Computer simulations of an impurity in a granular gas under planar Couette flow

We present in this work results from numerical solutions, obtained by means of the direct simulation Monte Carlo (DSMC) method, of the Boltzmann and Boltzmann--Lorentz equations for an impurity immersed in a granular gas under planar Couette flow. The DSMC results are compared with the exact solution of a recent kinetic model for the same problem. The results confirm that, in steady states and over a wide range of parameter values, the state of the impurity is enslaved to that of the host gas: it follows the same flow velocity profile, its concentration (relative to that of the granular gas) is constant in the bulk region, and the impurity/gas temperature ratio is also constant. We determine also the rheological properties and nonlinear hydrodynamic transport coefficients for the impurity, finding a good semi-quantitative agreement between the DSMC results and the theoretical predictions.