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

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

2002-10-10

arxiv.org/abs/cond-mat/0210226v2

Phys. Rev. E 67, 021308 (2003)

Physics

Condensed Matter

Statistical Mechanics

5 figures. to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.67.021308

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).

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