Viscosity of a sheared correlated (near-critical) model fluid in confinement. (26th July 2017)

• Record Type: Journal Article
• Authors: Rohwer, Christian M; Gambassi, Andrea; Krüger, Matthias
• Is Part Of: Journal of physics. Volume 29:Number 33(2017)
• Publication Date: 2017-07-26
• Subjects: fluctuation phenomena -- shear flow -- confinement -- viscosity -- long-ranged correlations; Condensed matter -- Periodicals; Matière condensée -- Périodiques; Vaste stoffen; Vloeistoffen; Natuurkunde; Electronic journals; Computer network resources; 530.4105
• DOI: 10.1088/1361-648X/aa6e75
• Languages: English
• ISSNs: 0953-8984

Abstract

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 ℓ / L, where ℓ 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.