Applications and generalizations of the foam drainage equation

Some new analytic results concerning the foam drainage equation are described. The temporal approach to the equilibrium profile of the foam is shown to be exponential, in agreement with numerical calculations. The effect 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 effect of confinement in a cylindrical tube.