Hydrodynamics of inelastic Maxwell models

Abstract

An overview of recent results pertaining to the hydrodynamic description (both Newtonian and non-Newtonian) of granular gases described by the Boltzmann equation for inelastic Maxwell models is presented. The use of this mathematical model allows us to get exact results for different problems. First, the Navier--Stokes constitutive equations with explicit expressions for the corresponding transport coefficients are derived by applying the Chapman--Enskog method to inelastic gases. Second, the non-Newtonian rheological properties in the uniform shear flow (USF) are obtained in the steady state as well as in the transient unsteady regime. Next, an exact solution for a special class of Couette flows characterized by a uniform heat flux is worked out. This solution shares the same rheological properties as the USF and, additionally, two generalized transport coefficients associated with the heat flux vector can be identified. Finally, the problem of small spatial perturbations of the USF is analyzed with a Chapman--Enskog-like method and generalized (tensorial) transport coefficients are obtained.

40 pages, 10 figures; v2: final version published in a special issue devoted to "Granular hydrodynamics"

References in corpus (13)

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Cited by in corpus (14)

• Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases
• Impurity in a sheared inelastic Maxwell gas
• Granular gas of inelastic and rough Maxwell particles
• Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients
• Generalized transport coefficients for inelastic Maxwell mixtures under shear flow
• Moment theories for a d-dimensional dilute granular gas of Maxwell molecules
• Collisional rates for the inelastic Maxwell model: application to the divergence of anisotropic high-order velocity moments in the homogeneous cooling state
• Anomalous transport of impurities in inelastic Maxwell gases
• Navier-Stokes transport coefficients for driven inelastic Maxwell models
• Exact transport coefficients from the inelastic rough Maxwell model of a granular gas
• High-degree collisional moments of inelastic Maxwell mixtures. Application to the homogeneous cooling and uniform shear flow states
• Shear-rate dependent transport coefficients in granular suspensions
• 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