Transport coefficients for inelastic Maxwell mixtures

Abstract

The Boltzmann equation for inelastic Maxwell models is used to determine the Navier-Stokes transport coefficients of a granular binary mixture in $d$ dimensions. The Chapman-Enskog method is applied to solve the Boltzmann equation for states near the (local) homogeneous cooling state. The mass, heat, and momentum fluxes are obtained to first order in the spatial gradients of the hydrodynamic fields, and the corresponding transport coefficients are identified. There are seven relevant transport coefficients: the mutual diffusion, the pressure diffusion, the thermal diffusion, the shear viscosity, the Dufour coefficient, the pressure energy coefficient, and the thermal conductivity. All these coefficients are {\em exactly} obtained in terms of the coefficients of restitution and the ratios of mass, concentration, and particle sizes. The results are compared with known transport coefficients of inelastic hard spheres obtained analytically in the leading Sonine approximation and by means of Monte Carlo simulations. The comparison shows a reasonably good agreement between both interaction models for not too strong dissipation, especially in the case of the transport coefficients associated with the mass flux.

9 figures, to be published in J. Stat. Phys

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Cited by in corpus (24)

• Navier-Stokes transport coefficients of $d$-dimensional granular binary mixtures at low density
• Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases
• Frequency-dependent fluctuation-dissipation relations in granular gases
• Third and fourth degree collisional moments for inelastic Maxwell models
• System of elastic hard spheres which mimics the transport properties of a granular gas
• Simple shear flow in inelastic Maxwell models
• Shear-rate dependent transport coefficients for inelastic Maxwell models
• Hydrodynamics of inelastic Maxwell models
• Maxwell and very hard particle models for probabilistic ballistic annihilation: hydrodynamic description
• Non-equilibrium phase transition in a sheared granular mixture
• Dynamics of Annihilation I : Linearized Boltzmann Equation and Hydrodynamics
• Impurity in a sheared inelastic Maxwell gas
• Granular gas of inelastic and rough Maxwell particles
• Energy non-equipartition in multicomponent granular mixtures
• Generalized transport coefficients for inelastic Maxwell mixtures under shear flow
• Anomalous transport of impurities in inelastic Maxwell gases
• Navier-Stokes transport coefficients for driven inelastic Maxwell models
• High-degree collisional moments of inelastic Maxwell mixtures. Application to the homogeneous cooling and uniform shear flow states
• Exact transport coefficients from the inelastic rough Maxwell model of a granular gas
• A note on the violation of the Einstein relation in a driven moderately dense granular gas
• Tracer diffusion coefficients in a sheared inelastic Maxwell gas
• Inelastic Maxwell models for monodisperse gas-solid flows
• Kinetic model for transport in granular mixtures
• Dissipation process of binary mixture gas in thermally relativistic flow