Third Sound and Stability of 3He–4He Mixture Films

In this paper, we study third sound in 3He–4He mixture films on several representative substrates: Nuclepore, glass, Li, and Na. This work extends previous more technical work which focused on the strongly binding substrates Nuclepore and glass. We proceed from a first-principles, microscopic theory utilizing the variational, hypernetted chain/Euler-Lagrange (HNC–EL) theory as applied to inhomogeneous boson systems. We calculate chemical potentials for both the 4He superfluid film and the physisorbed 3He. Numerical density derivatives of the chemical potentials lead to the sought-after third sound speeds. On all substrates, the third sound speeds show a series of oscillations driven by the layered structure of the 4He film, this is the case even for the very weakly binding Na substrate despite fairly structureless chemical potentials. We study the effect on the third sound response of adding a small amount of 3He to the film. We find, in agreement with our previous results, that the effect of the 3He depends sensitively on the particular 4He film coverage. The third sound speed can either increase or decrease. In fact, in some regimes, the added 3He destabilizes the film and can drive “layering transitions” leading to quite complicated geometric structures of the film in which the outermost layer consists of phase-separated regimes of 3He and 4He. Finally, we examine the range of applicability of the usual film-averaged hydrodynamic description. We find that at least up to film thicknesses of six liquid layers, there is no regime in which the usual hydrodynamic expression is applicable.