Sound wave propagation in transition-regime micro- and nanochannels

We present an extension of the existing continuum theory for sound wave propagation in dilute gases in “narrow” two-dimensional channels to arbitrary Knudsen numbers; the theory provides predictions for the wavelength and attenuation coefficient as a function of the oscillation frequency. A channel is considered narrow in the context of wave propagation when its height is much smaller than the characteristic diffusion length based on the wave frequency. This criterion is easily satisfied by small scale (transition-regime) channels for most frequencies of interest. Numerical simulations for a dilute monoatomic gas using the direct simulation Monte Carlo are used to verify the theoretical results. Good agreement is found between theory and simulation.