dorsal/arxiv
View SchemaThin film dynamics on a vertically rotating disk partially immersed in a liquid bath
| Authors | K. Afanasiev, A. Münch, B. Wagner |
|---|---|
| Categories | |
| ArXiv ID | physics/0605109 |
| URL | https://arxiv.org/abs/physics/0605109 |
Abstract
The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that drags a thin film out of the bath is set up. From this, a dimension-reduced extended lubrication approximation that includes the meniscus region is derived. This problem constitutes a generalization of the classic drag-out and drag-in problem to the case of axisymmetric flow. The resulting nonlinear fourth-order partial differential equation for the film profile is solved numerically using a finite element scheme. For a range of parameters steady states are found and compared to asymptotic solutions. Patterns of the film profile, as a function of immersion depth and angular velocity are discussed.
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"date_modified": "2026-03-02T18:01:07.402000Z",
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"abstract": "The axisymmetric flow of a thin liquid film is considered for the problem of\na vertically rotating disk that is partially immersed in a liquid bath. A model\nfor the fully three-dimensional free-boundary problem of the rotating disk,\nthat drags a thin film out of the bath is set up. From this, a\ndimension-reduced extended lubrication approximation that includes the meniscus\nregion is derived. This problem constitutes a generalization of the classic\ndrag-out and drag-in problem to the case of axisymmetric flow. The resulting\nnonlinear fourth-order partial differential equation for the film profile is\nsolved numerically using a finite element scheme. For a range of parameters\nsteady states are found and compared to asymptotic solutions. Patterns of the\nfilm profile, as a function of immersion depth and angular velocity are\ndiscussed.",
"arxiv_id": "physics/0605109",
"authors": [
"K. Afanasiev",
"A. M\u00fcnch",
"B. Wagner"
],
"categories": [
"physics.flu-dyn",
"physics.comp-ph"
],
"title": "Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath",
"url": "https://arxiv.org/abs/physics/0605109"
},
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