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Gravity-driven thin-film flow on a flexible substrate

Published online by Cambridge University Press:  30 August 2013

P. D. Howell,
J. Robinson and
H. A. Stone
P. D. Howell*
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford OX1 3LB, UK
J. Robinson
Affiliation:
Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
H. A. Stone
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: howell@maths.ox.ac.uk
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Abstract

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We study the flow of a thin liquid film along a flexible substrate. The flow is modelled using lubrication theory, assuming that gravity is the dominant driving force. The substrate is modelled as an elastic beam that deforms in two dimensions. Steady solutions are found using numerical and perturbation methods, and several different asymptotic regimes are identified. We obtain a complete characterization of how the length and stiffness of the beam and the imposed liquid flux determine the profile of the liquid film and the resulting beam deformation.

JFM classification

Materials Processing Flows: CoatingLow-Reynolds-number flows: Lubrication theoryInterfacial Flows (free surface): Thin films

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 732 , 10 October 2013, pp. 190 - 213
Copyright
©2013 Cambridge University Press 

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