The Surface Evolver was used to compute the equilibrium microstructure of dry soap foams with random structure and a wide range of cell-size distributions. Topological and geometric properties of foams and individual cells were evaluated. The theory for isotropic Plateau polyhedra describes the dependence of cell geometric properties on their volume and number of faces. The surface area of all cells is about 10% greater than a sphere of equal volume; this leads to a simple but accurate theory for the surface free energy density of foam. A novel parameter based on the surface-volume mean bubble radius is used to characterize foam polydispersity. The foam energy, total cell edge length, and average number of faces per cell all decrease with increasing polydispersity. Pentagonal faces are the most common in monodisperse foam but quadrilaterals take over in highly polydisperse structures.

• Received 22 June 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.208301