Emulsions, Microemulsions and Foams (Part V) -...

NPTEL Chemical Engineering Interfacial Engineering Module 6: Lecture 5

Joint Initiative of IITs and IISc Funded by MHRD 1/20

Emulsions, Microemulsions and Foams

(Part V)

Dr. Pallab Ghosh

Associate Professor

Department of Chemical Engineering

IIT Guwahati, Guwahati–781039

India



Table of Contents

Section/Subsection Page No. 6.5.1 Rheology of microemulsions 3

6.5.2 Applications of microemulsions 5

6.5.3 Foams 5–18

6.5.3.1 Preparation of foams 8

6.5.3.2 Measurement of foam stability 10

6.5.3.3 Structure of foams 12

6.5.3.4 Foam drainage 15

6.5.3.5 Application of foams 17

Exercise 19

Suggested reading 20



6.5.1 Rheology of microemulsions

The rheological properties, particularly the viscosity, characterize a

microemulsion system. Viscosity is the practically relevant quantity for various

applications of microemulsions, e.g., pumping the materials and their use as

hydraulic fluids. Apart from experimental data (many of which are related to

tertiary oil recovery), there are theoretical models for microemulsion viscosity as

function of phase composition.

The viscosity of a microemulsion system largely depends on its structure, i.e., the

size and shape of the droplets, their concentration and interaction among the

droplets. One can obtain information on these parameters by rheological

measurements.

Einstein’s equation of viscosity for the dispersion of small rigid spheres was

presented in Lecture 5 of Module 1. This equation has been modified by Taylor

(1932) for a dispersion of spherical droplets in another liquid.

2.51 s d

rs d

(6.5.1)

where r is the relative viscosity (i.e., the ratio of the viscosity of the

microemulsion system and viscosity of the pure solvent), s is the viscosity of

the solvent, d is the viscosity of the dispersed phase and is the volume

fraction of the dispersed material.

Equation (6.5.1) reduces to Einstein’s equation for the hard spheres for which

d .

Thomas (1965) proposed the following equation for relative viscosity at high

volume fractions.

21 21 2.5 10.05 expr C C (6.5.2)

where 1C and 2C are adjustable constants, which can vary from one system to

another. This equation has been found to describe well the viscosity of spherical

objects such as glass beads, polystyrene lattices and oil-in-water microemulsions.

For small spheres, Thomas (1965) found that 31 2.73 10C and 2 16.6C .



Equations (6.5.1) and (6.5.2) were developed assuming the droplets to be

spherical. Many microemulsions indeed have spherical droplets. However,

microemulsions may contain prolate, oblate and rod-like structures. The viscosity

of a dispersion of rigid rods can be calculated from the equation given by Doi and

Edwards (1978).

Example 6.5.1: For the microemulsion system, tetradecyldimethylamine oxide

(TDMAO)decanewater, the variation of relative viscosity with volume fraction (of

surfactant plus decane) at 298 K is given below.

r r

0.029 1.11 0.142 1.82

0.057 1.24 0.213 2.9

0.086 1.38 0.283 5.74

0.114 1.57 0.354 15.05

Fit Eq. (6.5.2) to these data and determine the constants. Present your results graphically.

Solution: The best-fit curve is shown in Fig. 6.5.1.

Fig. 6.5.1 Variation of relative viscosity with .

The constants, 1C and 2C , of Eq. (6.5.2) were determined by regression analysis. Their

values are: 21 1.8 10C and 2 18.3C .



Microemulsions usually show Newtonian behavior, i.e., the observed shear rate is

proportional to the applied shear stress (Attwood et al., 1974; Kumar and Mittal,

1999). However, in concentrated systems, and especially when the microemulsion

contains elongated structures that interact strongly, non-Newtonian behavior can

be observed.

6.5.2 Applications of microemulsions

Microemulsions have been extensively studied as a part of academic research as

model systems for surfactant aggregation structures, and for industrial and semi-

industrial uses.

Microemulsions have found extensive use in enhanced oil recovery,

pharmaceuticals, cosmetics, foods and textile industries.

Several important reactions have been carried out in microemulsions such as the

synthesis of nanoparticles (which will be discussed in Module 9), polymerization

and enzymatic reactions.

Microemulsion-based washing and cleaning is a well known technique.

Microemulsions have good prospects for soil remediation.

Microemulsion structures can be effectively used in materials science for the

preparation of catalysts and semiconductors, and advanced mesoporous inorganic

materials.

