Pressure distribution of gaseous slip flow in microchannel

A slip boundary condition for gaseous flow in microchannel was proposed, in which a function of Knudsen number takes the place of Knudsen number that is used in common slip boundary condition. The function satisfies two necessary conditions. Firstly, it should be in the same order as Knudsen number when Knudsen number is small. Secondly, it should be unity when Knudsen number goes to infinite. An analytical formula about pressure distribution of gaseous slip in microchannel was derived with the proposed boundary condition. Furthermore, the validity of the formula was verified in comparison with the experimental data. At last, because the dimensionless pressure at outlet should be unity, a modified pressure distribution formula was proposed, which has better agreement with the experimental data.