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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
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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

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References

Asadullah, M. 1986 Viscous flow near a stationary contact line. Ph.D. dissertation, University of Essex.
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