SIMPLE SHEARING FLOW OF 3-DIMENSIONAL FOAMS AND HIGHLY CONCENTRATED EMULSIONS WITH PLANAR FILMS

Simple shearing flow of a ''dry,'' perfectly ordered, three-dimensiona l foam composed of planar films is considered. The undeformed spatiall y periodic cell structure is formed by regular tetrakaidecahedra, whic h have six square surfaces and eight regular hexagonal surfaces. The e lastic-plastic response of the foam is modeled by assuming that all su rfaces remain planar and that the angle between connected surfaces doe s not change during elastic deformation. An explicit expression for th e stress tensor that is valid up to the elastic limit is determined. P ast the elastic limit, the foam structure and macroscopic stress are p iecewise continuous functions of strain. Discontinuities in structure and stress are associated with topological (T1) changes in the film ne twork structure that occur when the area of an individual film vanishe s. These T1 changes, which reduce surface energy and result in the swi tching of cell neighbors, are essential mechanisms for yield behavior in foam flow. The foam structure is determined for all values of shear strain by choosing initial cell orientations that lead to periodic be havior with strain. The shear stress evaluated from a strain energy me thod differs from that obtained by volume averaging the local surface tension forces; this inconsistency arises because a foam with planar f ilms cannot satisfy the equilibrium requirement that three films meet at equal angles of 120-degrees.