Moderately dense granular gas of inelastic rough spheres

TL;DR

This paper develops a comprehensive kinetic theory for moderately dense inelastic and rough granular gases, deriving detailed balance equations and transport coefficients based on the Enskog equation and Grad's distribution function.

Contribution

It introduces a 29-field kinetic theory for dense granular gases of inelastic rough spheres, connecting microscopic properties to macroscopic transport coefficients.

Findings

Derived balance equations for 29 scalar fields.

Obtained explicit expressions for transport coefficients.

Extended theory to elastic rough spheres case.

Abstract

A kinetic theory for moderately dense gases of inelastic and rough spherical molecules is developed from the Enskog equation where a macroscopic state is characterized by 29 scalar fields which correspond to the moments of the distribution function: mass density, hydrodynamic velocity, pressure tensor, absolute temperature, translational and rotational heat fluxes, hydrodynamic angular velocity and angular velocity flux. The balance equations for the 29 scalar fields are obtained from a transfer equation derived from the Enskog equation where the kinetic and potential parts of the new moments of the distribution function and production terms are calculated from Grad's distribution function for the basic fields. The transition from the 29 field theory to an eight field theory -- with mass density, hydrodynamic velocity, absolute temperature and hydrodynamic angular velocity -- leads to the determination of the transport coefficients of the Navier-Stokes and Fourier laws. The transport coefficients are functions of the normal and tangential restitution coefficients and of the local equilibrium radial distribution function. The transport coefficients in the limiting case of elastic rough spheres is also determined.