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A plate oscillating across a liquid interface: effects of contact-angle hysteresis

Published online by Cambridge University Press:  21 April 2006

G. W. Young  and
S. H. Davis
G. W. Young
Affiliation:
Department of Mathematics, University of Akron, Akron, OH 44325, USA
S. H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60201, USA
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Abstract

We consider the oscillatory motion of a solid plate into and out of a bath of liquid. Assuming that the displacement amplitude of the plate motion is small and that the capillary number is small, the problem reduces to solving an interfacial boundaryvalue problem for the response of the contact line. The characteristic contact angle versus contact-line speed relationship includes contact-angle hysteresis which is assumed small and comparable to the amplitude of the plate motion. Sinusoidal and square-wave plate motions are considered. We find that the contact line moves with the plate if the contact line is fixed, but has relative motion otherwise. It would then advance part of the time, recede part of the time, and remain stationary in the transition periods. Further, we find that both contact-angle hysteresis and steepening of the contact angle with increasing contact-line speed are dissipative effects.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 174 , January 1987 , pp. 327 - 356
Copyright
© 1987 Cambridge University Press

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