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Viscous interactions of many neutrally buoyant spheres in Poiseuille flow

Published online by Cambridge University Press:  21 April 2006

Jeffrey A. Schonberg ,
Donald A. Drew  and
Georges Belfort
Jeffrey A. Schonberg
Affiliation:
Department of Chemical Engineering and Environmental Engineering and Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Donald A. Drew
Affiliation:
Department of Chemical Engineering and Environmental Engineering and Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Georges Belfort
Affiliation:
Department of Chemical Engineering and Environmental Engineering and Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
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Abstract

A theory is developed to predict the motion of N neutrally buoyant spheres suspended in laminar flow between parallel plates. The spheres are at large separation yet nearer each other than the duct walls, and the Reynolds number is small. In this parameter range, viscous interactions are larger than inertial effects, and can be represented in terms of a superposition of ‘strainlets’. Several examples are given to show this viscous interaction effect. Near the leading edge of a front of spheres or near the trailing edge significant lateral migration velocities can occur, being at least one order of magnitude larger than inertially induced migration velocities. This phenomenon may have a negative effect on ‘chromatographic’ separation schemes, affecting particle concentration, recovery and resolution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 167 , June 1986 , pp. 415 - 426
Copyright
© 1986 Cambridge University Press

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