Lecture 5

NPTEL Chemical Engineering Interfacial Engineering Module 1: Lecture 5

Joint Initiative of IITs and IISc Funded by MHRD 1/21

Colloidal Materials: Part IV

Dr. Pallab Ghosh

Associate Professor

Department of Chemical Engineering

IIT Guwahati, Guwahati–781039

India



Table of Contents

Section/Subsection Page No. 1.5.1 Hofmeister series 3

1.5.2 Electroviscous effect 3

1.5.3 Gelation 4

1.5.4 Imbibition 5

1.5.5 Syneresis 5

1.5.6 Gold number 6

1.5.7 Rheological properties of colloidal dispersions 8–16

1.5.7.1 Einstein’s equation of viscosity 11

1.5.7.2 Mark–Houwink equation for colloidal polymers 13

1.5.7.3 Deborah number 14

1.5.7.4 Peclet number 15

1.5.8 Surfactants 16–18

1.5.8.1 Properties of surfactants 17

1.5.8.2 Adsorption and micellization 18

Exercise 19

Suggested reading 21



1.5.1 Hofmeister series

Small amounts of electrolytes diminish the -potentials of lyophilic sols, but

coagulation does not take place. If a large amount of electrolyte is added to a

lyophilic system, the dispersed substance precipitates. This is known as salt-out,

which is different from the coagulation observed with the lyophobic colloids.

It is believed that the stability of the lyophilic systems depends upon their charge

and hydration. Large amounts of electrolytes dehydrate the particles in addition to

reducing their -potentials. It is generally accepted that salting-out depends on

the nature of the ions. Based on experimental observations, a series has been

created for anions and cations reflecting their ability to salt out. This series is

known as Hofmeister series.

Cations: Mg++ > Ca++ > Sr++ > Ba++ > Li+ > Na+ > K+ > Rb+ > Cs+

Anions: Citrate= > Tartrate= > SO4= > Acetate > Cl > NO3

> ClO3 > I > CNS

Salt-out of a hydrophilic sol frequently produces a liquid aggregate in place of a

solid. This sometimes appears in the form of viscous drops. This phenomenon is

known as coacervation and the droplets are known as coacervates.

The coacervates are formed most readily when two hydrophilic sols carrying

opposite charges (e.g., gelatin at pH < 4.7 and gum acacia sol) are mixed in

suitable proportions. It is believed that the shells of tightly-bound water

molecules surrounding the particles prevent them from coagulation. On the other

hand, the electrostatic attraction holds a number of particles together.

Redispersion of coacervates can be achieved by the addition of iodide or

thiocyanate ions which favor hydration of the particles. Otherwise, ions of high

valence can be added, which would diminish the -potential of either sol.

1.5.2 Electroviscous effect

The lyophilic sols have significantly higher viscosity than the lyophobic sols.

This is due to the extensive solvation of the dispersed-phase particles, which

increases the resistance to flow. The viscosity of very dilute lyophilic sols (e.g.,

gamboge, mastic and protein) obeys the Einstein’s equation.



The addition of a small amount of an electrolyte to a lyophilic sol produces a

marked decrease in viscosity. For example, KCl at 2 mol/m3 concentration can

decrease the viscosity of an agar-agar sol by 20%. Experiments with salts

containing ions of different valence have shown that the influence increases with

the increasing valence of the counterion.

Therefore, it can be surmised that the decrease in viscosity is associated with the

electrostatic double layer surrounding the colloid particles. A small amount of

electrolyte cannot appreciably affect the solvation of the particles. Therefore, it is

evident that the -potential is an important factor in determining the viscosity of

the dispersion. The role of electrical charge of the particles on the viscosity of the

sol is known as electroviscous effect.

