RESUMO
Analytical solutions describing propagation of monochromatic acoustic waves inside long pores of simple geometries and narrow flat slits are obtained with accounting for gas rarefaction effects. It is assumed that molecular nature of gas is important in Knudsen layers near solid boundaries. Outside the Knudsen layers, the continuum approach is used. This model allows for extension of acoustic analysis to regions of low pressures and microscopic cross-sectional sizes of channels. The problem is solved using linearized Navier-Stokes equations with the boundary conditions that resulted from the first-order approximation with respect to small Knudsen number Kn. For slits and pores of circular and square cross sections, the theoretical dependencies of the dynamic density in the low-frequency range are compared with those that resulted from known experimental data on steady-state flows of rarefied gases in uniform channels. Despite the formal restriction Kn << 1 of asymptotic analysis, the theoretical model agrees well with experiments up to Kn approximately 5. It is shown that the molecular phenomena affect acoustic characteristics of micro-channels and pores starting from relatively small Knudsen numbers Kn > 0.01, especially at low frequencies. The obtained results may be used for analyses of acoustic properties of waveguides, perforated panels, micro-channels and pores in wide range of gas pressures as well as for stationary flows of rarefied gases through long uniform pipes etc.
