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

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

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


© 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.
Original languageEnglish (US)
Pages (from-to)407-430
Number of pages24
JournalJournal of Fluid Mechanics
StatePublished - Nov 11 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


Dive into the research topics of 'A pinned or free-floating rigid plate on a thin viscous film'. Together they form a unique fingerprint.

Cite this