2007/07/25 by James W. Dufty, Dufty, James W.
Engineering · Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Granular flow and fluidized beds #Material Dynamics and Properties #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.0707.3714
openalex publication_date 2007/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Granular fluids consist of collections of activated mesoscopic or macroscopic particles (e.g., powders or grains) whose flows often appear similar to those of normal fluids. To explore the qualitative and quantitative description of these flows an idealized model for such fluids, a system of smooth inelastic hard spheres, is considered. The single feature distinguishing granular and normal fluids being explored in this way is the inelasticity of collisions. The dominant differences observed in real granular fluids are indeed captured by this feature. Following a brief introductory description of real granular fluids and motivation for the idealized model, the elements of nonequilibrium statistical mechanics are recalled (observables, states, and their dynamics). Peculiarities of the hard sphere interactions are developed in detail. The exact microscopic balance equations for the number, energy, and momentum densities are derived and their averages described as the origin for a possible macroscopic continuum mechanics description. This formally exact analysis leads to closed, macroscopic hydrodynamic equations through the notion of a "normal" state. This concept is introduced and the Navier-Stokes constitutive equations are derived, with associated Green-Kubo expressions for the transport coefficients. A parallel description of granular gases is described in the context of kinetic theory, and the Boltzmann limit is identified critically. The construction of the "normal" solution to the kinetic equation is outlined, and Navier-Stokes order hydrodynamic equations are re-derived for a low density granular gas.