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Moffatt vortices induced by the motion of a contact line

Published online by Cambridge University Press:  04 April 2014

E. Kirkinis*
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3125, USA School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Queensland 4001, Australia
S. H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3125, USA
*
Email address for correspondence: ekirkinis@gmail.com

Abstract

A recent hydrodynamic theory of liquid slippage on a solid substrate (Kirkinis & Davis, Phys. Rev. Lett., vol. 110, 2013, 234503) gives rise to a sequence of eddies (Moffatt vortices) that co-move with a moving contact line (CL) in a liquid wedge. The presence of these vortices is established through secular equations that depend on the dynamic contact angle $\alpha $ and capillary number Ca. The limiting case $\alpha \rightarrow 0$ is associated with the appearance of such vortices in a channel. The vortices are generated by the relative motion of the interfaces, which in turn is due to the motion of the CL. This effect has yet to be observed in experiment.

Type
Rapids
Copyright
© 2014 Cambridge University Press 

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