Osmotic stabilization of concentrated emulsions and foams

In the absence of coalescence, coarsening of emulsions land foams) is contr olled by molecular diffusion of the dispersed-phase species from one emulsi on droplet (or foam bubble) to another. Previous studies of dilute emulsion s have shown how the osmotic pressure of a trapped species within droplets can overcome the Laplace pressure differences that drive coarsening, and "o smotically stabilize" the emulsion. Webster and Cates (Langmuir 1998, 14, 2 068-2079) gave rigorous criteria for osmotic stabilization of mono- and pol ydisperse emulsions, in the dilute regime. We consider here whether analogo us criteria exist for the osmotic stabilization of mono- and polydisperse c oncentrated emulsions and foams. We argue that in such systems the pressure differences driving coarsening are small compared to the mean Laplace pres sure. This is confirmed for a monodisperse 2D model, for which an exact cal culation gives the pressure in bubble i as P-i = P + Pi + P-i(G), with P th e atmospheric pressure, IT the osmotic pressure, and P-i(G) a "geometric pr essure" that reduces to the Laplace pressure only for a spherical bubble, a nd depends much less strongly on bubble deformation than the Laplace pressu re itself. In fact, for Princen's 2D emulsion model, P-i(G) is only 5% larg er in the dry limit than the dilute limit. We conclude that osmotic stabili zation of dense systems typically requires a pressure of trapped molecules in each droplet that is comparable to the Laplace pressures the same drople ts would have if they were spherical, as opposed to the much larger Laplace pressures actually present in the system. We study the coarsening of foams and dense emulsions when there is an insufficient amount of the trapped sp ecies present. Various rate-limiting mechanisms are considered, and their d omain of applicability and associated droplet growth rates discussed. In a concentrated foam or emulsion, a finite yield threshold for droplet rearran gement among stable droplets may be enough to prevent coarsening of the rem ainder.