Anomalous transport of impurities in inelastic Maxwell gases

Abstract

A mixture of dissipative hard grains generically exhibits a breakdown of kinetic energy equipartition. The undriven and thus freely cooling binary problem, in the tracer limit where the density of one species becomes minute, may exhibit an extreme form of this breakdown, with the minority species carrying a finite fraction of the total kinetic energy of the system. We investigate the fingerprint of this non-equilibrium phase transition, akin to an ordering process, on transport properties. The analysis, performed by solving the Boltzmann kinetic equation from a combination of analytical and Monte Carlo techniques, hints at the possible failure of hydrodynamics in the ordered region. As a relevant byproduct of the study, the behaviour of the second and fourth-degree velocity moments is also worked out.

The title has been changed. The paper has been enlarged with respect to our first version. 13 pages, 9 figures. To be published in EPJE

References in corpus (9)

• Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
• Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
• Velocity Distributions of Granular Gases with Drag and with Long-Range Interactions
• The Boltzmann equation for driven systems of inelastic soft spheres
• Navier-Stokes transport coefficients of $d$-dimensional granular binary mixtures at low density
• The rich behavior of the Boltzmann equation for dissipative gases
• Granular mixtures modeled as elastic hard spheres subject to a drag force
• Growth and Structure of Stochastic Sequences
• Velocity fluctuations in a one dimensional Inelastic Maxwell model