Avalanches and diffusion in bubble rafts

Energy dissipation distributions and particle displacement statistics are studied in the mean-field version of Durian's bubble model. A two-dimensional (2D) bi-disperse mixture is simulated at various strain rates, , and packing ratios, ϕ , above the rigidity onset at . Well above , and at sufficiently low , the system responds in a highly bursty way, reminiscent of other dynamically critical systems with a power-law distribution of energy dissipation. As one increases at fixed ϕ or tunes at fixed , the bursty behavior vanishes. Displacement distributions are non-Fickian at short times but cross to a Fickian regime at a universal strain, , independent of and ϕ . Despite the profound differences in short-time dynamics, at intermediate Δ γ the systems exhibit qualitatively similar spatial patterns of deformation with lines of slip extending across large fractions of the simulation cell. These deformation patterns explain the observed diffusion constants and the universal crossover time to Fickian behavior.