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Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid

Published online by Cambridge University Press:  21 April 2006

H. A. Stone  and
L. G. Leal
H. A. Stone
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Present address: Division of Applied Sciences, Harvard University, Cambridge, MA 02138 USA.
L. G. Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

In this paper we examine some general features of the time-dependent dynamics of drop deformation and breakup at low Reynolds numbers. The first aspect of our study is a detailed numerical investigation of the ‘end-pinching’ behaviour reported in a previous experimental study. The numerics illustrate the effects of viscosity ratio and initial drop shape on the relaxation and/or breakup of highly elongated droplets in an otherwise quiescent fluid. In addition, the numerical procedure is used to study the simultaneous development of capillary-wave instabilities at the fluid-fluid interface of a very long, cylindrically shaped droplet with bulbous ends. Initially small disturbances evolve to finite amplitude and produce very regular drop breakup. The formation of satellite droplets, a nonlinear phenomenon, is also observed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 198 , January 1989 , pp. 399 - 427
Copyright
1989 Cambridge University Press

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