coalescence; i.e., the mean bubble size increases. In both A theoretical model is presented for the drainage, collapse, and cases, the interfacial area available, which plays an important coalescence in standing foams. The foam is assumed to consist of role in determining the utility of foams in applications such pentagonal dodecahedra and coalescence is assumed to occur due as foam fractionation, decreases. In addition, the adsorbed to a variation in the sizes of the films which constitute the faces surfactant in the collapsed films is released into the liquid of these polyhedra. Even in a monodispersed foam containing in the Plateau border channels and moves out of the foam. bubbles having the same volume, the film areas are not identical, Several theoretical models of foam behavior have apbut are distributed randomly about a mean. This leads to a nonunipeared in literature. A fairly comprehensive account of the formity of film-drainage rates and hence of film thicknesses within any volume element in the foam. Smaller films drain faster and theoretical work in this area up to 1993 can be found in the rupture earlier, causing the bubbles containing them to coalesce. review by Narsimhan and Ruckenstein (1). Much of the The evolution of coalescence is monitored via the mean bubble work, however, has dealt with steady state foam columns volume which varies in the vertical direction. The model is also (2, 3) and relatively few efforts (4-14) have been made to able to predict the evolution of the surfactant concentration profile model the dynamic phenomena occurring in a standing foam. as it changes due to coalescence and collapse. Simulations are The most notable among the earlier papers on drainage in performed to examine the effect of various parameters, such as standing foams are those of Krotov (7) and Narsimhan (8). the apparent diffusion coefficient of the surfactant, the distribution Krotov was the first to recognize the effect of Plateau border of film sizes, and the concentrations of surfactant and salt in the suction (capillary pressure) on foam drainage and formufoaming solution on the drainage and collapse behavior of the lated the basic drainage equations and boundary conditions.
foam.