Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-27T09:08:06.891Z Has data issue: false hasContentIssue false
  • English
  • Français

Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop

Published online by Cambridge University Press:  21 April 2006

P. A. Durbin
P. A. Durbin
Affiliation:
NASA Lewis Research Center, Cleveland, OH 44135, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

It has previously been shown that the no-slip boundary condition leads to a singularity at a moving contact line and that this forces one to admit some form of slip. Present considerations on the energetics of slip due to shear stress lead to a yield stress boundary condition. A model for the distortion of the liquid state near solid boundaries gives a physical basis for this boundary condition. The yield stress condition is illustrated by an analysis of a slender drop rolling down an incline. That analysis provides a formula for the frictional drag resisting the drop movement. With the present boundary condition the length of the slip region becomes a property of the fluid flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 197 , December 1988 , pp. 157 - 169
Copyright
© 1988 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

Batchelor, G. K.1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Dussan V., E. B. 1976 J. Fluid Mech. 77, 665–684.
Dussan V., E. B. & Chow, R. T. 1983 J. Fluid Mech. 137, 1–29.
Dussan V., E. B. & Davis, S. H. 1974 J. Fluid Mech. 65, 71–95.
Elliot, G. E. P. & Riddleford, A. C.1967 J. Colloid Interface Sci. 23, 389–398.
Eyring, H. & Jhon, M. S.1969 Significant Liquid Structures. John Wiley Press.
Greenspan, H. P.1978 J. Fluid Mech. 84, 125–143.
Hocking, L. M.1976 J. Fluid Mech. 76, 801–817.
Hocking, L. M.1981 Q. J. Mech. Appl. Maths 34, 37–55.
Huh, C. & Mason, S. G.1977 J. Fluid Mech. 81, 401–419.
Huh, C. & Scriven, L. E.1971 J. Colloid Interface Sci. 35, 85–101.
Lamb, H.1932 Hydrodynamics. Dover Press.
Lowndes, J.1980 J. Fluid Mech. 101, 631–645.