Modified Sonine approximation for granular binary mixtures

TL;DR

This paper introduces a modified Sonine approximation within the Chapman-Enskog framework to better predict hydrodynamic transport coefficients in granular binary mixtures, especially under strong dissipation conditions.

Contribution

The authors develop a new Sonine approach replacing the Maxwell-Boltzmann distribution with the homogeneous cooling state distribution to improve theoretical predictions.

Findings

Modified Sonine approximation yields more accurate transport coefficients.

Numerical simulations confirm improved agreement with theory.

Method is reliable at high dissipation levels.

Abstract

We evaluate in this work the hydrodynamic transport coefficients of a granular binary mixture in $d$ dimensions. In order to eliminate the observed disagreement (for strong dissipation) between computer simulations and previously calculated theoretical transport coefficients for a monocomponent gas, we obtain explicit expressions of the seven Navier-Stokes transport coefficients with the use of a new Sonine approach in the Chapman-Enskog theory. Our new approach consists in replacing, where appropriate in the Chapman-Enskog procedure, the Maxwell-Boltzmann distribution weight function (used in the standard first Sonine approximation) by the homogeneous cooling state distribution for each species. The rationale for doing this lies in the fact that, as it is well known, the non-Maxwellian contributions to the distribution function of the granular mixture become more important in the range of strong dissipation we are interested in. The form of the transport coefficients is quite common in both standard and modified Sonine approximations, the distinction appearing in the explicit form of the different collision frequencies associated with the transport coefficients. Additionally, we numerically solve by means of the direct simulation Monte Carlo method the inelastic Boltzmann equation to get the diffusion and the shear viscosity coefficients for two and three dimensions. As in the case of a monocomponent gas, the modified Sonine approximation improves the estimates of the standard one, showing again the reliability of this method at strong values of dissipation.