Rayleigh Problem in Superfluid Helium

Abstract

On the basis of the two-fluid hydrodynamics, an analogue of the well-known Rayleigh equation was obtained for the dynamics of a spherical cavity in superfluid helium. With the aim of choosing a correct set of variables, a thorough analysis of the momentum flux tensor and energy flux has been carried out. The mass flux density or the mass average velocity, associated with it, and the velocity of the normal component, were chosen as independent variables. Due to the nonlinear character of the momentum flux tensor, several additional terms appeared in the equation for the evolution of the interface in comparison with the classical Rayleigh equation. These additional terms led to fundamental difference in the dynamics of vapor film in comparison with a classical fluid. For instance, one of the new terms led to an interesting effect of anomalous suppression or, depending on the configuration, anomalous enhancement of oscillations of the interface, observed in many works. Besides the additional anomalous decay or anomalous enhancement, there is also additional pressure, associated with the relative velocity in superfluid helium. The result obtained indicates the need to revise some results on the dynamics of a cavity in superfluid helium.