Impurity in a granular gas under nonlinear Couette flow

TL;DR

This paper investigates the transport properties of an impurity in a granular gas under nonlinear Couette flow, developing a hydrodynamic model validated by Monte Carlo simulations that remains accurate under extreme conditions.

Contribution

The authors derive a hydrodynamic solution for impurity transport in granular gases under nonlinear flow, validated by simulations, extending the applicability beyond traditional regimes.

Findings

Hydrodynamic solution accurately describes impurity transport in bulk.

Solution valid for high shear rates and inelasticities.

Preliminary Boltzmann simulations support the model's reliability.

Abstract

We study in this work the transport properties of an impurity immersed in a granular gas under stationary nonlinear Couette flow. The starting point is a kinetic model for low-density granular mixtures recently proposed by the authors [Vega Reyes F et al. 2007 Phys. Rev. E 75 061306]. Two routes have been considered. First, a hydrodynamic or normal solution is found by exploiting a formal mapping between the kinetic equations for the gas particles and for the impurity. We show that the transport properties of the impurity are characterized by the ratio between the temperatures of the impurity and gas particles and by five generalized transport coefficients: three related to the momentum flux (a nonlinear shear viscosity and two normal stress differences) and two related to the heat flux (a nonlinear thermal conductivity and a cross coefficient measuring a component of the heat flux orthogonal to the thermal gradient). Second, by means of a Monte Carlo simulation method we numerically solve the kinetic equations and show that our hydrodynamic solution is valid in the bulk of the fluid when realistic boundary conditions are used. Furthermore, the hydrodynamic solution applies to arbitrarily (inside the continuum regime) large values of the shear rate, of the inelasticity, and of the rest of parameters of the system. Preliminary simulation results of the true Boltzmann description show the reliability of the nonlinear hydrodynamic solution of the kinetic model. This shows again the validity of a hydrodynamic description for granular flows, even under extreme conditions, beyond the Navier-Stokes domain.