Power-Law Scaling in Granular Rheology

We propose a new form of the constitutive equation for simple granular materials which is independent of packing fraction. By measuring coarse-grained continuum fields in discrete element method simulations of frictional particles, we have found that rescaling the stress ratio μ by a power of dimensionless granular temperature Θ makes the data from many different flow geometries collapse to a master curve which depends only on the inertial number I. This power-law structure appears robust to varying interparticle friction (roughness) in both 2D and 3D systems. Its functional form reflects the key physical idea that stronger velocity fluctuations (agitations) soften the granular material and assist flow. Our rheology fits and extends the frameworks such as kinetic theory and the nonlocal granular fluidity model. Finally, we show how this equation can be used to predict the velocity field in inclined chutes where flow depends on two spatial coordinates.