Coarsening of Two Dimensional Foam on a Dome

TL;DR

This study investigates bubble growth and topology in a 2D foam on a dome, revealing size-dependent growth of six-sided bubbles and altered topological distributions compared to flat space, aligning with modified theoretical predictions.

Contribution

It provides experimental evidence for size-dependent growth rates of six-sided bubbles on a dome, confirming a modified von Neumann's law and analyzing topological differences from flat space coarsening.

Findings

Six-sided bubbles grow with size-dependent rates.

Fewer 3-5 sided bubbles, more 6+ sided bubbles compared to flat space.

Good agreement with Aboav-Weaire law for neighbor sides.

Abstract

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. 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 3, 4, and 5 sided bubbles, and more 6 and greater sided bubbles, 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.