1.5.3 Gelation

The cooling of a not-too-dilute lyophilic sol (e.g., gelatin or agar-agar) results in

the formation of a gel. A gel can also be obtained by the addition of electrolytes

under suitable conditions to lyophobic sols which exhibit some lyophilic

character (e.g., silicic acid and ferric oxide). The gels do not differ fundamentally

in their structure and properties from gelatinous precipitates. The gelation process

is accompanied by a large increase in viscosity.

Two types of gels can be distinguished: elastic and rigid gels. Partial dehydration

of an elastic gel (e.g., gelatin) leads to the formation of an elastic solid. The

original sol can be generated readily by the addition of water (and subsequent

warming, if necessary). Rigid gels (e.g., silica gel) become glossy or powdery,

and lose their elasticity on drying. Furthermore, mere addition of water may not

regenerate the sol. The walls of the capillaries formed upon the dehydration of

elastic gels are supple, but they are stiff for the rigid gels. Dehydrated silica gel

has a honeycomb structure with fine capillaries, which renders it a valuable

adsorbing agent. The dehydration and rehydration of the partially dried gels is the

most important distinction between the elastic and nonelastic gels.



1.5.4 Imbibition

A gel imbibes a considerable amount of liquid when placed in a suitable liquid.

The volume of the liquid imbibed can be several times the volume of the original

gel. Imbibition is thus accompanied by a large increase of volume. For this

reason, this phenomenon is often called swelling. This can produce a large

amount of pressure. For example, if dry gelatin is placed in a tight porous vessel

and kept in water, swelling can break the vessel! However, the net volume

decreases in the imbibition process.

Sulfate, tartrate, citrate and acetate inhibit the swelling of gelatin and similar gels,

and their inhibiting effect decreases in the sequence mentioned. On the other

hand, chloride, chlorate, nitrate, bromide, iodide and thiocyanate favor the

imbibition of water, and the effect of chloride is the least. For iodide solutions,

the gel often disperses at the room temperature and forms the sol spontaneously.

Otherwise, the swollen gel is warmed to form the sol.

The Hofmeister series gives the order of temperature to which the gel must be

heated in presence of the anions to convert it to sol.

Imbibition of liquid by porous media has important applications in the cleaning

and deposition. Fig. 1.5.1 illustrates the imbibition of different liquids on a

porous micropatterened surface.

Fig. 1.5.1 Imbibition of liquids by polygonal spreading on surfaces (source: L. Courbin, E. Denieul, E. Dressaire, M. Roper, and A. Ajdari, Nature, 6, 661, 2007;

reproduced by permission of Macmillan Publishers, 2007).

1.5.5 Syneresis

Many gels exude small amounts of liquid on standing (e.g., concentrated silicic

acid gels and dilute gels of gelatin and agar-agar). This phenomenon was first



observed by Thomas Graham, and he called it syneresis. Examples of syneresis

are drainage of lymph from a contracting clot of blood, and collection of whey on

the surface of yoghurt. Syneresis in jam is shown in Fig. 1.5.2.

Syneresis is believed to be due to the exudation of water held by the capillary

forces between the heavily-hydrated particles constituting the framework of the

gel.

Fig. 1.5.2 Measurement of syneresis in jam.

1.5.6 Gold number

When a lyophilic sol is added to a lyophobic sol, the sensitivity of the latter

towards electrolytes is altered. Some lyophilic sols enhance the stability of the

lyophobic sols and render them less sensitive towards electrolytes.

The protective effect of a lyophilic sol is different for different lyophobic sols.

Zsigmondy set up a standard by which the protective capacity can be expressed. It

is known as gold number. The gold number of a lyophilic sol is the amount (in

mg) of the dispersed phase of the lyophilic sol (in dry condition) which ought to

be added to a 10 cm3 standard gold sol (0.0053% 0.0058%) to prevent it from

turning to blue (from red) upon the addition of 1 cm3 of a 10% solution of sodium

chloride.



The change in color reflects the onset of coagulation. Therefore, a low value of

the gold number indicates good protective ability of the lyophilic colloid. Gold

numbers of some lyophilic sols are presented in the Table 1.5.1.