6.5.3 Foams

Foam is a dispersion of gas bubbles in liquid in which at least one dimension falls

within the colloidal size range. A foam typically contains either very small

bubbles or, more commonly, quite large gas bubbles separated by thin liquid

films, as shown in Fig. 6.5.2.



(a) (b)

Fig. 6.5.2 (a) microfoam, and (b) foam in tea.

The thin films are known as lamellae or laminae. The concentrated foams in

which the liquid films are thinner than the bubble sizes, and the gas bubbles are

polyhedral, are known as polyederschaum. Low-concentration foams in which the

liquid films have thicknesses on the same scale or larger than the bubble sizes and

the bubbles are approximately spherical, are known as kugelschaum or gas

emulsions.

The three-dimensional foam bubbles are spherical in wet foams (i.e., those with

gas volume fraction, g , up to 0.74, which is the maximum volume fraction

possible for an internal phase made up of uniform incompressible spheres). The

foam bubbles have distorted shape in drier foams ( 0.74 0.83g ). In still drier

foams, the foam cells take on a variety of polyhedral shapes (i.e., 0.83g ).

Foams not only contain gas, liquid and surfactant, but can contain dispersed oil

droplets and nano-sized solid particles as well.

An agent (e.g., a surfactant) that stabilizes a foam is known as foaming agent. The

foaming agent can make it easier to form a foam or provide stability against

coalescence of the bubbles. Sometimes it is also termed as foam booster,

whipping agent and aerating agent. A substance that acts to prevent formation of

foam is known as antifoam agent. It is also known as antifoamer or foam

inhibitor.

Defoamers or foam breakers are substances which cause collapse of foams, e.g.,

poly(dimethylsiloxane), (CH3)3SiO[(CH3)2SiO]iR (where R represents any of a

number of organic functional groups).



Various mechanisms have been proposed regarding the effect of defoamers on the

stability of foams. The most widely accepted mechanism of foam destabilization

in the presence of oil is that the oil drops enter and spread at the airwater

interface of the foam films, thereby rupturing the film.

Two coefficients, entering and spreading, have been derived from the change of

free energy when the oil drop enters the airwater interface or spreads at the

interface. If the entering coefficient is positive, the oil drop enters the airwater

interface. If the spreading coefficient is positive, the oil drop spreads as a duplex

film on each side of the original film and forms a weak spot on the film that leads

to rupture.

Another theory proposes that the stability of the film formed between the

airwater interface and an approaching oil drop (termed as pseudoemulsion film)

is the governing factor behind the foam stability.

Let us consider a foam having polyhedral shape as shown in Fig. 6.5.3.

Fig. 6.5.3 Common foam made from soap solution.

The structure is not always a regular polyhedron. In fact, most foams contain a

distribution of shapes and sizes. If we assume that the surface tension is the same

at every lamellar surface, the geometric laws that govern the assemblage of foam

cells, are as follows.

(i) Three, and only three, liquid surfaces meet along an edge. The three

surfaces are equally inclined to one another all along the edge at 2 3 rad.

The surfaces need not be planar. If curved, the 2 3 rad angle is formed by

the tangents to the surfaces at any point on the line of contact. This angle is



known as Steiner angle. The border where the lamellae meet is termed

Plateau border (named after J. Plateau, who did pioneering research on the

equilibrium between three lamellae nearly 150 years ago) (see Fig. 6.5.4).

It plays a very important role in film drainage.

Fig. 6.5.4 Structure of foam lamella.

(ii) In three dimensions, four, and only four, of those edges meet at a point. The

angles at which the four edges meet are equally inclined to one another in

space. Hence, they meet mutually at the tetrahedral angle, 1.9 rad.

These two conditions are known as Plateau’s conditions. These conditions are

not independent, because one follows as a corollary of the other [see the article

by Almgren and Taylor (1976)].

Observations of foams under dynamic conditions have shown that whenever

many films happen to come together, a rearrangement takes place immediately

to restore junctions of only three films at the Plateau borders.

6.5.3.1 Preparation of foams

The easiest way to prepare foam in the laboratory is to mix a gas and a liquid

together in a container and then shake. A foam can be formed in a liquid if

bubbles of gas are injected faster than the rate at which liquid between the

bubbles can drain away. Although the bubbles coalesce as soon as the liquid

between them has drained away, a temporary dispersion can form. An example is

the foam formed when bubbles are vigorously blown into a viscous oil. It should

be remembered that like the emulsions, foams are not thermodynamically stable:

eventually they all collapse. However, in carefully controlled environments, it has



been possible to make surfactant-stabilized static bubbles with lifetimes of

months and years!

