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On liquid films on an inclined plate

Published online by Cambridge University Press:  18 August 2010

E. S. BENILOV ,
S. J. CHAPMAN ,
J. B. MCLEOD ,
J. R. OCKENDON  and
V. S. ZUBKOV
E. S. BENILOV*
Affiliation:
Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
S. J. CHAPMAN
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, UK
J. B. MCLEOD
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, UK
J. R. OCKENDON
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, UK
V. S. ZUBKOV
Affiliation:
Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
*
†Email address for correspondence: eugene.benilov@ul.ie
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Abstract

This paper examines two related problems from liquid-film theory. Firstly, a steady-state flow of a liquid film down a pre-wetted plate is considered, in which there is a precursor film in front of the main film. Assuming the former to be thin, a full asymptotic description of the problem is developed and simple analytical estimates for the extent and depth of the precursor film's influence on the main film are provided. Secondly, the so-called drag-out problem is considered, where an inclined plate is withdrawn from a pool of liquid. Using a combination of numerical and asymptotic means, the parameter range where the classical Landau–Levich–Wilson solution is not unique is determined.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 53 - 69
Copyright
Copyright © Cambridge University Press 2010

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References

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