2007/01/31 by Francisco Vega Reyes, Vicente Garzó, Vicente Garzo +2 · 1 citation
Engineering · Physics and Astronomy · #Boltzmann constant #Boltzmann equation #Classical mechanics #Dimensionless quantity #Drag #Elastic collision #Granular flow and fluidized beds #Hard spheres #Inelastic collision #Lattice Boltzmann Simulation Studies #Particle Dynamics in Fluid Flows #Physics #Quantum mechanics #SPHERES #Thermodynamics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.75.061306
published as Phys. Rev. E 75, 061306 (2007) · The title has been changed, 4 figures, and to be published in Phys. Rev. E
arxiv created 2007/04/24 · openalex publication_date 2007/06/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Granular gaseous mixtures under rapid flow conditions are usually modeled as a multicomponent system of smooth inelastic hard disks (two dimensions) or spheres (three dimensions) with constant coefficients of normal restitution alphaij. 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 disks or spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. For each collision term ij, the model has two parameters: a dimensionless factor betaij modifying the collision rate of the elastic hard spheres, and the drag coefficient zetaij. Both parameters are determined by requiring that the model reproduces the collisional transfers of momentum and energy of the true inelastic Boltzmann operator, yielding betaij=(1+alphaij)2 and zetaij proportional, variant1-alphaij/2, where the proportionality constant is a function of the partial densities, velocities, and temperatures of species i and j. 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. The discrepancies between both descriptions are seen to be similar to those found for monocomponent gases. 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.