Hydrodynamic modes of superfluid helium adsorbed on Nuclepore

A theory is presented to describe sound propagation in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ adsorbed on Nuclepore, a planar porous substrate. The theory predicts the dependence of the sound velocity on film thickness. For thin films the sound speed is lower than on an equivalent nonporous substrate while for thick films the reverse holds. The transition between these regimes occurs when the fluid in the pores capillary condenses. The predictions of the theory are in qualitative agreement with the experimental results of Hallock and co-workers.