The general methods for generation of foam are as follows [see Schramm

(2005)].

(i) bubbling gas into a liquid or solution

(ii) causing a stream of liquid to fall onto a pool of liquid or solution engulfing

air bubbles

(iii) suddenly reducing the pressure on a solution of dissolved gas, causing rapid

nucleation and growth of gas bubbles within the solution

(iv) turbulent mixing with a stirrer such that air is whipped into a liquid

(v) co-injecting liquid and gas into a mechanical foam generator which uses

pressure drop, turbulence and/or tortuous flow methods to cause bubble

pinch-off and sub-division.

Most foams are prepared with the aid of a foaming agent. The foaming agent may

comprise one or more of surfactants, macromolecules and finely divided solids. It

is needed to reduce the surface tension and thereby facilitate formation of a large

amount of interfacial area with the minimal requirement of mechanical energy to

create it. The surfactant provides a protective film at the surface of the bubbles

which prevents their coalescence. Stability against coalescence can be further

enhanced by the inclusion of agents that increase the viscosity and retard

evaporation, e.g., addition of glycerine to a foaming solution makes the foam

more stable. Several scientists have suggested that high surface viscosity

stabilizes foams.

Micro-foams (also known as colloidal gas aphrons) can be prepared by

dispersing gas into a surfactant solution under high shear. Under the appropriate

conditions of turbulent wave break-up, it is possible to create a dispersion of very

small gas bubbles, each surrounded by a film of surfactant molecules. Under

ambient conditions, the bubble diameters are typically in the range of 50 to 300

m. Sebba (1971) has presented a simple method for preparing micro-foams in

the laboratory by entrainment of gas bubbles in a dilute surfactant solution.



The gas volume fraction in a foam is expressed by foam quality. In three-phase

systems, when the foam contains solid particles as well, the term slurry quality is

used to give the volume fraction of gas and solid, i.e., g s g s lV V V V V ,

where gV , sV and lV denote the volumes of gas, solid and liquid phases,

respectively.

6.5.3.2 Measurement of foam stability

The stability of foam is usually tested by the following methods.

(i) the lifetime (i.e., coalescence time) of single bubbles

(ii) the steady-state foam volume under given conditions of gas flow, shaking

or shearing

(iii) the rate of collapse of a static column of foam (known as the RossMiles

test)

In the first method, a bubble is allowed to coalesce on a flat air–water interface

(i.e., bubble–interface coalescence). Also, two bubbles can be kept in contact

until they coalesce (i.e., binary coalescence). Detailed experimental and

theoretical studies have been made on these methods [see Chaudhari and

Hofmann (1994)]. This method is similar to the study of coalescence of drops

discussed in the Lectures 2 and 3 of this module. Similar to that observed for the

drops, stochastic distributions of coalescence time are always observed in these

experiments. The stability of the bubbles in different foam systems can be

compared by the mean values of the distributions.

In the second method, foam is generated by flowing gas through a porous orifice

into a test solution. The steady state foam volume maintained under constant gas

flow rate into the column is then measured. This technique is frequently used to

assess the stability of evanescent foams.

In the static foam test proposed by Ross and Miles (as described in ASTM

D1173-07), foam is generated by filling a pipette with a given volume of a

foaming solution. Then the solution is allowed to fall a specified distance into a



separate volume of the same solution that is contained in a receiver vessel. The

details of the ‘foam pipet’ and the ‘foam receiver’ are shown in Fig. 6.5.5.

(a) (b)

Fig. 6.5.5 The static foam test apparatus (ASTM D1173-07): (a) foam pipet, and (b) foam receiver.

Foam is produced as the solution from the pipette falls on the solution in the

receiver. The volume of foam that is produced immediately upon draining of the

pipette is termed initial foam volume. This volume is measured. The decay in

foam volume after some time is also measured. From these data, the rate of

collapse of the foam column can be calculated.

The rate of drainage of foam is often expressed in terms of foam number. A foam

is formed in a vessel and thereafter the remaining foam volume is measured as a

function of time. The foam number is the volume of bulk liquid that has separated

after a specified interval, expressed as a percentage of the original volume of

liquid foamed.



