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.