The structure of foam cells: Isotropic Plateau polyhedra

S. Hilgenfeldt, A. M. Kraynik, D. A. Reinelt, J. M. Sullivan

Research output: Contribution to journalArticle

Abstract

A mean-field theory for the geometry and diffusive growth rate of soap bubbles in dry 3D foams is presented. Idealized foam cells called isotropic Plateau polyhedra (IPPs), with F identical spherical-cap faces, are introduced. The geometric properties (e.g., surface area 3, curvature R, edge length L, volume V) and growth rate script G sign of the cells are obtained as analytical functions of F, the sole variable. IPPs accurately represent average foam bubble geometry for arbitrary F ≥ 4, even though they are only constructible for F = 4,6,12. While H/V1/3, L/V1/3 and script G sign exhibit F1/2 behavior, the specific surface area S/V2/3 is virtually independent of F. The results are contrasted with those for convex isotropic polyhedra with flat faces.

Original languageEnglish (US)
Pages (from-to)484-490
Number of pages7
JournalEurophysics Letters
Volume67
Issue number3
DOIs
StatePublished - Aug 1 2004

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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