Can liquid foams and emulsions be modeled as packings of soft elastic particles?

Abstract

When two immersed bubbles are pushed against each other, a facet is formed at their contact, leading to an increase of interfacial energy and hence a repulsive interaction force. Foams (and concentrated emulsions) in mechanical equilibrium may thus be modeled as an assembly of soft elastic interacting particles. Such a model has been used in many studies of their structure and mechanical properties, in particular near the jamming transition (or wet limit) where the contact forces are so small that bubbles remain roughly spherical. We review analytical ab initio models and simulations, based on the equilibration of pressure and surface tension forces or, equivalently, minimization of interfacial energy. Two-body interaction behavior dominates asymptotically at packing fractions approaching the jamming transition, but the interaction is intrinsically anharmonic and cannot be captured by a power law. This phenomenon was first identified by D. Morse and T. Witten: we offer a detailed analysis and transparent derivation of their classic result. For packing fractions well above the jamming transition point, the coupling among contacts mediated by bubble volume conservation has a significant impact on the macroscopic elastic response of foam. This effect is captured by a many-body interaction law, derived from first principles. Applications are explored in two and three dimensions, as are future directions for this kind of theory.

Keywords: Elasticity; Emulsions; Foams; Jamming.