Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-09T21:25:06.290Z Has data issue: false hasContentIssue false
  • English
  • Français

Steady viscous flow near a stationary contact line

Published online by Cambridge University Press:  21 April 2006

Ian Proudman  and
Mir Asadullah
Ian Proudman
Affiliation:
Department of Mathematics, University of Essex, Wivenhoe Park, Colchester, Essex CO4 3SQ, UK
Mir Asadullah
Affiliation:
Basic Sciences Department, University of Engineering and Technology, Peshawar, Pakistan
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper presents the asymptotic solution, near a stationary contact line at a plane boundary, for steady viscous incompressible flow of two immiscible liquids. The eigenvalues which determine this Stokes flow are determined by the contact angle α of the more viscous liquid and the ratio μ of the two viscosities. The dominant eigenvalues are found for all values of α and μ. As μ → 0 the results agree with those of Moffatt's (1964) one-phase theory for the case μ = 0 only when α > 81°. For α < 81° the two sets of results are qualitatively different. In particular, the eddy structure corresponding to complex eigenvalues occurs only in the α-range (34°, 81°). As μ increases from 0 to 1, this range steadily decreases to zero, which is located at 60°. The transport of energy across the liquid interface is almost always from the obtuse-angled sector to the acute-angled sector, irrespective of α, μ, and the location of the global power supply.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 187 , February 1988 , pp. 35 - 43
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

Asadullah, M. 1986 Viscous flow near a stationary contact line. Ph.D. dissertation, University of Essex.
Dean, W. R. & Montagnon, P. E. 1949 On the steady motion of viscous liquid in a corner. Proc. Camb. Phil. Soc. 45, 389–394.Google Scholar
Hooper, A., Duffy, B. R. & Moffatt, H. K. 1982 Flow of fluid of non-uniform viscosity in converging and diverging channels. J. Fluid. Mech. 117, 283–304.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1–18.Google Scholar
Moffatt, H. K. & Duffy, B. R. 1980 Local similarity solutions and their limitations. J. Fluid Mech. 96, 299–313.Google Scholar