foam and foam Films

Shape of Films and Bubbles in Foam References Chapter 2 Expermineta1 Methods Involved in the Study of Foam Films 2.1.1.. Line tension at a circular liquid film Non-Equilibrium Properti

F o a m and F o a m F i l m s

Theory, Experiment, Application

S T U D I E S IN I N T E R F A C E S C I E N C E

S E R I E S E D I T O R S

D M ~ b i u s and R M i l l e r

Vol I

Dynamics of Adsorption at Liquid Interfaces

Theory, Experiment, Application

by S.S Dukhin, G Kretzschmar and R Miller

Vol z

An Introduction to Dynamics of Colloids

by J.K.G Dhont

Vol 3 Interfacial Tensiometry

by A.I Rusanov and V.A Prokhorov

Vol 4

New Developments in Construction and Functions of Organic Thin Films edited by T Kajiyama and M Aizawa

Vol 5 Foam and Foam Films

Theory, Experiment, Application

by D Exerowa and P.M Kruglyakov

Vol 6 Drops and Bubbles in Interfacial Research edited by D M6bius and R Miller

Theory, Experiment, Application

D O T C H I EXEROWA

Institute of Physical Chemistry Bulgarian Academy of Sciences

Sofia Bulgaria

PYOTR M KRUGLYAKOV

State Academy of Architecture and Building

Penza Russia

I 9 9 8

E L S E V I E R

ELSEVIER SCIENCE B.V

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ISBN: o 444 81922 3

© 1998 Elsevier Science B.V All rights reserved

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No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products,

instructions or ideas contained in the material herein

This book is printed on acid-flee paper

Mrs Roumyana Stoyanova and Dr Khristo Khristov, and was edited by Dr Emil Manev The authors appreciate highly their dedicated work and express their deep gratitude

D Exerowa P.M Kruglyakov

Sofia, September 1997

vi

It is sure4 6 e t t e r t o strive f o r a complete understandiy

of the phenomena than t o despair of the human mind

After Stephen Hawking

(Hack Holes and Baby Universes and Other Essays

Bantam Books, New York, 1993)

Preface

Ackmwledgemenls

and Gas Phases of Foams

1.1 Methods for Foam Generation

1.2 Shape of Films and Bubbles in Foam

References

Chapter 2 Expermineta1 Methods Involved in the Study of Foam Films

2.1.1 Thin Liquid Films: Microinterferometric Technique

2.1.2 Measuring cells for formation and study of microscopic

2.1.3 Determination of foam film thickness

2.1.6, Foam film study with a-particle irradiation

2.1.7 Fluorescence recovery after photobleaching (FRAP)

2.2.3 Techniques for measurement of the lateral electrical

conductivity of foam films

2.2.6 X-ray reflectivity of foam films

foam films

surfactants

Physical Chemistry of Foams Films

3.1.2 Ftane-parallel thin liquid fiIms

viii Contents

3.2

3.3

3.4

3.1.3 Thermodynamics of foam films

3.1.4 Mechanical model of the foam film and its adjacent

meniscus 3.1.5 Contact angles

3.1.6 Line tension at a circular liquid film

Non-Equilibrium Properties of Foam Films

3.2.1 Kinetics of thinning of foam films

3.2.1.1 Asymmetric drainage of foam films 3.2.1.2 Kinetics of formation of foam films 3.2.2 Kinetics of rupture of foam films

3.2.2.1 Critical thickness of film rupture 3.2.2.2 Critical thickness of rupture and black spot formation in microscopic foam films Surface Forces in Foam Films

3.3.1 Disjoining pressure isotherm and experimental

verification of the DLVO-theory 3.3.2 Potential of the diffuse electric layer at solution/air

interface 3.3.3 Surface forces in foam films from amphiphilic block

copolymers 3.3.3.1 Transition from electrostatic to steric stabilisation

in foam films from ABA triblock copolymers 3.3.3.2 Dynamic method for surface force measurment in foam films from ABA triblock copolymers 3.3.3.3 Disjoining pressure in foam films from ABA triblock copolymers

Black Foam Films (Nano Black Films)

3.4.1 Surface forces in black foam film

3.4.1.1 Isotherms of disjoining pressure of black films from non-ionic surfactant solutions

3.4.1.2 Isotherms of disjoining pressure of black films from phospholipids

3.4.1.3 Isotherms of disjoining pressure of black films from ionic surfactant solutions

3.4.2 Transition from common black to Newton black films

3.4.2.1 Two equilibrium states of black foam films 3.4.2.2 Experimental investigations of CBF/NBF transition 3.4.2.3 Metastable black foam films

3.4.2.4 Elestrostatic origin of the transition to NBF 3.4.2.5 Main differences between CBF and NBF 3.4.2.6 Thickness transition in foam films 3.4.3 Relationship between black foam film formation and the

properties of the surfactant adsorption layers 3.4.3.1 Properties of the adsorption layers

3.4.3.2 Probability for observation of black foam films depending on the adsorption layer state 3.4.3.3 Formation of black foam films from an insoluble surfactant monolayer

