A mathematical model for an expanding foam

A theoretical and numerical model is presented for the shape evolution of the thin liquid films separating the gas bubbles in a foam. The motion is due to capillary action, surface tension gradients, and the overall expansion of the foam. The expansion is the result of the increase in gas content with time. Process modeling is accomplished via the solution of three coupled partial differential equations. Two time scales are included in the model: a process time and a drying or curing time. It is demonstrated that the amount of surfactant is the dominant control mechanism for the final film thickness. If sufficient surfactant is present, the films will be shown to dilate uniformly in space. A number of known features of expanding foams are reproduced by the model.