Higher order lubrication model between slip walls

Abstract

A higher order lubrication model between slip walls is proposed for predicting the flow fields that cannot be described by the standard lubrication models based on the thin-gap approximation. The analysis shows that when considering the non-negligible pressure gradient in the surface-normal direction, the local pressure can be separated into (i) the base contribution by the modified Reynolds lubrication equation and (ii) the higher order component varying in both longitudinal and wall-normal directions, which takes the form proportional to the longitudinal derivative of the local velocity of the Couette–Poiseuille flow. For both (i) and (ii), the effect of the slip boundaries appears as the apparent displacements of the no-slip solid walls, and for (i) additional terms (to the no-slip case) also appear. The validity of the higher order slip-wall lubrication model is established by comparing the analytical prediction of the pressure with the fully resolved numerical results in a relatively wide region between a no-slip corrugated wall and a flat plate with varying slip length: the contribution of the higher order term is identified as the decreased lubrication pressure due to velocity slip. The model also successfully predicts the trend of pressure change between the varying slip case and a more realistic system with constant slip length for a channel, where the thin-gap approximation does not hold.