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

Trinh, Philippe H.; Wilson, Stephen K.; Stone, Howard A.

Type

Article

Authors

Trinh, Philippe H.
Wilson, Stephen K.
Stone, Howard A.

KAUST Grant Number

KUK-C1-013-04

Date

2014-11-11

Online Publication Date

2014-11-11

Print Publication Date

2014-12

Permanent link to this record

http://hdl.handle.net/10754/597377

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Abstract

© 2014 Cambridge University Press. 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.

Citation

Trinh PH, Wilson SK, Stone HA (2014) A pinned or free-floating rigid plate on a thin viscous film. Journal of Fluid Mechanics 760: 407–430. Available: http://dx.doi.org/10.1017/jfm.2014.526.

Sponsors

The authors are grateful to Dr P. Howell and Dr D. Vella (University of Oxford) for valuable discussions. This work was begun while SKW was a Visiting Fellow in the Department of Mechanical and Aerospace Engineering at Princeton University, and completed while SKW was a Visiting Fellow and PHT was a Short Term Visitor at the Oxford Centre for Collaborative Applied Mathematics (OCCAM) at the University of Oxford. This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). SKW is presently a Leverhulme Trust Research Fellow (2013-2015) supported by award RF-2013-355. HAS acknowledges partial support from NSF grant CBET 1132835.