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Flow past periodic arrays of spheres at low Reynolds number

Published online by Cambridge University Press:  25 March 1997

HONGWEI CHENG  and
GEORGE PAPANICOLAOU
HONGWEI CHENG
Affiliation:
Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544, USA. e-mail: hongwei@cherrypit.princeton.edu
GEORGE PAPANICOLAOU
Affiliation:
Department of Mathematics, Stanford University, Stanford CA 94305, USA. e-mail: papanico@math.stanford.edu
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Abstract

We calculate the force on a periodic array of spheres in a viscous flow at small Reynolds number and for small volume fraction. This generalizes the known results for the force on a periodic array due to Stokes flow (zero Reynolds number) and the Oseen correction to the Stokes formula for the force on a single sphere (zero volume fraction). We use a generalization of Hasimoto's approach that is based on an analysis of periodic Green's functions. We compare our results to the phenomenological ones of Kaneda for viscous flow past a random array of spheres.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 335 , 25 March 1997 , pp. 189 - 212
Copyright
© 1997 Cambridge University Press

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