Effective heights and tangential momentum accommodation coefficients of gaseous slip flows in deep reactive ion etching rectangular microchannels

The behavior of a rarefied, compressible flow in long, constant cross section channels provides an opportunity to study complex gas dynamics in a simple geometry that allows analytical solutions. The problem of a rarefied, compressible flow in near unity aspect ratio rectangular cross section channels has been all but ignored despite it being a common flow geometry. We present analytical expressions for the mass flow rate in long, straight and uniform rectangular cross section microchannels in the slip flow regime. Using these analytical expressions, we extract the tangential momentum accommodation coefficient (TMAC) as well as the effective channel dimensions to account for a slight curvature of one of the walls of the rectangle. These expressions are effective in near unity aspect ratio rectangular microchannels made by deep reactive ion etching. The dependence of the flow behavior on the channel height to width aspect ratio is discussed as is the effect of the slight deviation from a rectangular cross section. The obtained TMAC results are consistent with values found by previous researchers using similar materials. Finally, a method of determining TMACs in channels consisting of non-homogenous materials or processing methods is presented.