Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases

Abstract

The hydrodynamic Burnett equations and the associated transport coefficients are exactly evaluated for generalized inelastic Maxwell models. In those models, the one-particle distribution function obeys the inelastic Boltzmann equation, with a velocity-independent collision rate proportional to the $\gamma$ power of the temperature. The pressure tensor and the heat flux are obtained to second order in the spatial gradients of the hydrodynamic fields with explicit expressions for all the Burnett transport coefficients as functions of $\gamma$, the coefficient of normal restitution, and the dimensionality of the system. Some transport coefficients that are related in a simple way in the elastic limit become decoupled in the inelastic case. As a byproduct, existing results in the literature for three-dimensional elastic systems are recovered, and a generalization to any dimension of the system is given. The structure of the present results is used to estimate the Burnett coefficients for inelastic hard spheres.

16 pages, 5 figures; v2: new Appendix (D) and new references added

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Cited by in corpus (8)

• Higher-order moment theories for dilute granular gases of smooth hard-spheres
• Transport coefficients of solid particles immersed in a viscous gas
• Granular gas of inelastic and rough Maxwell particles
• Moment theories for a d-dimensional dilute granular gas of Maxwell molecules
• Exact transport coefficients from the inelastic rough Maxwell model of a granular gas
• Inelastic Maxwell models for monodisperse gas-solid flows
• Translational and rotational non-Gaussianities in homogeneous freely evolving granular gases
• Exact Rheology of Uniform Shear Flow in a Gas of Inelastic and Rough Maxwell Particles