Continuum-based slip model and its validity for micro-channel flows

In this paper, the low Mach number he- lium and nitrogen flows in micro-channels are inves- tigated numerically with variations of inlet to outlet pressure ratios, aspect ratios, out pressures and fluid mediums by using different continuum-based slip models. Theoretical solutions based on perturbation expansions of the Navier-Stokes equations have been developed under different order slip conditions. The validity of slip models has been examined by the corresponding experiments and the DSMC method at different Knudsen numbers. Simulations have shown good predictions of the compressibility, rarefaction and thermal creep effects on micro-channel flows with the present slip models. The higher order slip models relatively decrease the rarefaction effects comparing with a first-order slip model. Both of the Knudsen number and the Reynolds number have been identified as key parameters, which govern the rarefaction effects and thermal creep effects, respec- tively. The present slip models have been also dem- onstrated to be appropriate for micro-channel nitro- gen flows with the Knudsen number less than 0.15, and the higher order slip conditions improve the Na- vier-Stokes predictions in the slip flow regime with Kn<0.08. However, the continuum-based slip models significantly under-predict the rarefaction effects in the transitional flow regime as the Knudsen number exceeds 0.2.