Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-19T12:47:42.639Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of wetting: local contact angles

Published online by Cambridge University Press:  26 April 2006

P. G. De Gennes ,
X. Hua  and
P. Levinson
P. G. De Gennes
Affiliation:
Collège de France, F-75231 Paris Cedex 05, France
X. Hua
Affiliation:
Collège de France, F-75231 Paris Cedex 05, France
P. Levinson
Affiliation:
Collège de France, F-75231 Paris Cedex 05, France
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss the motion of a triple line for a fluid spreading on a flat solid surface in conditions of partial wetting: the equilibrium contact angle θe is assumed to be finite but small: 0 < θe [Lt ] 1. We distinguish four regions: (1) a molecular domain of size a (≈ a few Ångströms) very near the triple line, where the continuum description breaks down; (2) a proximal region (of length a/θ2e and height a/θe) where the long-range Van der Waals forces dominate; (3) a central region, where capillary forces and Poiseuille friction are the only important ingredients; (4) a distal region where macroscopic features (related to the size of the droplet, or to gravitational forces) come into play. In regions (2, 3, 4) the flow may be described in a lubrication approximation, and with a linearized form of the capillary forces. We restrict our attention to low capillary numbers Ca and expand the profiles to first order in Ca near the static solution. The main results are: (a) the logarithmic singularity which would have occurred in a simple wedge picture is truncated by the long-range forces, at a fluid thickness a/θe. This effect is more important, at small θe, than the effects of slippage which have often been proposed to remove the singularity, and which would lead to a truncation thickness comparable with the molecular size a; (b) in the central region, the local slope θ(x) grows logarithmically with the distance x from the triple line; (c) one can match explicitly the solutions in the central and distal region: we do this for one specific example: a plate plunging into a fluid with an incidence angle exactly equal to θe. In this case we show that, far inside the distal region, the perturbation of the slope decays like 1/x2.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 212 , March 1990 , pp. 55 - 63
Copyright
© 1990 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

Berry, M.: 1974 J. Phys. A 7, 231.
Cox, R. G.: 1966 J. Fluid Mech. 168, 169.
Dussan, V. E. B.: 1979 Ann. Rev. Fluid Mech. 11, 371–400.
Dussan, V. E. B.: 1976 J. Fluid Mech. 77, 665.
Fermigier, M.: 1989 Dynamique d'une interface liquide dans un capillaire. Thèse, Université Paris 6.
de Gennes, P. G.: 1979 C. R. Acad. Sci. Paris B 288, 219.
de Gennes, P. G.: 1985 Rev. Mod. Phys. 57, 827.
de Gennes, P. G.: 1986 Z. Kolloid Polymer Sci. 264, 463.
Hardy, W.: 1919 Phil. Mag. 38, 49.
Hocking, L. M.: 1977 J. Fluid Mech. 79, 209.
Hocking, L. M. & Rivers, A., 1982 J. Fluid Mech. 121, 425.
Hoffmann, R.: 1975 J. Colloid Interface Sci. 50, 228.
Huh, C. & Scriven, L. E., 1971 J. Colloid Interface Sci. 35, 85.
Joanny, J.-F.: 1984 Le mouillage. Thése, Paris.
Lelah, M. & Marmur, A., 1981 J. Colloid Interface Sci. 82, 518.
Ngan, C. & Dussan, V. E. B. 1982 J. Fluid Mech. 118, 27.
Tanner, L.: 1979 J. Phys. D 12, 1473.
Teletzke, G. F., Davies, H. T., Scriven, L. E.: 1988 Rev. Phys. Appl. 23, 989.