Cohesive Properties of Thin Films of Liquids Adhering to a Solid Surface BY J. F. PADDAY Research Laboratories Kodak Limited Wealdstone Harrow Middlesex England Received 6th April 1970 The process of forming and rupturing a thin liquid film at a solid surface is described thermo- dynamically for both high and low energy solid surfaces. In part 1 the build-up of thin films on high-energy surfaces from the first monolayer is considered and reviewed. Components of the surface free energy of formation of the thin film (disjoining pressure) are defined. For curved surfaces the disjoining forces should be combined with the Laplace capillary pressure to give a correct form of the Kelvin equation. It is suggested from the early work of Bangham and Deryaguin that thin liquid layers have anomalous physical properties.These studies are discussed in relation to the thickness of the liquid films. In part 2 new experimental evidence of the critical rupture thickness of thin liquid films on low energy surface is presented. A number of pure liquids rupture spontaneously on low energy surfaces such as wax or polytetrafluoroethylene at very great thicknesses (0.01 cm). The effects of aqueous salt and surfactant solutions suggest these long-range forces are electrical in origin. We first consider the process of thinning of a thick uniform layer of liquid in contact with a pure smooth horizontal solid surface as shown in fig. 1. It is assumed \ B C FIG. 1 .-The processes of disjoining and rupture. A formation of a thin stable layer ; B formation of a metastable layer with sessile drop or lens on a wetted surface ; C unstable thin layer with the formation of a dry patch.that only vapour is present above the liquid surface and that the solid is completely wet when immersed below the surface of the liquid. If now the liquid thickness is successively reduced one of three phenomena occurs either (A) the solid surface is 64 J . F. PADDAY 65 spread with and holds a uniform thin layer of liquid which is stable at all thicknesses ; (B) or a thin layer is formed which when reduced to some critical thickness dis- proportionates to form a very thin layer in contact with a thicker lens or sessile drop; (C) or at some relatively great thickness the liquid layer in contact with the solid spontaneously breaks to leave a dry patch with a wetting meniscus in contact with it as shown in fig.1. The phenomena of fig. 1A and B are invariably associated with high-energy surfaces and are considered in part I of this paper. The phenomenon of fig. 1C is associated with low energy surfaces and is considered separately in part 2. PART I.-THIN FILMS ON HIGH ENERGY SURFACES Hardy appears to have been one of the earliest investigators of properties of thin films of liquids in contact with solids. He was concerned primarily with observa- tions with lubrication but discovered the dual thickness films (fig. 1B) and likened their behaviour to the formations of lenses of non-spreading oils on water. It became clear from this early work of Hardy and later Bangham and Fakhoury that to form stable or metastable thin films it was necessary to spread liquids on high-energy surfaces such as mica clean glass or silica and charcoal.Bangham 2-4 and his coworkers investigated the build-up of successive layers of condensed vapour to give a film of type A fig. 1. The partial vapour pressures recorded by Bangham and Mosallam did not exceed 0.7 of saturation and the film thicknesses they obtained were less than 20A. They thus never made their films thick enough to investigate the region of condensation on these surfaces where the condensed vapour was of the same thickness as a receding liquid film. Bangham also attempted to estimate the surface tension of much thicker films formed by a liquid receding on a solid surface. He claimed that the thinner of the two films in situation B of fig. 1 had a lower surface tension as measured from the angle of contact between the thick and thin However these wetting studies tended to be of a phenomenological nature and some of his experiments on the break up of liquid films on freshly cleaved mica could not be confirmed by the author .Over the same period Deryaguin and his coworkers investigated the properties of thin films of liquid on high-energy ~olids.~-lO Deryaguin introduced the term wedging-apart pressure ” later known as “ disjoining pressure ” to describe the equilibrium force required to remove a small increment of thickness of the thin liquid layer. 