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.
ASJC Scopus subject areas
- Physics and Astronomy(all)