Correction of second-order slip condition for higher Knudsen numbers by approximation of free-molecular diffusion

The computational predictions of channel and pipe flows with classical models and no-slip condition at the wall reach excellent results for lower Knudsen numbers (Kn) only. Linear slip models reach a very good approximation of measurement results over the region of 10−3 < Kn < 10−1. The numerical results of higher-order slip models match experimental data up to Kn ≈ 1. The present work derives an analytical model for the transition from the slip regime to the free-molecular flows by the superposition of diffuse molecular boundary reflection and the molecular diffusion inside the bulk flow. The methodology of the present publication models the mass flow resulting from the molecular diffusion for the approximation of the mass flow in microchannels and micropipes for the regime of molecular mass flows (1 < Kn < 100) in an excellent way. The present model shows good agreement with the former models, measurement data, and direct simulation Monte Carlo results for the complete region from the transitional regime up to free-molecular flow (10−2 < Kn < 102).