Table 1.5.1 Gold numbers of some lyophilic sols

Sol Gold number

Gelatin 0.005–0.01

Hemoglobin 0.03–0.07

Albumin 0.1–0.2

Gum arabic 0.15–0.25

Dextrin 6–20

Potato starch > 25

Historically, gold number has some very important applications, although many

of them have been replaced by more accurate modern analytical techniques. For

example, albumins have higher gold numbers than globulins. Consequently, the

changes occurring in blood plasma in tetanus, where the albumins are converted

into globulins, can easily be detected by determining the gold number.

The protective effect of lyophilic colloids has been attributed to a homogeneous

encircling of the suspended particle by the particles of the protective colloid,

forming a protective sheath. According to Zsigmondy, this theory is applicable to

coarse particles only, not to the fine colloids such as the red gold sols. Zsigmondy

observed that particles of gelatin did not form a sheath around the gold particles.

However, one particle of gelatin adsorbed several gold particles. He, therefore,

suggested that the stability was due to the mutual adsorption of the particles of

hydrophobic and hydrophilic colloids. The union of the particles of the two

colloids formed a complex which imparted the stability.



1.5.7 Rheological properties of colloidal dispersions

The flow behavior of the colloid dispersions is important in numerous

applications in our daily life and in chemical industries. The particles present in

the dispersion exert a significant influence on its flow properties. Therefore, the

colloid dispersions can display a wide range of rheological behavior.

Charged dispersions and sterically-stabilized colloids show elastic behavior. If the

interparticle interaction is not important, the behavior of the dispersion resembles

ordinary viscous liquids. Most of the colloid dispersions can be classified as

Newtonian and non-Newtonian fluids.

The rheological behavior of fluids can be expressed by their profiles of shear

stress s versus shear rate at a constant temperature and pressure as

illustrated in Fig. 1.5.3.

Fig. 1.5.3 Shear stress versus shear rate behavior.

The simplest relation between shear stress and shear rate is,

s (1.5.1)

This is known as Newton’s law of viscosity. The proportionality constant, , is

known as viscosity. Gases and many liquids (e.g., water) obey Newton’s law of

viscosity, and these fluids are known as Newtonian fluids.

The flow behavior of most colloidal dispersions, however, does not follow this

simple behavior. The deviations occur mainly due to two factors: (i) interparticle

hydrodynamic interactions, and (ii) colloidal forces (electrostatic or steric)



between the particles. The hydrodynamic effects exist even for neutral particles

when the concentration is large. The electrical and steric interactions can be

important in dilute dispersions if the range of the forces is large enough.

For a Newtonian fluid, the slope of the s versus curve is constant. Therefore,

the viscosity does not vary with shear rate. However, for non-Newtonian fluids

such a plot can be non-linear, and the slope varies from point to point. Therefore,

the viscosity of such fluids depends upon the shear rate even at constant

temperature and pressure.

The non-Newtonian fluids can be divided into two categories: (i) fluids whose

s behavior is independent of time, (ii) fluids whose s behavior depends

upon time, and (iii) viscoeleastic fluids. The non-Newtonian fluids such as

Bingham plastic, pseudoplastic and dilatant belong to the first category. Their

s behavior does not depend on the history of the fluid, and a given sample

of the material shows the same behavior no matter how long the shear stress has

been applied. Polymer solutions and paper pulp in water are examples of

pseudoplastic fluid. Dispersions of starch and sand are examples of dilatant fluid.

Examples of Bingham plastic fluid are clay dispersions, drilling mud and

toothpaste.

