Structure of random monodisperse foam

The Surface Evolver was used to calculate the equilibrium microstructure of random monodisperse soap froth, starting from Voronoi partitions of randomly packed spheres. The sphere packing has a strong influence on foam properties, such as E (surface free energy) and [f] (average number of faces per cell). This means that random foams composed of equal-volume cells come in a range of structures with different topological and geometric properties. Annealing-subjecting relaxed foams to large-deformation, tension-compression cycles-provokes topological transitions that can further reduce E and [f]. All of the foams have [f]less than or equal to14. The topological statistics and census of cell types for fully annealed foams are in excellent agreement with experiments by Matzke. Geometric properties related to surface area, edge length, and stress are evaluated for the foams and their individual cells. Simple models based on regular polygons predict trends for the edge length of individual cells and the area of individual faces. Graphs of surface area vs shape anisotropy for the cells reflect the geometrical frustration in random monodisperse foam, which is epitomized by pentagonal dodecahedra: they have low surface area but do not pack to fill space.