Gaseous Flows in Rectangular Microchannels: Experimental Validation of a Second-Order Slip Flow Model

Abstract

A precise analytical model for gaseous flows in microchannels is of great interest for various applications, as for example when these microchannels are parts of a complex fluidic microsystem. However, a decrease in the channel hydraulic diameter leads to an increase in the rarefaction effects. If the Knudsen number becomes higher than about 0.1, it is generally admitted that the Navier-Stokes equation, even with first-order slip flow boundary conditions, are no longer valid. In order to keep an analytical model for higher Knudsen numbers, a resolution of the Navier-Stokes equation with second-order boundary conditions has been proposed in rectangular microchannels. An experimental setup has been designed for the measurement of gaseous microflows under controlled temperature and pressure conditions. Data relative to nitrogen and helium flows through rectangular microchannels are presented and analyzed. The microchannels have been etched by DRIE in silicon and closed with Pyrex by anodic bounding. Their depths range from 4.5 to 0.5 μm, with aspect ratios from 1 to 9%. It is shown that for aspect ratios higher than 1%, a plane flow model is no longer accurate, and that the proposed rectangular model should be used. The different sources of uncertainty that could occur during the experiments are discussed. A method is proposed to eliminate the principal one, that is the uncertainty when measuring the dimensions of the microchannel cross-section. Theoretical and experimental mass flow rates are compared, and it is shown that in rectangular microchannels, the second-order model is valid up to about 0.25, whereas the first-order model is no longer accurate for Knudsen numbers higher than 0.05. The best fit has been found for a tangential momentum accommodation coefficient σ = 0.93 , both with helium and nitrogen. Perspectives of this work are also presented.