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Enskog kinetic theory for monodisperse gas–solid flows

Published online by Cambridge University Press:  27 September 2012

V. Garzó ,
S. Tenneti ,
S. Subramaniam  and
C. M. Hrenya
V. Garzó
Affiliation:
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
S. Tenneti
Affiliation:
Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
S. Subramaniam
Affiliation:
Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
C. M. Hrenya*
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309, USA
*
†Email address for correspondence: hrenya@colorado.edu
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Abstract

The Enskog kinetic theory is used as a starting point to model a suspension of solid particles in a viscous gas. Unlike previous efforts for similar suspensions, the gas-phase contribution to the instantaneous particle acceleration appearing in the Enskog equation is modelled using a Langevin equation, which can be applied to a wide parameter space (e.g. high Reynolds number). Attention here is limited to low Reynolds number flow, however, in order to assess the influence of the gas phase on the constitutive relations, which was assumed to be negligible in a previous analytical treatment. The Chapman–Enskog method is used to derive the constitutive relations needed for the conservation of mass, momentum and granular energy. The results indicate that the Langevin model for instantaneous gas–solid force matches the form of the previous analytical treatment, indicating the promise of this method for regions of the parameter space outside of those attainable by analytical methods (e.g. higher Reynolds number). The results also indicate that the effect of the gas phase on the constitutive relations for the solid-phase shear viscosity and Dufour coefficient is non-negligible, particularly in relatively dilute systems. Moreover, unlike their granular (no gas phase) counterparts, the shear viscosity in gas–solid systems is found to be zero in the dilute limit and the Dufour coefficient is found to be non-zero in the elastic limit.

JFM classification

Granular media: Granular media Multiphase and Particle-laden Flows: Particle/fluid flow Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 129 - 168
Copyright
©2012 Cambridge University Press

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