Stability of soap films

In this chapter we shall show how the observed phenomena may be explained by means of elementary catastrophe theory. In principle, the discussion will be confined to examination of non-chemical systems. However, some of the discussed problems, such as a stability of soap films, a phase transition in the liquid-vapour system, diffraction phenomena or even non-linear recurrent equations, are closely related to chemical problems. This topic will be dealt with in some detail in the last section. The discussion of catastrophes (static and dynamic) occurring in chemical systems is postponed to Chapters 5, 6 these will be preceded by Chapter 4, where the elements of chemical kinetics necessary for our purposes will be discussed. 

A simple example of a physical system exhibiting in certain circumstances sensitivity to arbitrarily small changes in control parameters is a soap film stretched on a thin wire frame. We shall demonstrate that such 

We shall examine properties of two systems of this type. Let the first system consist of a soap film stretched on two rings having the same diameter R (Fig. 28). 

The system described above belongs to a class of models with potential. The properties of stationary states of the system are totally determined by the condition of a minimum of potential energy of the system. In this case, the potential energy is proportional to the surface area of the film. Since the gravitational field is a potential field, accounting for the effect of gravitational forces on the film also leads to a certain model with potential. 

In the considered case the soap film takes the shape of a surface of revolution, see Fig. 28. The area of revolution, S, is given by the equation 112 

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Many of the considered problems, such as the problem of stability of soap films, the liquid-vapour phase transition, the diffraction phenomena, descriptions of the heartbeat or the nerve impulse transmission, catastrophes described by non-linear recurrent equations have a close relation to chemical problems. 

During the First World War Sir James Dewar, who is primarily known for his work in the field of low temperature physics and for the creation of the Dewar flask, was unable to continue his researches into low-temperature phenomena. So he investigated the draining and stability of soap films. His assistant and colleague during this period was Mr. A. S. C. Lawrence who summarized their joint work in his book. Soap Films, a study of molecular individuality fi... 

The stability of soap films is determined by the amphipathic ions in the surface. If a soap film is perturbed from equilibrium so that the area of an element of film increases, the surface density of amphipathic ions will decrease. That is, the number of ions per unit area will diminish and consequently the surface will behave more like the surface of water. Hence the surface tension of the surface element will increase because the surface tension of water is greater than that of soap solution. This increased force in the region of increased area will restore the surface to its former equilibrium configuration. This stabilizing effect was first observed by Marangoni and is known as the Marangoni effect. 

The relative stability of soap films is partially due to their elasticity. To see this, we consider a film with an equilibrium state represented by the surface excess T and the dissolved surfactant concentration c. A local stretching disturbs these parameters. If the disturbance occurs on a short time scale, the soap molecules do not have time to diffuse out from the inner fluid to the surface, so the same number of soap molecules remains both inside and at the surface. As the area increases, Tg decreases, which results in an increase of the surface tension according to Eq. (2.11), thus opposing the stretching. This process is called the Marangoni elasticity and explains the film stability to rapid disturbances. If the time scale of the stretching is... 

That electrostatic double-layer forces play a dominant role in the stabilization of soap films can be demonstrated by measuring the change in film thickness with a variation of the salt concentration. With increasing ionic strength, the Debye length decreases and we expect the film to shrink in thickness. Such experiments were... 

Water-in-oil macroemulsions have been proposed as a method for producing viscous drive fluids that can maintain effective mobility control while displacing moderately viscous oils. For example, the use of water-in-oil and oil-in-water macroemulsions have been evaluated as drive fluids to improve oil recovery of viscous oils. Such emulsions have been created by addition of sodium hydroxide to acidic crude oils from Canada and Venezuela. In this study, the emulsions were stabilized by soap films created by saponification of acidic hydrocarbon components in the crude oil by sodium hydroxide. These soap films reduced the oil/water interfacial tension, acting as surfactants to stabilize the water-in-oil emulsion. It is well known, therefore, that the stability of such emulsions substantially depends on the use of sodium hydroxide (i.e., caustic) for producing a soap film to reduce the oil/water interfacial tension. 

In this situation, the equilibrium thickness at any given height h is determined by the balance between the hydrostatic pressure in the liquid (hpg) and the repulsive pressure in the film, that is n = hpg. Cyril Isenberg gives many beautiful pictures of soap films of different geometries in his book The Science of Soap Films and Soap Bubbles (1992). Sir Isaac Newton published his observations of the colours of soap bubbles in Opticks (1730). This experimental set-up has been used to measure the interaction force between surfactant surfaces, as a function of separation distance or film thickness. These forces are important in stabilizing surfactant lamellar phases and in cell-cell interactions, as well as in colloidal interactions generally. 

