The superfluidity of liquid ${}^3\text{H}\text{e}$ in a high-porosity aerogel has been studied using a fourth-sound resonance technique. This technique has two significant advantages: it can directly determine the superfluid density and it can derive the transport properties of the viscous normal-fluid component. The temperature dependence of the resonance frequency revealed suppression of superfluidity and that a finite normal-fluid fraction exists even at $T=0$. The motion of the normal-fluid component has also been investigated. As $T\to 0$, the energy loss becomes very small, despite a finite amount of the normal-fluid component remaining. This implies that the normal-fluid component is highly constrained by the aerogel, and hence the dissipation mechanism cannot be described in terms of the conventional hydrodynamic model. We have succeeded to explain these results by introducing a frictional relaxation model to describe our observations, and found that the flow field changes from being parabolic (Hagen-Poiseuille viscous flow) to flat (Drude frictional flow) on introducing an aerogel. Numerical calculation of the relaxation time using the quasiclassical Green’s-function method reproduces experimental results.

• Received 2 June 2010

DOI:https://doi.org/10.1103/PhysRevB.82.054521