Shubha Tewari

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 (T1) 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.

Signatures of incipient jamming in collisional hopper flows

Many disordered systems experience a transition from a fluid-like state to a solid-like state following a sudden arrest in dynamics called jamming. In contrast to jamming in spatially homogeneous systems, jamming in hoppers occurs under extremely inhomogeneous conditions as the gravity-driven flow of grains enclosed by rigid walls converges towards a small opening. In this work, we study velocity fluctuations in a collisional flow near jamming using event-driven simulations. The average flow in a hopper geometry is known to have strong gradients, especially near the walls and the orifice. We find, in addition, a spatially heterogeneous distribution of fluctuations, most striking in the velocity autocorrelation relaxation times. At high flow rates, the flow at the center has lower kinetic temperatures and longer autocorrelation times than at the boundary. Remarkably, however, this trend reverses itself as the flow rate slows, with fluctuations relaxing more slowly at the boundaries though the kinetic temperatures remain high in that region. The slowing down of the dynamics is accompanied by increasing non-Gaussianity in the velocity distributions, which also have large spatial variations.

Growing length scale in gravity-driven dense granular flow

We report simulations of a two-dimensional, dense, bidisperse system of inelastic hard disks falling down a vertical tube under the influence of gravity. We examine the approach to jamming as the average flow of particles down the tube is slowed by making the outlet narrower. Defining coarse-grained velocity and stress fields, we study two-point temporal and spatial correlation functions of these fields in a region of the tube where the time-averaged velocity is spatially uniform. We find that fluctuations in both velocity and stress become increasingly correlated as the system approaches jamming. We extract a growing length scale and time scale from these correlations.