Probing porous media with first and second sound. II. Acoustic properties of water-saturated porous media

Abstract

The ultrasonic properties (reflection/transmission and bulk attenuation/speed) of porous and permeable media saturated with a Newtonian fluid, namely water, are considered. The frequency dependence of the transmission amplitudes of pulses is measured through a slab of thickness d₁, repeated for another slab of thickness d₂ for a given material. With these two measurements on two different thicknesses, it is possible in principle to separate bulk losses from reflection/transmission losses for compressional waves in these materials. The bulk properties are calculated from the Biot theory for which all of the input parameters have been measured separately; the attenuations are particularly sensitive to the values of Λ, determined from second‐sound attenuation measurements reported in the companion article. There is excellent quantitative agreement between the theoretical and experimental values in the cases considered; there are no adjustable parameters involved. The reflection and transmission coefficients are reported for some of the multiply reflected pulses and their amplitudes are compared with those calculated from the Deresiewicz–Skalak and Rosenbaum boundary conditions appropriate to either the open‐pore or sealed‐pore surfaces, as the case may be. Again, there is excellent quantitative agreement between theory and experiment. Compared with the open‐pore boundary conditions, it is noted that there is a large reduction, both theoretically and experimentally, in the efficiency with which the slow compressional wave is generated when the sealed‐pore boundary conditions apply, but this efficiency is not reduced to zero.