{
  "annotation_id": "8f338842-4594-41f4-96c5-cea51d0614ca",
  "date_created": "2026-03-02T18:01:07.402000Z",
  "date_modified": "2026-03-02T18:01:07.402000Z",
  "file_hash": "48b65e84d7f33bc3d76553b198242865248f1400730c54da40b5c137f7337eb2",
  "private": false,
  "record": {
    "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"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6cda3ee4-b109-404f-9238-4f445fbef40d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}