Granular mixtures modeled as elastic hard spheres subject to a drag force

Abstract

Granular gaseous mixtures under rapid flow conditions are usually modeled by a multicomponent system of smooth inelastic hard spheres with constant coefficients of normal restitution. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. The Navier--Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman--Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions.

arXiv commentThe title has been changed, 4 figures, and to be published in Phys. Rev. E

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• Energy Production Rates of Multicomponent Granular Gases of Rough Particles. A Unified View of Hard-Disk and Hard-Sphere Systems
• Impurity in a sheared inelastic Maxwell gas
• Generalized transport coefficients for inelastic Maxwell mixtures under shear flow
• Impurity in a granular gas under nonlinear Couette flow
• Computer simulations of an impurity in a granular gas under planar Couette flow
• Anomalous transport of impurities in inelastic Maxwell gases
• Rheology of a dilute binary mixture of inertial suspension under simple shear flow
• Kinetic model for transport in granular mixtures
• Exact results for non-Newtonian transport properties in sheared granular suspensions: inelastic Maxwell models and BGK-type kinetic model