Slip velocity and stresses in granular Poiseuille flow via event-driven simulation

Abstract

Event-driven simulations of inelastic smooth hard disks are used to probe the slip velocity and rheology in gravity-driven granular Poiseuille flow. It is shown that both the slip velocity (U(w)) and its gradient (dU(w)/dy) depend crucially on the mean density, wall roughness, and inelastic dissipation. While the gradient of slip velocity follows a single power-law relation with Knudsen number, the variation in U(w) with Kn shows three distinct regimes in terms of Knudsen number. An interesting possibility of Knudsen-number-dependent specularity coefficient emerges from a comparison of our results with a first-order transport theory for the slip velocity. Simulation results on stresses are compared with kinetic-theory predictions, with reasonable agreement of our data in the quasielastic limit. The deviation of simulations from theory increases with increasing dissipation which is tied to the increasing magnitude of the first normal stress difference (N(1)) that shows interesting nonmonotonic behavior with density. As in simple shear flow, there is a sign change of N(1) at some critical density and its collisional component and the related collisional anisotropy are responsible for this sign reversal.