On the other hand, the s curves for the non-Newtonian fluids belonging to

the second category depend upon how long the shear has been applied. These

fluids can be divided into two categories, viz. thixotropic and rheopectic. The

thixotropic fluids show a decrease in viscosity with time under a constant applied

shear stress. The classic example of thixotropic behavior is displayed by the

flocculated sols of iron (III) oxide, alumina and bentonite clay gels, which can be

‘liquefied’ on shaking and ‘solidified’ on standing. Many paints show thixotropic

behavior. In these colloid systems, there is a time-dependent aligning to match

the induced flow. The behavior of rheopectic fluids is opposite: the apparent

viscosity increases with time by the application of shear. Certain clay suspensions

and gypsum pastes, which thicken or solidify while shaken but sets slowly on

standing, are examples of rheopectic fluid.



The relation between shear stress and shear rate for many non-Newtonian liquids

can be expressed by the power-law model.

s pk (1.5.2)

where is called flow-behavior index and pk is called consistency index. This

model is also known as Ostwaldde Waele model. For 1 and pk , this

model predicts Newtonian flow behavior.

The Ostwaldde Waele equation can be written as,

s , 1pk (1.5.3)

where is known as apparent viscosity. For pseudoplastic fluids, 1 , and the

apparent viscosity decreases with increasing rate of shear. For dilatant fluids

1 , the apparent viscosity increases with increasing shear rate.

The Bingham plastic fluid behaves like a solid until a minimum yield stress 0s

is applied, and subsequently the shear stress varies linearly with shear rate.

0s s B (1.5.4)

If the dispersion is such that the behavior is non-linear once the flow starts,

the HershelBulkley model can be used.

0s s H (1.5.5)

Example 1.5.1: The data on the variation of viscosity with shear rate for a mixture of an

anionic surfactant and a nonionic surfactant are given in the following table.

1s Pa s 1s Pa s

0.11 680.2 6.62 13.6

0.18 482.8 10.80 9.1

0.41 184.7 16.80 6.0

0.67 114.8 27.30 3.7

1.04 76.3 42.40 2.0

1.61 46.8 65.75 1.2



2.49 31.1 102.10 0.8

4.06 20.5

Determine the parameters of the Ostwaldde Waele model from these data.

Solution: From Eq. (1.5.3) we have,

1pk

ln ln 1 lnpk

The plot of ln versus ln is shown in Fig. 1.5.4.

Fig. 1.5.4 Variation of ln with ln .

From this plot, the slope and the intercept are 0.98 and 4.4, respectively. Therefore, the

parameters of the Ostwaldde Waele model are, 0.02 and 81.45pk Pa s.

1.5.7.1 Einstein’s equation of viscosity

Albert Einstein derived an equation for the viscosity of an infinitely-dilute

dispersion of very small rigid spheres. His theory is based upon the following

assumptions: (i) density and viscosity of the fluid are constant, (ii) the flow



velocity is low, (iii) no slippage of the liquid at the surface of the spheres, and (iii)

the spheres are large enough compared to the liquid molecules so that the liquid

can be regarded as continuum.

The Einstein’s equation of viscosity is,

1 2.5d

(1.5.6)

where is the viscosity of the pure liquid, d is the viscosity of the dispersion

and is the volume fraction of the spheres. Equation (1.5.6) has been found to

agree well with many experimental results reported in the literature.

Deviation from Einstein’s equation can result from factors such as electroviscous

effect, swelling, flocculation, and adsorption of water on the surface of the

particles.

For dispersions with higher volume fractions of the particles, Einstein’s equation

can be extended as,

2 31 21 2.5d k k

(1.5.7)

Equation (1.5.7) gives a better fit to the data for dispersions which are not very

dilute. Several attempts have been made to extend Einstein’s equation for

concentrated dispersions.

Equation (1.5.6) can be written in terms of the molar volume of the colloid as,

1 2.5dsp mv c

(1.5.8)

where sp is the specific viscosity, mv is the molar volume and c is the

concentration.

Example 1.5.2: The specific viscosity of a dispersion of glass spheres having 160 m

diameter in water varies with the volume fraction of the spheres as given below.

