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Some recent progress in the study of liquid foams is reviewed in outline. Calculations of foam conductivity are presented, which further improve upon the approximation recently proposed by us, in accounting for the nonlinearity in the dependence of conductivity on liquid fraction.

We present a new analysis of the dependence of electrical conductivity on liquid fraction for a foam. Ignoring the contribution of the films to both the liquid content and the conductivity, we consider only the network of liquid-filled Plateau borders and the junctions at which they meet. The effect of the junctions is calculated in the form of a vertex correction to both the conductivity and liquid fraction of the network. The correction is sufficient to account for the deviation from the linear formula of Lemlich for liquid fractions up to about 10%.

Some new analytic results concerning the foam drainage equation are described. The temporal approach to the equilibrium pro le of the foam is shown to be exponential, in agreement with numerical calculations. The e¬ect of including the equilibrium distribution of the liquid fraction as an initial condition is discussed, with respect to the progress of a solitary wave of liquid through a foam column. Existing analysis is further extended to allow for a variation of bubble sizes within the column and numerical calculations are compared with experimental results. We then consider the extension of the foam drainage equation into two and three dimensions and in particular the e¬ect of con nement in a cylindrical tube.

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