Foam microrheology: from honeycombs to random foams

Foam includes a broad range of materials from shaving cream to the flexible polyurethane that cushions our seats. This overview covers two decades of research on the rheology of liquid foam from a micromechanical point of view. These highly structured, multiphase fluids exhibit rich rheological response that can be related to geometry and mechanics at the cell level. Properties of interest include the shear modulus, yield stress, and non-Newtonian viscosity. Theories based on the simple liquid honeycomb in 2D illustrate cell-level mechanisms that are also important in 3D. These include energy storage in expanding surfaces that causes elasticity, irreversible topological transitions within the foam structure that produce yield phenomena, and the interplay between cell distortion and film-level viscous flow that is responsible for viscoelasticity. Static 3D structures ranging in complexity from the Kelvin cell to the elegant Weaire-Phelan structure to random polydisperse foams are calculated with the Surface Evolver, a computer program developed by K.A. Brakke. Excellent agreement with experimental data on foam structure and shear modulus is demonstrated. Simulations involving large quasistatic deformations of Kelvin and Weaire-Phelan foams in simple shearing flow are compared with 2D results. The geometry and rheological consequences of Plateau borders in wet foams are described. The fluid mechanics of bubbles growing in a viscous fluid reveals the evolution of foam structure that controls behavior in the solid state. Simulated soap froth structure is used as a template to develop finite element models of cellular solids. The micromechanical approach that is described has established a firm theoretical foundation for developing structure-property-processing relationships for foamed polymers.