Dimple formation and behavior during axisymmetrical foam film drainage

Abstract

Draining foam or emulsion f h are generally of nonuniform thickness. A thick region or 'dimple forme in the central part of a circular film. It is separated from the Plateau border by a thinner 'barrier We have developed a new numerical model to simulate the entire drainage process, including the film formation. The model assumes that drainage is arieymmetric and that the fluid interfaces are immobile. The initial conditions are a pair of static hemispherical menisci. Fluid is withdrawn at a constant rate for a specified time to form a film. The condition for the transition from a nearly plane-parallel f i to a dimpled film in the absence of disjoining pressure was determined. The ratio of the minimum to maximum thickness in the film and a dimensionless rate of drainage are correlated with the ratio of the maximum possible curvature in the dimple to the curvature in the meniscus. The rate of drainage is always less than that given by the Reynolds theory for drainage between a pair of disks that is pressed by a pressure equal to the capillary pressure. When the film is approximately plane-parallel, the pressure drop from the center of the film to the Plateau border is less than half of that predicted by the Reynolds theory and there is a significant pressure gradient beyond the nominal film radius. When a dimple forms, most of the resistance to flow is in the thin barrier ring. The presence of disjoining pressure makes a qualitative difference in film drainage. Low electrolyte concentrations in a film containing ionic surfactant produce a repulsive disjoining pressure that inhibits formation of the thin barrier ring and thus of the dimple itaelf. The film drains rapidly to ita equilibrium thickness. For high electrolyte concentration, the disjoining pressure is dominated by van der Waals attraction. As a result a thin annular fiIm forms that forces the dimple into a lens with a finite contact angle. These types of behavior are observed experimentally.