Abstract
When a fluid of kinematic viscosity ν and sound velocity αf flows in one direction in rigid-walled ducts and tubes at a radial frequency ω, the slowness s1 of the sound wave propagation or diffusion is directly related to the permeability K=iν/α2fωs21. A similar relation between the dynamic flow permeability and sound wave speed is given for porous media, based on a spatial average over a length scale D of the order of several pore and grain sizes. Model slownesses in ducts and tubes are obtained to calculate K(ω) for compressible fluids. In the long wavelength regime (i.e., channel size much smaller than wavelength) the correction due to compressibility is independent of channel size and is of the order of 2νω/ α2f. This correction is negligible for frequencies below the MHz range for gases and highly viscous fluids and negligible below the GHz range for water.
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