Elastic behavior of confined soap froth.

The elastic response of ordered 3D soap froth, in which N layers of cells are confined between two rigid walls, is analyzed. Surface Evolver simulations are used to compute the equilibrium structure, which consists of a layer of Fejes-Toth cells at each wall and N - 2 core layers of Kelvin cells. The reference state corresponds to the plate spacing ho that achieves isotropic stress; and the foam confinement is varied by changing h.

A geometric exploration of stress in deformed liquid foams.

We explore an alternate way of looking at the rheological response of a yield stress fluid: using discrete geometry to probe the heterogeneous distribution of stress in soap froth. We present quasi-static, uniaxial, isochoric compression and extension of three-dimensional random monodisperse soap froth in periodic boundary conditions and examine the stress and geometry that result. The stress and shape anisotropy of individual cells is quantified by Q, a scalar measure derived from the interface tensor that gauges each cell's contribution to the global stress.

Statistical mechanics of two-dimensional shuffled foams: geometry-topology correlation in small or large disorder limits.

Bubble monolayers are model systems for experiments and simulations of two-dimensional packing problems of deformable objects. We explore the relation between the distributions of the number of bubble sides (topology) and the bubble areas (geometry) in the low liquid fraction limit. We use a statistical model [M.

The Einstein shear viscosity correction for non no-slip hyperspheres.

We calculate the effective shear viscosity of a dilute dispersion of n-dimensional non no-slip hyperspheres, first for hyperdrops, second for slippery hyperspheres, and third for porous hyperspheres.

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.

Deformation of Platonic foam cells: effect on growth rate.

The diffusive growth rate of a polyhedral cell in dry three-dimensional foams depends on details of shape beyond cell topology, in contrast to the situation in two dimensions, where, by von Neumann's law, the growth rate depends only on the number of cell edges. We analyze the dependence of the instantaneous growth rate on the shape of single foam cells surrounded by uniform pressure; this is accomplished by supporting the cell with films connected to a wire frame and inducing cell distortions by deforming the wire frame. We consider three foam cells with a very simple topology; these are the Platonic foam cells, which satisfy Plateau's laws and are based on the trivalent Platonic solids (tetrahedron, cube, and dodecahedron).

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.

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.