6.5.3.3 Structure of foams

Lord Kelvin showed (circa 1887) that tetrakaidecahedron is the ideal cell in a dry,

polyhedral and monodisperse foam. This polyhedron has eight doubly-curved

hexagonal faces and six quadrilateral faces with bowed edges.

The curved surfaces are a requirement of the minimization of surface energy.

This structure also satisfies the Plateau’s conditions given in Section 6.5.3.

Kelvin’s minimal tetrakaidecahedron is actually a slightly distorted plane-faced

isotropic or orthic tetrakaidecahedron, which is obtained by truncating the six

corners of a regular octahedron each to such a depth as to reduce its eight original

(equilateral triangular) faces to equilateral equiangular hexagons.

The orthic tetrakaidecahedron itself is an unsatisfactory foam cell because it does

not satisfy Plateau’s conditions. In the minimal tetrakaidecahedron, the corners of

the orthic polyhedron are maintained. The quadrilateral faces remain planar but

acquire bowed-out noncircular edges, each having a total turning angle of ~ 9

rad. The corners of each nonplanar, wavy hexagon are still in one plane, while the

hexagon contains three straight lines, i.e., its three long diagonals.

However, the statistical distribution of polygon faces on packed soap bubbles

differs markedly from Kelvin’s tetrakaidecahedron, and the bubbles show a

predominance of the pentagonal faces. Interestingly, studies of metal crystallites

and vegetable cells also show similar distributions. It may be due to the small

deviations from monodispersity or the disturbing effect of the container walls.

The stringent requirements for the occurrence of the minimal tetrakaidecahedron

structure are: every part of the boundary of the group must be either infinitely

distant from the place considered, or be so adjusted as not to interfere with the

homogeneousness of the interior distribution of cells.

Princen and Levinson (1987) suggested a possible reason why the Kelvin’s

tetrakaidecahedron, in spite of satisfying the mathematically-correct conditions of

space-filling and minimum partitional area, fails to match the structure of foams.

According to them, upon drainage of the continuous phase from between the

initially spherical bubbles in face-centered cubic packing, the system may get

trapped in an intermediate, less ordered structure that, although at a local surface



area minimum, may be energetically separated from the Kelvin’s structure by a

high barrier. Evidence for this may be found in the great difficulty one encounters

in trying to build a 15-bubble cluster that has a Kelvin’s tetrakaidecahedron at its

center.

Williams (1968) has pointed out that topological transformations of vertices and

sides permit a number of other space-filling polyhedra to be derived from

Kelvin’s tetrakaidecahedron. Such derived polyhedra have fewer elements of

symmetry than their parent polyhedron, but one of them can be singled out that

closely matches the naturally occurring distributions of faces. This

tetrakaidecahedron is designated as -tetrakaidecahedron, shown in Fig. 6.5.6.

Fig. 6.5.6 The transition from Kelvin’s tetrakaidecahedron (called -tetrakaidecahedron) (a), to -tetrakaidecahedron (c), through a polyhedron (b),

with four quadrilateral, four pentagonal and six hexagonal faces (Williams, 1968) (reproduced by permission from The American Association for the Advancement

of Science, 1968).

It can be mechanically derived from the Kelvin’s -tetrakaidecahedron by taking

any edge common to two hexagons plus the edges that meet at each end of this

edge [Figure (a)], rotating them 2 rad and reconnecting them. The resultant

polyhedron [Figure (b)] with four quadrilateral, four pentagonal and six

hexagonal faces will also pack to fill space. The same operation is then performed

with the same group of edges on the opposite side of the polyhedron.

The -tetrakaidecahedron retains the same average number of sides per face

(5.143), faces (14), vertices (24) and edges (36) as the Kelvin’s

tetrakaidecahedron. However, it has two quadrilateral, eight pentagonal and four

hexagonal faces, which reproduces the predominance of the pentagonal faces that



is observed in all polyhedral aggregates, which is so lacking in Kelvin’s

tetrakaidecahedron.

Williams’ -tetrakaidecahedra pack together as a body-centered tetragonal lattice.

It is not isometric, therefore, if it were metastably composed of soap films, would

rearrange spontaneously to an assembly of Kelvin’s polyhedra. This would occur

because the -tetrakaidecahedron has a smaller isoperimetric quotient than

Kelvin’s.

The relative surface area and isoperimetric coefficient for several polyhedra are

shown in Table 6.5.1. The relative surface area is defined as 0A A , where A is

the surface area of the polyhedron and 0A is the surface area of the sphere having

the same volume as the polyhedron. The isoperimetric coefficient is defined as,

2 336 V A , where V is the volume of the polyhedron.

