{
  "id": "1903.04799",
  "version": "v1",
  "published": "2019-03-12T09:39:56.000Z",
  "updated": "2019-03-12T09:39:56.000Z",
  "title": "A Lattice Boltzmann Model for Squirmers",
  "authors": [
    "Michael Kuron",
    "Philipp Stärk",
    "Christian Burkard",
    "Joost de Graaf",
    "Christian Holm"
  ],
  "comment": "9 pages, 7 figures",
  "categories": [
    "physics.flu-dyn",
    "cond-mat.soft",
    "physics.comp-ph"
  ],
  "abstract": "The squirmer is a simple yet instructive model for microswimmers, which employs an effective slip velocity on the surface of a spherical swimmer to describe its self-propulsion. We solve the hydrodynamic flow problem with the lattice Boltzmann (LB) method, which is well-suited for time-dependent problems involving complex boundary conditions. Incorporating the squirmer into LB is relatively straight-forward, but requires an unexpectedly fine grid resolution to capture the physical flow fields and behaviors accurately. We demonstrate this using four basic hydrodynamic tests: Two for the far-field flow---accuracy of the hydrodynamic moments and squirmer-squirmer interactions---and two that require the near field to be accurately resolved---a squirmer confined to a tube and one scattering off a spherical obstacle---which LB is capable of doing down to the grid resolution. We find good agreement with (numerical) results obtained using other hydrodynamic solvers in the same geometries and identify a minimum required resolution to achieve this reproduction. We discuss our algorithm in the context of other hydrodynamic solvers and present an outlook on its application to multi-squirmer problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-12T09:39:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lattice boltzmann model",
      "hydrodynamic solvers",
      "basic hydrodynamic tests",
      "unexpectedly fine grid resolution",
      "complex boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}