Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-09T21:42:54.513Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Davis, S. H. 1980 J. Fluid Mech. 98, 225.
Dussan V., E. B. 1979 Ann. Rev. Fluid Mech. 11, 371.
Dussan V., E. B. 1985 J. Fluid Mech. 151, 1.
Dussan V. E. B. & Chow, R. T.-P. 1983 J. Fluid Mech. 137, 1.
Dussan V. E. B. & Davis, S. H. 1974 J. Fluid Mech. 65, 71.
Guastalla, J. 1957 In Proc. Second International Congress of Surface Activity, III (ed. J. H. Schulman), pp. 143–152. Academic.
Johnson, R. E. & Dettre, R. H. 1969 In Surface and Colloid Science, vol. 2 (ed. E. Matijevic), pp. 85–153. Wiley-Interscience.
Johnson, R. E., Dettre, R. H. & Brandreth, D. A. 1977 J. Colloid Interface Sci. 62, 205.
Murphy, E. D. 1984 The moving Wilhelmy plate: a theoretical study. M.S. thesis, University of Pennsylvania, Philadelphia, Pennsylvania.
Penn, L. S. & Miller, B. 1980a J. Colloid Interface Sci. 77, 574.
Penn, L. S. & Miller, B. 1980b J. Colloid Interface Sci. 78, 238.
Princen, H. M. 1969 In Surface and Colloid Science, vol. 2 (ed. E. Matijevic), pp. 1–84. Wiley-Interscience.
Weiland, R. H. & Davis, S. H. 1981 J. Fluid Mech. 107, 261.
Young, G. W. 1985 Dynamics and Stability of Flows with Moving Contact Lines. Ph.D. thesis, Northwestern University, Evanston, Illinois.