Kinetic Theories for Collisional Grain Flows

Authored by: James T. Jenkins

Handbook of Granular Materials

Print publication date:  October  2015
Online publication date:  March  2016

Print ISBN: 9781466509962
eBook ISBN: 9781466509979
Adobe ISBN:

10.1201/b19291-6

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Abstract

There is an obvious analogy between the colliding macroscopic grains of a granular material with high energy and the agitated molecules of a dense gas. This is supported by the experimental observation that when a granular material is rapidly sheared, the shear and normal stresses required to maintain the motion vary with the square of the shear rate (Bagnold 1954, Savage 1972, Savage and McKeown 1983, Savage and Sayed 1984, Hanes and Inman 1985). The interpretation of these observations is that, at high shear rates, the dominant mechanism of momentum transfer is collision between grains, with the interstitial liquid or gas playing a relatively minor role. In this chapter, we explore how methods from the kinetic theory of dense gases (e.g., Reif 1969, Chapman and Cowling 1970) have been adopted and extended to derive balance laws, constitutive relations and boundary conditions for systems of macroscopic, dissipative, grains. Our intention is to provide an accessible overview of continuum theories that have their origin in the collisions between pairs of spherical particles and the simplest relevant statistical characterizations of the likelihood of such interactions. More elaborate and exhaustive treatments of the kinetic theory for granular flows exist. The book by Brilliantov and Pöschel (2004) is an example, and the review of Goldhirsch (2003) provides access to many others.

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