Kinetic theory of mixtures of inelastic rough hard spheres

Santos, A.¹ and Kremer, G.²

¹ Dep. Physics - University of Extremadura, Spain; ² Universidade Federal do Paraná, Brasil

The simplest model of a granular fluid consists of identical, inelastic smooth hard spheres with a constant coefficient of normal restitution. Kinetic theory tools have successfully been applied to this model and interesting properties have been analyzed. Obviously, the model can be made closer to reality by introducing more ingredients, such as polydispersity and/or roughness. These two ingredients are especially interesting because they unveil an inherent breakdown of energy equipartition in granular fluids, even in homogeneous and isotropic states. The aim of this talk is to explore the combined effect of both ingredients in a kinetic theory description. We will consider a dilute mixture of inelastic rough hard spheres of arbitrary number densities, masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution. After constructing the Boltzmann equation for the mixture, the collisional moments associated with the translational and rotational temperatures will be expressed in terms of average values. Next, those average values will be estimated by assuming a Maxwellian velocity distribution, allowing us to express the cooling rates in terms of the partial temperatures and the mechanical parameters of the mixture. Finally, the results will be applied to the homogeneous cooling state of a binary mixture and the influence of inelasticity on the temperature ratios will be analyzed.