Enskog kinetic theory for a model of a confined quasi-two-dimensional granular fluid

TL;DR

This paper derives the Navier-Stokes transport coefficients for a confined quasi-two-dimensional granular gas using Enskog kinetic theory, extending previous low-density results to moderate densities with explicit formulas.

Contribution

It provides the first derivation of transport coefficients for this specific granular fluid model at moderate densities using the Chapman-Enskog method.

Findings

Explicit expressions for transport coefficients are obtained.

Results are valid for states with stationary temperature.

The theory extends previous low-density results to moderate densities.

Abstract

The Navier-Stokes transport coefficients for a model of a confined quasi-two-dimensional granular gas of smooth inelastic hard spheres are derived from the Enskog kinetic equation. A normal solution to this kinetic equation is obtained via the Chapman-Enskog method for states close to the local homogeneous state. The analysis is performed to first order in spatial gradients, allowing the identification of the Navier-Stokes transport coefficients associated with the heat and momentum fluxes. The transport coefficients are determined from the solution to a set of coupled linear integral equations analogous to those for elastic collisions. These integral equations are solved by using the leading terms in a Sonine polynomial expansion. The results are particularized to the relevant state with stationary temperature, where explicit expressions for the Navier-Stokes transport coefficients are given in terms of the coefficient of restitution and the solid volume fraction. The present work extends to moderate densities previous results [Brey \emph{et al.} Phys. Rev. E \textbf{91}, 052201 (2015)] derived for low-density granular gases.