Randomfoams are modeled as spatially periodic structures, but unlike ordered systems, the representative volume (cubic unit cell) contains up to 1000 bubbles jammed together in a disordered packing. The bubbles in the foam shown at left are constrained to have equal volume (monodisperse). The first step in modeling a random foam involves filling space with Voronoi polyhedra produced from random packings of spheres. Two methods for packing hard spheres are used: random sequential adsorption (RSA) produces relatively loose packings and classical hard-sphere molecular dynamics produces random close packing (RCP) of higher densities.
The second step in producing a stable foam is to relax the Voronoi structure by minimizing the surface area or surface free energy of the foam. There are many topological transitions (neighbor switches) that occur during the relaxation process. The surface free energy of the foam can be reduced even further by annealing the foam, which involves subjecting the relaxed foam to large-deformation, tension-compression cycles that provoke further topological transitions.
In monodisperse foams, most bubbles have 12 to 16 faces and most faces have 4 to 6 edges (triangular faces and heptagonal faces are rare except in the initial Voronoi structures). The probabilities p(f) that a bubble has ffaces and p(n) that a face has n edges as determined from many foam structures are graphed at right. The data distinguishes between types of foam structures, V (Voronoi), R (relaxed), RA (relaxed and annealed), and the two methods for making the Voronoi polyhedra discussed above. The topological statistics are compared with the experimental observations of Matzke (Am. J. Botany 33, 58 (1946)).
See Random Monodisperse Foam (pdf) for more details. Professor Reinelt and Dr. Kraynik at Sandia National Laboratories have been collaborating on foam research for many years.