Report: A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales

Rarefied gas flows in channels, pipes, and ducts with smooth surfaces are studied in a wide range of Knudsen number (Kn) at low Mach number (M) with the objective of developing simple, physics-based models. Such flows are encountered in microelectromechanical systems (MEMS), in nanotechnology applications, and in low-pressure environments. A new general boundary condition that accounts for the reduced momentum and heat exchange with wall surfaces is proposed and its validity is investigated. It is shown that it is applicable in the entire Knudsen range and is second-order accurate in Kn in the slip flow regime. Based on this boundary condition, a universal scaling for the velocity profile is obtained, which is used to develop a unified model predicting mass flow rate and pressure distribution with reasonable accuracy for channel, pipe, and duct flows in the regime (0 Kn). A rarefaction coefficient is introduced into this two-parameter model to account for the increasingly reduced intermolecular collisions in the transition and free-molecular regimes. The new model is validated with comparisons against direct-simulation Monte Carlo results, linearized Boltzmann solutions, and experimental data.