Shear viscosity for a heated granular binary mixture at low-density

TL;DR

This paper analyzes the shear viscosity of a heated granular binary mixture at low density using Boltzmann kinetic theory, employing Chapman-Enskog and DSMC methods, and finds excellent agreement between theory and simulation.

Contribution

It provides a detailed theoretical and numerical analysis of shear viscosity in heated granular mixtures, extending previous free cooling studies to driven systems.

Findings

Theoretical expressions for shear viscosity are derived using Chapman-Enskog.

Numerical DSMC simulations validate the theoretical results.

Excellent agreement between theory and simulation across parameters.

Abstract

The shear viscosity for a heated granular binary mixture of smooth hard spheres at low-density is analyzed. The mixture is heated by the action of an external driving force (Gaussian thermostat) which exactly compensate for cooling effects associated with the dissipation of collisions. The study is made from the Boltzmann kinetic theory, which is solved by using two complementary approaches. First, a normal solution of the Boltzmann equation via the Chapman-Enskog method is obtained up to first order in the spatial gradients. The mass, heat, and momentum fluxes are determined and the corresponding transport coefficients identified. As in the free cooling case [V. Garz\'o and J. W. Dufty, Phys. Fluids {\bf 14}, 1476 (2002)], practical evaluation requires a Sonine polynomial approximation, and here it is mainly illustrated in the case of the shear viscosity. Second, to check the accuracy of the Chapman-Enskog results, the Boltzmann equation is numerically solved by means of the Direct Simulation Monte Carlo (DSMC) method. The simulation is performed for a system under uniform shear flow, using the Gaussian thermostat to control inelastic cooling. The comparison shows an excellent agreement between theory and simulation over a wide range of values of the restitution coefficients and the parameters of the mixture (masses, concentrations, and sizes).