3.4.4 Bilayer Black Foam Films (NBF)

3.4.4.1 Comparison of the lifetime/surfactant concentration dependence of CBF and NBF

3.4.4.2 Theory of rupture of amphiphile bilayers 3.4.4.3 Experimental results on stability of amphiphile bilayers

3.4.4.4 Phase transitions in phospholipid foam bilayers 3.4.4.5 Linear energy of holes in amphiphile bilayers 3.4.4.6 Linear energy of the contact line black foam film/

bulk liquid 3.5 Diffusion Processes in Foam Films

3.5.1 Gas permeability of foam films

3.5.2 Gas permeability of NBF

3.5.3 Lateral diffusion in phospholipid black foam films

3.5.4 Lateral diffusion of vacancies in NBF

3.6 Similarity of Foam Films with Emulsion and Asymmetric Thin

4.1 Relation between the geometrical (structural) parameters of a foam

and its physicochemical characteristics

4.2 Determination of foam expansion ratio (foam density)

4.3 Determination of pressure in foam Plateau borders

4.4 Determination of foam dispersity

4.5 Study of foam liquid distribution and Plateau border profiles

References

Chapter 5 Foam Drainage

5.1 A brief characterisation of foam drainage

5.2 Techniques for the study of foam drainage

5.3 Foam drainage at high pressure drop

5.3.1 Hydrodynamic model of a foam

5.3.2 Liquid flow through polyhedral foams with different types

of foam films 5.3.2.1 Liquid flow in gravitational field 5.3.2.2 Liquid flow under pressure drop

x Contents

5.3.3 Equations for drainage under pressure drop

5.3.4 Foam drainage and the kinetics of establishing equilibrium

pressure in the foam liquid phase: experimental studies 5.3.4.1 Kinetics of establishing pressure in the foam liquid phase

5.3.4.2 Influence of the type of foam films on foam drainage

5.4 Gravitational drainage of a foam

5.4.1 Equations of gravitational drainage

5.4.2 Initial stage of drainage

5.4.3 Influence of the foam structure and the properties of the

foaming solution on the drainage rate 5.4.4 Drainage of three-phase foams

5.5 Influence of internal foam collapse on drainage

References

Chapter 6 Foam Collapse

6.1 Techniques involved in the study of the kinetics of internal foam

collapse

6.2 Internal foam collapse at diffusion gas transfer

6.3 Coalescence and structural rearrangement

6.4 Kinetics of internal foam collapse

6.5 Decay of the foam column

6.5.1 Foam column decay in gravitational field

6.5.2 Influence of Plateau border pressure on foam column

destruction 6.5.3 Foam breakdown in centrifugal field

6.6 Comparison between the rate of internal foam collapse and the

decrease in foam volume

References

Chapter 7 Foam Stability and the Stabilising Ability of Surfactants

7.1 Definition of the term foam stability and foaming ability of solutions

7.2 Characteristics of stability related to foam column decay

7.3 Kinetic factors of foam stability

7.4 Thermodynamic factors of foam stability

7.5 Model approach to the study of foam stability and analysis of

the stabilising factors

7.5.1 Role of foam films in the stability of foams

7.5.2 Stability of a real foam

7.6 Physicochemical properties of surfactants and the stabilising ability

of their solutions

7.6.1 Foam stabilising properties of surfactants determined by

Foam Pressure Drop Technique and Ross-Miles Test

7.6.2 Effect of the isoelectric state at the solution/air interface on

the stability of foams from nonionic surfactants 7.7 Dependence of the foaming ability on the mode of foam formation

and the properties of the surfactant solutions

7.8 Foaming ability of solutions and foam stability

7.9 Stabilising ability and hydrophile-lipophile balance of surfactants

7.10 Stability of dynamic foams

7.11 Foamed emulsions with large volume fraction of the disperse phase

Chapter 9 Foam Breakdown by Antifoams

9.1 Techniques for determination of the defoaming efficiency of

substances

9.2 Adsorption (Homogeneous) mechanism of foam breakdown

9.3 Defoaming in Heterogeneous Systems

9.3.1 Inhibition of black spot formation in microscopic foam

films 9.3.2 Role of antifoam spreading

9.3.3 Mechanism of heterogeneous defoaming

9.4 Defoaming ability of solid hydrophobic particles

9.5 Inversion of the defoaming ability of alcohols

References

Chapter 10 Technological Application of Foams: Physicochemical Ground

10.1 Classification of foams and films by the properties determining their

technological application

10.2 General principles of regulation of the physicochemical properties

of foams

10.3 Accumulation and separation of surfactants in a foam

10.3.1 Classification of the methods of surface separation

10.3.2 Characteristics of the effectiveness of accumulation,

separation and purification of surfactant solutions 10.3.3 Experimental studies on the accumulation of individual

surfactants and mixtures

xii Contents

10.3.4 Foam separation of surfactant components from mixtures

10.4 Optimisation of the processing properties of solidifying foams

10.4.1 Thermal insulators from frozen aqueous foams

10.4.2 Oligomer polymer foams

10.5 Examples of foam inhibition in the process of extraction and in

emulsion metalworking fluids

10.6 Examples of the use of natural products as foaming agents

10.7 Use of foams in petroleum and gas industries

References

Chapter 11 Black Foam Films: Application in Medicine

11.1 Black Film Method for assessment of foetal lung maturity

11.2 Phase state of foam bilayer (NBF) from amniotic fluid

11.3 A new hypothesis of the structure and stability of alveolar surface

11.4 Black Film Method for assessment of therapeutic surfactants

PREFACE

The first book on soap foams and bubbles appeared at the end of the nineteenth century (Boys, 1890) The gist of its contents has become considerably outdated but, nevertheless, it has lost neither its attraction nor its cognitive value to this very day - a fact that has been confirmed

by its undergoing numerous republications The results of the ongoing investigations on macroscopic films have been systematised and summarised in K.J Mysels et al.'s monograph, while the microscopic films have been surveyed in a number of reviews by A Scheludko, I.S Clunie et al and others The processes of foam formation and collapse, especially those with practical implications, have been dealt with by J.J Bikerman et al (1953), E Manegold (1953, in German), J.J Bikerman (1973), V.K Tikhomirov (1975, 1983), K.V Kann (1989) and P.M Kruglyakov and D Exerowa (1990), the last three having been published in Russian A series of monographic collections, editors R.J Akers (1976), L.L Schramm (1984), A.J Wilson (1989), N.R Morrou (1990), R.K Prud'homme and S.A Khan (1995) have also treated these topics Moreover, a multitude of books and brochures on the practical applications of foam in various industrial branches like fire-fighting, flotation, oil-production, dust-collection, have come out at different times There are a great many cases when we have based ourselves on the books by J.N Israelachvili (1985), B.V Derjaguin, N.V Churaev and V.M Muller (1987), B.V Derjaguin (1989) which are primarily devoted to surface forces theories, as well as the monograph by S.S Dukhin, G Kretzschmar and R Miller (1995) on adsorption phenomena at liquid interfaces This provoked us to examine some of the above mentioned issues less exhaustively

