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

TL;DR

This study uses lattice-gas automaton simulations to analyze granular flow in channels, revealing non-parabolic velocity profiles, non-uniform density distributions, and new scaling laws for density variations based on driving force and system parameters.

Contribution

It introduces a novel simulation approach to characterize granular flow profiles and proposes a phenomenological scaling theory explaining the observed density and velocity behaviors.

Findings

Velocity profiles are non-parabolic and depend on the velocity ratio.

Maximal velocity scales linearly with driving force, with a non-zero intercept.

Density near boundaries exceeds that at the center, with width scaling as a function of system parameters.

Abstract

We have performed two-dimensional lattice-gas-automaton simulations of granular flow between two parallel planes. We find that the velocity profiles have non-parabolic distributions while simultaneously the density profiles are non-uniform. Under non-slip 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 ($u_{max}$) at the center is a linear function of the driving force (g) as $u_{max} = \alpha g - \delta$ with non-zero $\delta$ 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 ($\epsilon$) and the width of the system (L) as $g^{\mu} L^{\nu}/\epsilon$ with exponents $\mu = 1.4 \pm 0.1$ and $\nu = 0.5 \pm 0.1$. A phenomenological theory based on a scaling argument is presented to interpret these findings.