Roth A E, Jones C D, Durian D J
Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Aug;86(2 Pt 1):021402. doi: 10.1103/PhysRevE.86.021402. Epub 2012 Aug 6.
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.
在本文中，我们报告了关于两个半球之间狭窄间隙中包含的干泡沫粗化过程中气泡的生长速率以及气泡拓扑结构的统计情况。与平坦空间中的粗化情况不同，在平坦空间中六边形气泡既不生长也不收缩，而我们观察到六边形气泡会随时间增长，其速率取决于它们的大小。这一结果与J. E. 阿夫龙和D. 莱文 [《物理评论快报》69, 208 (1992)] 所预测的对冯·诺依曼定律的修正相符。对于边数不同的气泡，除了可能的七边形外，生长速率数据中的噪声过多，以至于无法证明与平坦空间中的粗化存在差异。就气泡拓扑结构的统计而言，与平坦空间中粗化的稳态分布相比，我们发现三边、四边和五边形气泡较少，而六边形或更多边形的气泡较多。我们还发现，对于n边形气泡的相邻气泡边数的平均值，与阿博阿夫 - 韦尔定律总体上吻合良好。
