Professor Torquato has worked extensively on the characterization of disordered microstructures, such as the random packing of hard spheres. A related question, which has received much less attention, is how such packings rearrange in slow, dense flows, such as gravity-driven granular drainage. Dilute granular flows are routinely described by collisional kinetic theory, but the physical picture of dense flows is fundamentally different, due to long-lasting, many-body contacts. Here, we argue that particles undergo cooperative random motion in response to diffusing "spots" of free volume. The spot hypothesis precisely relates diffusion and cage-breaking to volume fluctuations and spatial velocity correlations, as confirmed by drainage experiments in our Dry Fluids Laboratory. A spot-based Monte Carlo algorithm also faithfully reproduces brute-force ("discrete element") simulations, with 1000 times less computational effort. The continuum limit of the spot model provides a new non-local partial differential equation for diffusion, with microscopically determined parameters. The spot mechanism may apply more generally to other dense amorphous materials, such as metallic glasses, where particles are geometrically constrained by their nearest neighbors.
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