Gaseous slip flow in long microchannels

An analytic and experimental investigation into gaseous flow with slight rarefaction through long microchannels is undertaken. A two-dimensional (2-D) analysis of the Navier-Stokes equations with a first-order slip-velocity boundary condition demonstrates that both compressibility and rarefied effects are present in long microchannels. By undertaking a perturbation expansion in ε, the height-to-length ratio of the channel, and using the ideal gas equation of state, it is shown that the zeroth-order analytic solution for the streamwise mass flow corresponds well with the experimental results. Also, the effect of slip upon the pressure distribution is derived, and it is obtained that this slip velocity leads directly to a wall-normal migration of mass. The fabrication of wafer-bonded microchannels that possess well-controlled surface structure is described, and a means for accurately measuring the mass how through the channels is presented. Experimental results obtained with this mass-flow measurement technique for streamwise helium mass flow through microchannels 52.25-μm wide, 1.33-μm deep, and 7500-μm long for a pressure range of 1.6-4.2 atmospheres (outlet pressures at atmospheric) are presented and shown to compare favorably with the analysis