Instability of thin liquid films between membranes

Abstract

The conditions for instability of the thin liquid film between two plane-parallel membranes were derived taking into account the influence of the membrane tension, the membrane bending elasticity, the film viscosity and the disjoining pressure. It was shown that the liquid film could be unstable if the negative (attractive) disjoining pressure is predominant. The characteristic timeτ m of growth of perturbation due to thermal or other fluctuations of the membrane shape increases with increasing the film viscosity, the membrane tension and the membrane bending elasticity, and decreasing the film thickness and the negative disjoining pressure. It is of the order of 10−2÷103 sec. When the membranes approach each other at certain value of the average film thicknessh cr called critical, the fastest growing perturbations lead to formation of a liquid film with smaller (or zero) thickness. It was found that the critical thickness increases with increasing the negative disjoining pressure and the membrane area and decreasing the membrane tension and the bending elasticity having typical values of the order of 10−6÷10−5 cm. The case of a membrane approaching a solid plane was also considered. Excluding the small differences in numerical coefficients the results are similar to the case of two identical membranes.