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The velocity of ‘large’ viscous drops falling on a coated vertical fibre

Published online by Cambridge University Press:  25 November 2013

Liyan Yu  and
John Hinch
Liyan Yu*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
John Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: liyan.yu@cantab.net
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Abstract

Kalliadasis & Chang (J. Fluid Mech., vol. 261, 1994, pp. 135–168) showed within lubrication theory that if a liquid film is thicker than a critical value then drops will accelerate and grow, whereas with thinner films the drops fall at a constant velocity. As the thickness of the film increases to the critical value, the drops move faster and are larger. We revisit their asymptotic analysis of these large drops. While we recover their results for the leading-order and first correction, we do not agree on further corrections. In particular we find it necessary to evaluate the third correction, which they do not consider, before we obtain a first approximation to the dependence of the speed on the non-dimensional control parameter. We proceed to two further corrections in order to improve this first approximation to the speed.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Waves/Free-surface Flows: Solitary waves Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 737 , 25 December 2013 , pp. 232 - 248
Copyright
©2013 Cambridge University Press 

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References

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