Second-order slip laws in microchannels for helium and nitrogen

Abstract

We perform gas flow experiments in a shallow microchannel, 1.14±0.02 μm deep, 200 μm wide, etched in glass and covered by an atomically flat silicon wafer. The dimensions of the channel are accurately measured by using profilometry, optical microscopy and interferometric optical microscopy. Flow-rate and pressure drop measurements are performed for helium and nitrogen, in a range of averaged Knudsen numbers extending up to 0.8 for helium and 0.6 for nitrogen. This represents an extension, by a factor of 3 or so, of previous studies. We emphasize the importance of the averaged Knudsen number which is identified as the basic control parameter of the problem. From the measurements, we estimate the accommodation factor for helium to be equal to 0.91±0.03 and that for nitrogen equal to 0.87±0.06. We provide estimates for second-order effects, and compare them with theoretical expectations. We estimate the upper limit of the slip flow regime, in terms of the averaged Knudsen number, to be 0.3±0.1, for the two gases.