Impurity in a Granular Fluid

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.