Document Type

Article

Publication Date

11-1989

Publication Title

Journal of Rheology

Abstract

We extend methods from the kinetic theory of gases to obtain a general constitutive relation for the collisional source of second moment in dilute flows of identical, smooth, highly inelastic spheres. In the derivation, we base all statistical averaging on an anisotropic Maxwellian distribution function, which is sensitive to all components of the full second moment of fluctuation velocity and is not based on the assumption that the fluctuations are nearly isotropic. In the case of homogeneous shear flow, we combine the constitutive relation with the balance equation for full second moment to determine, for prescribed values of shear rate, coefficient of restitution, and solid fraction, both exact numerical and approximate closed‐form solutions for the second moment and pressure tensor. Most striking are the resulting normal pressure differences, which are predicted by this theory but not by kinetic theories for nearly elastic particles.

Volume

33

Issue

8

First Page Number

1293

Last Page Number

1306

DOI

10.1122/1.550052

Publisher Statement

© 1989, American Institute of Physics. Available on publisher's site at http://dx.doi.org/10.1122/1.550052

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