Inelastic Maxwell models for monodisperse gas-solid flows

TL;DR

This paper derives exact expressions for transport coefficients in inelastic Maxwell models of monodisperse gas-solid flows, considering the effects of an interstitial gas phase and comparing with previous hard sphere results.

Contribution

It provides explicit, exact formulas for Navier-Stokes transport coefficients in inelastic Maxwell models with gas-solid interactions, extending previous approximate methods.

Findings

Transport coefficients depend explicitly on restitution and friction coefficients.

Hydrodynamic regime can be reached independently of initial conditions.

Results are consistent with previous hard sphere models in steady state.

Abstract

The Boltzmann equation for $d$-dimensional inelastic Maxwell models is considered to analyze transport properties for monodisperse gas-solid suspensions. The influence of the interstitial gas phase on the dynamics of solid particles is modeled via a viscous drag force. The Chapman-Enskog method is applied to solve the inelastic Boltzmann equation to first order in the deviations of the hydrodynamic fields from their values in the homogeneous cooling state. Explicit expressions for the Navier-Stokes transport coefficients are \emph{exactly} obtained in terms of both the coefficient of restitution and the friction coefficient characterizing the amplitude of the external force. The conditions under which a hydrodynamic regime independent of the initial conditions is reached are widely discussed. Finally, the results derived here are compared with those previously obtained for inelastic hard spheres in steady state conditions by using the so-called first Sonine approximation.