Granular Temperature Controls Local Rheology of Vibrated Granular Flows

We use numerical simulations to demonstrate a local rheology for dense granular flows under shear and vibration. Granular temperature has been suggested as a rheological control but has been difficult to isolate. Here, we consider a granular assembly that is subjected to simple shear and harmonic vibration at the boundary, which provides a controlled source of granular temperature. We find that friction is reduced due to local velocity fluctuations of grains. All data obey a local rheology that relates the material friction coefficient, the granular temperature, and the dimensionless shear rate. We also observe that reduction in material friction due to granular temperature is associated with reduction in fabric anisotropy. We demonstrate that the temperature can be modeled by a heat equation with dissipation with appropriate boundary conditions, which provides complete closure of the system and allows a fully local continuum description of sheared, vibrated granular flows. This success suggests local rheology based on temperature combined with a diffusion equation for granular temperature may provide a general strategy to model dense granular flows.