The Stochastic Flow Rule and Rate Sensitivity in Dense Granular Flows.

The Stochastic Flow Rule (SFR) is a constitutive law which, when used with limit-state Mohr-Coulomb plasticity for stresses, gives predictions for the mean velocity field in quasi-2D dense granular flows. It is based on a simple microscopic flow mechanism, where ``spots'' of free volume perform random walks along slip-lines, biased by stress imbalances upon local fluidization. The SFR has recently been shown to predict dense granular flows in diverse geometries--- e.g. draining silos, annular Couette cells, and plate-dragging experiments--- without the use of fitting parameters. However, a significant rheological change occurs in certain geometries--- e.g. inclined plane flow and gravity-free horizontal shear flow--- where the packing fraction is nearly uniform and a distinct stress/strain-rate relationship arises. In this talk, we review the SFR and propose a simple explanation of when and why rate sensitivity occurs, depending on the slip-line geometry. We also postulate how rate-dependent terms may be combined with the SFR to create a more universal theory of dense flows.