Non-equilibrium phase transition in a sheared granular mixture

TL;DR

This paper investigates a non-equilibrium phase transition in a sheared granular mixture, revealing a transition between disordered and ordered phases characterized by the impurity's energy share, using an exact solution of the inelastic Boltzmann equation.

Contribution

It provides the first exact analytical description of a phase transition in a sheared granular mixture, highlighting the breakdown of energy equipartition in the ordered phase.

Findings

Disordered phase has finite temperature ratio.

Ordered phase exhibits diverging temperature ratio.

Impurity energy share transitions sharply at the phase boundary.

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.