2001/06/30 by Andrés Santos, Andres Santos, James W. Dufty · 2 citations
Engineering · Materials Science · Physics and Astronomy · #Granular flow and fluidized beds #Material Dynamics and Properties #Particle Dynamics in Fluid Flows #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.64.051305
published as Phys. Rev. E 64, 051305 (2001) · 28 pages, 12 figures included
arxiv created 2001/09/04 · openalex publication_date 2001/10/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that the homogeneous cooling state (HCS) for a heavy impurity particle in a granular fluid supports two distinct phases. The order parameter straight phi;(s) is the mean square velocity of the impurity particle relative to that of a fluid particle, and the control parameter xi* is the fluid cooling rate relative to the impurity collision rate. For xi*<1 there is a "normal" phase for which straight phi;(s) scales as the fluid/impurity mass ratio, just as for a system with elastic collisions. For xi*>1 an "ordered" phase occurs in which straight phi;(s) is finite even for vanishingly small mass ratio, representing an extreme violation of energy equipartition. The phenomenon can be described in terms of a Landau-like free energy for a second order phase transition. The dynamics leading to the HCS is studied in detail using an asymptotic analysis of the Enskog-Lorentz kinetic equation near each phase and the critical domain. Critical slowing is observed with a divergent relaxation time at the critical point. The stationary velocity distributions are determined in each case, showing a crossover from Maxwellian in the normal phase to an exponential quartic function of the velocity that is sharply peaked about the nonzero straight phi;(s) for the ordered phase. It is shown that the diffusion coefficient in the normal phase diverges at the critical point and remains so in the ordered phase. This is interpreted as a transition from diffusive to ballistic dynamics between the normal and ordered phases.