Symmetric mode instability of the slipflow model for flows in a microchannel with a vanishing Reynolds number

The slipflow model is usually used to study microflows when the Knudsen number lies between 0.01 and 0.1. The instability due to microscale effect seems to have never been studied before. In this paper we present preliminary results for the instability (not physical instability) of this model when applied to microchannel flow with a vanishing Reynolds number. The present paper is restricted to symmetrical mode. Both first-order and second-order slip boundary conditions will be considered. The project supported by the National Natural Science Foundation of China (10025210) and Tsinghua Project for Basic Research (2002)