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.