Coarsening of Foams Driven by Concentration Gradients of Gases of Different Solubilities.

Abstract

The evolution of a foam driven by the transfer of two gases of different solubilities across the soap films is studied. A bamboo foam, or a train of films, is used as a model system; it is made of a poorly soluble gas and put into contact with a reservoir of a soluble gas at an initial time. The measurement of the time evolution of the volume of each bubble shows that the foam swells as it progressively incorporates the soluble gas. The dynamics is modeled from the gas fluxes across each film. The continuous limit of this model at a large number of bubbles is studied in detail: it gives an effective nonlinear diffusion equation, which fits the data very well. The corresponding diffusion constant, given by the product of the permeability of the soluble gas and the initial size of the bubbles, is shown to be the key parameter governing the coarsening dynamics of the foam.