SIMPLE SHEARING FLOW OF A DRY KELVIN SOAP FOAM

Simple shearing flow of a dry soap foam composed of identical Kelvin c ells is analysed. An undeformed Kelvin cell has six planar quadrilater al faces with curved edges and eight non-planar hexagonal faces with z ero mean curvature. The elastic-plastic response of the foam is modell ed by determining the bubble shape that minimizes total surface area a t each value of strain. Computer simulations were performed with the S urface Evolver program developed by Brakke. The foam structure and mac roscopic stress are piecewise continuous functions of strain. Each dis continuity corresponds to a topological change (T1) that occurs when t he film network is unstable. These instabilities involve shrinking fil ms, but the surface area and edge lengths of a shrinking film do not n ecessarily vanish smoothly with strain. Each T1 reduces surface energy , results in cell-neighbour switching, and provides a film-level mecha nism for plastic yield behaviour during foam flow. The foam structure is determined for all strains by choosing initial foam orientations th at lead to strain-periodic behaviour. The average shear stress varies by an order of magnitude for different orientations. A Kelvin foam has cubic symmetry and exhibits anisotropic linear elastic behaviour; the two shear moduli and their average over all orientations are G(min) = 0.5706, G(max) = 0.9646, and (G) over bar = 0.8070, where stress is s caled by T/V-1/3, T is surface tension, and V is bubble volume. An app roximate solution for the microrheology is also determined by minimizi ng the total surface area of a Kelvin foam with flat films.