Planar foam films

To understand drainage we have to discuss the pressure inside the liquid films. At the contact line between liquid films, a channel is formed. This is called the Plateau border. Due to the small bending radius (rP in Fig. 12.18), there is a significant Laplace pressure difference between the inside of the compartment and the liquid phase. The pressure inside the liquid is significantly smaller than in the gas phase. As a result, liquid is sucked from the planar films into the Plateau s border. This is an important effect for the drainage of foams because the Plateau borders act as channels. Hydrodynamic flow in the planar films is a slow process [574], It is for this reason that viscosity has a drastic influence on the evolution of a foam. Once the liquid has reached a Plateau border the flow becomes much more efficient. The liquid then flows downwards driven by gravitation. 

Based on the analysis of deformation of an idealised foam vertex, composed of six planar films, Stamenovich and Wilson obtained an expression for the shear modulus... 

Reinelt, D.A. (1993) Simple shearing flow of tree-dimensional foams and highly concentrated emulsions with planar films. / Rhed., 37 (6), 1117-1139. 

In the opposite case, when the surfactant is soluble in the continuous phase, the Marangoni effect becomes operative and the rate of film thinning becomes dependent on the surface (Gibbs) elasticity (see Equation 4.293). Moreover, the convection-driven local depletion of the surfactant monolayers in the central area of the film surfaces gives rise to fluxes of bulk and surface diffusion of surfactant molecules. The exact solution of the problem [651,655,689,739,740,787] gives the following expression for the rate of thinning of symmetrical planar films (of both foam and emulsion type) ... 

Figure 7.8 Schematic of a foam film (a) and a film on a solid surface (b).The region ofthe meniscus (C), the transition regions (T), and the planar films (F) are indicated.

One possible explanation of the observed dependence might be that the film rupture in om systems occurs by passing below the barrier II (Fig. 13c). Indeed, Bergeron [45] showed with large planar foam films (studied by the porous plate method) that in some systems II aI corresponded to an actual maximum of the calculated curve IlAs(fj), whereas in other systems ns was well below the maximum of the calculated nAs(fj) cmves (for a possible explanation see Ref. 45). Such a possibility is offered by different theoretical models of film rupture, in which the formation of imstable spots in large liquid films by various mechanisms is considered [40,45-47]. However, all these models are developed for large planar films and cannot be applied directly to om system without a careful analysis of the role of film curvature in the film rupture process. Fmther experimental and theoretical work is under way to reveal the actual mechanism of film rupture, to develop an adequate model of this process, and to explain the observed linear dependence of Has versus 1// eef-... 

Fig. 3.42 Region of two-dimensional foam formed by a PSi35-PNaA26 Langmuir-Blodgett film within the confines of a planar surface micelle domain (Meszaros et al 1994). 

An approach that is almost diametrically opposed to the earlier models of Khan and Armstrong, and Kraynik and Hansen, was advanced by Schwartz and Princen (108). In this model, the films are negligibly thin, so that all the continuous phase is contained in the Plateau borders, and the surfactant tiuns the film surfaces immobile as a result of surface-tension gradients. Hydrodynamic interaction between the films and the Plateau borders is considered to be crucial. This model, believed to be more realistic for common sur factant-stabilized emulsions and foams, draws on the work of Mysels et al. (109) on the dynamics of a planar, vertical soap film being pulled out of, or pushed into, a bulk solution via an intervening Plateau border. An important result of their analysis is commonly referred to as FrankeTs law, which relates the film thickness, 2h., to the pulling velocity, U, and may be written in the form ... 

As will become evident from the discussion that follows, essentially only the value of Aafh) in Equation 1.32 is of interest to us. For this reason, Aa h) can be viewed as a primary characteristic describing film properties and the interactions between surfaces. Unfortunately, for solid planar parallel surfaces, such measurements are nearly impossible the experimental integration of n(fi) between macroscopic surfaces requires that the surfaces remain flat and parallel to the precision of fractions of an angstrom in the course of measuring very small forces. While this is impossible for solid surfaces, such measurements are quite possible and indeed broadly utilized in the investigation of liquid films emulsion films, foam films, and wetting films. In all of these cases, a flat and parallel state can be maintained because of the high mobility of the interfaces. 

Here Pl is the density of the foaming liquid and is the radius of the bubble. Equation 4.2 implies that the time is independent of the height of the film above the planar liquid surface at which the bubble is resting. In actuality, the film would become relatively thin at the top of the bubble. Failure to account for this effect is a consequence of incomplete consideration of continuity by Shearer and Akers [5] in the derivation of Equation 4.2. 

Foam is an agglomeration of a large number of different bubbles (Plate 4.13). Each bubble in the foam is a polyhedral cell with a number of different faces. Each face is curved as a result of the excess pressure across it. If the pressure in two adjacent cells is the same, the excess pressure across the surface is zero and the separating surface is planar. The foam will contain, only, three film surfaces intersecting along lines at 120° and four lines of soap film meeting at a point with adjacent lines intersecting at 109° 28. ... 

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