Harvard Applied Mechanics Colloquium
Wednesday, April 21, 2004
Title: A Theory of Cooperative Diffusion in Dense Granular Flows
Speaker: Martin Z. Bazant (MIT, Applied Math)
Abstract:
Dilute granular flows are routinely described by the kinetic theory of
(inelastic) gases and classical hydrodynamics, but dense flows require
a fundamentally different approach, due to long-lasting, many-body
contacts. In the case of silo drainage, many continuum models have
been proposed for the mean flow, but no statistical theory is
available. Here, we propose that particles undergo cooperative random
motion in diffusing ``spots'' of free volume, extending across several
particle diameters. The continuum limit of the Spot Model provides
new, non-local partial differential equations for tracer diffusion in
dense flows. The theory directly relates diffusion and cage-breaking
to volume fluctuations, in agreement with particle-tracking
experiments in the MIT Dry Fluids Lab. It also provides a simple
explanation of density waves, caused by weak short-ranged repulsion
between spots. Direct evidence for spots comes from our observation of
spatial velocity correlations in experimental and computational flows.
The basic idea of a spot of cooperative diffusion may also apply to
other dense, disordered materials, such as metallic glasses.