Physical Review E
The von Neumann-Mullins law for the area evolution of a cell in the plane describes how a dry foam coarsens in time. Recent theory and experiment suggest that the dynamics are different on the surface of a three-dimensional object such as a sphere. This work considers the dynamics of dry foams on the surface of a sphere. Starting from first principles, we use computer simulation to show that curvature-driven motion of the cell boundaries leads to exponential growth and decay of the areas of cells, in contrast to the planar case where the growth is linear. We describe the evolution and distribution of cells to the final stationary state.
Ryan, Shawn D.; Zheng, Xiaoyu; and Palffy-Muhoray, Peter, "Curvature-driven Foam Coarsening on a Sphere: A Computer Simulation" (2016). Mathematics Faculty Publications. 299.