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Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate Reynolds numbers

Published online by Cambridge University Press:  26 April 2006

David S. Dandy  and
L. Gary Leal
David S. Dandy
Affiliation:
Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551, USA
L. Gary Leal
Affiliation:
Department of Chemical Engineering, Caltech, Pasadena, CA 91125, USA
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Abstract

Numerical solutions have been obtained for steady streaming flow past an axisymmetric drop over a wide range of Reynolds numbers (0.005 [les ] Re [les ] 250), Weber numbers (0.005 [les ] We [les ] 14), viscosity ratios (0.001 [les ] λ [les ] 1000), and density ratios (0.001 [les ] ζ [les ] 1000). Our results indicate that at lower Reynolds numbers the shape of the drop tends toward a spherical cap with increasing We, but at higher Re the body becomes more disk shaped with increasing We. Unlike the recirculating wake behind an inviscid bubble or solid particle, the eddy behind a drop is detached from the interface. The size of the eddy and the separation distance from the drop depend on the four dimensionless parameters of the problem. The motion of the fluid inside the drop appears to control the behaviour of the external flow near the body, and even for cases when λ and ζ [Lt ] 1 (a ‘real’ bubble), a recirculating wake remains unattached.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 208 , November 1989 , pp. 161 - 192
Copyright
© 1989 Cambridge University Press

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