In the present monograph, we have attempted to both explain and describe the processes running in the foams and their equilibrium properties on the basis of quantitative regularities of electrostatic, molecular, etc interactions, physicochemical, hydrodynamic and other surface phenomena However, considering the complex nature of foam properties, it has, understandably, proved impossible for a number of properties and processes, still awaiting quantitative explanation

The treatment of foam films is important in its own right, thin liquid films being an effective tool and a luring scientific topic in surface and colloid science In all justice we must say that nowadays this scientific domain exists wholly in its own account and its numerous practical

xiv

applications are just one more proof of that Thin liquid films, and foam films in particular, allow for direct measurement of the surface forces at play inside them (both DLVO and non-DLVO forces), establishing their mutual impact etc., leading in turn to the most critical application possible of surface forces theory, while on the other hand stimulating theoretical analyses Special attention has been paid to the transition from long-range to short-range molecular interactions in thin liquid films which continues to be unfailingly informative about the operation of surface forces A new approach to the study of amphiphile (foam, emulsion and membrane) bilayers on the basis of short-range molecular forces has been set forth, enabling the authors to examine stability and permeability in terms of a uniform point of view by advancing a hole nucleation theory This has also made possible to determine the molecular parameters of the bilayer by measuring experimentally the macroscopic parameters

The contents of this monograph have been drawn, primarily, from the findings contained

in the authors and their co-workers studies, including those resulting from the method of Foam Pressure Drop Technique, developed by P.M Kruglyakov, Khr Khristov and D Exerowa On the other hand, the book treats fairly thoroughly the whole array of physicochemical properties of foam and foam films by pulling on both outstanding older works and the latest achievements in the research of foams and other disperse systems (especially emulsions) and surface phenomena Understandably enough, scrutinising the various foam and film properties has not been sufficiently uniform which bears on both the state of the art and the authors' interests It is the authors' conviction that tradition and continuity are of paramount importance in scientific progress, thus attempting to include into the book the contributions of the authors pioneering in this domain Alongside the literature in English, the monograph draws on, more thoroughly than usual, scientific results and methods, published in Bulgarian and Russian, therefore, inaccessible

to the majority of readers and not having exerted an overwhelming influence on future works but, which may, hopefully, be elaborated further One of the outstanding features of the monograph is the circumstantial elucidation of the role of foam films in the various processes and phenomena in the foam itself and a comparison of the foam and foam film properties from different perspectives Another original trait of the book is the formulation of the general scientific principles, underlying the regulation of the physicochemical parameters of foam and foam films and the technological application of foams based on them Of course, the applications of foam are

so numerous that they could hardly be outlined comprehensively in a single book Fore.that reason the delineation of foam applications has been limited to a finite number of areas, mainly to those

in which the principles of regulating the technological parameters, postulated by the authors can

be utilised or to those which have remained untouched so far There is also a short review section, classifying "useful" foams in terms of their most essential property, proving indispensable to the given field of application It is also worth remarking that the principal regularities, outlined in the field of foam films may turn out to be applicable as a model system to study surface phenomena,

to carry out physicochemical description of amphiphile molecules (surfactants, phospholipids and polymers), to apply in biomedicine etc

Finally, having in mind that each imperfection could be swallowed more easily when taken in small doses, we would like to express our regret that this book turned out longer than originally intended

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ACKNOWLEDGEMENTS

D Exerowa is a student of A Scheludko's who has inscribed his name among the pioneers of the quantitative study of thin liquid films Both authors are indebted to A Scheludko for the invaluable knowledge and the original approach to the scientific quest and wish to render deep homage to his memory The authors feel grateful and will remember the frequent conversations with the late B.V Derjaguin who gave them valuable knowledge and inspired the quantitative approach in their research D Exerowa is particularly indepted to K Mysels for giving the lead towards striving for pioneer scientific quest

The authors would particularly like to express their gratefulness to Khr Khristov, T Kolarov, R Cohen, Z Lalchev, A Nikolova, B Balinov, R Sedev, R Ivanova, R Yankov, all from Bulgaria, and to L.L Kuznetsova, A.I Bulavchenko, V.A Safonov, N.G Vilkova, T.N Khaskova, all from Russia, for their particularly prolific and beneficial participation in the studies which made this book possible The authors highly appreciate the joint work with their foreign colleagues T Yamanaka (Japan), K Malysa (Poland), V.M Muller and Z.M Zorin (Russia), H.-

J Mtiller (Germany), Th.F Tadros (UK) and E Scarpelli (USA), the results of which are included in this book The authors are also indebted to their colleagues D Platikanov, B Radoev and E Manev for their precious help and invaluable discussions when writing the respective sections, related to their own investigations or joint research D Exerowa expresses her gratitude

to D Kashchiev for their joint work on the development of the hole-nucleation theory of rupture

of amphiphile bilayers, and for the agreable and fruitful discussions

We owe Borislav Toshev deep indebtedness for writing Section 3.1, entitled Elements of the Thermodynamics of Foam Films, where he advances a new approach to handling thin liquid film thermodynamics

Last but not least, we wish to express our deep and cordial thanks to R Stoyanova and Khr Khristov for translating and laying out this book, and to E Manev for doing the editing job

