2nd New England Area Granular Materials Workshop Yale University, June 3, 2004 Title: A theory of cooperative diffusion in dense granular flows Speaker: Martin Z. Bazant (Applied Mathematics, MIT) Abstract: Although diffusion in fast, dilute granular flows may be described by variations of classical kinetic theory, recent experiments suggest that slow, dense flows require a fundamentally different approach, due to long-lasting, many-body contacts. In the case of slow silo drainage, many continuum models have been proposed for the mean flow, but no microscopic theory of fluctuations is available. Here, we propose describe a statistical theory of dense flows in which particles undergo cooperative random motion in response to diffusing ``spots'' of free volume. The Spot Model may be either used in Monte Carlo simulations or analyzed in the continuum limit, where some new partial differential equations arise. The theory predicts spatial velocity correlations, athermal diffusion and cage breaking controlled by free volume and geometry-dependent density waves. Particle-tracking experiments in the MIT Dry Fluids Lab provide strong support for the spot hypothesis.