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The motion of a spherical liquid drop at high Reynolds number

Published online by Cambridge University Press:  28 March 2006

J. F. Harper  and
D. W. Moore
J. F. Harper
Affiliation:
Department of Mathematics, University of Bristol
Now at the Department of Mathematics, Victoria University of Wellington, New Zealand.
D. W. Moore
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

The steady motion of a liquid drop in another liquid of comparable density and viscosity is studied theoretically. Both inside and outside the drop, the Reynolds number is taken to be large enough for boundary-layer theory to hold, but small enough for surface tension to keep the drop nearly spherical. Surface-active impurities are assumed absent. We investigate the boundary layers associated with the inviscid first approximation to the flow, which is shown to be Hill's spherical vortex inside, and potential flow outside. The boundary layers are shown to perturb the velocity field only slightly at high Reynolds numbers, and to obey linear equations which are used to find first and second approximations to the drag coefficient and the rate of internal circulation.

Drag coefficients calculated from the theory agree quite well with experimental values for liquids which satisfy the conditions of the theory. There appear to be no experimental results available to test our prediction of the internal circulation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 2 , 3 May 1968 , pp. 367 - 391
Copyright
© 1968 Cambridge University Press

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