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Drops of power-law fluids falling on a coated vertical fibre

Published online by Cambridge University Press:  19 June 2014

Liyan Yu Open the ORCID record for Liyan Yu [Opens in a new window]  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: [email protected]
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Abstract

We study the solitary wave solutions in a thin film of a power-law fluid coating a vertical fibre. Different behaviours are observed for shear-thickening and shear-thinning fluids. For shear-thickening fluids, the solitary waves are larger and faster when the reduced Bond number is smaller. For shear-thinning fluids, two branches of solutions exist for a certain range of the Bond number, where the solitary waves are larger and faster on one and smaller and slower on the other as the Bond number decreases. We carry out an asymptotic analysis for the large and fast-travelling solitary waves to explain how their speeds and amplitudes change with the Bond number. The analysis is then extended to examine the stability of the two branches of solutions for the shear-thinning fluids.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Waves/Free-surface Flows: Solitary waves Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 751 , 25 July 2014 , pp. 184 - 215
Copyright
© 2014 Cambridge University Press 

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