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Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow

Published online by Cambridge University Press:  20 April 2006

D. J. Jeffrey  and
Y. Onishi
D. J. Jeffrey
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, U.K. Present Address: Pulp and Paper Research Institute and Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. West, Montreal, PQ, Canada H3A 2K6.
Y. Onishi
Affiliation:
Department of Mechanical Engineering, University of Osaka Prefecture, Sakai 591, Japan
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Abstract

Two unequal rigid spheres are immersed in unbounded fluid and are acted on by externally applied forces and couples. The Reynolds number of the flow around them is assumed to be small, with the consequence that the hydrodynamic interactions between the spheres can be described by a set of linear relations between, on the one hand, the forces and couples exerted by the spheres on the fluid and, on the other, the translational and rotational velocities of the spheres. These relations may be represented completely by either a set of 10 resistance functions or a set of 10 mobility functions. When non-dimensionalized, each function depends on two variables, the non-dimensionalized centre-to-centre separation s and the ratio of the spheres’ radii λ. Two expressions are given for each function, one a power series in s−1 and the other an asymptotic expression valid when the spheres are close to touching.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 139 , February 1984 , pp. 261 - 290
Copyright
© 1984 Cambridge University Press

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