Drainage and Coalescence in Standing Foams

A theoretical model is presented for the drainage, collapse, and coalescence in standing foams. The foam is assumed to consist of pentagonal dodecahedra and coalescence is assumed to occur due to a variation in the sizes of the films which constitute the faces of these polyhedra. Even in a monodispersed foam containing bubbles having the same volume, the film areas are not identical, but are distributed randomly about a mean. This leads to a nonuniformity of film-drainage rates and hence of film thicknesses within any volume element in the foam. Smaller films drain faster and rupture earlier, causing the bubbles containing them to coalesce. The evolution of coalescence is monitored via the mean bubble volume which varies in the vertical direction. The model is also able to predict the evolution of the surfactant concentration profile as it changes due to coalescence and collapse. Simulations are performed to examine the effect of various parameters, such as the apparent diffusion coefficient of the surfactant, the distribution of film sizes, and the concentrations of surfactant and salt in the foaming solution on the drainage and collapse behavior of the foam.