Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow
Physical Review Fluids
This work utilizes soft-particle discrete element simulations to examine the rheology of steady two-dimensional granular flows with reference to a unidirectional shear flow, which has been extensively employed for validating the local visco-plastic model of Jop et al. [Nature 441, 727--730 (2006)]. The μ-I scaling proposed by Jop et al. is found to be valid in both two-dimensional and unidirectional flows, as observed in previous studies, however, each flow type results in a different curve.
... e μ, ratio of the shear stress magnitude to the pressure, is the friction coefficient and I is the dimensionless inertial number, which is proportional to the ratio of the magnitude of the rate of strain tensor, γ̇, to the square root of the pressure. The friction coefficient is found not to scale in a simple way with the flow classification parameter ψ, which characterizes the local flow type. All the data collapse to a single curve using the scaling proposed by Zhang and Kamrin [Phys. Rev. Lett. 118, 058001 (2017)], in which the scaled granular fluidity (f=1/(μ T), where T ∝ u/γ̇ and u is the fluctuation velocity) is found to depend only on the solid fraction ϕ. The data for variation of ϕ with inertial number I collapse to a single curve for all the flows.