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

Under steady shear, a foam relaxes stress through intermittent rearrangements of bubbles accompanied by sudden drops in the stored elastic energy. We use a simple model of foam that incorporates both elasticity and dissipation to study the statistics of bubble rearrangements in terms of energy drops, the number of nearest neighbor changes, and the rate of neighbor-switching $\mathrm{}\left(T1\mathrm{}\right)\mathrm{}$ events. We do this for a two-dimensional system as a function of system 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 strain, independent of both system size and dissipation mechanism. These results are in good qualitative agreement with experiments on two-dimensional and three-dimensional foams. In contrast, we find for progessively wetter foams that the event size distribution broadens into a power law that is cut off only by system size. This is consistent with criticality at the melting transition.