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

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 et al. Phys. Rev. E 91, 052201 (2015)] derived for low-density granular gases.