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Drops climbing uphill on an oscillating substrate

Published online by Cambridge University Press:  07 March 2011

E. S. BENILOV  and
J. BILLINGHAM
E. S. BENILOV*
Affiliation:
Department of Mathematics, University of Limerick, Ireland
J. BILLINGHAM
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
*
†Email address for correspondence: eugene.benilov@ul.ie
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Abstract

Recent experiments by Brunet, Eggers & Deegan (Phys. Rev. Lett., vol. 99, 2007, p. 144501 and Eur. Phys. J., vol. 166, 2009, p. 11) have demonstrated that drops of liquid placed on an inclined plane oscillating vertically are able to climb uphill. In the present paper, we show that a two-dimensional shallow-water model incorporating surface tension and inertia can reproduce qualitatively the main features of these experiments. We find that the motion of the drop is controlled by the interaction of a ‘swaying’ (odd) mode driven by the in-plane acceleration and a ‘spreading’ (even) mode driven by the cross-plane acceleration. Both modes need to be present to make the drop climb uphill, and the effect is strongest when they are in phase with each other.

JFM classification

Interfacial Flows (free surface): Capillary flows Drops and Bubbles: Drops Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 674 , 10 May 2011 , pp. 93 - 119
Copyright
Copyright © Cambridge University Press 2011

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References

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