Math. Model. Nat. Phenom.
Volume 6, Number 1, 2011Instability and patterns. Issue dedicated to the memory of A. Golovin
|Page(s)||17 - 47|
|Published online||09 June 2010|
Theory of Dilute Binary Granular Gas Mixtures
School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University,
Ramat-Aviv Tel Aviv 69978,
1 Corresponding author. E-mail: firstname.lastname@example.org
A computer-aided method for accurately carrying out the Chapman-Enskog expansion of the Boltzmann equation, including its inelastic variant, is presented and employed to derive a hydrodynamic description of a dilute binary mixture of smooth inelastic spheres. Constitutive relations, formally valid for all physical values of the coefficients of restitution, are calculated by carrying out the pertinent Chapman-Enskog expansion to sufficient high orders in the Sonine polynomials to ensure numerical convergence. The resulting hydrodynamic description is applied to the analysis of a vertically vibrated binary mixture of particles (under gravity) differing only in their respective coefficients of restitution. It is shown that even with this “minor”difference the mixture partly segregates, its steady state exhibiting a sandwich-like configuration.
Mathematics Subject Classification: 76P05 / 82B40 / 82C40 / 82C70
Key words: kinetic theory / granular gases / mixtures / segregation / Chapman-Enskog expansion / hydrodynamics
© EDP Sciences, 2010
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