Slip length and problem of anomalous velocity profiles

The most used expression for the slip length in the slip flow regime where slip conditions are needed for flow prediction comes from a Maxwell description of kinetic boundary conditions and depends on one coe dient only. Even if generally associated to the tangential accommodation coe dient, this coe dient equals any kind of kinetic property accommodation coe dients. The slip length so predicted by Maxwell increases strongly for the small values of the Maxwell accommodation coe dient whereas it seems, according to experiments that the slip length keeps a finite value and remains of the mean free path magnitude order. In addition, this enhancement of the Maxwell slip length for the small values of the Maxwell accommodation coe dient leads to some anomalous behaviors in theoretical flow predictions such as the so called inverted velocity profile in the cylindrical Couette flow of rarefied gas. In this work, we consider the calculation of the slip velocity based on another modelling of the gaz/surface interaction which involves distinguishable accommodation co-e dients for the normal and the tangential momentum components. The result shows that the slip length remains in the magnitude order of the mean free path when the values of the various momentum accommodation coe dients are varying. Then, the flow anomalous behaviors exhibited in flow fields where the boundary effects become important should be due to the unsuitable application of the Maxwell diffuse-specular boundary conditions for small values of the Maxwell accommodation coe dient. These anomalous behaviors should disappear when more accurate description of the boundary conditions was used.