Direct simulation Monte Carlo-based expressions for the gas mass flow rate and pressure profile in a microscale tube

The direct simulation Monte Carlo (DSMC) method of Bird is used to develop simple closed-form expressions for the mass flow rate and the pressure profile for the steady isothermal flow of an ideal gas through a microscale tube connecting two infinite reservoirs at different pressures but at the temperature of the tube wall. Gas molecules reflect from the tube wall according to the Maxwell model (a linear combination of specular and diffuse reflections at the wall temperature) with a unity or sub-unity value of the accommodation coefficient (the probability that molecules reflect diffusely from the wall). The DSMC-based expressions have four parameters. Two parameters are specified so that the mass flow rate reduces to the known expression in the free-molecular regime. One parameter was previously determined by comparison to DSMC simulations in the slip regime. The remaining parameter is determined by comparison to DSMC simulations for pressures spanning the transition regime with several values of the acc...