Third-sound velocity in thin 3He-4He mixture films

The linearized hydrodynamics equations for a flat superfluid 3He-4He mixture film are derived. It is more complex than in pure 4He film: there is one new variable, the concentration of which presents spatial variations near the substrate walls. Interactions of the film with the gas and substrate are included. An approximate solution for the third-sound velocity is then obtained for thin films in the low-frequency limit, neglecting dissipation due to vortex motion. This solution, as for 4He, should be useful for any analysis of third-sound experiments in mixture films