An accurate von Neumann's law for three-dimensional foams

Sascha Hilgenfeldt, Andrew M. Kraynik, Stephan A. Koehler, Howard A. Stone

Research output: Contribution to journalArticleAcademicpeer-review

136 Citations (Scopus)
166 Downloads (Pure)


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 F1/2 for large F, in contrast to the conjectured linear dependence. Accounting for foam disorder in the model further improves the agreement with data.
Original languageUndefined
Pages (from-to)2685-2688
Number of pages4
JournalPhysical review letters
Issue number12
Publication statusPublished - 2001


  • METIS-202589
  • IR-36627

Cite this