The Elastic Landau-Levich Problem on a Slope
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Journal Title
Journal of Fluid Mechanics
ISSN
0022-1120
Publisher
Cambridge University Press
Volume
883
Number
A40
Type
Article
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AM
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Warburton, K., Hewitt, D., & Neufeld, J. (2019). The Elastic Landau-Levich Problem on a Slope. Journal of Fluid Mechanics, 883 (A40)https://doi.org/10.1017/jfm.2019.910
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The elastic analogue of the Landau-Levich dip-coating problem, in which a plate is withdrawn from a bath of fluid on whose surface lies a thin elastic sheet, is analysed for angle of withdrawal θ to the horizontal.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 El^3/4 /(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 Finally, the circumstances under which the assumption of a steady solution is no longer valid are discussed, and the time-dependent solution is described.
Sponsorship
NERC (NE/L002507/1)
NERC (NE/L002507/1)
Identifiers
External DOI: https://doi.org/10.1017/jfm.2019.910
This record's URL: https://www.repository.cam.ac.uk/handle/1810/300181
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