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An analytical solution for the profile and volume of a small drop or bubble symmetrical about a vertical axis

Published online by Cambridge University Press:  12 April 2006

A. K. Chesters
A. K. Chesters
Affiliation:
Laboratory for Aero- and Hydrodyanmics, Delft University of Technology, The Netherlands
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Abstract

A solution for the profile of a small drop or bubble symmetrical about a vertical axis and at rest in a second fluid is obtained as a first-order perturbation of a circle. At the end of the drop opposite the apex, the perturbation approach breaks down and a matching zero-gravity solution is used. The results agree with numerical solutions and indicate that the pendant-drop profile of maximum volume fitting a given small vertical tube intersects the exit plane at very nearly 90°. This enables the maximum volume to be determined accurately from a force balance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 4 , 5 August 1977 , pp. 609 - 624
Copyright
© 1977 Cambridge University Press

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References

Bashforth, F. & Adams, H. 1883 The Theories of Capillary Action. Cambridge University Press.
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