The velocity boundary condition at a liquid/solid interface is an old but challenging problem for over one hundred years. The classical fluid mechanics assumes that no wall slip occurs at the liquid/solid interfaces, i.e., the so called no-slip boundary condition. The validity of this assumption has been doubted for over a century. Early experimental measurements observed that wall slips occur for mercury flowing in very narrow, fused quartz capillaries, as well as for water flowing at a glass surface treated with dimethyldichlorosilane. During the last few years, both experimental observation [1] and molecular dynamics simulation [2] found that wall slips occur not only on poorly wetting surfaces but also on wetting surfaces.In the present paper boundary slip for a fluid flow at a smooth solid surface is numerically analyzed using a limiting shear stress model and complementary algorithm. The physical model is a smooth sphere approaching a flat plane. The wall slip velocity is controlled by the liquid/solid interface limiting shear stress, which is different from the so-called slip length model [3] where slip length controls the wall slip velocity. In our numerical methods, no iterative process is needed. The fluid pressure, boundary slip velocity and boundary shear stress are obtained at the same time. It is found that almost perfect agreements exist between the present theoretical predictions and the existing experimental observations for wall slip. It is found that the predicted hydrodynamic force in the case of wall slip is one order smaller than that predicted by the classical fluid hydrodynamic theory. This work not only provides a new model for the scientific research of wall slips occurring in both a simple flow and complex flow of fluids, but also gives a reliable numerical method for fluid hydrodynamics simulation considering wall slips. The present slip model gives a new way to search the wall slip mechanisms and let us think again the possibility of the so-called slip length model.
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