Analytical models of single bubbles and foam

Abstract

We investigate the use of analytic models of three-dimensional bubbles with deformable surfaces to study the energy of foams in equilibrium. While the idea of modelling the surfaces of bubbles as deformable minimal surfaces in threedimensions has been explored before, this work has been limited to the mathematically exact case of a bubble with just two contacts, an unrealistic case for real three dimensional bulk foams. Here we demonstrate that by geometrically decomposing a bubble into a collection of Z circular cones with the same total volume as the original bubble, we can successfully extend this approach to estimate the energy of a bubble in a foam with any number of neighbouring bubbles over the entire range of liquid fraction. We model the interaction between bubbles as they come into contact as a constant volume deformation. The results of this approximate geometrical model are found to agree, both qualitatively and quantitatively, with the results of Surface Evolver simulations ...