Velocity and density profiles of granular flow in channels using a lattice gas automaton

Abstract

We have performed two-dimensional lattice-gas-automaton simulations of granular flow between two parallel planes. We find that the velocity profiles have nonparabolic distributions, while simultaneously the density profiles are nonuniform. Under nonslip boundary conditions, deviation of velocity profiles from the parabolic form of Newtonian fluids is found to be characterized solely by ratio of maximal velocity at the center to the average velocity, though the ratio depends on the model parameters in a complex manner. We also find that the maximal velocity (${\mathrm{u}}_{\mathrm{max}}$) at the center is a linear function of the driving force (g) as ${\mathrm{u}}_{\mathrm{max}}$=\ensuremath{\alpha}g-\ensuremath{\delta} with nonzero \ensuremath{\delta} in contrast with Newtonian fluids. Regarding density profiles, we observe that densities near the boundaries are higher than those in the center. The width of higher densities (above the average density) relative to the channel width is a decreasing function of a variable which scales with the driving force (g), energy dissipation parameter (\ensuremath{\epsilon}), and the width of the system (L) as ${\mathrm{g}}^{\mathrm{\ensuremath{\mu}}}$${\mathrm{L}}^{\ensuremath{\nu}}$/\ensuremath{\epsilon} with exponents \ensuremath{\mu}=1.4\ifmmode\pm\else\textpm\fi{}0.1 and \ensuremath{\nu}=0.5\ifmmode\pm\else\textpm\fi{}0.1. A phenomenological theory based on a scaling argument is presented to interpret these findings.