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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-09-01
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| Series: | Fluids |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2311-5521/6/9/318 |
| _version_ | 1797519359842713600 |
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| author | Selin Duruk Edouard Boujo Mathieu Sellier |
| author_facet | Selin Duruk Edouard Boujo Mathieu Sellier |
| author_sort | Selin Duruk |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T07:41:45Z |
| format | Article |
| id | doaj.art-9763049f091b4b81a76c5561034979eb |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T07:41:45Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-9763049f091b4b81a76c5561034979eb2023-11-22T13:01:52ZengMDPI AGFluids2311-55212021-09-016931810.3390/fluids6090318Thin Liquid Film Dynamics on a Spinning SpheroidSelin Duruk0Edouard Boujo1Mathieu Sellier2Department of Mechanical Engineering, University of Canterbury, Christchurch 8041, New ZealandLaboratory of Fluid Mechanics and Instabilities, EPFL, 1015 Lausanne, SwitzerlandDepartment of Mechanical Engineering, University of Canterbury, Christchurch 8041, New ZealandThe 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.https://www.mdpi.com/2311-5521/6/9/318thin liquid filmnonlinear dynamicsexternal forcingcurved substratecoating |
| spellingShingle | Selin Duruk Edouard Boujo Mathieu Sellier Thin Liquid Film Dynamics on a Spinning Spheroid Fluids thin liquid film nonlinear dynamics external forcing curved substrate coating |
| title | 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_short | Thin Liquid Film Dynamics on a Spinning Spheroid |
| title_sort | thin liquid film dynamics on a spinning spheroid |
| topic | thin liquid film nonlinear dynamics external forcing curved substrate coating |
| url | https://www.mdpi.com/2311-5521/6/9/318 |
| work_keys_str_mv | AT selinduruk thinliquidfilmdynamicsonaspinningspheroid AT edouardboujo thinliquidfilmdynamicsonaspinningspheroid AT mathieusellier thinliquidfilmdynamicsonaspinningspheroid |