DataSheet1_Average evolution and size-topology relations for coarsening 2d dry foams.CSV

Two-dimensional dry foams coarsen according to the von Neumann law as dA/dt ∝ (n − 6) where n is the number of sides of a bubble with area A. Such foams reach a self-similar scaling state where area and side-number distributions are stationary. Combining self-similarity with the von Neumann law, we derive time derivatives of moments of the bubble area distribution and a relation connecting area moments with averages of the side-number distribution that are weighted by powers of bubble area. To test these predictions, we collect and analyze high precision image data for a large number of bubbles squashed between parallel acrylic plates and allowed to coarsen into the self-similar scaling state. We find good agreement for moments ranging from 2–20.

二维干泡沫遵循冯·诺依曼定律（von Neumann law）发生熟化，其演化关系为dA/dt ∝ (n − 6)，其中n为面积为A的气泡的边数。此类泡沫可达到自相似标度态，此时面积分布与边数分布均处于稳态。结合自相似性与冯·诺依曼定律，我们推导得到气泡面积分布各阶矩的时间导数，以及将面积矩与以气泡面积幂次加权的边数分布平均值相联系的关系式。为验证上述理论预测，我们采集并分析了大量气泡的高精度图像数据：这些气泡被挤压于平行亚克力板之间，并发生熟化直至达到自相似标度态。我们发现，在2至20阶的矩区间内，理论与实验结果吻合良好。