Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation

Abstract

The linear integral equations defining the Navier-Stokes (NS) transport coefficients for polydisperse granular mixtures of smooth inelastic hard disks or spheres are solved by using the leading terms in a Sonine polynomial expansion. Explicit expressions for all the NS transport coefficients are given in terms of the sizes, masses, compositions, density and restitution coefficients. In addition, the cooling rate is also evaluated to first order in the gradients. The results hold for arbitrary degree of inelasticity and are not limited to specific values of the parameters of the mixture. Finally, a detailed comparison between the derivation of the current theory and previous theories for mixtures is made, with attention paid to the implication of the various treatments employed to date.

26 pages, to be published in Phys. Rev. E

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• Does the Chapman--Enskog expansion for sheared granular gases converge?
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• Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient
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• Enskog kinetic theory of binary granular suspensions: heat flux and stability analysis of the homogeneous steady state
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• Transport properties in a model of confined granular mixtures at moderate densities
• Kinetic model for transport in granular mixtures
• Diffusion of intruders in a granular gas thermostatted by a bath of elastic hard spheres
• Kinetic theory of polydisperse granular mixtures: influence of the partial temperatures on transport properties. A review
• Mean-squared displacements of rough particles in polydisperse granular gases
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