Nonlinear boundary slip of fluid flowing over solid surface

A general nonlinear slip of fluid flow at a solid surface is proposed in the present paper. The theoretical prediction shows that the slip length keeps as a constant (an initial slip length) at a small shear rate, then increases with the shear rate, and finally is approximately proportional to the slip velocity at a high shear rate. The nonlinear slips occurring at both of the simple flow in a parallel sliding system and a complex flow between two approaching spheres are investigated. It is found that the initial slip length controls the slip behavior at a small shear rate, but a critical shear rate controls the boundary slip at the high shear rate. Our theoretical predictions are in well agreement with the experimental measurements of boundary slips for both a simple fluid and a complex fluid.