66 DISJOINING PRESSURE OF THIN FILMS OF LIQUIDS ON SOLIDS The process of joining a thin liquid film to a solid surface is shown in fig. 2. Rupture in effect is the “ reverse ” of this process. The disjoining process differs from rupture in that only a small increment of liquid thickness is removed and not the whole layer.The steps of the process are taken as first the formation of the free liquid film (A-B) followed by the bringing into contact of the solid surface with the thin film (B-C). Thereafter specific interactions or solution may take place between solid and thin film (C-D) and finally adsorption forces may lead to the build-up of a electric potential at each interface of the thin layer (D-E). Deryaguin and Shcherbakov Duyvis,l Kitchener and Sheludko l4 have all given thermodynamic accounts of the disjoining process. They define the dis- joining pressure as the change of free energy with thickness and break it down into SP1-C 66 COHESIVE PROPERTIES OF THIN FILMS components. Deryaguin and Obuchov expression define this disjoining pressure ll by the where y is the specific surface free energy of the thin liquid film yo is the specific surface free energy of an infinitely thick film and h is the thickness of the layer.A B C .' . .. I. - - . - + **. . . . . *. .. . .. -. . .. ' * .. .. '. ' .. I .,* 'liquid .. 4 TTLL -1 . .. * *. - . -* TT,s ' - . .. *.. . . 1 -. - - .. - . - E D I FIG. 2.-Steps in the formation of a thin film. A-B formation of thin liquid film ; B-C adhesion of thin films to solid surface ; G-D reorientation of thin liquid layer by specific interactions ; D-E adsorption of electric charge. Provided that the structure of the bulk liquid is retained in the thin layer it is possible to inter-relate disjoining pressure with changes in surface tension but Deryaguin and his coworkers have consistently maintained that thin liquid films adhering to solid surface are either totally oriented in the thin layer (Deryaguin's a- phase) or are partially oriented over a fraction of the total thickness of the film (Deryaguin's P-phase) the remainder of the layer containing unoriented or bulk liquid.Hence on Deryaguin's evidence it is incorrect to consider disjoining pressure as involving a change in surface tension alone. A more general definition of dis- joining pressure is derived by Deryaguin and Shcherbakov l1 in terms of the chemical potential of the inolecules forming the thin film and the total free energy w of the thin film. Their equation was RTln (PIP,) = ul1,(6w/6h) (2) where v is the molar volume of the substance forming the thin layer P is the vapour pressure in equilibrium with the thin film and P the saturated vapour pressure at the temperature T.The term -6w/61z is the disjoining pressure and is equivalent to TI of eqn (1). Eqn (2) applies equally to the adsorption of the first monolayer of vapour on the solid surface and to successive build-up of condensed vapour into a true liquid layer. It thus allows the vapour pressure to be used to derive the disjoining pressure when direct measurement is not possible. COMPONENTS OF THE DISJOINING PRESSURE Sheludko l4 and Kitchener l3 split the disjoining pressure ll into two components ; a term IT for the van der Waals interactions and a term 17, for the component due to electrical double layer repulsion. It is more convenient to split the van der Waals term into two components one ITLL for the disjoining pressure of the liquid film in the absence of any solid (equivalent to process A to B of fig.2); and the other, J . F . PADDAY 67 nSL (equivalent to process B to C of fig. 2) for the effect of the solid on this film. In the absence of electrical charges and of specific interactions ELL must always be negative and nSL always positive. To take account of the change in bulk properties in the film that is consistently claimed by many workers a component of the disjoining pressure n is introduced. This component represents the change in free energy of the thin layer due to orienta- tion solvation or other specific interactions between the solid and the thin liquid film. Although measurement of this component may well prove difficult its value must be positive for high energy surfaces.The contribution of the electrostatic pressure IT, has been derived by Langmuir,ls Frumkin,l6 Verwey and Overbeek,I7 Deryaguin and Landau and She1udk0.l~ Generally n, was derived for two interacting electrical double layers of the same charge sign and density such as those that stabilize thin soap films. Read and Kitchener l 9 calculated n, of a thin water film at a silica surface taking into account the difference in potential between the solid-liquid and liquid-air interfaces. They pointed out that the usual assumption of constant potentials leads to physically improbable consequences because the negative charge at one surface was much greater than at the other. The counterions of the surface of high charge would render the surface