Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow

We consider the rheology of steady two-dimensional granular flows, in different geometries, using discrete element method-based simulations of soft spheres. The flow classification parameter (psi), which defines the local flow type (ranging from pure rotation to simple shear to pure extension), varies spatially, to a significant extent, in the flows. We find that the material behaves as a generalized Newtonian fluid. The mu-I scaling proposed by Jop et al. [Nature (London) 441, 727 (2006)] is found to be valid in both two-dimensional and unidirectional flows, as observed in previous studies; however, the data for each flow geometry fall on a different curve. The results for the two-dimensional silo flow indicate that the viscosity does not depend directly on the flow type parameter, psi. We find that the scaling based on granular fluidity [Zhang and Kamrin, Phys. Rev. Lett. 118, 058001 (2017)] gives good collapse of the data to a single curve for all the geometries. The data for the variation of the solid faction with inertial number show a reasonable collapse for the different geometries.