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Navier–Stokes Transport Coefficients of d-Dimensional Granular Binary Mixtures at Low Density

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Abstract

The Navier–Stokes transport coefficients for binary mixtures of smooth inelastic hard disks or spheres under gravity are determined from the Boltzmann kinetic theory by application of the Chapman–Enskog method for states near the local homogeneous cooling state. It is shown that the Navier–Stokes transport coefficients are not affected by the presence of gravity. As in the elastic case, the transport coefficients of the mixture verify a set of coupled linear integral equations that are approximately solved by using the leading terms in a Sonine polynomial expansion. The results reported here extend previous calculations (Garzó, V., Dufty, J.W. in Phys. Fluids 14:1476–1490, 2002) to an arbitrary number of dimensions and provide explicit expressions for the seven Navier–Stokes transport coefficients in terms of the coefficients of restitution and the masses, composition, and sizes of the constituents of the mixture. In addition, to check the accuracy of our theory, the inelastic Boltzmann equation is also numerically solved by means of the direct simulation Monte Carlo method to evaluate the diffusion and shear viscosity coefficients for hard disks. The comparison shows a good agreement over a wide range of values of the coefficients of restitution and the parameters of the mixture (masses and sizes).

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Authors and Affiliations

  1. Departamento de Física, Universidad de Extremadura, 06071, Badajoz, Spain

    Vicente Garzó

  2. Departamento de Electrónica e Ingeniería Electromecánica, Universidad de Extremadura, 06071, Badajoz, Spain

    José María Montanero

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  1. Vicente Garzó
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  2. José María Montanero
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Correspondence to Vicente Garzó.

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Garzó, V., Montanero, J.M. Navier–Stokes Transport Coefficients of d-Dimensional Granular Binary Mixtures at Low Density. J Stat Phys 129, 27–58 (2007). https://doi.org/10.1007/s10955-007-9357-2

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  • DOI: https://doi.org/10.1007/s10955-007-9357-2

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