of low charge positive and thereby induce attraction.However it is certain that ITel must be positive when the two interacting surfaces of the thin film are of like charge. Similarly ITel must be negative when the two surfaces are of opposite charge. A curved liquid-air surface of radius Y will possess a capillary pressure given by 2y/r and a vapour pressure P different from the saturated value P,. The capillary pressure is associated with the liquid-air-interface and may be used as a direct measure of the disjoining pressure lo l9 when the curved surface is free from thin film perturbations. However when a curved liquid-air surface approaches a flat surface film as with a Wilhelmy plate then there will be a transition region however small where the capillary pressure diminishes and disjoining pressure increases.ln this region we suppose in the first instant that the disjoining and capillary pressures are additive so that where r and r 1 are the principal radii of curvature which possess a negative value when the liquid-air interface is concave and a positive value when convex. For thick films ll is zero and eqn (3) reduces to the Kelvin equation. The contributions ITLL ITsL IT and n, are all complex functions of /z and each will vary according to whether the thin film is flat or curved. Although 1111 and ITel are probably interrelated we assume additivity such that (4) = ~ L L + X ~ L + ~ 1 + riel. When ll is negative the thin film is unstable. positive but d2w/6h2 must be negative. For stability not only must II be REGIONS OF STABLE THIN FILMS The thin liquid film adhering to a long perfectly-wetted Wilhelmy plate will be considered following the model of Read and Kitchener.lg Such a plate is shown in fig.3 and here it will be used to distinguish certain zones of the thin films. If it is assumed that only pure vapour is in contact with the liquid and that the vapour is an 68 COHESIVE PROPERTIES OF THIN FILMS ideal gas the vapour pressure P at any height I above the free surface bulk liquid is given by (RTIu,) In (PIP,) = - I gp. ( 5 ) The hydrostatic height may thus be used as a measure of the disjoining pressure. Combining eqn (3) (4) and (9 - - At flat films the first term is zero and disjoining pressure is the main component whereas for thick films the first term predominates and all other terms are zero. ' p / CM. PS - I08 - 107 0.000; - - I d 0484 -lo5 0.930 -I& 0.993 -I$ 0.3993 -lo2 0.9999 -I0 0-99999 1 L WILNELMY PLATE l - r h rfNkt.4 10'0 lo8 I06 104 B.E.T.EANGHAM DERYACUIN a ZORIN i 20 6 0 100 400 2oC 1500 UNKNOWN REGION ZORlN L CHURAEV OERYAGUIN L KUSSAKOV READ L KITCHENER KELVIN / LAPLACE . .. FIG. 3.-Regions of stable thin films on a Wilhelmy plate. Where the Wilhelmy plate meets the free surface of liquid a cylindrical meniscus will be formed. At some height above the free surface equal to the capillary constant a the liquid meniscus will meet the flat thin film. The shape of the meniscus in this region is governed by the Laplace equation because all II terms of eqn (6) are too small to matter. This region is the meniscus zone of the " thin films " and may be located anywhere up the side of the Wilhelmy plate merely by bringing a second Wilhelmy plate into close proximity so that capillary rise is obtained.At some height say lo8 cm above this zone the partial vapour pressure is so small that the solid Wilhelmy surface may be regarded as practically " clean ',. Between these two zones lies a series of regions of different disjoining pressure in which all experimental data may be placed. The first region below the " clean'' zone may be regarded as that region in which the first monolayer of adsorbed vapour condenses on the solid surface. Descending further one enters the B.E.T. region where partial vapour pressure increases to a value of about 0.7 and multilayer adsorption sets in. J . F. PADDAY 69 Bangham's 2o system of adsorbed water vapour on glass and mica covered a range of partial vapour pressures not exceeding 0.7 and therefore falls in to this B.E.T.region. He ascertained the thickness of his adsorbed layers as being no greater than 20 8 ; hence the anomalous properties of condensed or adsorbed water claimed by Bangham refer specifically to the first few layers and not to the much thicker layers of Deryaguin and Zorin 21 and those by which anomalous water was formed as reported by Fedyakin 22 and by D e r y a g ~ i n . ~ ~ However Bangham claimed anomalous properties for the much thicker layers he obtained with receding wetting films. The results of Deryaguin and Zorin 21 on thin films of water and other liquids on glass fall into the next region of partial vapour pressure 0.7 to 0.99. This is the region where capillary condensation