Rheological properties of the soft disk model of 2D foams

Abstract

The soft-disk model previously developed and applied by Durian D. J. Durian, Phys. Rev. Lett. 75, 4780 1995 is brought to bear on problems of foam rheology of longstanding and current interest, using twodimensional systems. The questions at issue include the origin of the Herschel-Bulkley relation, normal stress effects dilatancy , and localization in the presence of wall drag. We show that even a model that incorporates only linear viscous effects at the local level gives rise to nonlinear power-law dependence of the limit stress on strain rate. With wall drag, shear localization is found. Its nonexponential form and the variation of localization length with boundary velocity are well described by a continuum model in the spirit of Janiaud et al. Phys. Rev. Lett. 97, 038302 2006 . Other results satisfactorily link localization to model parameters, and hence tie together continuum and local descriptions.