Improved models of solid foams based on soap froth

Abstract

Random Laguerre tessellations are widely used to model the cell systems of solid foams because they enable the reproduction of the cell-volume distributions found in real materials. However, the tessellations have planar cell faces, which over constrain the orientations of cell edges and adversely affect the distribution of edge lengths. The Surface Evolver was used to compute equilibrium microstructures of soap froth by minimizing the total surface area of Laguerre tessellations while preserving their cell-volume distributions. The resulting soap froth structures are more realistic than Laguerre tessellations because the edges of a face do not lie in the same plane and there are significantly fewer short edges. The edge-length distributions of soap froth models are in better agreement with experimental measurements of solid foams with open cells than those with closed cells. We argue that surface tension forces, which control area minimization, are more important during the formation of open-cell foams while viscous forces are more important during the formation of closed-cell foams but are not accounted for in existing models of foam formation. The distributions of other geometric characteristics, such as cell surface area, cell diameter, number of faces per cell and number of edges per face, are not adversely affected by area minimization.