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Effective viscosity of a periodic suspension

Published online by Cambridge University Press:  20 April 2006

Kevin C. Nunan  and
Joseph B. Keller
Kevin C. Nunan
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305 Present address: Thomas J. Watson Research Center, Yorktown Heights, New York.
Joseph B. Keller
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305
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Abstract

The effective viscosity of a suspension is defined to be the four-tensor that relates the average deviatoric stress to the average rate of strain. We determine the effective viscosity of an array of spheres centred on the points of a periodic lattice in an incompressible Newtonian fluid. The formulation involves the traction exerted on a single sphere by the fluid, and an integral equation for this traction is derived. For lattices with cubic symmetry the effective viscosity tensor involves just two parameters. They are computed numerically for simple, body-centred and face-centred cubic lattices of spheres with solute concentrations up to 90% of the close-packing concentration. Asymptotic results for high concentrations are obtained for arbitrary lattice geometries, and found to be in good agreement with the numerical results for cubic lattices. The low-concentration asymptotic expansions of Zuzovsky also agree well with the numerical results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 142 , May 1984 , pp. 269 - 287
Copyright
© 1984 Cambridge University Press

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