Worsening of the membrane wetting by water}
100 m�
100 m�
Emulsification in Protein Solutions
Beta Lactoglobulin (BLG) and Na-Caseinate [3]
Regimeofadsorption:
BLG:diffusional
Na-Caseinate:barrier [4]
{Lower interfacial tension �ow} � {smaller angle �}
1 �m pore diameter
Droplet diameter, �m
1 10 100
Num
ber o
f dro
plet
s
0
20
40
60
80
100
120
140Na CaseinateBLGdm = 5.8 �m
dm = 33 �m
Square root of time, t1/2 (s1/2)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Inte
rfac
ial t
ensi
on (m
N/m
)
22
24
26
28
30
32Na-caseinate BLG Best fit
SUMMARY AND CONCLUSIONS
Condition for producing small and monodisperse drops:
1. The applied pressure difference should be slightly greaterthan the critical pressure: �P � �Pcr ;
2. The dynamic contact angle � should be as small as possiblecos� = (�so � �sw)/�ow ;
3. The surfactant should adsorb fast at the expanding oil-waterinterface.
References
[1] T. Nakashima, M. Shimizu, M. Kukizaki (Eds.) “Membraneemulsification operational manual,” 1st Edition, Dept. of Chemistry,Industrial Research Institute of Miyazaki Prefecture, Miyazaki, 1991.
[2] Pu, B., Chen, D. “A study of the measurement of surface and interfacialtension by the maximum liquid drop volume method. I. Using a back-suction syringe technique,” J. Colloid Interface Sci. 235 (2001) 265.
[3] N. C. Christov, D. N. Ganchev, N. D. Vassileva, N. D. Denkov, K. D.Danov, and P. A. Kralchevsky, “Capillary Mechanisms in MembraneEmulsification: Oil-in-Water Emulsions Stabilized by Tween 20 and MilkProteins”, Colloids and Surfaces A (2002) � in press.
[4] K. D. Danov, D. S. Valkovska, and P. A. Kralchevsky, “AdsorptionRelaxation for Nonionic Surfactants under Mixed Barrier-Diffusion andMicellization-Diffusion Control”, J. Colloid Interface Sci. 251 (2002)18–25.