D Exerowa P.M Kruglyakov

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INTRODUCTION

Foam is a widely familiar gas/liquid disperse system Like other disperse systems, such as suspensions and emulsions, the foam is characterised by a highly developed interface, determining its properties A rewarding investigation of a broad range of surface phenomena could be carried out in terms of foam and foam films, establishing both the general regularities, qualifying the various interfaces, and the specific ones, relating to the water/gas interface, which are equally relevant to biology, ecology, geology and a number of other scientific and technological domains, touching upon colloid science

The contacts between the gas bubbles in the liquid when foaming, as well as the contacts between the emulsion drops and the suspension particles, occur through various thick and thin liquid layers (films), usually containing surfactants The properties of disperse systems (foams, emulsions, suspensions) are largely determined by the properties of these films Furthermore, the problem of foam stability is distinct from the problem of colloid solution and emulsion stabilities whose behaviour is strongly dependent on the process of particle collision In contrast to other disperse systems, the individual bubbles in the foam contact immediately after its generation resulting in formation of foam films that being an essential structural element of the foam, determine to a great extent foam stability With the Plateau borders and the vertexes, the films form a unified capillary system All the most essential foam processes, including those determining gas bubble expansion and their lifetime, bear on the thickness, structure and physicochemical properties of foam films

The study of the physicochemical properties of the thin liquid films inside the foam itself,

is a task of utmost difficulty Basing oneself on the findings from foam investigations, one could only approximately evaluate film thickness, structure and composition, failing to determine the liquid distribution among films and borders in the foam A number of essential thermodynamic parameters, such as the film tension, the contact angles between the films and the bulk phase, the difference in the surfactant amount adsorbed in the thin and thick films, as well as many other directly measurable characteristics of foams (and emulsions) still defy our investigations Considerable progress in the study of thin film properties, including the reasons for their stability,

has recently been made owing to the investigations on model microscopic films: single thin films, obtained by a special technique and proved to be a practically adequate model of the film structure in a polyhedral foam It has become possible to perform direct and precise measurements of the various film parameters (thickness, tension, contact angles, diffuse electric layer potential, etc.) The application of the model systems has permitted a sufficiently comprehensive study of the hydrodynamics of non-equilibrium films, the surface forces of different origin: electrostatic, van der Waals, hydration, steric, hydrophobic, etc., the dependence

of black film thickness and composition on the surfactant kind, electrolyte concentration, pH and temperature Furthermore, the existence of different types of foam films has been established and the transition between them A theory of bilayer black foam film rupture has been developed The thinnest-black films have been found to play a particularly important role in the formation of highly stable foams They are used as models in the study of surface phenomena at various interfaces, molecular interactions between two contacting phases at short distances, including at bilayer contact This fact in itself is of the utmost importance in studying the formation and stability of concentrated disperse systems and in modelling the contact between the two biomembranes For this reason the book discusses different aspects of black foam films and some intriguing perspectives for future development, for instance, as a self-organising nanomolecular system, have been pointed out

The physicochemical properties of foam and foam films have attracted scientific interest

as far back as a hundred years ago though some investigations of soap foams were carried out in the seventeen century Some foam forming recipes must have been known even earlier The foundations of the research on foam films and foams have been laid by such prominent scientists

as Hook, Newton, Kelvin and Gibbs Hook's and Newton's works contain original observations

on black spots in soap films

The first systematic study of the various properties of soap films has been conducted by the Belgian scientist Plateau Using the findings from investigations on the structure and properties of differently shaped films, he was the first to draw attention to that part of the film which contacts the surface holding the film It came to be called Plateau border Plateau studied the impact of various external effects (like the stream of air, evaporation, etc.) on the behaviour of

foam films (1861) In his view, the reason for the long lifetime of soap films, i.e their high stability, was related to their surface viscosity and proposed a special method to measure it Marangoni (1871) was the one to account for the conclusions from Plateau's observations by the compression or, respectively, the expansion of the surfactant monolayer, i.e those monolayer properties which are now known as the Marangoni effect (of dynamic elasticity), having acquired wide popularity Another reason for film stability (equilibrium elasticity) has been established by Gibbs (1878), who is also responsible for a number of significant ideas concerning soap film stability The first theory of soap film rupture has been put forward by Dupre (1869) In the early twentieth century, the works of Johonnot (1906), Rickenbacher 19.16) and Perrin (1918) have shed additional light by showing the existence of two varieties of black films without indicating the reasons for their formation and stability There were attempts, first by Plateau, then by Reynolds, to determine the radius of the molecular action studying the dependence of the surface tension of the film on its thickness However, the sensitivity of the techniques employed was insufficient and the object of study was improperly chosen, so they were not successful in finding the tension difference

Further progress in the foam film research was achieved in the second half of twentieth century with the studies of Derjaguin, Mysels, Scheludko and many other scientists whose work has been referred to repeatedly in the present monograph They have contributed to reaching the contemporary understanding of the foam films and foams

Foam is widely applied in a large variety of industrial branches and the claims put forward

to it are largely dependent on its technological applications which are often mutually exclusive A case in point is flotation foam which, as a rule, being quite unstable and containing dissolved substances, guarantees the selective mineral particle extraction from suspensions Frozen foams which have been used in the thermal insulation of paint ground coats are expected to have, prior

to crystallisation, low expansion ratio and low drainage rate On the contrary, foam designed to carry out adsorption concentration or foam chromatography should be readily dried and highly stable Foam, resistant to strong and quick deformations and the impact of organic liquids and of solid particles of various kinds, has proved to be invaluable in washing away gas pipes, in cleaning greased products, in carrying out enhanced oil recovery as well as in dust collection

xxii

The scientific principles for regulating the physicochemical properties of foams targeted at producing foams, possessing the indispensable technological and exploitation qualities, has powerfully established itself This problem could be solved by determining the quantitative relationships between the essential foam structure parameters (expansion ratio, dispersity, bubble shape, film thickness and capillary pressure) and the kinetic regularities of the processes, controlling foam stability (drainage, gas diffusion transfer into the foam, coalescence and the rupture of the film and the collapse of the foam as a whole) Consequently, to optimise the properties of foam, it is necessary to create efficient methods to investigate the structure of parameters and processes, running in the foams, under conditions corresponding to their application, for instance, when in contact with organic liquids, when flowing in porous media, when frozen, etc

