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Plane simple shear of smooth inelastic circular disks: the anisotropy of the second moment in the dilute and dense limits

  • J. T. Jenkins (a1) and M. W. Richman (a2)
Abstract

We consider a plane, steady, homogeneous flow of circular disks. The disks are identical, smooth, and inelastic. We adopt the assumption of molecular chaos and introduce an anisotropic Maxwellian velocity distribution function based on the full second moment of the velocity fluctuations. In the limits of dilute and dense flows, we determine approximate analytic solutions of the balance law for the second moment that result in stresses whose qualitative behaviour and magnitudes are in good agreement with numerical simulations.

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© 1988 Cambridge University Press
References
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Goldreich, P. & Tremaine S. 1978 The velocity dispersion in Saturn's rings Icarus 34, 227–239.
Hoover, W. G. & Alder B. J. 1967 Studies in molecular dynamics. IV. The pressure, collision rate, and their number dependence for hard disks. J. Chem. Phys. 46, 686–691.
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Jenkins, J. T. & Richman M. W. 1985a Grad's 13-moment system for a dense gas of inelastic spheres. Arch. Rat. Mech. Anal. 87, 355–377.
Jenkins, J. T. & Richman M. W. 1985b Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28, 3485–3494.
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Walton, O. R. & Braun R. L. 1986 Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30, 949–980.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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