Table 6.5.1 Relative surface area and isoperimetric coefficient for various bodies

Body 0A A

Sphere 1.0000 1.0000

Icosahedron 1.0646 0.8288

Kelvin’s tetrakaidecahedron 1.0970 0.7575

Orthic tetrakaidecahedron 1.0990 0.7534

Rhombic dodecahedron 1.1053 0.7405

Pentagonal dodecahedron 1.0984 0.7547

Octahedron 1.1826 0.6046

Cube 1.2407 0.5236

Tetrahedron 1.4900 0.3023

These two quantities are related by the following equation.

1 3

0

1A

A

(6.5.3)



Williams (1968) reported that the value of 0A A would be 4% higher than that of

-tetrakaidecahedron to enclose the same volume. This feature makes it

impossible to produce with soap films a cluster of 15 equal-sized bubbles having

an enclosed -tetrakaidecahedron. Hence, Williams’ minimal -

tetrakaidecahedron, with its good agreement with the distribution of faces found

in foams and other natural packings, and its agreement with the space-filling

requirement, does not meet the condition of minimum surface area that the

surface tension imposes. Therefore, from the discussion presented in this section,

it appears that no single polyhedral cell can be abstracted from foam that meets

all the requirements.

Note that many scientists have used foam structures different from

tetrakaidecahedron in various models (e.g., drainage of foams). Many of them

have used the pentagonal dodecahedral shape of the bubbles: a symmetric cluster

of thirteen equal bubbles contains a minimal pentagonal dodecahedron at its

center (which is known as the Dewar cluster). This structure, however, does not

fill space without voids.

6.5.3.4 Foam drainage

Because the gas bubbles are polyhedral in shape, the liquid in foam can be

divided into films and Plateau borders. At the Plateau borders, the gasliquid

interface is quite curved. This generates a low pressure region in the Plateau area,

as predicted by the YoungLaplace equation (see Section 2.3.2).

Since the interface is flat along the thin film region, a higher pressure exists there.

This pressure difference forces liquid to flow towards the Plateau borders,

causing thinning of the films, and motion in the foam. This is schematically

shown in Fig. 6.5.7.



Fig. 6.5.7 Pressure difference across the curved surfaces in foam lamellae, and flow of liquid towards the Plateau borders.

Haas and Johnson (1967) assigned separate roles to films and Plateau borders

during the drainage process. They showed that flow through the films due to

gravity was negligible. Instead, the films drain into the adjacent Plateau borders

due to the curvature effect. The Plateau borders, in turn, form a network, through

which the liquid flows due to gravity. This mechanism of foam drainage has been

accepted by many scientists, however, the details and complexity vary.

Different shapes of the Plateau border have been assumed: Haas and Johnson

(1967) assumed the Plateau border to be circular whereas, Desai and Kumar

(1982) assumed it to be triangular.

Various assumptions have been made on the rigidity of the walls of the Plateau

border. Haas and Johnson (1967), and Hartland and Barber (1974) assumed them

to be rigid. On the other hand, Desai and Kumar (1982) have treated them as

partially mobile, and the mobility depends upon the surface viscosity. They

divided the Plateau border into two categories: the nearly-horizontal and the

nearly-vertical Plateau borders. Different roles were assigned to these two types.

It was assumed that the films drained into all the Plateau borders equally.

The horizontal Plateau borders receive the liquid from the films and drain it into

the vertical Plateau borders. The vertical Plateau borders receive liquid from the

films, from the horizontal Plateau borders as well as the vertical Plateau borders

above, and discharge it into the vertical Plateau borders below them.

Gururaj et al. (1995) assumed the -tetrakaidecahedron structure of the foam cells

and developed a network model of static foam drainage.



The role of surface elasticity on foam stability has been studied in several works

(Malysa et al., 1981; Huang et al., 1986). To quantify foam stability, Malysa et

al. (1981) used a parameter termed retention time, which was defined as the slope

of the linear part of the plot of gas flow rate versus the gas volume contained in

the system. It characterizes the frothability of the flotation frothers.

They found that the retention time varied almost linearly with the Marangoni

elasticity (see Section 5.2.2). Fig. 6.5.8 depicts their results for n-octanol and n-

octanoic acid solutions.

Fig. 6.5.8 Variation of retention time with Marangoni dilatational elasticity (Malysa et al., 1981) (adapted by permission from Elsevier Ltd., © 1981).

