Non-continuum effects on a squeezed gas film in a two-dimensional acoustic resonator

Abstract

We study the effect of gas rarefaction and wall confinement on the propagation of vibroacoustic disturbances in a microchannel, generated by non-uniform (localized) time-harmonic oscillations of one of the channel walls. The problem is studied in the entire range of gas rarefaction rates, combining continuum and free-molecular limit analyses with direct simulation Monte Carlo calculations. Gas rarefaction is found to strongly increase the signal decay rate, varying between a slowly decaying propagating wave parallel to the channel walls at continuum conditions, to a near-source confined acoustic perturbation in the free-molecular regime. The impact of the stationary scattering wall is examined in detail, and the effect of replacing between fully diffuse and specular boundary reflections is found to slightly reduce the decay rate of the signal. The frequency dependence of the force generated by the gas film on the channel walls is calculated. Here, gas rarefaction smooths the transition between resonance and antiresonance behaviours observed in the continuum regime. A model set-up of a fully specular channel with a point delta source is examined, for which closed-form expressions are found for the effect of the stationary wall on the hydrodynamic perturbations and the acoustic force. These expressions assist in rationalizing the fundamental effect of the scattering wall on the system response.