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Effect of microstructural anisotropy on the fluid–particle drag force and the stability of the uniformly fluidized state

Published online by Cambridge University Press:  26 October 2012

William Holloway ,
Jin Sun  and
Sankaran Sundaresan
William Holloway*
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
Jin Sun
Affiliation:
School of Engineering, University of Edinburgh, Edinburgh EH9 3JL, Scotland, UK
Sankaran Sundaresan
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: [email protected]
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Abstract

Lattice-Boltzmann simulations of fluid flow through sheared assemblies of monodisperse spherical particles have been performed. The friction coefficient tensor extracted from these simulations is found to become progressively more anisotropic with increasing Péclet number, $Pe= \dot {\gamma } {d}^{2} / D$, where $\dot {\gamma } $ is the shear rate, $d$ is the particle diameter, and $D$ is the particle self-diffusivity. A model is presented for the anisotropic friction coefficient, and the model constants are related to changes in the particle microstructure. Linear stability analysis of the two-fluid model equations including the anisotropic drag force model developed in the present study reveals that the uniformly fluidized state of low Reynolds number suspensions is most unstable to mixed mode disturbances that take the form of vertically travelling waves having both vertical and transverse structures. As the Stokes number increases, the transverse-to-vertical wavenumber ratio decreases towards zero; i.e. the transverse structure becomes progressively less prominent. Fully nonlinear two-fluid model simulations of moderate to high Stokes number suspensions reveal that the anisotropic drag model leads to coarser gas–particle flow structures than the isotropic drag model.

JFM classification

Complex Fluids: Complex Fluids Instability: Instability Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 27 - 49
Copyright
©2012 Cambridge University Press

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