As it is well known, science has made a significant step forward owing to the powerful link between colloid science and the study of biological structures and materials Thus, an opportunity arises for these findings to be applied in medicine, both by creating new diagnostic methods, and by gaining an insight into the mechanism of crucial physiological processes and biostructures whose biological functions are essential It is exactly these matters that are dealt with in the last chapter of the book which makes the reader well aware of the fact that the black foam film has an alveolar analogue in vivo indicating what the future prospect for advancement

in that domain Many of the results on the molecular interactions obtained employing thin liquid films, in the first place being the black foam films, can ground the understanding of the formation and stability of biostructures

FORMATION AND STRUCTURE OF FOAMS PRESSURE IN THE LIQUID

AND GAS PHASES OF FOAMS

Foam is a disperse system, consisting of gas bubbles, separated by liquid layers Dispersion of gas in liquid in which the gas content is low and the thickness of liquid layers is commensurable to gas bubble size is called gas emulsion or spherical foam ("kugelschaum"

by Manegold [1 ]) The shape of bubbles in the gas emulsion is spherical (if their size is not very big) and there is no contact between them

Gas emulsions [2-4] are formed during several technological processes (gas adsorption and desorption, liquid boiling, polymer processing, carbonated beverages, etc.) They are also formed in nature: gas emitted from swamps and water basins at degradation of organic matter,

in rough sea, recovery of oil containing dissolved gases, etc

Gas emulsions in which the dispersion medium is of low viscosity are referred to as short-living disperse systems Because of the significant difference in the densities of gas and liquid they quickly separate into pure dispersion medium and foam The latter either decays rapidly or transforms into polyhedral foam, depending mainly on the kind and concentration

of surfactants in the foaming solution Long-living spherical foams can be formed by high viscosity liquids, for example, molten glass submitted to quick cooling raises sharply its viscosity thus impeding the movement, contact and coalescence of individual gas bubbles Transformation of gas emulsion into polyhedral foam begins when the gas content in foam becomes higher that 50-75% It is not possible to obtain stable (long-living) foams from pure liquid Stable polyhedral foams are formed only in the presence of an appropriate surfactant (or surfactant mixtures) Introduction of a surfactant into a liquid significantly changes the properties of gas dispersions and liquid films It lowers the surface tension at the gas/liquid interface, facilitates the dispersion of gas and reduces the size of bubbles, changes the velocity and regime of bubble rise

The main stages of foam formation can be established through observing the behaviour

of a certain number of rising bubbles When bubbles are formed o r created in a surfactant solution, an absorption of the surfactant starts at their interface Reaching the liquid surface each bubble forms a hemispherical liquid film which consists of two surfactant adsorption

2 Chapter 1

layers and a liquid core between them (Fig 1.1) The surfactant adsorption layers ensure long lifetime of the liquid films formed With the increase in the number of bubbles at the surface they begin to draw closer Furthermore, the capillary attraction between bubbles helps the process of bubble contact and deformation, resulting in thin liquid film formation between neighbouring bubbles Thus, a monolayer of gas bubbles is formed at the surface, followed by

a second layer, and so on until a three-dimensional foam is obtained When other methods of foam formation are employed (for example, injection of gas through gauzes, wetted with surfactant solution) gas bubbles acquire a polyhedral shape in the process of creation

as well as destruction of the foam column occurs when the foam is open to the atmosphere The most important parameters characterising a polyhedral foam are expansion ratio, dispersity and foam stability The expansion ratio n is the ratio between the foam volume VF

and the volume of the liquid content VL in it

n - v~ _ ~v~ + v~~ = l + V ~ (1.1)

where V c is the gas volume in the foam

Foam dispersity is characterised by the average bubble size, by bubble size distribution

or by the specific foam surface e There are three different specific foam surfaces

Under identical conditions of foam formation equal volumes of different foaming solutions yield different amounts of foam The foaming ability of a solution is a property characterising each particular surfactant solution This property can be expressed quantitatively by the volume of foam (or the foam column height), obtained under certain conditions (foaming method, temperature, surfactant concentration, pH, etc.) from a definite volume of the foaming solution Sometimes the term "foaming ability" is treated more widely:

as a complex characteristic, involving both the maximum foam volume, obtained under definite conditions and the foam lifetime

Dispersions of gas in solids are also called foams but the foam cells (bubbles) formed are isolated from one another An example of such foams are the natural porous materials, cellular concrete, cellular glass and polymer foams However, if in such disperse systems both phases are continuous (such as in many foamed polymers), they are called sponges Many porous materials are partially sponge and partially solid foam The properties of solid foams differ drastically from those of foams with liquid dispersion medium At the same time the strength and other physical and mechanical characteristics of solid foams depend significantly

4 Chapter 1

on the properties of the liquid foams they are obtained from as a result either of chemical reactions (polymerisation, hydration, etc.) or crystallisation (formation of frozen foams)

Alike other disperse systems foams can be obtained by condensation and dispersion methods

Condensation method for generating a foam involves creation of gas bubbles in the solution by decreasing external pressure or by increasing temperature (up to achieving a supersaturation of the solution) or as a result of a chemical reaction

In the dispersion method the foam results from dispersing gas into bubbles by injecting

it into the foaming solution through capillaries, porous plates, gauzes or tissues (barbotage or pneumatic methods) or by blowing gas through gauzes, wetted with a surfactant solution Gas dispersion can be obtained also by shaking a vessel partially filled up with a solution, by simultaneous flow of gas and liquid in a tube, by mechanical mixing of gas and liquid with a stirrer, perforated disks or other devices, by pouring liquid on the surface of the same solution,

by sucking gas in a flowing liquid, etc

Numerous variants of both methods have found wide application The apparatus and equipment used for foam generation both in laboratory and industrial scales are described in details in [5-12] That is why only the most important methods for foam generation and the areas of their application are briefly described below

