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Granular mixtures modeled as elastic hard spheres subject to a drag force.
MedLine Citation:
PMID:  17677254     Owner:  NLM     Status:  PubMed-not-MEDLINE    
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 alpha{ij}. 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 beta{ij} modifying the collision rate of the elastic hard spheres, and the drag coefficient zeta{ij}. Both parameters are determined by requiring that the model reproduces the collisional transfers of momentum and energy of the true inelastic Boltzmann operator, yielding beta{ij}=(1+alpha{ij})2 and zeta{ij} proportional, variant1-alpha{ij}/{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.
Francisco Vega Reyes; Vicente Garzó; Andrés Santos
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Publication Detail:
Type:  Journal Article     Date:  2007-06-26
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  75     ISSN:  1539-3755     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2007 Jun 
Date Detail:
Created Date:  2007-08-06     Completed Date:  2007-09-27     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  061306     Citation Subset:  -    
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.
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