2018/09/30 by Alberto Megías, Andrés Santos
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Angular velocity #Classical mechanics #Computer science #Curse of dimensionality #Degrees of freedom (physics and chemistry) #Geometry #Granular flow and fluidized beds #Hard spheres #Kinetic energy #Material Dynamics and Properties #Mathematics #Particle Dynamics in Fluid Flows #Physics #Planar #Plane (geometry) #Quantum mechanics #SPHERES #cond-mat.soft
paper · pdf · doi:10.1063/1.5119584
published as AIP Conference Proceedings 2132, 080003 (2019) · 11 pages, 1 figure; contributed paper at the 31st International Symposium on Rarefied Gas Dynamics (Glasgow, UK, July 23-27, 2018)
openalex created_date 2018/09/27 · openalex publication_date 2019/01/01 · arxiv created 2019/08/12 · arxiv updated 2019/08/14 · openalex updated_date 2026/08/05
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 ξijtr and ξijrot (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 ξijtr=ξij of smooth d-dimensional spheres are also recovered.