Influence of initial film radius and film thickness on the rupture of foam films

Abstract

The initial thickness and radius of the film that forms upon close contact of two foam bubbles are known to influence the thinning dynamics and lifetime of the film. Various scalings of lifetime tr, with initial radius Rfilm and thickness ho, have been proposed in literature. In this paper, we present a hydrodynamic thin-film model that includes both surface tension, van der Waals forces, and drainage and that clarifies the various proposed scalings of lifetime. Our model equations were solved numerically for a range of Rfilm and ho as direct input parameters. Films with a large radius are found to thin locally at a dimple, while films with a small radius thin across the entire film. The observed dynamics and lifetime were interpreted by developing a simplified model that describes the early stage dimpled drainage and the late stage van der Waals thinning, using known similarity solutions. For large radii films, our simulations confirm earlier theoretical work on semi-infinite films that predicts tr∼Rfilm0h05/7. For small radii films, our numerical simulations show the opposite trend with lifetime being solely dependent on Rfilm, in fair agreement with the simplified model that predicts tr∼Rfilm10/7h00.