Sound propagation in a superfluid helium filled porous solid: theory and experiment

The propagation of sound in a superfluid helium filled porous solid was investigated theoretically and experimentally. Motivated by the (classical ) Biot theory for the propagation of elastic waves in a fluid saturated porous solid, a set of linearized two fluid equations, averaged over the fine structure of the solid, was developed. From these were derived dispersion relations for the transition from first sound to fourth sound (c1 → c4) and from second sound to diffusion (c2 → diffusion) in a superfluid helium filled porous solid as the viscous drag on the normal component varies from zero to infinity. The speed and attenuation of the c1 → c4 mode was measured from 1.1K to 2.15 K under saturation vapor pressure (SVP) in three packed powder samples ranging from 1 to 25 μ nominal grain diameter and in three sintered bronze sphere samples ranging from 75 to 500 μ nominal diameter, covering both sides of the transition. The speed and attenuation of the c2 → diffusion mode was measured from 1.4 K to 2.15 K under SVP in the 500 μ diameter sample, covering the c2 side of the transition. This experiment marks the first time the Biot structural factor δ of a porous solid has been directly determined