On the cavity evolution and the Rayleigh--Plesset equation in superfluid helium

Abstract

On the basis of the two-fluid hydrodynamics, an analogue of the famous Rayleigh-Plesse equation for the dynamics of a spherical bubble in superfluid helium is obtained. The mass flow velocity $v$ and the velocity of the normal component $v_{n}$ were chosen as independent variables. Due to the two-fluid nature of HeII, the cross terms in the evolution equation for the boundary position $\ R(t)$ appeared, which were absent in classical Rayleigh-Plesset equation in ordinary fluids. One of them renormilizes the coefficient in front of $(dR/dt)^{2}$. Another additional term formally coinciding with the viscous term, describes the attenuation of the boundary oscillations. This "extra-damping" term, greatly exceeding the usual viscous term, leads to a significant difference in the dynamics of cavity compared to HeI. In particular, this results in the interesting effect of abnormal suppression of oscillations of the vapor--liquid boundary observed in many works. There is also an additional term proportional to the squared velocity of the normal component, which is independent of the derivative $dR/dt$, and can be included in the pressure drop. Its physical meaning is that it describes a "Bernoulli" -like pressure created by the flow of a normal component. The obtained result declares that some results on the dynamics of the cavity in superfluid helium should be reviewed