Drainage waves structure in gas-liquid foam

The simple physical model of foam drainage suggested previously by the authors is developed. A non-linear partial differential equation is obtained to describe foam syneresis (drainage process). Special kinds of its solutions in the form of a travelling wave are analysed. It is proved that for such types of solutions the right boundary condition cannot equal zero. A possible explanation for this restriction is suggested. In the authors' opinion, the main reason for this unexpected result is the peculiarity of the Plateau-Gibbs borders form: a cross-section of the Plateau triangle cannot be equal to zero under any variation of foam parameters. In mathematical terms this is reflected in the appearance of a square root singularity in the evolutionary equation that leads to the conclusion made. Qualitative comparison with recent experimental data is presented. It proves the principal conclusion obtained by the authors. Copyright (C) 1996 Elsevier Science Ltd.