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|
The structure of foam cells: Isotropic Plateau polyhedra
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
Corresponding author: email@example.com
Accepted: 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 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 . While , and exhibit behavior, the specific surface area 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
© EDP Sciences, 2004
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