Granular Fluids

TL;DR

This paper explores the potential for applying hydrodynamic and statistical mechanics principles to granular matter, aiming to develop fundamental equations and transport coefficients for granular flows.

Contribution

It extends nonequilibrium statistical mechanics methods to granular systems, deriving nonlinear Navier-Stokes equations and transport coefficients for granular flows.

Findings

Derivation of nonlinear Navier-Stokes equations for granular matter

Expressions for transport coefficients in granular flows

Demonstration of hydrodynamic description applicability

Abstract

The terminology granular matter refers to systems with a large number of hard objects (grains) of mesoscopic size ranging from millimeters to meters. Geological examples include desert sand and the rocks of a landslide. But the scope of such systems is much broader, including powders and snow, edible products such a seeds and salt, medical products like pills, and extraterrestrial systems such as the surface regolith of Mars and the rings of Saturn. The importance of a fundamental understanding for granular matter properties can hardly be overestimated. Practical issues of current concern range from disaster mitigation of avalanches and explosions of grain silos to immense economic consequences within the pharmaceutical industry. In addition, they are of academic and conceptual importance as well as examples of systems far from equilibrium. Under many conditions of interest, granular matter flows like a normal fluid. In the latter case such flows are accurately described by the equations of hydrodynamics. Attention is focused here on the possibility for a corresponding hydrodynamic description of granular flows. The tools of nonequilibrium statistical mechanics, developed over the past fifty years for fluids composed of atoms and molecules, are applied here to a system of grains for a fundamental approach to both qualitative questions and practical quantitative predictions. The nonlinear Navier-Stokes equations and expressions for the associated transport coefficients are obtained.