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Modified Sonine approximation for granular binary mixtures

Published online by Cambridge University Press:  06 March 2009

VICENTE GARZÓ ,
FRANCISCO VEGA REYES  and
JOSÉ MARÍA MONTANERO
VICENTE GARZÓ*
Affiliation:
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
FRANCISCO VEGA REYES
Affiliation:
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
JOSÉ MARÍA MONTANERO
Affiliation:
Departamento de Ingeniería Mecánica, Energética y de los Materiales, Universidad de Extremadura, E-06071 Badajoz, Spain
*
†Email address for correspondence: vicenteg@unex.es
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Abstract

We evaluate in this work the hydrodynamic transport coefficients of a granular binary mixture in d dimensions. In order to eliminate the observed disagreement (for strong dissipation) between computer simulations and previously calculated theoretical transport coefficients for a monocomponent gas, we obtain explicit expressions of the seven Navier–Stokes transport coefficients by the use of a new Sonine approach in the Chapman–Enskog (CE) theory. This new approach consists of replacing, where appropriate in the CE procedure, the Maxwell–Boltzmann distribution weight function (used in the standard first Sonine approximation) by the homogeneous cooling state distribution for each species. The rationale for doing this lies in the well-known fact that the non-Maxwellian contributions to the distribution function of the granular mixture are more important in the range of strong dissipation we are interested in. The form of the transport coefficients is quite common in both standard and modified Sonine approximations, the distinction appearing in the explicit form of the different collision frequencies associated with the transport coefficients. Additionally, we numerically solve by the direct simulation Monte Carlo method the inelastic Boltzmann equation to get the diffusion and the shear viscosity coefficients for two and three dimensions. As in the case of a monocomponent gas, the modified Sonine approximation improves the estimates of the standard one, showing again the reliability of this method at strong values of dissipation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 623 , 25 March 2009 , pp. 387 - 411
Copyright
Copyright © Cambridge University Press 2009

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