Thin Liquid Film Dynamics on a Spinning Spheroid
The present work explores the impact of rotation on the dynamics of a thin liquid layer deposited on a spheroid (bi-axial ellipsoid) rotating around its vertical axis. An evolution equation based on the lubrication approximation was derived, which takes into account the combined effects of the non-u...
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2021
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Online Access: | https://doi.org/10.3390/fluids6090318 |
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ftmdpi:oai:mdpi.com:/2311-5521/6/9/318/ 2023-08-20T04:09:52+02:00 Thin Liquid Film Dynamics on a Spinning Spheroid Selin Duruk Edouard Boujo Mathieu Sellier 2021-09-06 application/pdf https://doi.org/10.3390/fluids6090318 EN eng Multidisciplinary Digital Publishing Institute https://dx.doi.org/10.3390/fluids6090318 https://creativecommons.org/licenses/by/4.0/ Fluids; Volume 6; Issue 9; Pages: 318 thin liquid film nonlinear dynamics external forcing curved substrate coating Text 2021 ftmdpi https://doi.org/10.3390/fluids6090318 2023-08-01T02:37:58Z The present work explores the impact of rotation on the dynamics of a thin liquid layer deposited on a spheroid (bi-axial ellipsoid) rotating around its vertical axis. An evolution equation based on the lubrication approximation was derived, which takes into account the combined effects of the non-uniform curvature, capillarity, gravity, and rotation. This approximate model was solved numerically, and the results were compared favorably with solutions of the full Navier–Stokes equations. A key advantage of the lubrication approximation is the solution time, which was shown to be at least one order of magnitude shorter than for the full Navier–Stokes equations, revealing the prospect of controlling film dynamics for coating applications. The thin film dynamics were investigated for a wide range of geometric, kinematic, and material parameters. The model showed that, in contrast to the purely gravity-driven case, in which the fluid drains downwards and accumulates at the south pole, rotation leads to a migration of the maximum film thickness towards the equator, where the centrifugal force is the strongest. Text South pole MDPI Open Access Publishing South Pole Fluids 6 9 318 |
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MDPI Open Access Publishing |
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ftmdpi |
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English |
topic |
thin liquid film nonlinear dynamics external forcing curved substrate coating |
spellingShingle |
thin liquid film nonlinear dynamics external forcing curved substrate coating Selin Duruk Edouard Boujo Mathieu Sellier Thin Liquid Film Dynamics on a Spinning Spheroid |
topic_facet |
thin liquid film nonlinear dynamics external forcing curved substrate coating |
description |
The present work explores the impact of rotation on the dynamics of a thin liquid layer deposited on a spheroid (bi-axial ellipsoid) rotating around its vertical axis. An evolution equation based on the lubrication approximation was derived, which takes into account the combined effects of the non-uniform curvature, capillarity, gravity, and rotation. This approximate model was solved numerically, and the results were compared favorably with solutions of the full Navier–Stokes equations. A key advantage of the lubrication approximation is the solution time, which was shown to be at least one order of magnitude shorter than for the full Navier–Stokes equations, revealing the prospect of controlling film dynamics for coating applications. The thin film dynamics were investigated for a wide range of geometric, kinematic, and material parameters. The model showed that, in contrast to the purely gravity-driven case, in which the fluid drains downwards and accumulates at the south pole, rotation leads to a migration of the maximum film thickness towards the equator, where the centrifugal force is the strongest. |
format |
Text |
author |
Selin Duruk Edouard Boujo Mathieu Sellier |
author_facet |
Selin Duruk Edouard Boujo Mathieu Sellier |
author_sort |
Selin Duruk |
title |
Thin Liquid Film Dynamics on a Spinning Spheroid |
title_short |
Thin Liquid Film Dynamics on a Spinning Spheroid |
title_full |
Thin Liquid Film Dynamics on a Spinning Spheroid |
title_fullStr |
Thin Liquid Film Dynamics on a Spinning Spheroid |
title_full_unstemmed |
Thin Liquid Film Dynamics on a Spinning Spheroid |
title_sort |
thin liquid film dynamics on a spinning spheroid |
publisher |
Multidisciplinary Digital Publishing Institute |
publishDate |
2021 |
url |
https://doi.org/10.3390/fluids6090318 |
geographic |
South Pole |
geographic_facet |
South Pole |
genre |
South pole |
genre_facet |
South pole |
op_source |
Fluids; Volume 6; Issue 9; Pages: 318 |
op_relation |
https://dx.doi.org/10.3390/fluids6090318 |
op_rights |
https://creativecommons.org/licenses/by/4.0/ |
op_doi |
https://doi.org/10.3390/fluids6090318 |
container_title |
Fluids |
container_volume |
6 |
container_issue |
9 |
container_start_page |
318 |
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1774723594466623488 |