Non-equilibrium phase transition in a sheared granular mixture

¹ Departamento de Física, Universidad de Extremadura - E-06071 Badajoz, Spain, EU
² Université Paris-Sud, Laboratoire de Physique Théorique et Modèles Statistiques (CNRS UMR 8626) Bâtiment 100, F-91405 Orsay cedex, France, EU

Received: 7 March 2011
Accepted: 26 April 2011

Abstract

The dynamics of an impurity (or tracer particle) immersed in a dilute granular gas under uniform shear flow is investigated. A non-equilibrium phase transition is identified from an exact solution of the inelastic Boltzmann equation for a granular binary mixture in the tracer limit, where the impurity carries either a vanishing (disordered phase) or a finite (ordered phase) fraction of the total kinetic energy of the system. In the disordered phase, the granular temperature ratio (impurity “temperature” over that of the host fluid) is finite, while it diverges in the ordered phase. To correctly capture this extreme violation of energy equipartition, we show that the picture of an impurity enslaved to the host fluid is insufficient.