{
  "id": "1009.5969",
  "version": "v1",
  "published": "2010-09-29T18:24:39.000Z",
  "updated": "2010-09-29T18:24:39.000Z",
  "title": "Doubly-periodic array of bubbles in a Hele-Shaw cell",
  "authors": [
    "Antônio M. P. Silva",
    "Giovani L. Vasconcelos"
  ],
  "comment": "15 pages, 12 figures",
  "doi": "10.1098/rspa.2010.0227",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "Exact solutions are presented for a doubly-periodic array of steadily moving bubbles in a Hele-Shaw cell when surface tension is neglected. It is assumed that the bubbles either are symmetrical with respect to the channel centreline or have fore-and-aft symmetry, or both, so that the relevant flow domain can be reduced to a simply connected region. By using conformal mapping techniques, a general solution with any number of bubbles per unit cell is obtained in integral form. Several examples are given, including solutions for multi-file arrays of bubbles in the channel geometry and doubly-periodic solutions in an unbounded cell.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-29T18:24:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hele-shaw cell",
      "doubly-periodic array",
      "relevant flow domain",
      "channel centreline",
      "fore-and-aft symmetry"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Proceedings of the Royal Society of London Series A",
      "year": 2011,
      "month": "Feb",
      "volume": 467,
      "number": 2126,
      "pages": 346
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011RSPSA.467..346S"
    }
  }
}