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Boundary conditions for free surface inlet and outlet problems

Published online by Cambridge University Press:  10 August 2012

M. Taroni ,
C. J. W. Breward ,
P. D. Howell  and
J. M. Oliver
M. Taroni*
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK
C. J. W. Breward
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK
P. D. Howell
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK
J. M. Oliver
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK
*
†Email address for correspondence: taroni@maths.ox.ac.uk
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Abstract

We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number it is well known that the flux scales with , but this classical result is non-uniform as the contact angle approaches . By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed.

JFM classification

Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 708 , 10 October 2012 , pp. 100 - 110
Copyright
Copyright © Cambridge University Press 2012

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