Toward a unified local rheology for sheared, vibrated granular flow

Dense granular flows are ubiquitous, but still lack complete local flow models. The best models relate material friction to local strain rate, but are known to fail for simple modifications like stress gradients or applied external perturbations like vibrations. In these cases, some nonlocal information is required about the flow state or boundary condition. In this talk, I will describe a series of particle based numerical simulations that include both vibrations and stress gradients. For applied vibration, we find that reduced material friction occurs only above a minimum vibration frequency, to break contacts, and a minimum amplitude, to disrupt the force network. When local field quantities are considered, we find that systems that include vibrations and stress gradients can be captured by a single, local rheology model that includes stress and strain rate as well as granular temperature, which is defined as the mean-square of velocity fluctuations of grains. We show that this temperature-based description is consistent with previous nonlocal fluidity models (which successfully describe systems with stress gradients). Temperature is generated both by shear and vibration and diffuses via a heat equation, which provides complete closure of the system and allows a fully local continuum description. We test a heat equation similar to existing kinetic theory, and find consistency with our results, at least in certain limits. Our results strongly suggest that a modified kinetic theory that directly treats temperature, appropriately modified for the dense flow regime, could be the way forward to describe arbitrary dense granular flows as well as a range of related soft matter systems.