usually takes place on porous solid surfaces.In the B.E.T. region and the region of capillary condensation the main contribu- tion to the total disjoining pressure was believed by both Bangham and by Deryaguin to be ITI i.e. a specific but long-range interaction which is much larger than the sum of the van der Waals attractions nSL+nLL. The results of Read and Kitchener,lg Deryaguin and Kussakov l o and Zorin and Churayev 24 fall in a region of much lower disjoining pressures and refer to much thicker layers of 200 to 5000A. Read and Kitchener attribute their low disjoining pressure at these thicknesses to electrostatic repulsion IT,, because the repulsion fell as ionic strength of added salt increased. The contributions of the other terms HSL IfLL and IT in Kitchener's experiments were regarded as zero at these much greater thicknesses.Zorin and Churayev 24 measured the thickness of thin water films on quartz at low disjoining pressures. Their stable film was 100 A thick and possessed a peripheral step 400A thick. This step could well correspond to the step found when a large clean sheet of glass is withdrawn from a basin of water and allowed to e q ~ i l i b r a t e . ~ ~ * ~ ~ The step on the plane glass sheet appears at about 10 cm above the free surface and corresponds to a disjoining pressure of about lo4 dyn but is attributed by Satterly and Turnbull 25 to contamination. This step might mark a change from electrostatic to interactive disjoining forces. Each of the terms of eqn (4) are a different function of the thickness h so that II the total disjoining pressure is unlikely to fall away smoothly.Deryaguin and Zorin 21 showed that it did so for the non-polar liquids CC14 and CsH6 where the disjoining pressure decreased steadily to zero in a manner qualitatively predictable from London's theory of dispersion forces. For these liquids one may assume that where ASL and ALL are the Hamaker constants for intermolecular interactions between solid-liquid and liquid-liquid molecules respectively. K is a constant which depends on the value of n which possesses a value of 3 when the dispersion forces are unretarded and a value of 4 when retarded. Approximate expressions for ITsL and IT, are given by Kitchener l 3 and Sheludko,14 and these lead to negligible forces when 12 is greater than 500w. Thin layers of polar liquid do not show the same trend.Water and n-alcohols are known to interact with polar surfaces such as glass or mica to produce positive value of IT (Deryaguins' a-phase or Bangham's aggregated phase). The stepwise increase or decrease of the stable film has been explained by Zorin 27 as due to the difference of IT for the two phases postulated by Deryaguin. In fig. 4A the lower isotherm refers to the disjoining isotherm of Deryaguin's a-phase and the upper film on mercury. Scheludko l 4 suggests that the same data may be explained as shown in fig. 4B without recourse to the two phases supposed by Deryaguin. 70 COHESIVE PROPERTIES OF THIN FILMS Between the thick or stepped region of low disjoining pressure and the capillary condensation region of very high disjoining pressure lies a large unknown region of disjoining pressures that has never it seems been investigated.In the region of capillary condensation where 0.7 <Pips < 0.99 the Kelvin equation may be tested experimentally. The Kelvin equation without disjoining effects leads to radii of curvature between 20 and 50 A. Deryaguin and Zorin show that disjoining effects extend to lOOA in this region. This is also the region of partial vapour pressure appropriate to the formation of Deryaguin's anomalous water. Thus any test of the Kelvin equation must take into account disjoining effects as given in eqn (3) and any application of disjoining pressure to curved surfaces must include the capillary pressure. h I *O Zorin h 1.0 9 PS Shelud ko FIG. 4.-Disjoining isotherm of benzene on mercury. A Zorin; B Sheludko (taken from Sheludko 14).PART 2.-RUPTURE OF THIN FILMS AT LOW ENERGY SURFACES A third type of liquid layer in contact with a solid surface that of fig. lC is that which spontaneously ruptures when the thickness is reduced below some critical value. This type of thin liquid film is formed only at low-energy surfaces and it appears to be associated with large critical rupture thickness i.e. 0.01-0.05 cm. Although negative disjoining pressures have been measured by Sheludko and Platikanov 28 the rupture process of fig. lC does not seem to be widely studied. The experiments by which the critical thickness of these films was observed are given here together with the principal results. EXPERIMENTAL The apparatus for measuring the critical rupture thickness shown in fig. 5 is basically that