{
  "id": "1909.09625",
  "version": "v1",
  "published": "2019-09-20T17:27:06.000Z",
  "updated": "2019-09-20T17:27:06.000Z",
  "title": "Corrector equations in fluid mechanics: Effective viscosity of colloidal suspensions",
  "authors": [
    "Mitia Duerinckx",
    "Antoine Gloria"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "Consider a colloidal suspension of rigid particles in a steady Stokes flow. In a celebrated contribution, Einstein argued that in the regime of dilute particles, the system behaves at leading order like a Stokes fluid with some explicit effective viscosity. In this contribution, we rigorously define a notion of effective viscosity, regardless of the dilute regime assumption. More precisely, we establish a homogenization result when particles are distributed according to a stationary and ergodic random point process. The main novelty is the introduction and analysis of suitable corrector equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-20T17:27:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "effective viscosity",
      "colloidal suspension",
      "fluid mechanics",
      "ergodic random point process",
      "steady stokes flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}