Hostname: page-component-6bf8c574d5-mggfc Total loading time: 0 Render date: 2025-02-14T10:37:40.566Z Has data issue: false hasContentIssue false
  • English
  • Français

The steady movement of a liquid meniscus in a capillary tube

Published online by Cambridge University Press:  12 April 2006

C. Huh  and
S. G. Mason
C. Huh
Affiliation:
Department of Chemistry, McGill University, Montreal, Canada Present address: Exxon Production Research Co., Houston, Texas 7701.
S. G. Mason
Affiliation:
Department of Chemistry, McGill University, Montreal, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

The steady movement of a liquid meniscus in a circular capillary tube has been examined theoretically for dynamic contact angles close to 90° with minute slippage of the liquid on the solid, thus relaxing the conventional no-slip boundary condition. The resulting flow field does not produce an unbounded force at the contact line, contrary to that with the no-slip condition. The interfacial velocity, wall stress, fluid pressure and the meniscus shape are calculated, and the significance of dynamic contact-angle measurements is discussed. A modified version of the classical Washburn equation which takes account of the meniscus also reveals the importance of slippage.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 3 , 13 July 1977 , pp. 401 - 419
Copyright
© 1977 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

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Bhattarcharji, S. & Savic, P. 1965 Proc. Heat Transfer Fluid Mech. Inst. p. 248.
Bulkley, R. 1931 J. Res. Nat. Bur. Stand. 6, 89.
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics, Blaisdell.
Derjaguin, B. V. & Fedyakin, N. N. 1969 Sov. Phys. Dokl. 13, 1053.
Dryden, H. L., Murnaghan, F. D. & Bateman, H. 1956 Bull. Nat. Res. Counc. no. 84. Rep. Comm. Hydrodyn. Dover.
Dussan, V. E. B. & Davis, S. H. 1974 J. Fluid Mech. 65, 71.
Elliott, G. E. P. & Riddiford, A. C. 1967 J. Colloid Interface Sci. 23, 389.
Garabedian, P. R. 1966 Comm. Pure Appl. Math. 19, 421.
Hansen, R. S. & Miotto, M. 1957 J. Am. Chem. Soc. 79, 1765.
Hansen, R. J. & Toong, T. V. 1971a J. Colloid Interface Sci. 36, 410.
Hansen, R. J. & Toong, T. V. 1971b J. Colloid Interface Sci. 37, 196.
Hoffman, R. L. 1975 J. Colloid Interface Sci. 50, 228.
Huh, C. & Scriven, L. E. 1971 J. Colloid Interface Sci. 35, 85.
Inverarity, G. 1969 Brit. Polymer J. 1, 245.
Miller, C. A. & Ruckenstein, E. 1974 J. Colloid Interface Sci. 48, 368.
Oliver, J. F., Huh, C. & Mason, S. G. 1977 To be published.
Pearson, J. R. A. 1966 Mechanical Principles of Polymer Melt Processing. Pergamon.
Rose, W. & Heins, R. W. 1962 J. Colloid Sci. 17, 39.
Schonhorn, H., Frisch, H. L. & Kwei, T. K. 1966 J. Appl. Phys. 37, 4967.
Taber, J. J. 1969 Soc. Pet. Eng. J. 9, 3.
Tolstoi, D. M. 1952a Dokl. Akad. Nauk SSSR 85, 1089.
Tolstoi, D. M. 1952b Dokl. Akad. Nauk SSSR 85, 1329.
Washburn, E. W. 1921 Phys. Rev. 17, 273.