Europhys. Lett.
Volume 67, Number 3, August 2004
Page(s) 484 - 490
Section Interdisciplinary physics and related areas of science and technology
Published online 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

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

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 $\mathcal{G}$ of the cells are obtained as analytical functions of F, the sole variable. IPPs accurately represent average foam bubble geometry for arbitrary $F\geq 4$, even though they are only constructible for F= 4,6,12 . While R/V1/3, L/V1/3 and $\mathcal{G}$ 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.

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

© EDP Sciences 2004