A Soluble Model for Foam Drainage

A model is set up which is believed to contain the essential physics of foam drainage. Mathematically, the model leads to a non-linear partial differential equation, which we were able to solve exactly by analytical methods for the physical boundary conditions relevant for recent experiments in which a dry foam is wetted by a steady addition of liquid. The solution represents a density wave of constant profile (or solitary wave) in qualitative accord with these experiments. The observed dependences of liquid fraction and wet/dry foam boundary velocity on input flow are reproduced by the model.