0.01 0.02 0.03 0.04 0.06 0.08 0.10

sp 0.02 0.04 0.07 0.08 0.14 0.19 0.24



Verify whether these data obey the Einstein’s equation of viscosity, or not.

Solution: The given data are plotted as shown in Fig. 1.5.5.

Fig. 1.5.5 Variation of specific viscosity with volume fraction.

The best-fit least squares straight line through the data (shown by the pink line) has slope

= 2.34, which very close to 2.5, as predicted by Einstein’s equation (shown by the green

line). Therefore, it can be concluded that the given data obey Einstein’s equation of

viscosity.

1.5.7.2 MarkHouwink equation for colloidal polymers

The polymer solutions have particle-size in the colloidal dimensions. Often there

is a considerable interaction between the solute (i.e., the macromolecule) and the

solvent. The viscosity of polymer solutions is distinct because such solutions,

even at a dilute concentration, can display high viscosity.

This may be caused by the very extensive solvation of the solute molecules,

which immobilizes the bound liquid, or the long polymer molecules may be

intertangling with each other as they move. Many polymers show a strong

propensity to imbibe the solvent.

The average molecular weight of polymer can be determined by dilute solution

viscometery. The MarkHouwink equation correlates the viscosity-average

molecular weight vM with the intrinsic viscosity of the solution as,



am vK M (1.5.9)

The intrinsic viscosity is defined as,

0

1Lim d

c c

(1.5.10)

The viscosity average molecular weight vM is defined as,

11 aai i

vi i

n MM

n M

(1.5.11)

The parameters mK and a are the characteristics of a particular polymersolvent

combination. In ordinary ‘good’ solvents, the constants mK and a are valid only

within a rather limited range of molecular weight. The values of mK and a for

many polymer systems are tabulated in the literature.

To determine these two parameters, is experimentally determined for several

known molecular weight fractions of the polymer by dilute solution viscometry.

1.5.7.3 Deborah number

The Deborah number is a dimensionless number used to describe the influence of

time on the observed flow properties.

Whether a material deforms under applied stress or not, depends on the

magnitude of the stress and the time of observation. Even some apparently-solid

materials flow if they are observed long enough (e.g., silicone putty).

In interacting dispersions, it is important to consider the time over which the flow

behavior is observed relative to the time scales over which the shear force alters

the local structure of the dispersion. Deborah number is the ratio of the relaxation

time of the material rt and the observation time ot .

De r

o

t

t (1.5.12)

The difference between solids and liquids is defined by the magnitude of De. If

the time of observation is very large, or, conversely, if the time of relaxation is



very small, the material is seen to be flowing. On the other hand, if the time of

relaxation of the material is larger than the time of observation, the material, for

all practical purposes, can be considered a solid.

The name of this number was coined by Markus Reiner in 1964 from a biblical

quote. Prophetess Deborah sang after the victory over the Philistines, “The

mountains flowed before the Lord.” It symbolizes the fact that the mountains

flow, as everything flows, and they flowed before the Lord (not before man) for

the simple reason that man in his short lifetime cannot see them flowing, but the

time of observation of the Lord is infinite.

1.5.7.4 Peclet number

The Peclet number is a very important dimensionless number for the colloid

dispersions. It compares the effect of shear with the effect of diffusion of the

particles.

In a quiescent colloidal dispersion, the particles move randomly due to Brownian

motion. An equilibrium statistical distribution of the particles is established,

which depends on the factors such as the volume fraction occupied by the

particles and the force of interaction between the particles. Now, if a shear is

imposed on the dispersion, the distribution of the particles is altered. The

Brownian motion of the particles tries to restore the equilibrium structure.

The time taken by a particle to diffuse a distance equal to its radius, sR , is of the

order of 2sR D , where D is the diffusion coefficient. This is the time-scale for

diffusion dt . The time-scale for shear flow st is 1 , where is the shear

rate.

