Hydrodynamics for a model of a confined quasi-two-dimensional granular gas

TL;DR

This paper derives hydrodynamic equations for a confined quasi-two-dimensional granular gas, explicitly calculating transport coefficients and analyzing the effects of inelastic collisions on energy transport.

Contribution

It introduces a generalized Chapman-Enskog method to derive hydrodynamics for inelastic hard spheres, including new terms for energy transport due to inelasticity.

Findings

Transport coefficients depend on restitution and velocity parameters.

An Euler transport term for energy transport is identified.

Hydrodynamic equations are specialized for steady states.

Abstract

The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and momentum fluxes are calculated to Navier-Stokes order, and the associated transport coefficients are explicitly determined as functions of the coefficient of normal restitution and the velocity parameter involved in the definition of the model. Also an Euler transport term contributing to the energy transport equation is considered. This term arises from the gradient expansion of the rate of change of the temperature due to the inelasticity of collisions, and vanishes for elastic systems. The hydrodynamic equations are particularized for the relevant case of a system in the homogeneous steady state. The relationship with previous works is analyzed.