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Pressure drop due to the motion of a sphere near the wall bounding a Poiseuille flow

Published online by Cambridge University Press:  29 March 2006

Peter M. Bungay  and
Howard Brenner
Peter M. Bungay
Affiliation:
Department of Chemical Engineering and Biotechnology Program, Carnegie–Mellon University, Pittsburgh, Pennsylvania 15213 Present address: University Medical Clinic, Montreal General Hospital, 1650 Cedar Avenue, Montreal 109.
Howard Brenner
Affiliation:
Department of Chemical Engineering and Biotechnology Program, Carnegie–Mellon University, Pittsburgh, Pennsylvania 15213
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Abstract

An expression is derived for the (low Reynolds number) additional pressure drop created by a relatively small sphere moving near the wall of a circular tube through which there is a Poiseuille flow. Two specific applications are examined: (i) the sedimentation of a homogeneous non-neutrally buoyant sphere in a quiescent fluid; and (ii) the motion of a neutrally buoyant sphere. In the latter case a pronounced increase in the additional pressure drop is predicted when the separation between the sphere and the tube wall is reduced to zero.

This analysis, which includes the behaviour for a sphere in contact with the tube wall, supplements previous ‘method of reflexions’ treatments valid only when the distance from the sphere centre to the wall is large compared with the sphere radius.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 1 , 21 August 1973 , pp. 81 - 96
Copyright
© 1973 Cambridge University Press

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