A simple and largely applied method for foam formation is dispersion of gas through porous plates (filters) placed at the lower parts of foam generation apparatus [5-10] This method is employed in flotation, in gas adsorption and dust collection in set-up with turbulent gas emulsion, and in the equipment for foam separation The dispersity of a foam thus obtained depends on: filter pore size or capillary diameter, hydrophility of the material used in the dispersion device construction, physicochemical properties of the foaming solution (surface tension, viscosity, surfactant concentration, etc.) and conditions of the dispersion process

At the onset of formation by barbotage methods the foam represents a gas emulsion The rate of its transformation into a polyhedral foam depends on the velocity of bubble rise and the consequent drainage of the "excess" liquid from the foam thus formed Bubble size,

gas volume fraction (gas concentration in the liquid) and surfactant concentration determine the velocity of bubble rise In the absence of surfactant the velocity of bubble rise u of individual gas bubbles is expressed by the equation of Hadamar and Rybczynski [e.g 13]

p2gR 2

902

6 Chapter 1

When the hydrodynamic conditions correspond to Re = 1500 (R = 2 - 10 mm) bubbles become strongly deformed when rising They acquire the shape of a flat ellipsoid and begin to vibrate and move on a spiral trajectory In fact their size does not influence the velocity of rise [14] The following relation was derived from the results on the velocity of rise of large bubbles reported in [16]

where VB is the bubble volume

When an ensemble of bubbles rise, the collective velocity depends also on the volume fraction of the dispersed gas qg In the absence of surfactant the collective velocity of bubble rise under Stokes hydrodynamic regime of bubble movement (Re < 0.5) is given by [15,17]

Depending on the volume rate of gas supply there are dynamic and "static" regimes of foam formation [7,18]* "Static" regime of foam formation is realised at low rate of the dispersed gas when bubbles are formed under conditions close to equilibrium (when the

*Other researchers report about three or four regimes of foam formation [8,10,19]

equilibrium value of surface tension is established) This regime corresponds to small Reynolds numbers (Re < 100) which characterise the rate of gas feed

disperse system 1 - Stokes rising regime in the presence of a surfactant; 2 - Stokes rising regime without a

8 Chapter 1

The ratio pgV / (2 n'rcr) is a criterion of the validity of the theory and according to the experimental results of different researchers it varies from 0.6 to 1.88 depending on the radius

of the capillary orifice and the properties of the liquid [8,21]

The best fit between experimental results and theory is achieved when both the change

in hydrostatic pressure along the height of the forming bubble at the moment of its detachment from the capillary orifice and the expansion of bubble during its rising are taken into account Surface tension and density of foaming solution (see Eq (1.9)) determine the size of bubbles when they are formed slowly The surfactant kind and concentration affect both the rate of formation of adsorption layers at bubble surface and the stability of foam obtained

In dynamic regime of foam formation the size and shape of bubbles depend to a great extent on the volume rate of gas supply [8,22] Gas consumption increases mainly on the account of increase in bubble volumes and at a certain critical volume rate, the gas begins to emerge from the capillary orifice in a continuous stream which afterwards is dispersed into individual bubbles [8,23,24] Under this regime the influence that liquid flow turbulence exerts on bubble size is greater than that of the capillary orifice diameter and the physical properties of the liquid

At high volume rate of gas supply Q, the bubble volume is given by the following expression [8,20]

a bubble formed by blowing gas through a capillary with a hydrophobic surface is 20 times higher that the volume of a bubble obtained from a capillary of the same size but with hydrophilic surface

Bubbling devices can be porous plates, cartridges from glass, ceramics, metal ceramics and plastics, and also various kinds of gauzes Interesting modification are the elastic plates in which the diameter of their orifices is altered with the pressure of gas injected through them It

should be noted that a strong dependence (usually undesirable) of bubble size on gas volume flow rate is observed when such plates are used for foam generation

Porous plates produced by sinteration of glass powders are widely used, especially in laboratories However, both the size of pores and their cross-section along the plate height vary in a wide range Hence, the number of active pores depends on gas pressure and surface tension of the solution Increase in pressure activates all smaller pores

Another result from the non-uniformity of the orifices along the pore height is the hysteresis observed in the dependence of the volumetric gas flow rate through the porous plate

on the applied pressure drop (Fig 1.3) This dependence shows that at applying identical pressure drop the rate is significantly lower when gas feed is done by increasing pressure than when it is decreased (after reaching a certain maximum pressure) The explanation is that the number of active pores increases with pressure rise

[7] Average pore size 5-15 ~m; the plate is immersed into distilled water at 40 cm depth; curve 1 - measurement

at pressure increase; curve 2 - measurement at pressure decrease

In order to reduce the size of bubbles formed by dispersion through filters, additional methods and devices are used, for example, rotating drums [8], horizontally situated filter pores, rotating cylinders causing solution movement [8], shock effects on the bubbles formed [25], round body devices placed over capillary or pore orifice outlet [26] Very small bubbles can be formed from thin capillaries with diameter up to 10 - 20 gm (sometimes up to 4 gin) or very fine filters However, the rate of foam formation when such capillaries or filters are employed is very low Simple injection type devices for generating highly dispersed foam

10 Chapter 1

(microfoam) with bubble size from 10 - 20 gm are described in [27, 28] In laboratory practice the polydispersity of a foam can be reduced by its homogenisation, for example with a "brush" (rotating brush) [29]

