Coarsening of a Two-dimensional Foam on a Dome

Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6396, USA(Dated: July 26, 2012)In this paper we report on bubble growth rates and on the statistics of bubble topology for thecoarsening of a dry foam contained in the narrow gap between two hemispheres. By contrast withcoarsening in at space, where six-sided bubbles neither grow nor shrink, we observe that six-sidedbubbles grow with time at a rate that depends on their size. This result agrees with the modi cationto von Neumann’s law predicted by J. E. Avron and D. Levine. For bubbles with a di erent numberof sides, except possibly seven, there is too much noise in the growth rate data to demonstratea di erence with coarsening in at space. In terms of the statistics of bubble topology, we ndfewer 3, 4, and 5 sided bubbles, and more 6 and greater sided bubbles, in comparison with thestationary distribution for coarsening in at space. We also nd good general agreement with theAboav-Weaire law for the average number of sides of the neighbors of an n-sided bubble.