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On the hydrodynamics of pairs of spheres falling along their line of centres in a viscous medium

Published online by Cambridge University Press:  28 March 2006

E. H. Steinberger ,
H. R. Pruppacher  and
M. Neiburger
E. H. Steinberger
Affiliation:
Cloud Physics Laboratory, Department of Meteorology, University of California, Los Angeles
H. R. Pruppacher
Affiliation:
Cloud Physics Laboratory, Department of Meteorology, University of California, Los Angeles
M. Neiburger
Affiliation:
Cloud Physics Laboratory, Department of Meteorology, University of California, Los Angeles
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Abstract

The velocities, accelerations and drag forces experienced by two equal spheres falling along their line of centres in a viscous fluid were determined for three groups of Reynolds numbers R in the range where it is commonly assumed that Stokes's approximation applies. For all groups, with R ranging between 0·060 and 0·216, both spheres continually acclerated as they fell, and the upper sphere fell faster and accelerated more than the lower one. In contrast to Stimson & Jeffery's (1926) theory, which is based on the Stokes approximation, and to most earlier experimenters, the drag-force coefficients of the upper sphere computed from the experiments were significantly smaller than those for the lower sphere. Oseen's theory for this case agreed with the experiments in some respects, but contrary to it the drag-force coefficient varied with R for the upper sphere as well as the lower sphere.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 4 , 23 December 1968 , pp. 809 - 819
Copyright
© 1968 Cambridge University Press

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