Sheared liquids in the nanoscale range

In this paper, we study two characteristic properties of thin confined liquids under shear: the induced velocity profile in the liquid at low shear rates, and the shear-dependent thinning of the effective viscosity. Our approach is based on the coupling between a time-dependent Ginzburg–Landau equation for a local order parameter and a local velocity field. Special attention is given to the role of the lateral nonuniformity of the liquid–wall interactions in determining these properties. We derive the Brinkman equation for the velocity profile and obtain a power low dependence of the viscosity on shear rate in the thinning regime, ηeff∼γ−α with 2/3≤α≤1.