Impurity in a sheared inelastic Maxwell gas

V. Garzó 1, E. Trizac 2

Physical Review E 85 (2012) 011302

The Boltzmann equation for inelastic Maxwell models is considered in order to investigate the dynamics of an impurity (or intruder) immersed in a granular gas driven by a uniform shear flow. The analysis is based on an exact solution of the Boltzmann equation for a granular binary mixture. It applies for conditions arbitrarily far from equilibrium (arbitrary values of the shear rate $a$) and for arbitrary values of the parameters of the mixture (particle masses $m_i$, mole fractions $x_i$, and coefficients of restitution $\alpha_{ij}$). In the tracer limit where the mole fraction of the intruder species vanishes, a non equilibrium phase transition takes place. We thereby identity ordered phases where the intruder bears a finite contribution to the properties of the mixture, in a region of parameter space that is worked out in detail. These findings extend previous results obtained for ordinary Maxwell gases, and further show that dissipation leads to new ordered phases.

  • 1. Departamento de Fisica,
    Universidad de Extremadura
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud