Viscosity of a sheared correlated (near-critical) model fluid in confinement

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.

16 pages, 10 figures. Title modified and minor typos fixed from previous version

References in corpus (12)

• Lattice Boltzmann simulations of soft matter systems
• The Casimir effect: from quantum to critical fluctuations
• Critical Casimir forces in colloidal suspensions on chemically patterned surfaces
• Tunability of Critical Casimir Interactions by Boundary Conditions
• Trapping colloids near chemical stripes via critical Casimir forces
• Critical Casimir forces steered by patterned substrates
• Colloidal aggregation and critical Casimir forces
• Relaxation phenomena at criticality
• Structure and dynamics of binary liquid mixtures near their continuous demixing transitions
• Transient Casimir forces from quenches in thermal and active matter
• Forces exerted by a correlated fluid on embedded inclusions
• A Gaussian theory for fluctuations in simple liquids

Cited by in corpus (3)

• Stresses in non-equilibrium fluids: Exact formulation and coarse grained theory
• Non-equilibrium forces following quenches in active and thermal matter
• Correlations and forces in sheared fluids with or without quenching