An Accurate von Neumann's Law for Three-Dimensional Foams

The diffusive coarsening of 2D soap froths is governed by von Neumann's law. A statistical version of this law for dry 3D foams has long been conjectured. A new derivation, based on a theorem by Minkowski, yields an explicit analytical von Neumann's law in 3D which is in very good agreement with detailed simulations and experiments. The average growth rate of a bubble with $F$ faces is shown to be proportional to $F^{1/2}$ for large $F$, in contrast to the conjectured linear dependence. Accounting for foam disorder in the model further improves the agreement with data.