Rotation of Liquid Helium at Low Reynolds Numbers

Abstract

Previous experiments on the transient and steady-state behavior of the free surface of helium II in a bucket suddenly set into rotation have shown that the normal and superfluid components are in common motion. This contradicts the simple two-fluid equations (neglecting mutual friction) and has been attributed to the fluid's having exceeded some "critical velocity." The principle of dynamical similarity suggests that such experiments should be scaled according to the Reynolds number, and analysis of previous experiments indicates that this parameter has always been rather high (>3.7×${10}^4$). The Reynolds number has been reduced to ∼1.4×${10}^3$ by reducing the radius of the container to 0.0255 cm. The experimental results show that under these conditions the two fluids are still in common motion. The shape of the free surface was much different than in wider containers due to the effects of surface tension, which limit further reduction of the Reynolds number in this manner.