On the application of the Boltzmann equation to the simulation of fluid structure interaction in micro-electro-mechanical-systems

A three-dimensional quasi-static Stokes model, with a correction based on the kinetic theory of rarefied gas, is used to evaluate the damping forces exerted by gas flows on the moving surfaces of micromechanical structures in a wide range of pressures. Numerical results are compared with the experimental data collected on a silicon biaxial accelerometer in the continuum and transitional flow regimes. Furthermore, rarefied gas flows in ultra-thin film slider bearings are studied through a generalized Reynolds equation based on the linearized Boltzmann equation which holds for arbitrary Knudsen numbers. Since the generalized Reynolds equation is a flow rate-based model and is obtained by calculating the fundamental flows in the lubrication film (i.e., the Poiseuille and Couette flows), the plane Poiseuille-Couette flow problem between parallel plates has been preliminarly investigated. General boundary conditions of Maxwell's type have been considered by allowing for bounding surfaces with different physical properties.