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 objectiv e of dev eloping simple, physics-based models. Such flows are encountered in microelectromechanical systems ( ) MEMS , in nanotechnology applications , and in low-pressure env ironments. A new general boundary condition that accounts for the reduced momentum and heat exchange with wall surfaces is proposed and its v alidity is inv estigated. 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 univ ersal scaling for the v elocity profile is obtained, which is used to dev elop 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 v alidated with comparisons against direct-simulation Monte Carlo results, linearized Boltzmann solutions, and experimental data.