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The Elastic Landau-Levich Problem on a Slope

Warburton, K; Hewitt, D; Neufeld, J; (2020) The Elastic Landau-Levich Problem on a Slope. Journal of Fluid Mechanics , 883 , Article A40. 10.1017/jfm.2019.910. Green open access

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Abstract

The elastic analogue of the Landau–Levich dip-coating problem, in which a plate is withdrawn from a bath of fluid on whose surface lies a thin elastic sheet, is analysed for angle of withdrawal θ to the horizontal. The flow is controlled by the elasticity number, El, which is a measure of the relative importance of viscous and bending stresses, and θ. The leading-order solution for small El is a steady profile in which the thickness of the film on the plate is found to vary as El3/4 /(1 − cos θ )5/8 . This prediction is confirmed in the limit θ � 1 by comparison with numerical simulation. Finally, the circumstances under which the assumption of a steady solution is no longer valid are discussed, and the time-dependent solution is described.

Type: Article
Title: The Elastic Landau-Levich Problem on a Slope
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/jfm.2019.910
Publisher version: https://doi.org/10.1017/jfm.2019.910
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: thin films, lubrication theory, coating
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10085578
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