Implementation of Morse–Witten theory for a polydisperse wet 2D foam simulation

Abstract

The Morse-Witten theory (D. Morse and T. Witten, EPL 22 (1993) 549-555) provides a formulation for the inter-bubble forces and corresponding deformations in a liquid foam, accurate in the limit of high liquid fraction. Here we show how the theory may be applied in practice, including allowing for polydispersity in the bubble sizes. The resulting equilibrated 2D structures are consistent with direct calculations, within the limitations of the theory. The path to developing a 3D model is outlined for future work.

The evolution of numerical methods for predicting the distribution of surfactant in the bubble-scale dynamics of foams

“…In these cases the Potts model [19] provides similar (but less accurate) information about the structure, again using minimization of energy, in a stochastic manner, and hence offers an easier route to simulating many realisations of a disordered foam. Recently, a "Morse-Witten" theory [20] for the way in which compressed droplets (or bubbles in this case) deform has been used to generate equilibrium structures of monodisperse [21,22] and polydisperse foams in which bubble deformation is small [23], up to 10% of the bubble diameter. It remains to be seen whether this method can provide a route to predicting foam flow.…”

Description of the buckling of a chain of hard spheres in terms of Jacobi functions

“…In the context of the present work, the contacts in direction perpendicular to the axis of the three-bubble chain provide a transverse confining potential for the chain. (For simulation details of the bubble packing see [22]. ).…”

“…Our work is also related to models used in studies of ''force chains'' in 2D or 3D granular materials [29,30], a wide class of materials that includes colloidal packings [31] and wet foams [22]. When these have a disordered structure, the larger contact forces form a random network of more or less straight chains, playing the major role in supporting an imposed stress.…”

“…An example of the sudden local buckling of a chain, induced by increasing compression, is shown in Fig. 1 for a two-dimensional packing of bubbles [22], as simulated by the Morse-Witten method [32,33]. Note that buckling takes place over a small range of compression.…”