Temperature scaling in a dense vibro-fluidised granular material

TL;DR

This paper derives an asymptotic theory for the temperature and density profiles of a dense, vibrated granular material, showing good agreement with simulations at high densities and extending understanding beyond dilute models.

Contribution

It introduces an asymptotic analytical solution for the temperature and density distribution in dense vibrated granular materials, incorporating elastic particle assumptions and virial equation of state.

Findings

Good agreement with simulation data at high densities

The Maxwell-Boltzmann velocity distribution is valid in the leading approximation

Predicts scaling relations of total dissipation in the granular bed

Abstract

The leading order "temperature" of a dense two dimensional granular material fluidised by external vibrations is determined. An asymptotic solution is obtained where the particles are considered to be elastic in the leading approximation. The velocity distribution is a Maxwell-Boltzmann distribution in the leading approximation. The density profile is determined by solving the momentum balance equation in the vertical direction, where the relation between the pressure and density is provided by the virial equation of state. The predictions of the present analysis show good agreement with simulation results at higher densities where theories for a dilute vibrated granular material, with the pressure-density relation provided by the ideal gas law, are in error. The theory also predicts the scaling relations of the total dissipation in the bed reported by McNamara and Luding (PRE v 58, p 813).