Hydrodynamics for inelastic Maxwell mixtures: Some applications
by Vicente Garzó   José María Montanero  

Vol. 2 No. 2 (2007) P.155~P.177

ABSTRACT

Hydrodynamic equations for a binary mixture of inelastic Maxwell models described by the Boltzmann equation are derived. The Navier-Stokes transport coecients are exactly obtained by solving the Boltzmann equation from the Chapman-Enskog method for states close to the (local) homogeneous cooling state (HCS). The knowledge of the transport coecients allows one to analyze two dierent problems. First, we solve the linearized hydrodynamic equations around the homogeneous (cooling) state and identify the conditions for stability as functions of the wave vector, the dissipation, and the parameters of the mixture. As happens for monocomponent systems, the analysis shows that the HCS is unstable to long enough wavelength perturbation. As a second problem, we explore the validity of Onsager's reciprocal relations of a granular binary mixture. As expected, since a granular system is not time reversal invariant, Onsager's reciprocal relations do not apply for inelastic collisions. The results show that the absence of the Gibbs state (non-Maxwellian behavior of the velocity distribution functions describing the HCS), the collisional cooling, and the occurrence of dierent kinetic temperatures for both species (breakdown of energy equipartition) are responsible for a violation of Onsager's relations.

KEYWORDS
Granular binary mixtures, Boltzmann equation, inelastic Maxwell models, Onsager's relations

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 82C40, 82C70

MILESTONES

Received: 2004-11-08
Revised : 2005-05-12
Accepted:

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