Critical Velocities for HE II

摘要

We propose a model to calculate the mass and heat flow of He II in a pipe connecting two baths. The each bath is maintained at constant temperature and pressure. The chemical potential difference is nonzero. When the velocities of the normal and superfluid components are above the critical value, the Gorter-Mellink equations provide a good approximation. These equations have unique solutions and the method is straightforward. When the velocities are below critical, the Landau equations are appropriate. These equations have no steady state solution when the chemical potential is nonzero. The equations do not specify how to find the velocity of the superfluid component and it is not clear how to determine when the flow is above or below the critical velocity. The model envisages two flow regimes in different parts of the flow path. One regime is above critical and is a solution of the Gorter-Mellink equations. It brings the chemical potential difference to zero. The remainder of the flow path is below critical with no gradient of chemical potential. There is a change in the profile of the superfluid component where the transition of flow regimes occurs and this allows a conservation of mass and heat flow.