Energy Production Rates of Multicomponent Granular Gases of Rough Particles. A Unified View of Hard-Disk and Hard-Sphere Systems.

Granular gas mixtures modeled as systems of inelastic and rough particles, either hard disks on a plane or hard spheres, are considered. Both classes of systems are embedded in a three-dimensional space (d = 3) but, while in the hard-sphere case the translational and angular velocities are vectors with the same dimensionality (and thus there are dtr = 3 translational and drot = 3 rotational degrees of freedom), in the hard-disk case the translational velocity vectors are planar (i.e., dtr = 2 translational degrees of freedom) and the angular velocity vectors are orthogonal to the motion plane (i.e., drot = 1 rotational degree of freedom). This complicates a unified presentation of both classes of systems, in contrast to what happens for smooth, spinless particles, where a treatment of d-dimensional spheres is possible. In this paper, a kinetic-theory derivation of the (collisional) energy production rates ξtr ij and ξrotij (where the indices i and j label different components) in terms of the numbers of degrees of freedom dtr and drot is presented. Known hard-sphere and hard-disk expressions are recovered by particularizing to (dtr, drot) = (3, 3) and (dtr, drot) = (2, 1), respectively. Moreover, in the case of spinless particles with d = dtr, known energy production rates ξtrij = ξij of smooth d-dimensional spheres are also recovered. [ABSTRACT FROM AUTHOR]