An analysis of surface curvature and growth laws for foam cells using the Surface Evolver
Physics Department, Trinity College - Dublin 2, Ireland
Accepted: 6 September 2000
The contributions of vertices, edges and faces to the sum rule expressed by the Gauss-Bonnet theorem are determined for typical cells, using the Surface Evolver. They compare well with an elementary theory. The resulting analytic approximation is used to derive a law of the Von Neumann type, relating cell growth to the number of vertices (or faces), similar to that found by Glazier in Potts model simulations. Contrary to results of the Potts model, this growth shows very little variation for bubbles with the same number of faces. This is the first time that a self-consistent theory describes successfully the curvature of foam cells and the growth law.
PACS: 82.70.Rr – Aerosols and foams / 02.40.Sf – Manifolds and cell complexes / 81.40.Cd – Solid solution hardening, precipitation hardening, and dispersion hardening; aging
© EDP Sciences, 2000