Thermal resonance model for micro-oscillators in the vicinity of a geometric boundary

Abstract

This study explores the damping behavior of micro-oscillators within the transitional flow regime between molecular flow and viscous flow, including the presence of a neighboring geometric boundary. The damping is described by a model based on standing thermal waves (STW), which form a thermal resonance depending on the pressure and on the gap width to the boundary. This concept was first introduced in a previous paper for a nitrogen atmosphere and is now examined for seven further gases (He, Ne, Ar, Kr, CO2, N2O, SF6). The distance between the micro-oscillator and the confining geometry, given by an Al plate, is in the range of 150 µm to 3500 µm. Fitting the thermal wave model to the experimental data shows very good agreement and explains the convex region for the measured quality factor Q in the transition from the molecular to the viscous flow regime. The evaluation of the thermal resonance model shows a strong correlation between the ambient pressure at which thermal resonance occurs and the thermal properties of the gas (i.e. thermal diffusivity a and adiabatic index κ) including the gap width h which is in agreement with the proposed theory. This opens up the possibility of using micro-oscillators to measure the thermal properties of gases in a very precise way, comparable to the thermal wave resonator cavity principle, but with a much simpler and smaller setup.