Most of the works on foam drainage have not included the effects of surface

forces on the drainage process. As noted by Narsimhan and Ruckenstein (1986),

the disjoining pressures arising due to these forces can strongly influence the

process of film thinning when the thickness of the film reduces below 100 nm.

The critical thickness of rupture is dependent on these forces (see Lecture 3 of

Module 5). Therefore, the models for foam drainage need to couple the

hydrodynamics of the foam bed with the instability of the thin liquid films to

predict the conditions for foam collapse.

6.5.3.5 Applications of foams

Foams are very commonplace in materials such as foods, shaving creams, fire-

fighting materials and detergents. Foams, as froths, are intimately involved in

many mineral separation processes.



Foams are widely used at many stages of petroleum recovery and processing such

as, oil-well drilling, reservoir injection and process-plant foams. In enhanced oil

recovery (EOR), a gas is injected in the form of a foam. Suitable foams can be

formulated with air, nitrogen, natural gas, carbon dioxide or steam. In a thermal

process, when a steam foam contacts residual crude oil, it tends to condense and

create water-in-oil emulsions. In a non-thermal process, the foam may emulsify

the oil and form an oil-in-water emulsion. This emulsion is then drawn up into the

foam structure.

Micro-foams have some interesting potential applications in soil remediation and

reservoir oil recovery.



Exercise

Exercise 6.5.1: Calculate the values of 0A A and isoperimetric coefficient for a cube.

Exercise 6.5.2: Show that, for a sphere, the isoperimetric coefficient is unity.

Exercise 6.5.3: Answer the following questions clearly.

1) What are Plateau’s conditions? Explain the significance of Plateau border. What

is Steiner angle?

2) Discuss three methods of preparation of foams.

3) Discuss the methods used for determining the stability of foams.

4) Explain the structure of foams. How can you obtain the -tetrakaidecahedron

structure from Kelvin’s minimal tetrakaidecahedron?

5) Explain why the Kelvin’s tetrakaidecahedron structure is rarely observed in

foams.

6) What is isoperimetric coefficient? What are its values for sphere and Kelvin’s

tetrakaidecahedron?

7) Explain the models of foam drainage. What is the role of Plateau borders in foam

drainage?

8) What is retention time? How is it related to the surface dilatational elasticity?



Suggested reading

Textbooks

P. Ghosh, Colloid and Interface Science, PHI Learning, New Delhi, 2009,

Chapter 9.

Reference books

L. E. Schramm, Emulsions, Foams, and Suspensions, Wiley-VCH, Weinheim,

2005, Chapter 2.

P. Kumar and K. L. Mittal (Editors), Handbook of Microemulsion Science and

Technology, Marcel Dekker, New York, 1999, Chapter 11.

Journal articles

D. Attwood, L. R. J. Currie, and P. H. Elworthy, J. Colloid Interface Sci., 46, 261

(1974).

D. D. W. Huang, A. Nikolov, and D. T. Wasan, Langmuir, 2, 672 (1986).

D. Desai and R. Kumar, Chem. Eng. Sci., 37, 1361 (1982).

D. G. Thomas, J. Colloid Sci., 20, 267 (1965).

F. J. Almgren (Jr.) and J. E. Taylor, Sci. Am., 235, 82 (1976).

F. Sebba, J. Colloid Interface Sci., 35, 643 (1971).

G. I. Taylor, Proc. R. Soc. London, Ser. A, 138, 41 (1932).

G. Narsimhan and E. Ruckenstein, Langmuir, 2, 230 (1986).

H. M. Princen and P. Levinson, J. Colloid Interface Sci., 120, 172 (1987).

K. Malysa, K. Lunkenheimer, R. Miller, and C. Hartenstein, Colloids Surf., 3,

329 (1981).

M. Doi and S. F. Edwards, J. Chem. Soc., Faraday Trans. II, 74, 918 (1978).

M. Gururaj, R. Kumar, and K. S. Gandhi, Langmuir, 11, 1381 (1995).

P. A. Haas and H. F. Johnson, Ind. Eng. Chem. Fundam., 6, 225 (1967).

R. E. Williams, Science, 161, 276 (1968).

R. V. Chaudhari and H. Hofmann, Rev. Chem. Eng., 10, 131 (1994).

S. Hartland and A. D. Barber, Trans. Inst. Chem. Engrs., 52, 43 (1974).

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