Dynamical model for nonlocal inertial-number rheology of dense granular flows

Dense granular materials present complicated fluid and solid behaviors. The materials flow above a yield stress which is greater than the magnitude when the flow stops, known as hysteresis. Nonlocal flow rheology emerges due to particle cooperative motions, resulting in flow-size dependence in quasistatic regime and long-range collision momentum transport in dense inertial regime. In this talk, we formulate a dynamical Ginzburg-Landau model of phase transition that can describe these features. We choose the inertial number I as a fluidization order parameter and derive the free energy functional using scaling arguments along with a yield-stress weakening mechanism. The model yields a nonmonotonic flow curve in a homogeneous flow environment, accounting for hysteresis and intermittency in the quasistatic regime. The model shows a generalized Bagnold stress revealing two nonlocal mechanisms: collisions among correlated structures within which fluidization spread. The model captures several salient features in inclined flow configuration including hysteretic starting and stopping heights, Pouliquen's inertial flow rule and flow-thickness dependent velocity shapes.