{
  "id": "2312.14613",
  "version": "v1",
  "published": "2023-12-22T11:14:42.000Z",
  "updated": "2023-12-22T11:14:42.000Z",
  "title": "Absolute and convective instabilities in a liquid film over a substrate moving against gravity",
  "authors": [
    "Fabio Pino",
    "Miguel Alfonso Mendez",
    "Benoit Scheid"
  ],
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "The drag-out problem for small Reynolds numbers (Re) admits the Landau-Levich-Derjaguin (LLD) solution for small capillary numbers (Ca), and Derjaguin's solution for large Ca. We investigate whether these solutions are absolutely or convectively unstable, solving the Orr-Sommerfeld eigenvalue problem. For Derjaguin's solution, we show that the instability is unconditionally convective for Kapitza number (Ka) smaller than 17 and becomes absolute for Ka>0.15 and Re^(1.7) for Re>10. For water (Ka=3400), the LLD solution is always convectively unstable. The absolute instability is observed only when the dip-coated film is additionally fed from above.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-22T11:14:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "liquid film",
      "convective instabilities",
      "substrate moving",
      "derjaguins solution",
      "orr-sommerfeld eigenvalue problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}