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Torque measurements on a stationary axially positioned sphere partially and fully submerged beneath the free surface of a slowly rotating viscous fluid

Published online by Cambridge University Press:  20 April 2006

J. G. Kunesh ,
H. Brenner ,
M. E. O'Neill  and
A. Falade
J. G. Kunesh
Affiliation:
Fractionation Research Inc., 1517 Fair Oaks Ave., South Pasadena, CA 91030
H. Brenner
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology Cambridge, MA 02139
M. E. O'Neill
Affiliation:
Department of Mathematics, University College, London WC1E 6BT
A. Falade
Affiliation:
Department of Mechanical Engineering, University of Lagos, Lago
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Abstract

Experimental measurements are presented for the hydrodynamic torque exerted on a stationary sphere situated at the axis of a slowly rotating viscous liquid at small rotary sphere Reynolds numbers (Re < 0.1) as a function of depth of submersion of the sphere below the free surface. Effects of free-surface proximity on the torque furnished the impetus for the study. Experiments were performed for different depths of sphere immersion beneath the free surface, varying from full to partial submersion. Rotation rates were maintained sufficiently low to approximate a planar interface. Torque measurements agreed well with existing theoretical predictions for both the interface-straddling and fully submerged sphere cases. In particular, the predicted continuity of the torque and its derivative at the interface-penetration point (where the sphere first starts to protrude through the free surface) was observed. Free-surface curvature as well as meniscus-curvature effects upon the torque were found to be negligible in the experiments, including even the extreme case where the sphere was in the almost fully withdrawn configuration.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 154 , May 1985 , pp. 29 - 42
Copyright
© 1985 Cambridge University Press

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