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The leading effect of fluid inertia on the motion of rigid bodies at low Reynolds number

Leshansky, A. M. and Lavrenteva, O. M. and Nir, A. (2004) The leading effect of fluid inertia on the motion of rigid bodies at low Reynolds number. Journal of Fluid Mechanics, 505 . pp. 235-248. ISSN 0022-1120.

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We investigate the influence of fluid inertia on the motion of a finite assemblage of solid spherical particles in slowly changing uniform flow at small Reynolds number, Re, and moderate Strouhal number, Sl. We show that the first effect of fluid inertia on particle velocities for times much larger than the viscous time scales as rootSl Re given that the Stokeslet associated with the disturbance flow field changes with time. Our theory predicts that the correction to the particle motion from that predicted by the zero-Re theory has the form of a Basset integral. As a particular example, we calculate the Basset integral for the case of two unequal particles approaching (receding) with a constant velocity along the line of their centres. On the other hand, when the Stokeslet strength is independent of time, the first effect of fluid inertia reduces to a higher order of magnitude and scales as Re. This condition is fulfilled, for example, in the classical problem of sedimentation of particles in a constant gravity field.

Item Type:Article
Additional Information:Copyright © 2004 Cambridge University Press. Reprinted with permission. Received 18 January 2002 and in revised form 11 December 2003. This work was supported by the fund for the promotion of research at the Technion – IIT. O.M.L. acknowledges the support of the Israel Ministry for Immigrant Absorption.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3626
Deposited By: Tony Diaz
Deposited On:22 Jun 2006
Last Modified:02 Oct 2019 23:05

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