Scheichl, B;
Bowles, R;
Pasias, G;
(2021)
Developed liquid film passing a smoothed and wedge-shaped trailing edge: small-scale analysis and the ‘teapot effect’ at large Reynolds numbers.
Journal of Fluid Mechanics
, 926
, Article A25. 10.1017/jfm.2021.612.
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Abstract
Recently, the authors considered a thin steady developed viscous free-surface flow passing the sharp trailing edge of a horizontally aligned flat plate under surface tension and the weak action of gravity, acting vertically, in the asymptotic slender-layer limit (J. Fluid Mech., vol. 850, 2018, pp. 924–953). We revisit the capillarity-driven short-scale viscous–inviscid interaction, on account of the inherent upstream influence, immediately downstream of the edge and scrutinise flow detachment on all smaller scales. We adhere to the assumption of a Froude number so large that choking at the plate edge is insignificant but envisage the variation of the relevant Weber number of O(1). The main focus, tackled essentially analytically, is the continuation of the structure of the flow towards scales much smaller than the interactive ones and where it no longer can be treated as slender. As a remarkable phenomenon, this analysis predicts harmonic capillary ripples of Rayleigh type, prevalent on the free surface upstream of the trailing edge. They exhibit an increase of both the wavelength and amplitude as the characteristic Weber number decreases. Finally, the theory clarifies the actual detachment process, within a rational description of flow separation. At this stage, the wetting properties of the fluid and the microscopically wedge-shaped edge, viewed as infinitely thin on the larger scales, come into play. As this geometry typically models the exit of a spout, the predicted wetting of the wedge is related to what in the literature is referred to as the teapot effect.
| Type: | Article |
|---|---|
| Title: | Developed liquid film passing a smoothed and wedge-shaped trailing edge: small-scale analysis and the ‘teapot effect’ at large Reynolds numbers |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/jfm.2021.612 |
| Publisher version: | https://doi.org/10.1017/jfm.2021.612 |
| Language: | English |
| Additional information: | © The Author(s), 2021. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | thin films, boundary layers, waves/free surface flows |
| 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/10129928 |
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