The Peclet number is defined as,

2 2Pe

1d s s

s

t R D R

t D

(1.5.13)

This ratio signifies the relative importance of shear and diffusion. If the Peclet

number is small, the Brownian motion dominates and the behavior of the particles



is dominated by the diffusional relaxation of the particles. On the other hand, if

the Peclet number is large, the shear-effect dominates the distribution.

1.5.8 Surfactants

A large number of phenomena at gasliquid, liquidliquid and liquid–solid

interfaces is controlled by a special class of organic compounds known as

surfactants or surface-active agents. These compounds have the unique property

that they tend to adsorb at the interface.

A surfactant is added in rather small quantities to the system. Nonetheless, it

alters the interfacial free energy significantly.

When the surfactant molecules adsorb at the interface, a significant reduction in

the tension results in most cases. Inorganic electrolytes can strongly influence the

adsorption of certain surfactants. Various intermolecular and surface forces are

responsible for these effects.

The traditional use of surfactants has been in household products, foods, coating

processes, petroleum industries, synthesis of microporous materials, and in

chemical reactions such as emulsion polymerization. At present, novel techniques

are being used to design new surfactants with specific chemical, biological,

electrochemical and photochemical properties.

Theoretical understanding of the surface activity has also progressed significantly

in the past decade, with high-speed computer simulations. The focus is on the

properties of multi-surfactant systems, behavior is electrolyte solutions, and in

concentrated surfactant solutions.



1.5.8.1 Properties of surfactants

A surfactant molecule has two parts: one part is soluble in the solvent, and the

other part is insoluble. The part of the urfactant molecule that has unfavorable

interaction with the solvent is known as the lyophobic part. On the other hand, the

part which has favorable interaction with the solvent is called the lyophilic part.

For example, consider a sodium stearate molecule [molecular formula:

CH3(CH2)16COO Na+]. In water, the lyophobic part is the hydrocarbon chain,

C17H35 whereas the lyophilic part is, COO. This type of structure is known as

amphipathic structure, as shown in Fig. 1.5.6. The part of a surfactant molecule

that is lyophilic in a polar solvent such as water, may be lyophobic in a

hydrocarbon solvent such as cyclohexane. Therefore, a surfactant that is useful in

water may not be effective in another solvent. In fact, it may not dissolve in

another solvent.

Fig. 1.5.6 Amphipathic structure of surfactant.

When the solvent is water, the lyophobic and lyophilic parts are called

hydrophobic and hydrophilic parts, respectively. Examples of hydrophilic head-

groups are COO and N(CH3)3+.

The hydrocarbon tail can be made of straight-chain alkyl groups, branched-chain

alkyl groups, long alkyl benzene chain, rosin derivative, alkene-oxide polymer,

polysiloxane group or lignin derivative.

If the hydrophobic group is very long, its solubility in water can be small. For

example, let us consider the sodium salts of fatty acids, which are the main

ingredients of soap. When the number of carbon atoms is less than 10, the soap is

readily soluble in water (however, its surface activity would be low). As the

number of carbon atoms increases (i.e., the hydrophobic tail becomes longer) the



solubility decreases. When the number of carbon atoms reaches 20, the soap is

almost insoluble in water.

1.5.8.2 Adsorption and micellization

When the surfactant molecules come in contact with water, they disrupt the

hydrogen bonds between the water molecules. This increases the free energy of

the system. Since this is thermodynamically unfavorable, the surfactant molecules

are sent away toward the airwater (or water–hydrocarbon) interface.

The air molecules are similar to the hydrophobic groups of the surfactant because

they are essentially nonpolar. This encourages the surfactant molecules to adsorb

at the airwater interface putting their hydrophobic tails in air, and hydrophilic

head-groups in water.

If a sufficient number of surfactant molecules is present in the medium, the

interface becomes covered with a closely-packed monolayer.

The long hydrophobic groups favor formation of assemblies known as micelles

and liquid crystalline phases. These are discussed in detail in Lecture 6, Module

1.



