LARGE ELASTIC DEFORMATIONS OF 3-DIMENSIONAL FOAMS AND HIGHLY CONCENTRATED EMULSIONS

We have developed a microrheological analysis for the nonlinear elastic behavior of a ’dry,’ perfectly ordered, three-dimensional foam composed of thin liquid films with uniform surface tension. The undeformed cell structure is based on Kelvin’s minimal tetrakaidecahedron, which contains six planar quadrilateral surfaces with curved edges and eight nonplanar hexagonal surfaces of zero mean curvature. Each film of the deformed foam has zero mean curvature, three films meet along an edge called a Plateau border at equal angles of 120°, and four Plateau borders join at each vertex. The nonlinear partial differential equation for film curvature is solved using finite difference methods. We consider uniaxial extension and examine a particular orientation of the foam that gives highly symmetric structures for all deformations up to the elastic limit. The elastic limit corresponds to a mathematical turning point at which the area of each film is finite; it does not coincide with the area of some films going smoothly to zero as expected from the theory for ’dry,’ two-dimensional foams. The surface area and complete stress tensor for the foam are evaluated. We have also developed an approximate analytical theory by assuming that the undeformed foam consists of regular tetrakaidecahedra and that the films remain planar during deformation. The elastic limit for the planar model does coincide with films vanishing smoothly. © 1993 Academic Press, Inc.