Journal
JOURNAL OF FLUID MECHANICS
Volume 712, Issue -, Pages 129-168Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2012.404
Keywords
granular media; particle/fluid flow; suspensions
Categories
Funding
- Ministerio de Educacion y Ciencia (Spain) [FIS2010-16587]
- FEDER
- Junta de Extremadura (Spain) [GR10158]
- US Department of Energy [DE-FC26-07NT43098]
- National Science Foundation [CBET-0318999, CBET-1134500]
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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.
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