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 former is less relevant, and (damped) Brownian particles are considered good fluid model systems. We formulate a general theoretical approach for rheology in confinement, based on the many particle diffusion equation, evaluated via classical density functional theory. We discuss the viscosity for the situation of two parallel walls in relative motion as a function of wall-to-wall distance.