Simple shearing flow of dry soap foams with tetrahedrally close-packed structure

The microrheology of dry soap foams subjected to quasistatic, simple sheari ng flow is analyzed. Two different monodisperse foams with tetrahedrally cl ose-packed (TCP) structure are examined: Weaire-Phelan (A15) and Friauf-Lav es (C15). The elastic-plastic response is evaluated by using the Surface Ev olver to calculate foam structures that minimize total surface area at each value of strain. The foam geometry and macroscopic stress are piecewise co ntinuous functions of strain. The stress scales as T/V-1/3, where T is surf ace tension and V is cell volume. Each discontinuity corresponds to large c hanges in foam geometry and topology that restore equilibrium to unstable c onfigurations that violate Plateau's laws. The instabilities occur when the length of an edge on a polyhedral foam cell vanishes. The length can tend to zero smoothly or abruptly with strain. The abrupt case occurs when a sma ll increase in strain changes the energy profile in the neighborhood of a f oam structure from a local minimum to a saddle point, which can lead to sym metry-breaking bifurcations. In general, the new structure associated with each stable solution branch results from an avalanche of local topology cha nges called T1 transitions. Each T1 cascade produces different cell neighbo rs, reduces surface energy, and provides an irreversible, film-level mechan ism for plastic yield behavior. Stress-strain curves and average stresses a re evaluated by examining foam orientations that admit strain-periodic beha vior. For some orientations, the deformation cycle includes Kelvin cells in stead of the original TCP structure; but the foam does not remain perfectly ordered. Bifurcations during subsequent T1 cascades lead to disorder and c an even cause strain localization. (C) 2000 The Society of Rheology. [S0148 -6055(00)00303-5].