{
  "id": "1702.01064",
  "version": "v1",
  "published": "2017-02-03T15:56:22.000Z",
  "updated": "2017-02-03T15:56:22.000Z",
  "title": "Viscosity of a sheared correlated model fluid in confinement",
  "authors": [
    "Christian M. Rohwer",
    "Andrea Gambassi",
    "Matthias Krüger"
  ],
  "comment": "16 pages, 10 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Second-order phase transitions are characterized by a divergence of the spatial correlation length of the order parameter fluctuations. For confined systems, this is known to lead to remarkable equilibrium physical phenomena, including finite-size effects and critical Casimir forces. We explore here some non-equilibrium aspects of these effects in the stationary state resulting from the action of external forces: by analyzing a model of a correlated fluid under shear, spatially confined by two parallel plates, we study the resulting viscosity within the setting of (Gaussian) Landau-Ginzburg theory. Specifically, we introduce a model in which the hydrodynamic velocity field (obeying the Stokes equation) is coupled to an order parameter with dissipative dynamics. The well-known Green-Kubo relation for bulk systems is generalized for confined systems. This is shown to result in a non-local Stokes equation for the fluid flow, due to the correlated fluctuations. The resulting effective shear viscosity shows universal as well as non-universal contributions, which we study in detail. In particular, the deviation from the bulk behavior is universal, depending on the ratio of the correlation length and the film thickness $L$. In addition, at the critical point the viscosity is proportional to $\\ell/L$, where $\\ell$ is a dynamic length scale. These findings are expected to be experimentally observable, especially for systems where the bulk viscosity is affected by critical fluctuations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-03T15:56:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sheared correlated model fluid",
      "confinement",
      "confined systems",
      "dynamic length scale",
      "second-order phase transitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}