{
  "id": "1704.02662",
  "version": "v1",
  "published": "2017-04-09T21:19:17.000Z",
  "updated": "2017-04-09T21:19:17.000Z",
  "title": "How to determine a boundary condition at a thin membrane for diffusion from experimental data",
  "authors": [
    "Tadeusz Kosztołowicz",
    "Sławomir Wąsik",
    "Katarzyna D. Lewandowska"
  ],
  "comment": "4 pages, 4 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We present a new method of deriving a boundary condition at a thin membrane for diffusion from experimental data. Based on experimental results obtained for normal diffusion of ethanol in water, we show that the derived boundary condition at a membrane contains a term with the Riemann--Liouville fractional time derivative of the $1/2$ order. Such a form of the boundary condition shows that a transfer of particles through a thin membrane is a `long memory process'. Presented method is an example that an important part of mathematical model of physical process may be derived directly from experimental data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-09T21:19:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thin membrane",
      "experimental data",
      "long memory process",
      "important part",
      "normal diffusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}