Abstract: Through a theoretical study,it is found that the incompressible slip flow model for flows in a microchannel with vanishing Reynolds numbers is unstable when the Knudsen number is larger than 1/9.The effect of the finite Reynolds numbers on the stability is considered.Results show that the critical Knudsen number for instability is an increasing function of the Reynolds numbers.

Key words: micro-flow, slip flow model, finite Reynolds number, stability, critical Knudsen number