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.