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Motion of a solid particle in a shear flow along a porous slab

Published online by Cambridge University Press:  23 October 2012

Sondes Khabthani ,
Antoine Sellier ,
Lassaad Elasmi  and
François Feuillebois
Sondes Khabthani
Affiliation:
Laboratoire Ingénierie Mathématique, École Polytechnique de Tunisie, rue El Khawarezmi, BP 743, La Marsa, Tunisia
Antoine Sellier
Affiliation:
LadHyX, École Polytechnique, 91128 Palaiseau CEDEX, France
Lassaad Elasmi
Affiliation:
Laboratoire Ingénierie Mathématique, École Polytechnique de Tunisie, rue El Khawarezmi, BP 743, La Marsa, Tunisia
François Feuillebois*
Affiliation:
LIMSI-CNRS, UPR 3251, BP 133, 91403 Orsay CEDEX, France
*
†Email address for correspondence: [email protected]
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Abstract

The flow field around a solid particle moving in a shear flow along a porous slab is obtained by solving the coupled Stokes–Darcy problem with the Beavers and Joseph slip boundary condition on the slab interfaces. The solution involves the Green’s function of this coupled problem, which is given here. It is shown that the classical boundary integral method using this Green’s function is inappropriate because of supplementary contributions due to the slip on the slab interfaces. An ‘indirect boundary integral method’ is therefore proposed, in which the unknown density on the particle surface is not the actual stress, but yet allows calculation of the force and torque on the particle. Various results are provided for the normalized force and torque, namely friction factors, on the particle. The cases of a sphere and an ellipsoid are considered. It is shown that the relationships between friction coefficients (torque due to rotation and force due to translation) that are classical for a no-slip plane do not apply here. This difference is exhibited. Finally, results for the velocity of a freely moving particle in a linear and a quadratic shear flow are presented, for both a sphere and an ellipsoid.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 271 - 306
Copyright
©2012 Cambridge University Press

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