{
  "id": "2410.07448",
  "version": "v1",
  "published": "2024-10-09T21:29:55.000Z",
  "updated": "2024-10-09T21:29:55.000Z",
  "title": "On the Propulsion of a Rigid Body in a Viscous Liquid Under the Action of a Time-Periodic Force",
  "authors": [
    "Mher M. Karakouzian",
    "Giovanni P. Galdi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "A rigid body $\\mathcal{B}$ moves in an otherwise quiescent viscous liquid filling the whole space outside $\\mathcal{B}$, under the action of a time-periodic force $\\boldsymbol{\\mathsf{f}}$ of period $T$ applied to a given point of $\\mathcal{B}$ and of fixed direction. We assume that the average of $\\boldsymbol{\\mathsf{f}}$ over an interval of length $T$ does not not vanish, and that the amplitude, $\\delta$, of $\\boldsymbol{\\mathsf{f}}$ is sufficiently small. Our goal is to investigate when $\\mathcal{B}$ executes a non-zero net motion; that is, $\\mathcal{B}$ is able to cover any prescribed distance in a finite time. We show that, at the order $\\delta$, this happens if and only if $\\boldsymbol{\\mathsf{f}}$ and $\\mathcal{B}$ satisfy a certain condition. We also show that this is always the case if $\\mathcal{B}$ is prevented from spinning. Finally, we provide explicit examples where the condition above is satisfied or not. All our analysis is performed in a general class of weak solutions to the coupled system body-liquid problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-09T21:29:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rigid body",
      "time-periodic force",
      "propulsion",
      "coupled system body-liquid problem",
      "non-zero net motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}