Gibbs-Plateau channel

If a small individual film is surrounded by broad Gibbs-Plateau channel, one may assume that channel surfaces closely resemble those of spherical shape, and hence r, = r2 = r, and pa = 2o / r. In the case when large film is surrounded by a narrow channel, the shape of channel surface is close to cylindrical, i.e. r, = r, r2 = °°, and pa = o / r. The film is in equilibrium with channels surrounding it when absolute values of capillary pressure, pa, and disjoining pressure, II, are equal. 

When of < 2o(negative excessive film tension, Aof < 0), stable films equilibrium with macroscopic phase form. In this case contact angle, 0, exists between the film and the Gibbs-Plateau channel (see Fig. VII-3) [12]. The value of this contact angle is given by... 

In the case of highly mobile interface between dispersed phase and dispersion medium (as in foams and emulsions) the condition of zero fluid flow velocity at interface (non-slip condition), determining the validity of Reynolds equation, may not be obeyed. In this case the decrease in the film thickness occurs at a greater rate. However, in foam and emulsion films stabilized by surfactant adsorption layers the conditions of fluid outflow from an interlayer are close to those of outflow from a gap between solid surfaces even in cases when surfactant molecules do not form a continuous solid-like film. This is the case because at surfactant adsorption below Tmax the motion of fluid surface leads to the transfer of some portions of surfactant adsorption layer from central regions of film to peripherical ones, adjacent to the Gibbs-Plateau channels. As a result, the value of adsorption decreases in the center of film, but increases at the periphery, which stipulates the appearance of the surface... 

When this condition is met, the liquid in the foam is redistributed due to its drainage from the films and disappearance of a part of the Gibbs-Plateau channels. 

The edges of foam cells are the Gibbs-Plateau borders (channels) filled with dispersion medium (see Chapter VII, 1). It was shown by Plateau that only three films may be joined by one border, and that the films must meet at 120°. The surface of Gibbs- Plateau border has a complex concave shape dictated by the condition requiring that the sum of two main curvatures remains constant. The capillary pressure under a concave surface is the reason for the lowered pressure in the Gibbs-Plateau border. 

Kuznetsova, L. L. and Kruglyakov, P. M., Study of the regularities of surfactant solutions flow along Plateau-Gibbs channels in foam, Doklady Phys. Chem., Vol. 260, No. 4,1981. 

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