Influence from polydispersity on the morphology of Voronoi and equilibrium foams

Abstract

Stochastic foam models are generated from Voronoi spatial partitioning, using the centers of equi-sized hard spheres in random periodic distributions as seed points. Models with different levels of polydispersity are generated by varying the packing of the spheres. Subsequent relaxation is then performed with the Surface Evolver software which minimizes the surface area for better resemblance with real foam structures. The polydispersity of the Voronoi precursors is conserved when the models are converted into equilibrium models. The relation between the sphere packing fraction and the resulting degree of volumetric polydispersity is examined and the relations between the polydispersity and a number of associated morphology parameters are then investigated for both the Voronoi and the equilibrium models. Comparisons with data from real foams in the literature indicate that the used method is somewhat limited in terms of spread in cell volume but it provides a very controlled way of varying the foam morphology while keeping it periodic and truly stochastic. The study shows several strikingly consistent relations between the spread in cell volume and other geometric parameters, considering the stochastic nature of the models.