Impurity in a Granular Fluid

TL;DR

This paper analyzes the velocity behavior of impurities in a granular fluid, revealing a phase transition related to impurity mass and detailed statistical properties of their velocity distributions.

Contribution

It provides an analytic solution for impurity velocity statistics in a granular fluid, identifying a phase transition and multiscaling behavior in the inelastic Maxwell model.

Findings

Velocity statistics of light impurities resemble the fluid background.

Temperature ratio diverges at a critical impurity mass.

Heavy impurities scatter off a static fluid background.

Abstract

We investigate velocity statistics of an impurity immersed in a uniform granular fluid. An analytic solution of the inelastic Maxwell model shows that a phase transition occurs in the cooling case. Light impurities have similar velocity statistics as the fluid background, although their temperature is generally different. Asymptotically, the temperature ratio increases with the impurity mass, and it diverges at some critical mass. Impurities heavier than this critical mass essentially scatter of a static fluid background. The impurity velocity distribution is generally characterized by multiscaling asymptotic behavior of its moments. Additionally, in the heavy impurity phase, it consists of modified replicas of the initial distribution.