Modeling the damping mechanism of MEMS oscillators in the transitional flow regime with thermal waves

Abstract

This paper investigates the damping behavior of a vibrating micro-oscillator caused by a surrounding gas in the transitional flow regime (0.01 < Kn < 0.1). In this regime, neither the continuum theory given by the Navier-Stokes equations nor the Boltzmann equation for the molecular flow regime can be applied to describe the damping effects correctly. We propose that the well-known Zener formalism developed for describing thermoelastic damping in solid oscillators can be adapted to include thermoacoustic effects in gases. In this newly proposed model, the damping is caused by thermal waves traveling from the micro-oscillator to a neighboring plate which is placed with a gap width ranging from 150 to 750 μm. This theoretical approach can be brought to a nearly perfect fit with the experimental data, including the observed concave zone of the quality factor plot within the transitional flow regime. The resonance frequency of thermal waves of gas within the gap is derived from standard wave theory, verifying the proportionalities extracted from the experimental results. Consequently, the theory in the transitional flow regime can be expanded by the thermal wave concept and the usage of MEMS oscillators for the thermal wave resonator cavity method (TWRC) is feasible.