Local Equation of State and Velocity Distributions of a Driven Granular Gas

TL;DR

This study uses simulations to explore the local equation of state and velocity distributions in a driven granular gas, revealing how inelasticity and system parameters influence local properties and velocity tail behaviors.

Contribution

It introduces a local constitutive equation for a driven granular gas and analyzes how inelasticity affects local and global properties, including velocity distributions.

Findings

Local constitutive relation depends on system parameters at high inelasticity.

At moderate inelasticity, the relation is approximately local and independent of global parameters.

Velocity distributions show non-scaling with local temperature and differ between velocity components.

Abstract

We present event-driven simulations of a granular gas of inelastic hard disks with incomplete normal restitution in two dimensions between vibrating walls (without gravity). We measure hydrodynamic quantities such as the stress tensor, density and temperature profiles, as well as velocity distributions. Relating the local pressure to the local temperature and local density, we construct a local constitutive equation. For strong inelasticities the local constitutive relation depends on global system parameters, like the volume fraction and the aspect ratio. For moderate inelasticities the constitutive relation is approximately independent of the system parameters and can hence be regarded as a local equation of state, even though the system is highly inhomogeneous with heterogeneous temperature and density profiles arising as a consequence of the energy injection. Concerning the local velocity distributions we find that they do not scale with the square root of the local granular temperature. Moreover the high-velocity tails are different for the distribution of the x- and the y-component of the velocity, and even depend on the position in the sample, the global volume fraction, and the coefficient of restitution.