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.
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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The elastic analogue of the Landau–Levich dip-coating problem, in which a plate is withdrawn from a bath of fluid on whose surface lies a thin elastic sheet, is analysed for angle of withdrawal θ to the horizontal.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 Finally, the circumstances under which the assumption of a steady solution is no longer valid are discussed, and the time-dependent solution is described.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 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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