Scaling Laws for Damping Forces Exerted by Different Gases in the Near- Free Molecular Flow Regimes

Abstract

Shear- and pressure-driven gas flows are encountered in several Micro-Electro-Mechanical-Systems (MEMS) applications, where the fluid is usually trapped under or around the vibrating micromechanical structure in extremely narrow gaps. The thin gas film is responsible for damping in these oscillating microstructures and its properties are of great importance to design, optimize and fabricate improved minute devices. Under such conditions, when the smallest characteristic length of MEMS is comparable with (or smaller than) the mean free path of the gas molecules, the traditional computational fluid dynamics methods, based on the Euler or the Navier-Stokes equations, fail in predicting the flows related to these devices. Therefore, in the present investigation, we solve directly the linearized Boltzmann equation in order to evaluate the damping forces exerted on a general two-dimensional configuration of a real biaxial accelerometer where different sets of plates induce a Poiseuille-like flow (microstructures that move in the direction perpendicular to their surfaces) as well as a Couette-like flow (microstructures that move in the direction parallel to their surfaces). A set of numerical experiments has been carried out in order to predict the scaling of damping forces by varying the relative dimensions of the geometrical configuration of the microdevice and the properties of the particular gas flowing through it, at different working pressures. Keywords: Boltzmann equation, damping forces, micro-electro-mechanical systems (MEMS).