Critical thickness and lifetimes of foams and emulsions: role of surface wave-induced thinning

Abstract

A theory is developed for predicting simultaneously the velocity of thinning, the critical thickness of rupture, and the lifetimes of the tangentially immobile foam and emulsion films. The theory accounts for the fact that thin free films are not plane-parallel, but are periodically nonhomogeneous in thickness. Based on the equations of motion, it is shown that the pumping of fluid generated by the oscillations of the finite amplitude surface waves enhances the velocity of thinning predicted by Reynolds' theory by up to several orders of magnitudes. In addition, for very thin films (thickness <500 Å), the growth of these "hydrodynamic" surface waves due to van der Waals dispersion forces increases even further the velocity of film thinning. The velocity of thinning obtained from the present theory varies inversely with about 8/10 power of the film radius, which is in agreement with the experimental observations. In contrast, Reynolds' velocity of thinning is inversely proportional to the square of the film radius. The thermal perturbations superimposed on the finite amplitude hydrodynamic surface waves also start to grow for very thin films due to the dispersion interactions. The growth rate of the thermal perturbations being much larger than the growth rate of the "hydrodynamic" surface waves, the former lead to the film rupture. The theory leads to an explicit correlation for the critical thickness as a function of the velocity of thinning, initial amplitude of thermal perturbations, viscosity, surface tension, and Hamaker constant. Finally, the velocities of thinning, critical thicknesses, and the lifetimes calculated from the present theory are all in qualitative and quantitative agreement with the hitherto unexplained experimental results.