{
  "id": "2310.08359",
  "version": "v1",
  "published": "2023-10-12T14:29:39.000Z",
  "updated": "2023-10-12T14:29:39.000Z",
  "title": "Bounds on the Spreading Radius in Droplet Impact: The Inviscid Case",
  "authors": [
    "Alidad Amirfazli",
    "Miguel D. Bustamante",
    "Yating Hu",
    "Lennon Ó Náraigh"
  ],
  "comment": "24 pages, 7 figures",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "We consider the classical problem of droplet impact and droplet spread on a smooth surface in the case of an ideal inviscid fluid. We revisit the rim-lamella model of Roisman et al. [\\textit{Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences}, 458(2022), pp.1411-1430.]. This model comprises a system of ordinary differential equations (ODEs); we present a rigorous theoretical analysis of these ODEs, and derive upper and lower bounds for the maximum spreading radius. Both bounds possess a $\\mathrm{We}^{1/2}$ scaling behaviour, and by a sandwich result, the spreading radius itself also possesses this scaling. We demonstrate rigorously that the rim-lamella model is self-consistent: once a rim forms, its height will invariably exceed that of the lamella. We introduce a rational procedure to obtain initial conditions for the rim-lamella model. Our approach to solving the rim-lamella model gives predictions for the maximum droplet spread that are in close agreement with existing experimental studies and direct numerical simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-12T14:29:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spreading radius",
      "droplet impact",
      "inviscid case",
      "rim-lamella model",
      "ideal inviscid fluid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}