Tortuosity measurements of porous ceramics using superfluid acoustics

The surface and bulk tortuosities of porous aluminum oxide ceramics have been measured using third sound and fourth sound propagation in superfluid Helium-4. The index of refraction of third sound measures the surface tortuosity, while the index of fourth sound measures the bulk tortuosity. The main feature observed is a rapid increase in the index of refraction of both sound modes as the pore-space percolation threshold is approached, to much higher values than previously observed. There is also an increase in the attenuation of both sounds, and a nonlinear dependence of the resonant frequencies on drive amplitude. The bulk tortuosity exceeds the surface tortuosity for porosities below 30%, a reversal of the behavior observed at high porosities. The overall results of this study suggest divergent behavior of both tortuosities near the percolation threshold, leading to a strong departure from the behavior predicted by Archie's law.