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Lift on a sphere moving near a wall in a parabolic flow

Published online by Cambridge University Press:  06 September 2010

SAMIR YAHIAOUI  and
FRANÇOIS FEUILLEBOIS
SAMIR YAHIAOUI
Affiliation:
Laboratoire PMMH, CNRS UMR 7636 – ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France
FRANÇOIS FEUILLEBOIS*
Affiliation:
LIMSI-CNRS, UPR 3251, B.P. 133, 91403 Orsay Cedex, France
*
†Email address for correspondence: francois.feuillebois@limsi.fr
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Abstract

The lift on a solid sphere moving along a wall in a parabolic shear flow is obtained as a regular perturbation problem for low Reynolds number when the sphere is in the inner region of expansion. Comprehensive results are given for the 10 terms of the lift, which involve the sphere translation and rotation, the linear and quadratic parts of the shear flow and all binary couplings. Based on very accurate earlier results of a creeping flow in bispherical coordinates, precise results for these lift terms are obtained for a large range of sphere-to-wall distances, including the lubrication region for sphere-to-wall gaps down to 0.01 of a sphere radius. Fitting formulae are also provided in view of applications. The migration velocity of an inertialess spherical particle is given explicitly, for a non-rotating sphere with a prescribed translation velocity and for a freely moving sphere in a parabolic shear flow. Values of the lift and migration velocity are in good agreement with earlier results whenever available.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 662 , 10 November 2010 , pp. 447 - 474
Copyright
Copyright © Cambridge University Press 2010

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