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Contact lines with a $18{0}^{\circ } $ contact angle

Published online by Cambridge University Press:  08 February 2013

E. S. Benilov  and
M. Vynnycky
E. S. Benilov*
Affiliation:
Mathematics Applications Consortium for Science and Industry, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
M. Vynnycky
Affiliation:
Mathematics Applications Consortium for Science and Industry, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
*
†Email address for correspondence: Eugene.Benilov@ul.ie
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Abstract

This work builds on the foundation laid by Benney & Timson (Stud. Appl. Maths, vol. 63, 1980, pp. 93–98), who examined the flow near a contact line and showed that, if the contact angle is $18{0}^{\circ } $, the usual contact-line singularity does not arise. Their local analysis, however, does not allow one to determine the velocity of the contact line and their expression for the shape of the free boundary involves undetermined constants. The present paper considers two-dimensional Couette flows with a free boundary, for which the local analysis of Benney & Timson can be complemented by an analysis of the global flow (provided that the slope of the free boundary is small, so the lubrication approximation can be used). We show that the undetermined constants in the solution of Benney & Timson can all be fixed by matching the local and global solutions. The latter also determines the contact line’s velocity, which we compute among other characteristics of the global flow. The asymptotic model derived is used to examine steady and evolving Couette flows with a free boundary. It is shown that the latter involve brief intermittent periods of rapid acceleration of contact lines.

JFM classification

Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 718 , 10 March 2013 , pp. 481 - 506
Copyright
©2013 Cambridge University Press

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