Thermal diffusion segregation of an impurity in a driven granular fluid

TL;DR

This paper investigates impurity segregation in driven granular fluids under steady states, comparing theoretical predictions from the Boltzmann equation with simulation results, demonstrating the reliability of Navier-Stokes granular hydrodynamics even at high inelasticities.

Contribution

It provides the first detailed comparison between inelastic Boltzmann theory and simulations for impurity segregation in driven granular fluids under different steady states.

Findings

Good agreement between theory and DSMC/MD simulations.

Navier-Stokes hydrodynamics accurately describes impurity dynamics.

Preliminary results extend understanding to moderate densities.

Abstract

We study segregation of an impurity in a driven granular fluid under two types of \emph{steady} states. In the first state, the granular gas is driven by a stochastic volume force field with a Fourier-type profile while in the second state, the granular gas is sheared in such a way that inelastic cooling is balanced by viscous heating. We compare theoretical results derived from a solution of the (inelastic) Boltzmann equation at Navier-Stokes (NS) order with those obtained from the Direct Monte Carlo simulation (DSMC) method and molecular dynamics (MD) simulations. Good agreement is found between theory and simulation, which provides strong evidence of the reliability of NS granular hydrodynamics for these steady states (including the dynamics of the impurity), even at high inelasticities. In addition, preliminary results for thermal diffusion in granular fluids at moderate densitis are also presented. As for dilute gases \cite{VGK14}, excellent agreement is also found in this more general case.