A Fluctuating Energy Model for Dense Granular Flows

Summary

We address the slow, dense flow of granular materials as a continuum with the incompressible Navier-Stokes equations plus the fluctuating energy balance for granular temperature. The pseudo-fluid is given an apparent viscosity, for which we choose an Arrhenius-like dependence on granular temperature; the fluctuating energy balance includes a ‘mobility enhancing’ term due to shear stress and a jamming, dissipative term which we assume to depend on the isotropic part of the stress tensor and on shear rate. After having proposed a ‘chemical’ interpretation of the phenomenology described by the model in terms of reaction rates, we report results for some 2-D standard geometries of flow, which agree semi-quantitatively with experimental and DEM observations. In particular, our model well reproduces the formation of stagnant zones of a characteristic shape (e.g. wedge-shaped static zones in a silo with flat bottom) without prescribing them a-priori with erosion techniques.