Navier-Stokes transport coefficients of $d$-dimensional granular binary mixtures at low density

TL;DR

This paper derives the Navier-Stokes transport coefficients for low-density granular binary mixtures in arbitrary dimensions using kinetic theory, confirming the theoretical results with numerical simulations.

Contribution

It extends previous theoretical calculations of transport coefficients to arbitrary dimensions and validates them with Monte Carlo simulations.

Findings

Transport coefficients are unaffected by gravity.

Good agreement between theory and simulations across various parameters.

Extension of previous work to higher dimensions.

Abstract

The Navier-Stokes transport coefficients for binary mixtures of smooth inelastic hard disks or spheres under gravity are determined from the Boltzmann kinetic theory by application of the Chapman-Enskog method for states near the local homogeneous cooling state. It is shown that the Navier-Stokes transport coefficients are not affected by the presence of gravity. As in the elastic case, the transport coefficients of the mixture verify a set of coupled linear integral equations that are approximately solved by using the leading terms in a Sonine polynomial expansion. The results reported here extend previous calculations [V. Garz\'o and J. W. Dufty, Phys. Fluids {\bf 14}, 1476 (2002)] to an arbitrary number of dimensions. To check the accuracy of the Chapman-Enskog results, the inelastic Boltzmann equation is also numerically solved by means of the direct simulation Monte Carlo method to evaluate the diffusion and shear viscosity coefficients for hard disks. The comparison shows a good agreement over a wide range of values of the coefficients of restitution and the parameters of the mixture (masses and sizes).