Coarsening of a two-dimensional foam on a dome.

In this paper we report on bubble growth rates and on the statistics of bubble topology for the coarsening of a dry foam contained in the narrow gap between two hemispheres. By contrast with coarsening in flat space, where six-sided bubbles neither grow nor shrink, we observe that six-sided bubbles grow with time at a rate that depends on their size. This result agrees with the modification to von Neumann's law predicted by J. E. Avron and D. Levine [Phys. Rev. Lett. 69, 208 (1992)]. For bubbles with a different number of sides, except possibly seven, there is too much noise in the growth rate data to demonstrate a difference with coarsening in flat space. In terms of the statistics of bubble topology, we find fewer three-, four-, and five-sided bubbles, and more bubbles with six or more sides, in comparison with the stationary distribution for coarsening in flat space. We also find good general agreement with the Aboav-Weaire law for the average number of sides of the neighbors of an n-sided bubble.