Competition and interaction of polydisperse bubbles in polymer foams

Abstract The effects of interactions between bubbles of different sizes during bubble growth in a polymeric foam are investigated. Two models are used: a two-dimensional simulation in which both the effects of gas diffusion through the polymer and bubble interactions through fluid stresses are included, and a three-dimensional model in which bubbles are assumed to interact only through direct competition for gas, and diffusion of gas into the bubbles is instantaneous. In the two-dimensional model, two different bubble sizes are used in a hexagonal array. For slow gas diffusion, the additional polymer stresses have little effect on the final bubble size distribution. For faster gas diffusion the growth occurs in two phases, just as was found in earlier work for isolated bubbles: an initial rapid viscous phase and a later phase controlled by the rate of polymer relaxation. In this later phase, polymers in the windows between neighbouring bubbles become highly stretched and these regions of high stress determine the dynamics of the growth. In the three-dimensional model we consider the effects of rheology on a pair of different-sized spherical bubbles, interacting only through competition for available gas. Viscoelastic effects result in a wider distribution of bubble volumes than would be found for a Newtonian fluid.