Theory of rheology in confinement

The viscosity of fluids is generally understood in terms of kinetic mechanisms, i.e., particle collisions, or thermodynamic ones as imposed through structural distortions upon, e.g., applying shear. Often the latter are more relevant, which allows a simpler theoretical description, and, e.g., (damped) Brownian particles can be considered good fluid model systems. We formulate a general theoretical approach for rheology in confinement, based on microscopic equations of motion and classical density functional theory. Specifically, we discuss the viscosity for the case of two parallel walls in relative motion as a function of the wall-to-wall distance, analyzing its relation to the slip length found for a single wall. The previously observed [A. A. Aerov and M. Krüger, J. Chem. Phys. 140, 094701 (2014).] deficiency of inhomogeneous (unphysical) stresses under naive application of shear in confinement is healed when hydrodynamic interactions are included.