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A pinned or free-floating rigid plate on a thin viscous film

Published online by Cambridge University Press:  11 November 2014

Philippe H. Trinh
Affiliation:
Oxford Centre for Industrial and Applied Mathematics (OCIAM), University of Oxford, Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
Stephen K. Wilson*
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK
Howard A. Stone
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
Email address for correspondence: s.k.wilson@strath.ac.uk

Abstract

A pinned or free-floating rigid plate lying on the free surface of a thin film of viscous fluid, which itself lies on top of a horizontal substrate that is moving to the right at a constant speed is considered. The focus of the present work is to describe how the competing effects of the speed of the substrate, surface tension, viscosity, and, in the case of a pinned plate, the prescribed pressure in the reservoir of fluid at its upstream end, determine the possible equilibrium positions of the plate, the free surface, and the flow within the film. The present problems are of interest both in their own right as paradigms for a range of fluid–structure interaction problems in which viscosity and surface tension both play an important role, and as a first step towards the study of elastic effects.

Type
Papers
Copyright
© 2014 Cambridge University Press 

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