described previously 29 for measuring spreading coefficients by the drop-height method.Instead of the solid surface E resting on the sample platform it was supported inside a glass container G on three glass chips broken from a microscope slide. The surface of the plane solid which was either a waxed glass microscope slide or a flat piece of polytetrafluoroethylene (Teflon) was mounted level. A 10 ml glass syringe was used to raise or lower the level of liquid in the glass container G. All apparatus was carefully cleaned and washed. Freshly distilled water checked for purity by surface-tension measurement and by shaking was poured into the vessel so as to cover the solid surface. The syringe was then J . F. PADDAY 71 used to lower the level of the liquid while at the same time its height was monitored with the pointer C.At some critical thickness the meniscus suddenly broke through to the Teflon. The critical rupture thickness was then measured as the distance between the pointer and the solid surface with an accuracy of fl .O p. The thickness at which breakdown took place was reproducible to within &3 % and was usually between 0.01 and 0.05 cin. Thick- nesses below 0.003 cm were regarded as being too small to measure to this method. The surface tension of water after disjoining was measured and found to be unaltered (within f0.05 dyn/cm) thus dispelling the possibility of artifacts caused by impurities. FIG. 5.-Apparatus for measuring the thickness of thin films on a low energy surface. A syringe B microscope with a vernier graticule ; C point adjustable in focus plane of the microscope ; D height adjustment of the microscope; E flat sample of low energy surface; F spreading liquid G glass vessel.RESULTS OF NEGATIVE RUPTURE PRESSURES It is believed that the phenomenon described measures a negative rupture pressure. In table 1 the critical rupture thickness h of a number of liquids on Teflon measured by this method are given. Even pure hydrocarbons and ethylene glycol ruptured spontaneously . TABLE CRITICAL RUPTURE THICKNESS OF PURE LIQUIDS ON TEFLON YL liquid p g/cm2 dyn/cm h cm water 1 .o 72 -0.051 benzene 0.88 29 -0.016 ethylene glycol 1.12 49 - 0.056 3 -decene 0.74 23 - 0.026 1 - tetradecene 0.775 27 - 0.027 1 -0ctadecene 0.79 28.4 - 0.027 That the process of rupture was not some artifact due to irregularities of the solid surface was shown by comparing the critical disjoining thickness of a flat and curved wax surface.The curved surface was formed by coating a watch-glass with paraffin wax. These results (table 2) indicate that the effect of curvature on the critical rupture thickness is relatively small and that therefore the effect of gross unevenness 72 COHESIVE PROPERTIES OF THIN FILMS of a solid surface cannot account for the large rupture thickness. The results of water rupturing on a Teflon and o n a wax surface (tables 1 and 2) show that the rupture thickness is critically dependent on the nature of the solid surface. TABLE 2.-cRITICAL RUPTURE THICKNESS OF WATER FILMS ON PARAFFIN WAX SURFACES h (cm) -0.032 flat surfaces - 0.03 1 curved surface (radius 6 cm) The effect of spreading aqueous solutions of KN03 tetradecyltrimethyamnionium bromide (t.t.a.b.) and the sodium salt of disec-octylsulphosuccinate (d.0.s.) on Teflon was also investigated.It was found that the critical rupture thicknesses of solution of KN03 followed closely those of solutions of t.t.a.b. as seen from fig. 6. At I I 0-5 10-4 10-3 10-2 to-’ mol/l. FIG. 6.-Critical rupture thickness of aqueous solution on teflon. x tetradecyltrimethylam- monium bromide ; 0 sodium dioctyl sulphosuccinate ; A KN03. concentration below 3 x M only small changes in thickness were observed but between 3 x and M the rupture pressure decreased suddenly and then increased to a value slightly greater than that of pure water. D.o.s. behaved differently. In the same concentration range the anionic surfactant d.0.s.produced a film that was stable at all measurable thicknesses and would not spontaneously disjoin (see fig. 6). In the concentration range 3 x to M both d.0.s. and t.t.a.b. adsorb at both the liquid-air and the low energy solid-liquid interfaces,30* 31 thus it is likely that the main contribution to these forces is the electric term arising from monolayers of adsorbed ionic surfactants. The comments of Dr. J. A. Kitchener are gratefully acknowledged. APPENDIX (ADDED IN PROOF) The following evidence was obtained from further experiments performed since writing the paper and was presented in the Discussion. SURFACE DEFORMATION PRIOR TO RUPTURE In a further series of experiments the rupture of a thin film of water at a curved wax surface was followed using a high-speed cine camera recording at approximately 10oO frames s-l while the liquid layer was continuously thinned.These sequences showed clearly that a FIG. 7.