On the modified Reynolds equation model for the prediction of squeeze-film gas damping in a low vacuum

The Reynolds equation coupled with an effective viscosity model is often employed to predict squeeze-film damping of plate resonators in a low vacuum. Due to the lack of a sound theoretical foundation, a study is carried out to evaluate the performance of such an approach in the free-molecule regime and results are presented in this paper. An experimentally validated Monte Carlo simulation approach for the simulation of air damping is developed and employed for this study. First, effective viscosity models are developed for a parallel-plate resonator and a rotational resonator based on experimental measurements. These models are then coupled with Reynolds equation and employed to simulate air damping of resonators of the same type but with differing dimensions. The results are compared with Monte Carlo simulation results. It has been found that the modified Reynolds equation approach cannot accurately compute air damping for a general class of resonators and hence cannot serve as a predictive tool. The deficiency lies in the effective viscosity model that is assumed to be a function of Knudsen number only. Possible extensions of the modified Reynolds equation approach in the highly rarefied regime are also discussed.