Issue Europhys. Lett. Volume 67, Number 3, August 2004 484 - 490 Interdisciplinary physics and related areas of science and technology http://dx.doi.org/10.1209/epl/i2003-10295-7 01 July 2004
Europhys. Lett., 67 (3), pp. 484-490 (2004)
DOI: 10.1209/epl/i2003-10295-7

## The structure of foam cells: Isotropic Plateau polyhedra

S. Hilgenfeldt1, A. M. Kraynik2, D. A. Reinelt3 and J. M. Sullivan4, 5

1  Applied Physics, University of Twente - P.O. Box 217 7500 AE Enschede, The Netherlands
2  Sandia National Laboratories, Department 9114 MS0834 Albuquerque, NM 87185-0834, USA
3  Department of Mathematics, Southern Methodist University Dallas, TX 75275-0156, USA
4  Department of Mathematics, University of Illinois - Urbana, IL 61801-2975, USA
5  Institut für Mathematik, Technische Universität Berlin - D-10623 Berlin, Germany

sascha@tn.utwente.nl

(Received 16 December 2003; accepted in final form 25 May 2004)

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 S, curvature R, edge length L, volume V) and growth rate of the cells are obtained as analytical functions of F, the sole variable. IPPs accurately represent average foam bubble geometry for arbitrary , even though they are only constructible for F= 4,6,12 . While R/V1/3, L/V1/3 and 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.

PACS
82.70.Rr - Aerosols and foams.
61.43.-j - Disordered solids.