Bridging the Rheology of Dense Granular Flows in Three Regimes

Using the discrete element method, simulations of simple shear flow of dense assemblies of soft, frictional particles have been carried out over a range of shear rates and volume fractions in order to characterize the rheology of granular flows in three regimes. In agreement with previous results for frictionless spheres [1], the pressure in each regime is found to obey an asymptotic power law relation with shear rate. These relations are then used to construct a blended pressure model. Additionally, we constitute the shear stress ratio in terms of two dimensionless groups: the inertia number [2], which governs the rheology of hard particles, and the ratio of shear time to the particle binary collision time, which characterizes the departure from hard-sphere behavior. The pressure and shear stress ratio relations form a rheological model that, in the hard-sphere limit, can be written as a modified kinetic theory for dense granular flows [3].\\[4pt] [1] T. Hatano, et al., J. Phys. Soc. Japan 76, 023001 (2007).\\[0pt] [2] da Cruz, F. et al., Phys. Rev. E 72, 021309 (2005).\\[0pt] [3] J. Jenkins, and D. Berzi, Granular Matter 12, 151 (2010).