Molecular dynamics simulations of vibrated granular gases

TL;DR

This paper uses molecular dynamics simulations to study vibrated granular gases, deriving an equation of state, analyzing velocity distributions, and examining energy non-equipartition in mixtures, providing insights into their heterogeneous behavior.

Contribution

It introduces a general equation of state for inelastic hard sphere mixtures and assesses the Random Restitution Coefficient model in vibrated granular gases.

Findings

Density and temperature profiles are heterogeneous due to boundary driving.

Velocity distributions exhibit non-Gaussian features.

Non-equipartition of energy is observed in binary mixtures.

Abstract

We present molecular dynamics simulations of mono- or bidisperse inelastic granular gases driven by vibrating walls, in two dimensions (without gravity). Because of the energy injection at the boundaries, a situation often met experimentally, density and temperature fields display heterogeneous profiles in the direction perpendicular to the walls. A general equation of state for an arbitrary mixture of fluidized inelastic hard spheres is derived and successfully tested against numerical data. Single-particle velocity distribution functions with non-Gaussian features are also obtained, and the influence of various parameters (inelasticity coefficients, density...) analyzed. The validity of a recently proposed Random Restitution Coefficient model is assessed through the study of projected collisions onto the direction perpendicular to that of energy injection. For the binary mixture, the non-equipartition of translational kinetic energy is studied and compared both to experimental data and to the case of homogeneous energy injection (``stochastic thermostat''). The rescaled velocity distribution functions are found to be very similar for both species.