Simulation of lubricant rheology in thin film lubrication Part 2: simulation of Couette flow

Abstract

In the second part of this two-part study, molecular dynamics simulations are performed for a fluid of spherical molecule in Couette flow. The simulation uses the same system as that in Part 1, but with the top wall translating in the x direction to generate a Couette flow. The shear equivalent viscosity η cs of a fluid is found to increase as film thickness decreases. The dependence is similar to that of the flow equivalent viscosity η ef obtained in Part 1, but the shear viscosity η cs exhibits a smaller value and slower increase rate. A further comparison between η cs and η ef shows that at the film thickness where the viscosity η ef diverges, the corresponding shear viscosity keeps a relatively small value, which is attributed to the larger shear rate applied in simulation of Couette flow. In a region where shear rate is low, the shear viscosity remains almost constant until a critical shear rate γ c is reached, then the ‘shear-thinning’ follows, i.e. the viscosity declines in a power-law, η cs ∼ γ − 2 3 , and the mean shear stress approaches a constant value—the ‘limiting shear stress’, If the film becomes molecularity thin, the lubricant behaves like a viscoelastic material, indicated by the considerable value of shear stress existing at the zero shear rate. The mean velocity profile of molecular flow shows a linear distribution, but with inflexions on the profile near the wall-fluid interface. When a very high shear rate is applied, however, the flow in thin films seems to be divided into two parts, half stays almost at rest and half is rapidly sheared. Once the stress exceeds the limiting shear stress, a slip in velocity appears at the solid-fluid interface.