Kelvin-Helmholtz Instability and Dissipation in a Phase-Separated 3He-4He Liquid Mixture

We study the behavior of the interface between the 3He-concentrated and 3He-dilute phases of a phase-separated 3He-4He liquid mixture in the presence of superflow in the d-phase. The superflow can produce a Kelvin-Helmholtz instability in the system. Here we consider two types of the instability: (i) quantized vortex in the superfluid liquid near the superfluid-normal interface; (ii) tangential flow of the superfluid component with respect to the normal fluid in the direction parallel to the interface. In these cases the Kelvin-Helmholtz instability has a threshold due to the surface tension and acceleration of the liquid in the direction normal to the interface. The acceleration is of centrifugal origin in (i) and gravitational one in (ii). The presence of the threshold results in quite different scales of characteristics distances. The centrifugal acceleration induces a scale of the order of the core radius b of several angstroms. The acceleration of gravity yields a scale of the capillary length ≃ 1.3 mm. In case (i) we obtain an instability of the vortex at a critical distance Rcr = bρd/(ρd − ρc). The vortex should disappear at distances smaller than Rcr. In case (ii) the interface becomes unstable provided the superfluid component flows in the direction tangential to the interface with a velocity exceeding its critical value ∼6.3 cm/s. There appear ripples with the wavelength of the order of the capillary constant. The instability threshold is found to be lower than in the absence of dissipation and independent of the magnitude of dissipation.