Tait, Properties of Matter, 1899, 256 for forms of films on frames, etc., see Searle, Proc. Cambr. PhiL Soc.9 1913, 17, 285 Michl, Phys. Z.9 1913, 14, 1218. For stability of thin films, Phillips and Rose-Innes, Proc. Phys. Soc., 1915, 27, 328. For pressure in a soap bubble, Kuenen, Proc. K. Akad. Wetens. Amsterdam, 1915,17, 946 Comm. Leiden, 1914,154 a). On the effect of evaporation on the stability of liquid films and froths, see Talmud and Suchowolskaja, Z. phys. Chem.9 1931, 154, 277 Neville and Hazlehurst, J. Phys. Chem.91937,41, 545. 

Mechanisms of Single-Foam Film Stability. Soap bubbles and soap films have been the focus of scientific interest since the days of Hooke and Newton (2—9). The stability and structure of foams are determined primarily by the relative rate of coalescence of the dispersed gas bubbles (10). The process of coalescence in foams is controlled by the thinning and rupture of the foam films separating the air bubbles. Experimental observations suggest that the lifetime (stability) of foam films is determined primarily by the thinning time rather than by the rupture time. Hence, if the approaching bubbles have equal size, the process of coalescence can be split into three stages ... 

Role of Adsorbed Surfactant Layer. Foams, irrespective of the nature of liquid and gas involved, require a third component for stabilization of thin films (lamellae) of the liquid. In the familiar case of aqueous soap films, this third component is the soap, a surface-active chemical that adsorbs at the gas—liquid interface and lowers the surface tension of water. The two effects, adsorption at the liquid surface and the depression of surface tension, are intimately linked and occur concomitantly. The adsorption is defined as the excess moles of solute per unit area of the liquid surface. In a binary system, this surface excess can be directly related to the lowering of surface tension by Gibbs adsorption equation ... 

In (5.107) and (5.108) we have assumed that a liquid cylinder has been deformed. In the case of the cylinder of soap film Eq. (5.108) is valid providing o is the film tension, a/. This factor will not effect the condition we shall derive for the stability of the soap film. Neglecting the weight of the fluid, the pressure difference between A and B is, from (5.107) and (5.108),... 

Though foam and emulsion films might exist for a long time, on some timescale they will collapse. The rupture of foam and emulsion films has been studied by various methods both experimentally [797] and theoretically [798]. It is obvious that the stability of foam films is influenced by surface forces. For example, in 1924 Bartsch reported that electrolytes decrease the life time of certain foams [799], presumably by decreasing electrostatic stabilization. Surface forces alone, however, do not determine the life time of a soap film. 

The repulsion between two double layers is important in determining the stability of colloidal particles against coagulation and in setting the thickness of a soap film (see Section VI-5B). The situation for two planar surfaces, separated by a distance 2d, is illustrated in Fig. V-4, where two versus x curves are shown along with the actual potential. 

Fig. 2. Effective interface potential (left) and corresponding disjoining pressure (right) vs film thickness as predicted by DLVO theory for an aqueous soap film containing 1 mM of 1 1 electrolyte. The local minimum in H(f), marked by °, gives the equiHbrium film thickness in the absence of appHed pressure as 130 nm the disjoining pressure 11 = —(dV/di vanishes at this minimum. The minimum is extremely shallow compared with the stabilizing energy barrier.

Berkman and Egloff explain that some additives increase the flexi-bihty or toughness of bubble walls, rather than their viscosity, to render them more durable. They cite as illustrations the addition of small quantities of soap to saponin solutions or of glycerin to soap solution to yield much more stable foam. The increased stability with ionic additives is probably due to elec trostatic repulsion between charged, nearly parallel surfaces of the hquid film, which acts to retard draining and hence rupture. 

In a gas and liquid system, when gas is introduced into a culture medium, bubbles are formed. The bubbles rise rapidly through the medium and dispersion of the bubbles occurs at surface, forming froth. The froth collapses by coalescence, but in most cases the fermentation broth is viscous so this coalescence may be reduced to form stable froth. Any compounds in the broth, such as proteins, that reduce the surface tension may influence foam formation. The stability of preventing bubbles coalescing depends on the film elasticity, which is increased by the presence of peptides, proteins and soaps. On the other hand, the presence of alcohols and fatty acids will make the foam unstable. 

As is known, if one blows air bubbles in pure water, no foam is formed. On the other hand, if a detergent or protein (amphiphile) is present in the system, adsorbed surfactant molecules at the interface produce foam or soap bubble. Foam can be characterized as a coarse dispersion of a gas in a liquid, where the gas is the major phase volume. The foam, or the lamina of liquid, will tend to contract due to its surface tension, and a low surface tension would thus be expected to be a necessary requirement for good foam-forming property. Furthermore, in order to be able to stabilize the lamina, it should be able to maintain slight differences of tension in its different regions. Therefore, it is also clear that a pure liquid, which has constant surface tension, cannot meet this requirement. The stability of such foams or bubbles has been related to monomolecular film structures and stability. For instance, foam stability has been shown to be related to surface elasticity or surface viscosity, qs, besides other interfacial forces. 

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