Statistics of shear-induced rearrangements in a two-dimensional model foam

Under steady shear, a foam relaxes stress through intermittent rearrangemen ts of bubbles accompanied by sudden drops in the stored elastic energy. We use a simple model of foam that incorporates both elasticity and dissipatio n to study the statistics of bubble rearrangements in terms of energy drops , the number of nearest neighbor changes, and the rate of neighbor-switchin g (T1) events. We do this for a two-dimensional system as a function of sys tem size, shear rate, dissipation mechanism, and gas area fraction. We find that for dry foams, there is a well-defined quasistatic limit at low shear rates where localized rearrangements occur at a constant rate per unit str ain, independent of both system size and dissipation mechanism. These resul ts are in good qualitative agreement with experiments on two-dimensional an d three-dimensional foams. In contrast, we find for progessively wetter foa ms that the event size distribution broadens into a power law that is cut o ff only by system size. This is consistent with criticality at the melting transition. [S1069-651X(99)06610-6].