{
  "id": "2007.02897",
  "version": "v1",
  "published": "2020-07-06T17:21:25.000Z",
  "updated": "2020-07-06T17:21:25.000Z",
  "title": "Stokes flow due to point torques and sources in a spherical geometry",
  "authors": [
    "Alexander Chamolly",
    "Eric Lauga"
  ],
  "comment": "30 pages, 8 figures",
  "categories": [
    "physics.flu-dyn",
    "cond-mat.soft"
  ],
  "abstract": "Solutions to the Stokes equations written in terms of a small number of hydrodynamic image singularities have been a useful tool in theoretical and numerical computations for nearly fifty years. In this article, we extend the catalogue of known solutions by deriving the flow expressions due to a general point torque and point source in the presence of a stationary sphere with either a no-slip or a stress-free (no shear) boundary condition. For an axisymmetric point torque and a no-slip sphere the image system simplifies to a single image point torque, reminiscent of the solution for a point charge outside an equipotential sphere in electrostatics. By symmetry, this also gives a simple representation of the solution due to an axisymmetric point torque inside a rigid spherical shell. In all remaining cases, the solution can be described by a collection of physically intuitive point and line singularities. Our results will be useful for the theoretical modelling of the propulsion of microswimmers and efficient numerical implementation of far-field hydrodynamic interactions in this geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-06T17:21:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stokes flow",
      "spherical geometry",
      "axisymmetric point torque inside",
      "single image point torque",
      "stokes equations written"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}