-Formation of dimple and rupture of a thin film of water on wax. Approx mag. x2. Radius of wax surface 7 cm. (a) Formation of dimple (towards left-hand edge of white patch) ; (b) rupture revealing wax surface below. To face page 73.1 J . F. PADDAY 73 local indentation of the water/air interface occurred at the position where the convex wax surface was nearest the liquid-air surface. In fig. 7 prints of two frames from this cine sequence are shown. The whitish patch is a specular reflection in the liquid/air interface produced by a powerful lamp. In the upper picture (a) the indentation is seen as a dimple in the surface near the edge of the specular reflection.Some 300 ms later the dimple broke through to the wax surface as shown in the lower picture (6). Once the wax was revealed the border expanded rapidly as a receding meniscus. Although these observations were performed on a dynamic system they served to show the formation of the dimple prior to rupture. A cross-section of it is shown in fig. 8(u). The dimple was also produced with I FIG. 8.-A apparent cross-section profile of the dimple of fig. 7(a) ; B apparent cross-section profile of deformation with wax that had been polished with cellulose fibres. the apparatus of fig. 5 but with the flat Teflon surface replaced by a convex glass surface coated with pure paraffin wax. Fig. 8(b) shows a second type of deformation obtained with a wax surface artificially polished.A dimple formed and appeared to be stable for many min- utes while observations were being made. Vibrations artificially induced at the liquid/air interface appeared to be damped out as they reached the dimple and only high energy knocks succeeded in forcing the dimple to break through prematurely. It was not found possible to estimate the depth of the dimple from the cine film but the appearance showed that the dimple penetrates a considerable part of the thickness of liquid layers Thus the thickness of the liquid film between the bottom of the dimple and the top of the convex wax-liquid interface will be considerably less than the critical disjoining thickness of tables 1 and 2. Furthermore the apparent negative disjoining forces at the bottom of the dimple will be balanced by a further restoring pressure P I given by where t is the depth of the dimple and r2 the radius of curvature (negative in value) at the bottom of the dimple.W. Hardy Proc. Roy. SOC. A 1912,86,610; 1923,104,25 ; 1925,108 1 ; 1926 112,62. D. H. Bangham and N. Fakhoury J. Chem. SOC. 1931 1324. D. H. Bangham N. Fakhoury and A. F. Mohamed Proc. Roy. SOC. A 1934 147 152 and 175. D. H. Bangham and S . Mosallam Proc. Roy. SOC. A 1938,165 552 ; 1938,166 558. D. H. Bangham and R. L. Razouk Trans. Faraday Soc. 1937,33 1459. D. H. Bangham and Z . Saweris Trans. Faraday SOC. 1938 34 554. B. V. Deryaguin J. Phys. Chem. 1932 ,3 29 ; 2. Phys. 1933 34 657 ; J. Phys. Chem. 1934 5,379 ; Sov. Phys. 1933 4,431. B. V. Deryaguin and E. Obuchov J. Colloid Chem. 1935,1,385 ; Actaphysicochim. 1936,1,5.B. V. Deryaguin and M. Kussakov Bull. Acad. Sci. U.R.S.S. 1936 471. B. V. Deryaguin and L. M. Shcherbakov Colloid J. U.S.S.R. (trans) 1961 23 33. lo B. V. Deryaguin and M. Kussakov Actuphysicochim. 1939 10,25. l2 E. M. Duyvis Thesis (Utrecht 1962). l3 J. A. Kitchener Endeavour 1962 22 118; Wetting S.C.I. Monograph no. 25 1967; (Soc. Chem. Ind. London 1967) p. 300. l4 A. Sheludko Adv. Colloid Interface Sci. 1967 1 391. l 5 I. Langmuir J. Chem. Phys. 1938 6,!873. 74 COHESIVE PROPERTIES OF THIN FILMS l 6 A. N. Frumkin Acta physicochim. 1938 9 3 13. l 7 E. J. W. Verwey and J . 1'. G. Overbeek TI2cor37 of the Stability of Lyophobic Colloids (Elsevier Amsterdam 1948). B. V. Deryaguin and L. Laundau Zhirr.. E x ~ p . Teor. Fig. 1941 11 802. l 9 A. D. Read and J. A. Kitchener J. Colloid Interface Sci. 1969 30 391. 2oD. H. Bangham J. Chem. Phys. 1946,14 352. 21 B. V. Deryaguin and Z. M. Zorin Proc. 2nd Znt. Congr. Surface Activity (London) 1957,2,145. 22 N. N. Fedyakin Colloid J. (trans.) 1962 24 425. 23 B. V. Deryaguin et al. Teor. Eksp. Khim. 1968 4 527. 24 Z. M. Zorin and N. V. Churayev Colloid J. (trans.) 1968 30 279. 2 5 J. Satterly and R. Turnbull Trans. Roy. Sac. Can. 1929 3 95. 26 R. S. Burdon Proc. Phys. SOC. 1926 38 148. 27 Z. M. Zorin KolloidZhur. 1963 25 624. 28 A. Sheludko and D. Platikanov Kolloid Zhur. 1961 175 150 ; Dokl. Akad. Nauk S.S.S.R. 29 J. F. Padday Rev. Sci. Znstr. 1959 26 256. 30 J. F. Padday Wetting S.C.1 Monograph no. 25 (SOC. Chem. Ind. London 1967) p. 234. 31 J. F. Padday Proc. 4th Int. Con.qr. Surface Active Substnnce 1964,2,299. 1961 138,415.