Simulations of vibrated granular medium with impact velocity dependent restitution coefficient

TL;DR

This paper presents numerical simulations of vibrated granular media using a velocity-dependent restitution coefficient, revealing how system behavior transitions from homogeneous to clustered states and differs from classical models.

Contribution

It introduces a velocity-dependent restitution coefficient in simulations, aligning results with experiments and highlighting deviations from traditional constant-coefficient models.

Findings

Scaling exponents decrease with particle number.

Results agree with experimental data.

Deviations from classical kinetic theory.

Abstract

We report numerical simulations of strongly vibrated granular materials designed to mimic recent experiments performed both in presence or absence of gravity. The coefficient of restitution used here depends on the impact velocity by taking into account both the viscoelastic and plastic deformations of particles, occurring at low and high velocities respectively. We show that this model with impact velocity dependent restitution coefficient reproduce results that agree with experiments. We measure the scaling exponents of the granular temperature, collision frequency, impulse, and pressure with the vibrating piston velocity as the particle number increases. As the system changes from a homogeneous gas state at low density to a clustered state at high density, these exponents are all found to decrease continuously with the particle number. All these results differ significantly from classical inelastic hard sphere kinetic theory and previous simulations, both based on a constant restitution coefficient.