A unified engineering model for steady and quasi-steady shear-driven gas microflows

We analyze one-dimensional plane Couette flows in the entire Knudsen regime with the objective of modeling shear-driven rarefied gas flows encountered in various microelectromechanical system (MEMS) components. Using the linearized Boltzmann solutions available in the literature and hard sphere direct simulation Monte Carlo (DSMC) results, we develop a unified empirical model that includes analytical expressions for the velocity distribution and shear stress for steady plane Couette flows. We also present extension of this model to time-periodic oscillatory Couette flows. Comparisons between the extended model and ensemble averaged unsteady DSMC computations show good agreements in the quasi-steady flow limit, where the Stokes number (beta) based on the plate separation distance and oscillation frequency is less than or equal to 0.25. Overall, the new model accurately predicts the velocity distribution and shear stress for steady and quasi-steady (beta less than or equal to 0.25) flows in a wide Knudsen number range (Kn less than or equal to 12), and it is strictly valid for low subsonic flows with Mach number less than or equal to 0.3.