Coarsening of two- and three-dimensional wet polydisperse foams

This paper investigates inter-bubble gas diffusion in two-dimensional (2D) and three-dimensional (3D) wet foams using the bubble dynamics model. The bubble dynamics model avoids the need to consider Tl type bubble rearrangement events in three dimensions explicitly. Foam bubbles are approximated as overlapping parallel cylinders (discs in cross-section) in two dimensions and overlapping spheres in three dimensions. Inter-bubble gas diffusion is modelled by calculating directly the gas transfer between adjacent bubbles and by taking the internal bubble pressure to be inversely proportional to the bubble radius. Scaling states for two initial bubble size distributions are examined. Good agreement is found between these results and existing experimental and simulation data. In both the 2D and 3D cases, the growth of a length scale, such as the average bubble size, in the scaling state converges to follow [R] similar to t(0.5). In 2D, the second moment of the neighbour distribution mu(2) in the scaling state is found to be 2.1 +/- 0.2 for both initial distributions, whereas for 3D foams mu(2) = 19 +/- 1 is reported.