Foam Structure: From Soap Froth to Solid Foams
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Foam Structure:
From Soap Froth to Solid Foams Andrew M. Kraynik
Abstract The properties of solid foams depend on their structure, which usually evolves in the fluid state as gas bubbles expand to form polyhedral cells. The characteristic feature of foam structure—randomly packed cells of different sizes and shapes—is examined in this article by considering soap froth. This material can be modeled as a network of minimal surfaces that divide space into polyhedral cells. The cell-level geometry of random soap froth is calculated with Brakke’s Surface Evolver software. The distribution of cell volumes ranges from monodisperse to highly polydisperse. Topological and geometric properties, such as surface area and edge length, of the entire foam and individual cells, are discussed. The shape of struts in solid foams is related to Plateau borders in liquid foams and calculated for different volume fractions of material. The models of soap froth are used as templates to produce finite element models of open-cell foams. Three-dimensional images of open-cell foams obtained with x-ray microtomography allow virtual reconstruction of skeletal structures that compare well with the Surface Evolver simulations of soap-froth geometry.
meet at equal dihedral angles of 120 at each cell edge, and (3) four edges join at equal tetrahedral angles of cos1(1/3) 109.47 at each cell vertex. The difficult problem of calculating the shape of minimal surfaces in disordered foams can be handled by the Surface Evolver4 computer software. Ordered foams provide a natural starting point for understanding structure and predicting properties. The Kelvin cell5 (Figure 1) is the only structure that satisfies Plateau’s laws and forms a perfectly ordered soap froth in which all cells have identical shapes and orientations. Kelvin cells pack on a bcc lattice and only contain quadrilateral and hexagonal faces. All of the cell edges and vertex regions have similar shapes. The Weaire–Phelan foam6 (Figure 1) has the lowest surface area of any known monodisperse structure. It contains eight cells: two pentagonal do-
Keywords: cellular solids, computer simulations, foams, structure–property relationships.
Introduction As is true with all random heterogeneous materials, it is necessary to understand the structure of foam in order to predict its properties. The microstructure of lowdensity foams is based on the packing of polyhedral cells that fill space;1,2 this characteristic distinguishes foams from other porous materials that are not cellular in nature. Many foams contain both open and closed cells, or have cell walls so thin that the properties of the foam are unaffected by their presence. Consequently, the key issue for foam properties centers on material distribution within the cell structure. Liquid and solid foams share many topological and geometric properties because solid foams typically evolve in the fluid state as gas bubbles form, expand, and deform under the influence of surface tension, viscous forces, phase change, and so on. In both
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