Effects of two transversal finite dimensions in long microchannel: Analytical approach in slip regime

An analytical approach has been developed to take account of the influence of the lateral walls on a stationary isothermal gas flow through a rectangular microchannel. The study concerns pressure-gradient-driven flows in channels where the length is large compared to the critical smallest dimension, namely, the channel height. The calculation of the bulk velocity is based on the Stokes equation treatment and uses the property of the Laplace operator. This novel method remains very easy to use when the second order term with respect to the Knudsen number is taken into account in the wall boundary conditions. The method is notably of high practical interest when applied to rectangular-cross-section microchannels that connect upstream and downstream high capacity reservoirs. The mass flow rates measured along such systems are fitted to first or second order polynomial forms following the mean Knudsen number of the flow. The present calculation also leads to a completely explicit second order expression for the mass flow rate. Thus, the first and second order experimental and theoretical coefficients can be identified immediately, allowing direct evaluations of physical gas-wall interaction features, in particular, the first, second order slip and the accommodation coefficients. An example of the implementation of the proposed technique is given. The slip and accommodation coefficients are extracted from the measurements of the mass flow rate through microchannels of rectangular cross-section.