Networklike propagation of cell-level stress in sheared random foams.

Quasistatic simple shearing flow of random monodisperse soap froth is investigated by analyzing surface evolver simulations of spatially periodic foams. Elastic-plastic behavior is caused by irreversible topological rearrangements (T1s) that occur when Plateau's laws are violated; the first T1 determines the elastic limit and frequent T1 avalanches sustain the yield-stress plateau at large strains. The stress and shape anisotropy of individual cells is quantified by Q, a scalar derived from an interface tensor that gauges the cell's contribution to the global stress. During each T1 avalanche, the connected set of cells with decreasing Q, called the stress release domain, is networklike and nonlocal. Geometrically, the networklike nature of the stress release domains is corroborated through morphological analysis using the Euler characteristic. The stress release domain is distinctly different from the set of cells that change topology during a T1 avalanche. Our results highlight the connection between the unique rheological behavior of foams and the complex large-scale cooperative rearrangements of foam cells that accompany distinctly local topological transitions.

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 (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 . All of the foams have

Structure of random foam.

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 R32 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.