Granular temperature controls local rheology of vibrated granular flows

TL;DR

This paper demonstrates that local rheology of vibrated granular flows can be described by a temperature-dependent model, linking granular temperature, friction, and shear rate, supported by numerical simulations.

Contribution

It introduces a local rheology model incorporating granular temperature and a heat diffusion equation, enabling a fully local continuum description of vibrated granular flows.

Findings

Friction decreases with increasing granular temperature.

Granular temperature obeys a heat equation with dissipation.

A local rheology model accurately describes vibrated granular flows.

Abstract

We use numerical simulations to demonstrate a local rheology for sheared, vibrated granular flows. We consider a granular assembly that is subjected to simple shear and harmonic vibration at the boundary. This configuration allows us to isolate the effects of vibration, as parameterized by 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, as suggested previously, combined with the new, empirical heat diffusion equation may provide a general strategy for dense granular flows.