Analysis of Compressible Laminar Flow In Micro-Channels

It is well established that compressibility effects play an important role in laminar flows through micro-channels.  An analytic solution to the vorticity-stream function form of the hydrodynamics equations is found for weakly compressible flow using a regular perturbation method.  In contrast to previous studies, the present analysis does not invoke the lubrication approximation and, consequently, predicts both a non-zero transverse velocity and a non-zero transverse pressure gradient.  Predicted velocity and pressure fields from the perturbation solution are compared to previously published analytical and numerical solutions.  Expressions for pressure drop are also given for compressible laminar flow in a channel that display significant deviations from the incompressible case.  In addition, experimental data from the literature for the flow of gases in microchannels are analyzed and compared with predictions from the analytical solution.  We find that a commonly used method for analyzing microchannel flow experiments obscures a rather simple dependence of pressure drop on the same dimensionless parameter used in the perturbation solution.