There are various equipment for foam generation that employ the method of gas blowing through porous plates or capillaries [6,7,11 ] One of the first equipment of this type is the aspiration foam generator of Tyutyunnikov and Kasyanova [30] A similar device that works with smaller volume of foaming solution is proposed by Japanese researchers [31] Apparatus in which dispersion devices are filters differ mainly by shape and capacity

of vessels, measuring instruments (electrodes, flowmetres, etc.), devices for air cleaning and drying and the way of thermostatting [8,10]

Fig 1.4 shows a scheme of apparatus for formation and investigation of foams (Foam Pressure Drop Technique, see Chapters 5 and 7) The pressure in foam Plateau borders is regulated with a glass porous plate [32-36] The foam is generated by injecting compressed air (purified and moistened) through porous plate 4 into the foaming solution in vessel 5 The foam produced is transferred along the glass tube to collecting vessel 6 (measuring cell), the bottom of which is a porous plate with a suitable pore size (5 - 50 gm) When foam properties are investigated platinum electrodes (for measuring electrical conductivity) and capillary micromanometer (for measuring pressure in Plateau borders) are placed in the lid of the measuring cell 6

A vessel made of sintered glass can also be used as a measuring cell [34, 35] In it the equilibrium pressure in Plateau borders is quickly reached and the effect of vessel walls on foam behaviour is omitted This cell is most efficient in the study of structured foams obtained from protein and saponin solutions Because of their rheological peculiarities such foams can decay close to the filter and detach from it if the measuring cell has a porous plate only at the bottom of the vessel

After the measuring cell is filled with foam to a specified level it is covered with the lid in order to ensure a vapour saturated atmosphere Then the space under the filter is connected through a glass cock with the buffer in which a definite reduced pressure is created and controlled by the vacuometer The liquid draining from the foam is collected in trap 7 Thus a definite reduced pressure in the Plateau borders is established

Recently a new technique has been introduced for the study of foam drainage under pressure drop The especially constructed apparatus allows automated calculation of foam expansion ratio at any instant of time (see Section 5.3.4)

Technique): 1 - pressure regulator, 2 - vessel for purification and wetting of gas, 3 - manometer, 4 - porous plate,

5 - vessel for foam production equipped with a outlet glass tube, 6 - vessel with a porous plate for collecting the foam, 6a - variant of the vessel for collecting the foam, made of sintered glass, 7 - trap, 8 - vacuometer, 9 - buffer; A - glass lid of vessel 6, equipped with electrodes 10 and micromanometer 11, used for foam investigation

Stream type foam generators (air-foam tubes) and foam generators in which the dispersing device is gauze have wide application, especially for fire-fighting and dust-catching foams [37-38]

In stream type generators [37-39] the foaming solution is fed under pressure through several injectors (diffuser) situated at a certain angle on the generator stem so that the solution streams cross at a given point (focus) W h e n streams collide they disperse, mix and suck in air from the orifices of the stem Such type of generators form foams with low expansion ratio but the foam can be thrown to a long distance though the solution is injected under relatively low pressures ( - 4-105 Pa)

There is a great variety in the construction of apparatus for foam generation employing dispersion of gas on gauzes In the simplest one both gas stream and foaming solution are fed simultaneously (modification of the method of Arbuzov and Grebenshchikov in which air is injected through a moistened porous plate) [40] The foaming solution is fed to the gauze either as drops by a sparger or the gauze is wetted with the solution Depending on the way of

12 Chapter 1

air feeding these generators can be: ejector type in which air is sucked in due to rarefaction caused by the stream of the solution, and others in which air is supercharged by means of a ventilator or a compressor The ejection type generators have high capacity and produce foams with expansion ratio about 100 - 200 Generators with supercharged air can produce foams with expansion ratio more than 1000 The capacity of these generators, depending on their construction and purpose, can vary from 10 to 15 000 dm -3 sec -1 In order to increase the distance to which high expansion ratio foam can be thrown out it is proposed [36] to combine

it with low expansion ratio foam The main characteristics of the air-mechanical foam generators are given in [8,38]

Usually the estimation of structural parameters of foam formed by dispersion through gauzes is done on the basis of liquid and gas material balance [36,38] Such calculations do not account for the properties of foaming solution and capillary pressures during the process

of foam formation That is why they cannot give reliable results

The dependence of expansion ratio of a foam formed through a gauze on gas consumption passes through an extremum [41,42]

In the pour test [43] foam is obtained by pouring the solution tested through a calibrated orifice from a definite height on the surface of the same solution (Fig 1.5) This method has been studied in details and has been adopted in several countries as a standard one for estimation of foaming ability of a solution (for example, solutions of detergents) This method has various modifications [5,6,8]

The method of beating up involves foam formation by reciprocating a perforated plate

or gauze (fixed on a piston) in the foaming solution [1,8] The piston is moved either manually or mechanically Several other methods based on mechanical agitation are also employed [9]

The mixing foam generators has been largely applied in the recent years In such generators the foam is produced by intensive mixing of liquid and gas, both flowing simultaneously in a tube or through porous media [44-49] The advantage of this method is that foam formation occurs together with its transportation which is very important in firefighting or in preparation of solidifying foams [44,46] Conditions under which a total gas dispersing is achieved and foam with a definite expansion ratio is obtained (the ratio between the tube length and diameter, average rate of flow and tube diameter and the minimum tangential tension) are reported in [46]

Foam can be obtained also by simultaneous movement of liquid and gas in a tube, filled up with spherical particles (for example, polystyrene grains [46], beadpacks [49]), in coarse-pored medium [47] or movement through natural soil, such as sand packs) [48] These ways of foam formation are used in modelling of enhanced oil recovery processes or controlling porous media permeability to gas [e.g 48,50]

Fig 1.5 Scheme of the apparatus for foam formation by the pour test: 1 - vessel, containing the foaming solution; 2 - graduated cylinder; 3 - thermostatting device; 4 - tubes; 5 - thermostat

