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Thin film flow over flexible membranes containing surface texturing: bio-inspired solutions

Lee, Y.C., Thompson, H.M. and Gaskell, P.H. (2009) Thin film flow over flexible membranes containing surface texturing: bio-inspired solutions. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 223 (JET552). pp. 337-345. ISSN 13506501

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Gravity-driven continuous thin liquid film flow over a flexible membrane containing surface topography is modelled using lubrication theory. The associated coupled nonlinear equation set, for the film thickness, pressure and membrane deflection, is solved using a state-of-the-art full approximation storage (FAS) multigrid algorithm with automatic mesh refinement and adaptive time-stepping, in order to maximise computational efficiency when fine-scale resolution is required while ensuring accurate mesh independent solutions at the micro-scale. The robustness of the approach is demonstrated through the solution of a series of problems and comparisons drawn with the same flow on an equivalent completely rigid membrane. It is shown that the former differs considerably from the latter in that the film thickness affects the shape of the flexible membrane, the compliance of which in turn impinges on the profile of the resulting free-surface disturbance.

Item Type: Article
Copyright, Publisher and Additional Information: © IMechE 2009. This is an author produced version of a paper subsequently published in 'Journal Of Engineering Tribology - Part J'. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: Thin film flow, Flexible membrane, Lubrication theory, Adaptive mesh refinement, Adaptive time-stepping, Multigrid
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds)
Depositing User: Mrs Fiona Slade
Date Deposited: 08 Mar 2010 14:43
Last Modified: 08 Feb 2013 17:06
Published Version: http://dx.doi.org/10.1243/13506501JET552
Status: Published
Publisher: Professional Engineering Publishing
Identification Number: 10.1243/13506501JET552
URI: http://eprints.whiterose.ac.uk/id/eprint/10472

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