Theory of helium under heat flow near the lambda point. II. Dynamics of phase change

The HeI-He II interface is a crucial aspect in the transformation processes between the superfluid and normal fluid phases. Its motion is investigated when temperatures and heat flows at boundaries deviate from those of a stationary coexistence state. As a unique feature, the heat flow to the interface from the He I side can be mostly transmitted to the He II side by thermal counterflow, and the latent heat generation (or absorption) at the interface becomes negligibly small. In any case the interfacial motion is so slow that the temperature on the He II side T/sub infinity/ is still given by the stationary relation T/sub lambda/-T/sub infinity/proportionalQ/sup 3/4/, where T/sub lambda/ is the critical temperatue and Q is the heat flow. The temperature profile and the interfacial position are calculated in some nonstationary cases. To this end a simple approximation scheme is developed. First, the interface can propagate with a constant velocity and the superfluid region can expand as a shock wave. Second, if the heat flow at the warmer boundary Q/sub w/ and that in the He II region Q/sub -/ are fixed at different values, the length of the He I region y/sub i/ changes in time as (d/dt)y/sup 1+p//sub i/ = constproportional Q/sub w/-Q/sub -/, where p = 1/(1-x/sub lambda/), and x/sub lambda/ is the critical exponent of the thermal conductivity. In particular, if y/sub i/ = 0 at t = 0 and Q/sub w/>Q/sub -/, the normal fluid region emerges as y/sub i/proportionalt/sup() 1/1+P/ at the warmer boundary. Third, if Q/sub -/ and the temperature at the warmer boundary are fixed, the interfacial position approaches an equilibrium position exponentially in time. The uniqueness of the problem arises from the superfluidity on the He II side and the strong critical singularity of the thermal conductivity on the He I side