A Dissipative Coulomb Model for Dense Granular Flows

We address the slow, dense flow of granular materials as a continuum with the incompressible Navier‐Stokes equations plus the fluctuating energy balance including granular temperature. The pseudo‐fluid is given an apparent viscosity which depends on an order parameter which we choose to be granular temperature. We derive the fluctuating energy balance following Babic [1]; this balance includes a ‘mobility enhancing’ term due to ‘viscous heating’ effects and a dissipative term which we assume, as a constitutive hypothesis, dependent on the isotropic part of the stress tensor and on shear rate, based on local friction considerations. For its particular structure the model is called Dissipative Coulomb Model. Solving the equation system we get an appreciable agreement with experiments in complex geometries (silos, hoppers). The model predicts also the typical behaviour of stresses in these configurations, thus predicting phenomena like the hourglass effect.