Thinning and rupture of ring-shaped films

Abstract

The problem of the thinning and stability of a film with a dimple is treated by using a simplified model. The model is based on a premise that all the energy dissipation takes place in the “barrier” ring with thickness h. Analytical solutions are obtained for the velocity of thinning and critical thickness of rupture in terms of the radius of the bubble, radius of curvature of the dimple, inner and outer radii of the ring, surface tension and disjoining pressure. The results suggest that the presence of a dimple increases the velocity of thinning and decreases the critical thickness of rupture, in general, as compared with a film without a dimple.