The flow factor approach model for the fluid flow in a nano channel

Abstract

The flow factor approach model was re-visited for the fluid flow in a nano slit pore. According to this model, the velocity profiles of the Couette and Poiseuille flows of a confined fluid were respectively calculated for different fluid–wall interactions and different wall separations. The calculation showed that the velocity profile across the film thickness of the Couette flow of a confined fluid is normally considerably distorted because of the fluid–wall interaction, compared with the conventional theory description. Such a distortion is more severe for a smaller wall separation. However, the calculated average velocity across the film thickness of the confined fluid in the Couette flow is still equal to that calculated from the conventional theory. For the same pressure gradient, the magnitude of the velocity of the Poiseuille flow calculated from this model is normally significantly smaller than that calculated from the conventional theory. Such a deviation is more severe for a stronger fluid–wall interaction. As a combined effect, the total volume flow rate through the wall gap of the confined fluid is greater than that calculated from the conventional theory when the Couette and Poiseuille flows are in contrary directions, while it is smaller than that calculated from the conventional theory when these two flows are in the same direction. Such differences are greater for stronger fluid–wall interactions. This may be one of the reasons why the generated hydrodynamic pressures and load-carrying capacity of a molecular-scale film lubricated contact both are greater than those calculated from conventional hydrodynamic lubrication theory. The results calculated from this model were compared with the molecular dynamics simulation results for the same operating conditions. Very good agreements between them were obtained.