An extended lubrication model for fluid flow in narrow gaps*

In this paper, to extend the applicable range of the lubrication theory, an extended lubrication equation is derived by considering the velocity component in surface-normal direction. The proposed equation is applied to the following two cases: the induced flows between a fixed flat plate and a curved object and by a sphere approaching to a plate. For the former case, the characteristics of the pressure distribution, particularly in the surface-normal direction, are reproduced successfully. For the latter case, the proposed equation is employed to model the flow between the sphere and plate. The effectiveness of the proposed equation is confirmed. A wider applicable range of the proposed equation comparing to that of the Reynolds lubrication equation is verified. The proposed equation predicts an applicable result for the ratio of the clearance width to the sphere radius being less than 0.5, while the Reynolds lubrication equation holds for a smaller range of the ratio being less than 0.1. This extended applicable range of the proposed equation is attributed to taking account of the velocity component in the surface-normal direction.