A great advantage of mixing foam generators is the possibility to regulate both foam expansion ratio and dispersity, though within a narrow range of alterations For example, at constant ratio of gas and liquid volumes the dispersity of foam increases when the consumption of liquid and gas rises [45]

The simplest relation between the volumes of foam formed and gas consumed is realised in the barbotage methods when the volume rate of gas supply is low (low Reynolds numbers) This dependence becomes more complicated when foam is generated by dispersion

of gas on gauzes In the other methods of foam formation mentioned: shaking a solution in closed vessel, beating up solution with various devices and pouring solution, the dependence foam volume vs solution properties and conditions of the foaming process is the least clear

1.2 SHAPE OF F I L M S AND BUBBLES IN F O A M

Geometrical shape of gas bubbles in foam depends on the ratio of gas and liquid volumes, on the degree of polydispersity and on bubble packing The results discussed below apply also for concentrated emulsions (considering density and interfacial tension)

In a monodisperse foam the deformation of spherical bubbles and formation of films at the places of their contact starts when the gas content in the system reaches 50% (vol.) for simple cubic bubble packing or 74% for close (face-centred) cubic or hexagonal packing (foam expansion ratio - 4) In a polydisperse foam the transition to polyhedral structure starts

at expansion ratio n 10-20, according to [ 10] but, as reported in [51 ], this can occur at n < 4, the latter being more probable The structure which corresponds to the transition of bubbles from spherical to polyhedral shape is called occasionally honeycomb structure

In order to clarify the conditions which determine the mechanical equilibrium of films, the contact of three gas bubbles in a surfactant solution (Fig 1.6,a) is to be considered When three bubbles get into contact simultaneously, they shift to assume positions determined by the capillary pressure and surface tension At the place of contact of two bubbles a circular film is formed and its size increases with further deformation of bubbles

Fig 1.6 Shape of contact area of gas bubbles: (a)- equilibrium state of three bubbles; (b)- unstable equilibrium of four bubbles; c - equilibrium state of four bubble; d - monolayer of polyhedral foam consisting of identical bubbles

At the place of contact of three films a Plateau border is formed (Plateau triangle, Fig 1.7) the shape of which represents a triangle between three contacting cylinders Since film

Fig 1.7

tensions y = 2or (or - surface tension) are equal, forces acting in one plane can balance one another only if the three angles between them are equal (first law of Plateau)

If four similar bubbles are brought into contact the four films formed (Fig 1.6,b) can

be balanced when the angle between them is 90 ~ but this structure is unstable The slightest change in pressure in any bubble disturbs force equilibrium and the contact area of these four films is transformed into a system with two Plateau borders, where three films meet (Fig 1.6,c) Thus the monolayer of polyhedral foam which can be formed from identical bubbles between two plates will have symmetrical and regular structure with a hexagonal packing (Fig 1.6,d)

The probability of formation of polyhedra (cells) of a definite shape was studied with the methods of statistical mechanics applying two variants of calculations [52] These theoretical considerations were done for a monolayer of a polydisperse foam Both variants gave a probability curve the maximum of which was at 6 side faces of the polyhedron The theoretical dependence fits well with the curve of probability for distribution of cell faces in a real foam monolayer [53]

Cross-section of Plateau border; the definition of radius R is given in Section 4.3

When two bubbles come into close contact in the liquid medium, the shape of the film formed depends on the bubble size and, respectively, on the excess (inner) pressure in them This has been already considered in details by Plateau [8,54] Fig 1.8 shows the contact between two bubbles If the bubble sizes and pressures in them are not equal (R~ < R2, p~ > P2) the foam film which separates them bends turning its convex surface towards the bubble with bigger radius (with the lower pressure) The radius of curvature of the separating film R3 is determined by the expressions

radius of curvature of the film

W h e n two bubbles are not c o m p l e t e l y submerged, each one is coated with a film (having two surfaces) and getting into contact the film formed b e t w e e n t h e m has a radius of curvature expressed by

R 3 = (R2 - R ! )

F r o m Eqs (1.12) and (1.13) it follows that the film separating two bubbles is flat only when the bubbles are of equal size W h e n the difference in size is large (R1 << R2), then RI -~ R3 Expressions (1.11) - (1.13) are valid w h e n the separating film is very thick and the film tension does not differ from the surface tensions of both bulk phases

In the calculation of the curvature of thin films the change in film tension should be taken into account Thus, for a bubble with thin films Eq (1.12) transforms [55] in

In [64] the possible stable configurations of films in polyhedral foams is discussed from the thermodynamic point of view that any disperse system tends to minimum surface energy Almgren and Taylor [64] modelled the shape of the films and the angles between them with wire devices and studied several film configurations They established that only film configurations which obey Plateau laws are stable with respect to minor deformations

The form of polyhedra that build up the real foam and the shape of Plateau borders continues to draw interest because of its complexity Gibbs [65] and Lord Kelvin [66] discussed the filling of space with regular geometrical bodies This is important also for crystallography, botany (cell structure) and other scientific fields According to Kelvin's ideas the space can be totally filled up by polyhedra consisting of six quadrilateral planar and eight nonplanar hexagonal faces of zero net curvature The calculation of surface area and volume

of the Kelvin's minimal tetrakaidecahedron is presented in [67] The total area of its surface A

= 35.65a 2, volume V = 17.42a~, (where a k is the distance from the centre of the hexagon to the middle of the edge of the polyhedron and it is related with the edge length by the expression a = 1.1596a~) The ratio A/Ao in this polyhedron is 1.097 (where Ao is the area of a sphere with the same volume) Reinelt and Kraynik [68] have obtained more precise values of

*The reason for formation of contact angles and the methods for their measurement are discussed in Chapter 2 and 3

**There is evidence in [60] that in low expansion ratio foam (q~- 0.89) borders with four faces are formed as a result of structural transformation