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On the creeping motion of two arbitrary-sized touching spheres in a linear shear field

Published online by Cambridge University Press:  29 March 2006

Avinoam Nir  and
Andreas Acrivos
Avinoam Nir
Affiliation:
Department of Chemical Engineering, Stanford University
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University
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Abstract

The Stokes equations describing the creeping motion of two arbitrary-sized touching spheres are solved exactly through the use of tangent-sphere coordinates. For the case of a linear shear field at infinity, explicit results covering the entire range of size ratios are presented for: (a) the forces and torques on the aggregate; (b) the hydrodynamic forces on the individual spheres comprising a freely suspended aggregate, which are in general non-zero; (c) the contribution of the pair to the bulk stress of a dilute suspension; and (d) under free suspension conditions, the velocity of any material point relative to that of the undisturbed flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 2 , 19 June 1973 , pp. 209 - 223
Copyright
© 1973 Cambridge University Press

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