Dynamics of the granular fluidity field

A collection of densely-packed solid grains such as sand, rice, and sugar can flow like liquids. A key issue for dense granular flows is rheology: what is the relation between stress and strain rate? The mu(I) rheology postulates a local rheology for steady-state inertial flows. Modified from the local rheology, the non-local granular fluidity (NGF) model has been proposed to explain non-local phenomena due to finite grain size. In the NGF model, an order parameter called ‘granular fluidity’ diffuses away following a partial differential equation in a form of the reaction-diffusion equation. This PDE, however, has only been verified in steady-states. Using the discrete element method, we observe dynamics of the order parameter in different configurations and verify the PDE of the NGF model in transient states.