{
  "id": "1404.2312",
  "version": "v1",
  "published": "2014-04-08T21:45:52.000Z",
  "updated": "2014-04-08T21:45:52.000Z",
  "title": "Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel",
  "authors": [
    "Giovani L. Vasconcelos",
    "Christopher C. Green"
  ],
  "comment": "11 pages, 2 figures",
  "categories": [
    "physics.flu-dyn",
    "math-ph",
    "math.MP",
    "nlin.PS"
  ],
  "abstract": "Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the flow region in a period cell. The conformal mappings are constructed using the generalized Schwarz-Christoffel formula for multiply connected polygonal domains in terms of products of Schottky-Klein prime functions. It is shown that previous solutions for multiple steady bubbles in a Hele-Shaw cell are all particular cases of the solutions described herein. Examples of specific bubble configurations are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-08T21:45:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact solutions",
      "hele-shaw channel",
      "periodic assembly",
      "conformal mappings",
      "auxiliary complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2312V"
    }
  }
}