Steady state velocity distributions of an oscillated granular gas

TL;DR

This study uses molecular dynamics simulations to analyze the steady-state velocity distributions in a vertically oscillated granular gas, revealing nearly height-independent distributions with stretched exponential high-energy tails influenced by restitution and friction parameters.

Contribution

It provides detailed characterization of the velocity distribution functions in a driven granular gas, highlighting the effects of restitution and friction on high-energy tail behavior.

Findings

Velocity distributions are nearly uniform above a certain height.

High-energy tails follow a stretched exponential form.

Frictionless models can mimic frictional behavior by adjusting restitution.

Abstract

We use a three-dimensional molecular dynamics simulation to study the single particle distribution function of a dilute granular gas driven by a vertically oscillating plate at high accelerations ($15g - 90g$). We find that the density and the temperature fields are essentially time-invariant above a height of about 35 particle diameters, where typically 20% of the grains are contained. These grains form the nonequilibrium steady state granular gas with a Knudsen number unity or greater. In the steady state region, the distribution function of horizontal velocities (scaled by the local horizontal temperature) is found to be nearly independent of height, even though the hydrodynamic fields vary with height. The high energy tails of the distribution functions are described by a stretched exponential $\sim \exp(-{\cal B}c_x^{\alpha})$, where $\alpha$ depends on the normal coefficient of restitution $e$ ($1.2 < \alpha < 1.6$), but $\alpha$ does not vary for a wide range of the friction parameter. We find that the distribution function of a {\it frictionless} inelastic hard sphere model can be made similar to that of a frictional model by adjusting $e$. However, there is no single value of $e$ that mimics the frictional model over a range of heights.