Stability, critical thickness, and the time of rupture of thinning foam and emulsion films

Abstract

A theory is developed to predict the critical thickness of rupture and the lifetimes of the tangentially immobile foam and emulsion films. The theory accounts for the stabilizing effects of film thinning on the growth of the surface corrugations and leads to an explicit expression for the critical thickness as a function of the velocity of thinning, amplitude of the surface corrugations, viscosity, surface tension, and Hamaker constant. The predictions of the theory are in both qualitative and quantitative agreement with the experimentally obtained critical thicknesses. The comparison of the theory with the data for critical thickness confirms an independent experimental observation that the velocity of film thinning depends inversely on the film radius (and not on the square of the film radius as predicted by Reynolds' law of film thinning). The stabilization due to drainage is found to be significant in determining the lifetimes of thin films, and the importance of this effect increases as the wavelength of the perturbation increases.The present theory in conjunction with the data for critical thickness predicts the lifetimes of foam films that are in agreement with the experimental data. Further, the Hamaker constant that is obtained byfitting the experimental data to the present theory is in excellent agreement with its predictions from the Lifshitz theory.