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Inertial instability of flows on the inside or outside of a rotating horizontal cylinder

Published online by Cambridge University Press:  01 November 2013

E. S. Benilov  and
V. N. Lapin
E. S. Benilov*
Affiliation:
Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
V. N. Lapin
Affiliation:
Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
*
†Email address for correspondence: [email protected]
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Abstract

We consider thin liquid films on the inside (rimming flows) or outside (coating flows) of a cylinder with horizontal axis, rotating about this axis. If the liquid’s net volume is small, such films are known to evolve towards a steady state with a smooth surface, whereas, for larger amounts, the flow develops a ‘shock’ similar to a tidal bore. In this work, smooth films are shown to be unstable. Since the strongest instability occurs at wavelengths comparable to the film’s thickness, our analysis is based on the full Navier–Stokes equations, not on the lubrication approximation (which has been traditionally used in this problem). It is also shown that, for cylinders of sufficiently small radii, the instability can be suppressed by surface tension.

JFM classification

Instability: Instability Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 736 , 10 December 2013 , pp. 107 - 129
Copyright
©2013 Cambridge University Press 

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