Sound wave propagation in rarefied molecular gases

Abstract

Sound wave propagation in rarefied flows of molecular gases confined in micro-channels is investigated numerically. We first validate the employed kinetic model against the experimental results and then systematically study the gas damping and surface force on the transducer as well as the resonance/anti-resonance in confined space. To quantify the impact of the finite relaxation rates of the translational and internal energies on wave propagation, we examine the roles of bulk viscosity and thermal conductivity in depth over a wide range of rarefactions and oscillation frequencies. It is found that the bulk viscosity only exerts influence on the pressure amplitude and its resonance frequency in the slip regime in high oscillations. In addition, the internal degree of freedom is frozen when the bulk viscosity of a molecular gas is large, resulting in the pressure amplitude of sound waves in the molecular gas being the same as in a monatomic gas. Meanwhile, the thermal conductivity has a limited influence on the pressure amplitude in all the simulated flows. In the case of the thermoacoustic wave, we prove that the Onsager–Casimir reciprocal relation also holds for molecular gases, i.e. the pressure deviation induced by the temperature variation is equal to the heat flux induced by the plate oscillation. Our findings enable an enhanced understanding of sound wave propagation in molecular gases, which may facilitate the design of nano-/micro-scale devices.