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The moving contact line: the slip boundary condition

Published online by Cambridge University Press:  11 April 2006

E. B. Dussan V.
E. B. Dussan V.
Affiliation:
Department of Chemical and Biochemical Engineering, University of Pennsylvania, Philadelphia
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Abstract

The singularity at the contact line which is present when the usual fluidmechanical modelling assumptions are made is removed by permitting the fluid to slip along the wall. The aim of this study is to assess the sensitivity of the overall flow field to the form of the slip boundary condition. Explicit solutions are obtained for three different slip boundary conditions. Two length scales emerge: the slip length scale and the meniscus length scale. It is found that on the slip length scale the flow fields are quite different; however, when viewed on the meniscus length scale, i.e. the length scale on which almost all fluidmechanical measurements are made, all of the flow fields appear the same. It is found that the characteristic of the slip boundary condition which affects the overall flow field is the magnitude of the slip length.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 77 , Issue 4 , 22 October 1976 , pp. 665 - 684
Copyright
© 1976 Cambridge University Press

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References

Ablett, R. 1923 An investigation of the angle of contact between paraffin wax end water. Phil. Mag. 46, 244.Google Scholar
Bascom, W. D., Cottington, R. L. & Singleterry, C. R. 1964 Dynamic surface phenomena in the spontaneous spreading of oils on solids. In Contact Angles, Wettability, and Adhesion (ed. R. E. Gould), p. 355. Washington, D.C.: Am. Chem. Soc.Google Scholar
Dussan, V.E. B., 1976 On the differences between a bounding surface and a material surface. J. Fluid Mech. 75, 609.CrossRefGoogle Scholar
Dussan, V.E. B., & Davis, S. H. 1974 On the motion of a fluid-fluid interface along a solid surface. J. Fluid Mech. 65, 71.Google Scholar
Elliot, G. E. P. & Riddiford, A. A. 1967 Dynamic contact angles. I. The effect of impressed motion. J. Colloid Interface Sci. 23, 389.Google Scholar
Goldstein, S. 1965 Note on the conditions at the surface of contact of a fluid with a solid body. In Modern Development in Fluid Mechanics, vol. 2, p. 676. Dover.Google Scholar
Hansen, R. J. & Toong, T. Y. 1971 Dynamic contact angle and its relationship to forces of hydrodynamic origin. J. Colloid Interface Sci. 37, 196.Google Scholar
Hansen, R. S. & Miotto, M. 1957 Relaxation phenomena and contact angle hysteresis. J. Am. Chem. Soc. 79, 1765.Google Scholar
Hoffman, R. L. 1975 A study of the advancing interface. I. Interface shape in liquidgas systems. J. Colloid Interface Sci. 50, 228.Google Scholar
Hue, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid liquidlfluid contact line. J. Colloid Interface Sci. 35, 85.Google Scholar
Jasper, J. J. 1972 J. Phys. Chem. Ref. 1, 841.Google Scholar
Johnson, R. E. & Dettre, R. H. 1964 Contact angle hysteresis. I. Study of an idealized rough surface. II. Contact angle measurements on rough surfaces. In Contact Angles, Wettability, and Adhesion (ed. R. E. Gould), p. 112. Washington, D.C.: Am. Chem. Soc.Google Scholar
Lopez, J., Miller, C. A. & Ruckenstein, E. 1976 Spreading kinetics of liquid drops on solids. J. Colloid Interface Sci. 56, 460.Google Scholar
Ludviksson, V. & Lightfoot, E. N. 1968 Deformation of advancing menisci. A.I.Ch.E. J. 14, 674.Google Scholar
Morse, P. M. & Fesebach, H. 1953 Methods of Theoretical Physics, part I. McGraw-Hill.Google Scholar
Rose, W. & Heins, R. W. 1962 Moving interfaces and contact angle rate-dependency. J. Colloid Sci. 17, 39.Google Scholar
Schonixorn, H., Frisch, H. L. & Kwei, T. K. 1966 Kinetics of wetting of surfaces by polymer melts. J. Appl. Phys. 37, 4967.Google Scholar
Schwartz, A. M. & Tejada, S. B. 1972 Studies of dynamic contact angle on solids. J. Colloid Interface Sci. 38, 359.Google Scholar
Tranter, C. J. 1948 The use of the Mellin transform in finding the stress distribution in an infinite wedge. Quart. J. Mech. Appl. Math. 1, 125.Google Scholar
Yarnold, G. D. & Mason, B. J. 1949 The angle of contact between water and wax. Proc. Phys. Soc. B62, 125.Google Scholar
Zisman, W. A. 1964 Relation of equilibrium contact angle to liquid and solid constitution. In Contact Angles, Wettability, and Adhesion (ed. R. E. Gould), p. 1. Washington, D.C.: Am. Chem. Soc.CrossRefGoogle Scholar