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On the deformation and drag of a falling viscous drop at low Reynolds number

Published online by Cambridge University Press:  28 March 2006

T. D. Taylor  and
Andreas Acrivos
T. D. Taylor
Affiliation:
Picatinny Arsenal, Dover, New Jersey
Andreas Acrivos
Affiliation:
Stanford University, Stanford, California
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Abstract

The motion at low Reynolds number of a drop in a quiescent unbounded fluid is investigated theoretically by means of a singular-perturbation solution of the axisymmetric equations of motion. Special attention is paid to the deformation of the drop. It is shown that for small values of the Weber number We the drop will first deform exactly into an oblate spheroid and then, with a further increase in We, into a geometry approaching that of a spherical cap. These results are quite insensitive to the ratio of the viscosities of the two fluid phases. The first-order effect of the deformation on the drag of the drop is also included in the analysis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 18 , Issue 3 , March 1964 , pp. 466 - 476
Copyright
© 1964 Cambridge University Press

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