Exercise

Exercise 1.5.1: The shear stress versus shear rate data for a dispersion of colloidal silica

Aerosil R805 (mean diameter = 32 nm) in polypropylene triol are given below at 298 K.

1s Pas 1s Pas 1s Pas

41 10 9.4 23 10 16.8 10 65.5

43 10 10.6 11 10 19.8 30 107.5

31 10 11.6 13 10 24.3 100 216.9

33 10 12.6 1 31.1

21 10 14.8 3 41.6

Fit an appropriate rheological model to these data.

Exercise 1.5.2: The intrinsic viscosities (at 298 K) of eleven molecular weight fractions

of cellulose nitrate dissolved in acetone are given below.

Mol. wt. 103

(kg/kmol)

(dm3/kg) Mol. wt. 103

(kg/kmol)

(dm3/kg)

77 123 846 1490

89 145 1270 2450

273 354 1550 3030

360 550 2510 3100

400 650 2640 3630

640 1060

Determine the MarkHouwink parameters from these data.

Exercise 1.5.3: The data on the relative viscosity with the volume fraction of a

dispersion of spheres of poly(methyl methacrylate) cross-linked with divinylbenzene in

benzene are tabulated below.



0.042 0.053 0.070 0.084 0.105 0.137 0.168

d 1.11 1.14 1.22 1.28 1.36 1.59 1.77

If d can be correlated with by equation (1.5.7), use the polynomial up to the term

containing 3 , and determine the parameters 1k and 2k . Discuss the importance of

swelling of the particles.

Exercise 1.5.3: Answer the following questions clearly.

(a) What is salt-out? How does it differ from coagulation?

(b) Explain the significance of Hofmeister series.

(c) What is coacervation?

(d) What is electroviscous effect?

(e) Explain gelation and imbibition.

(f) Explain the significance of gold number.

(g) Explain the difference between a Newtonian fluid and a non-Newtonian fluid.

What is the difference between pseudoplastic and dilatant fluids?

(h) What is the difference between a thixotropic fluid and a rheopectic fluid?

(i) Give one example each of (i) pseudoplastic (ii) Bingham plastic, and (iii) dilatant

fluids.

(j) Explain the power-law model.

(k) Explain Einstein’s equation of viscosity and its limitations.

(l) Explain MarkHouwink equation.

(m) Explain the significance of Deborah number.

(n) What is the significance of Peclet number?



Suggested reading

Textbooks

D. J. Shaw, Introduction to Colloid and Surface Chemistry, Butterworth-

Heinemann, Oxford, 1992, Chapter 4.

P. C. Hiemenz and R. Rajagopalan, Principles of Colloid and Surface Chemistry,

Marcel Dekker, New York, 1997, Chapter 4.

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

Chapters 2 & 3.

S. Glasstone, Textbook of Physical Chemistry, Macmillan Publishers, Delhi,

1986, Chapter 14.

Reference books

D. F. Evans and H. Wennerström, The Colloidal Domain: Where Physics,

Chemistry, Biology, and Technology Meet, Wiley-VCH, New York, 1994,

Chapter 1.

G. J. M. Koper, An Introduction to Interfacial Engineering, VSSD, Delft, 2009,

Chapter 5.

J. C. Berg, An Introduction to Interfaces and Colloids: The Bridge to

Nanoscience, World Scientific, Singapore, 2010, Chapter 3.

M. J. Rosen, Surfactants and Interfacial Phenomena, John Wiley, New Jersey,

2004, Chapter 1.

M. R. Porter, Handbook of Surfactants, Chapman and Hall, London, 1994,

Chapter 4.

Journal articles

L. Courbin, E. Denieul, E. Dressaire, M. Roper, A. Ajdari, and H. A. Stone,

Nature, 6, 661 (2007).

M. Reiner, Phys. Today, 17, 62 (1964).

N. L. Abbott, AIChE J., 47, 2634 (2001).

Lecture 5

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