Ultrasonic attenuation and pore microstructure in a liquid-He4—filled ceramic

We have measured the attenuation of transverse ultrasonic waves in a liquid-${}_{}{}^4{}_{}{}^{}\mathrm{He}$—filled porous ceramic, both above and below the superfluid transition temperature $T_{\lambda }$. We observed the attenuation due to motion of the viscous normal fluid component and determined its dependence on viscosity $\eta$, fluid density ${\rho }_f$, and sound frequency $\omega$. Our results are well described by an attenuation proportional to ${\rho }_f\omega$, and independent of $\eta$. This does not correspond to the expected behavior in either the low- or high-frequency regimes, and we interpret it to mean that the pore surface of our sample has features with a range of length scales comparable to the viscous penetration depth $\delta$ (200-600 Å). Although we only probe this narrow range of length scales, our results are consistent with a fractal dimension of 3 for the pore surface.