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Spindle-shaped drops in a viscous extensional flow

Published online by Cambridge University Press:  24 October 2008

J. D. Sherwood
J. D. Sherwood
Affiliation:
Unilever Research, Port Sunlight Laboratory, Merseyside
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Extract

We study the deformation of a long slender drop of viscosity ζμ suspended in another liquid of viscosity μ. Interfacial tension causes the drop to become spherical when there is no fluid motion. When the flow is weak the drop is slightly perturbed, and this case was studied by Taylor (7). Computing the flow around an exact sphere, he used the resulting imbalance in the normal stresses to predict the perturbed drop shape. When the drop is in viscid or slightly viscous (ζ ≪ 1), and when the flow is stronger, the drop becomes long and slender. Previous slender-body analyses (Taylor (8) Buckmaster (2, 3), Acrivos & Lo(1) and Hinch & Acrivos(5)) predict pointed ends, but break down in the neighbourhood of these ends. Here we adopt an approach similar to that of Taylor (7). The zero Reynolds number flow around a spindle-shaped drop with pointed ends is computed exactly. Interfacial tension does not quite balance the hydrodynamic stress, and the resulting imbalance in the normal stresses is used to predict a more accurate representation of the drop shape.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 3 , November 1981 , pp. 529 - 536
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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