Probing porous media with first and second sound. I. Dynamic permeability

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Abstract
The acoustic properties of first and second sound in He i i are used to probe the dynamic permeability k̃(ω), of porous media whose pores are large enough that the bulk properties of 4He are relevant. The measurements of phase velocity and attenuation, considered as functions of frequency and temperature, are in excellent agreement with the predictions based on a model k̃(ω) which involves four parameters: φ (porosity), α∞ (tortuosity), k0 (dc permeability), and Λ (dynamically connected pore size). The first three of these are measured by independent means; accurate values of Λ are extracted directly from the measurements in the high‐frequency region of the data where the observed temperature and frequency dependences of the modes are precisely those predicted on theoretical grounds. It is shown empirically that Λ is in fact closely related to the dc permeability k0 for all known data sets, thus supporting an earlier conjecture based on theoretical ideas.