Structure of random monodisperse foam

Abstract

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><or=14. 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.

The effect of pore size on cell adhesion in collagen-GAG scaffolds

“…The tetrakaidecahredon is a polyhedron that packs to fill space, approximates the structural features observed through experiment, nearly satisfies the minimum surface energy condition, and is often used for modeling low-density foams [30,32]. In addition, for the tetrakaidecahedral unit cell, the value of the dimensionless measure of total edge length per (unit volume) 1/3 for the unit cell is nearly identical to that observed for many random cellular structures [33], suggesting that the tetrakaidecahedral unit cell gives a good representation of the total edge length and can be used to model the specific surface area of random cellular structures such as the porous, CG scaffold. For an open-cell tetrakaidecahedron with edges of circular cross-section, the specific surface area is:…”

Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks

“…The data reported in [54], [55], and [56] are insufficient to provide definitive p-vector distributions for either polycrystalline aluminum or soap foam structures. However, they are sufficient to clearly distinguish those structures from the Poisson-Voronoi one.…”

“…Matzke [54] carefully recorded p-vector data for 1000 soap bubbles in a foam, and Williams and Smith [55] reported p-vector data for 91 individual cells in an aluminum polycrystal. More recently, Kraynik et al [56] reported p-vector data to characterize over 1000 simulated monodisperse foam bubbles, and we have reported the distribution of p-vectors in a set of 269,555 grains in simulated grain growth microstructures [33].…”

Networklike Propagation of Cell-Level Stress in Sheared Random Foams

“…The non-isotropic part of the effective macroscopic stress τ ij of a dry soap froth [31] is evaluated as…”

“…A method for simulating the equilibrium microstructure of random soap froth with controlled cell-size distributions [31][32][33] employs molecular dynamics to generate dense packings of rigid spheres, which are used to produce Laguerre (weighted-Voronoi) tessellations. The tessellations are initial conditions for the Surface Evolver [34], which minimizes surface area given cell volume constraints.…”