Heat Torques and Circulation in Superfluid Helium

The small torques experienced by heated cylinders immersed in rotating superfluid helium have been measured and the results are compared with the predictions made for "heat-exchange" torques by Penney and Overhauser. They have pointed out that whenever there is a net superfluid circulation about a heated object, the object should experience a torque proportional to the circulation and power input and inversely proportional to the absolute temperature. The measured torques show this expected dependence on power and temperature. The existence of such torques is inherent in the two-fluid thermohydrodynamics of He II and is a result of the transfer of superfluid angular momentum to the object as superfluid is converted to normal fluid at the heated surface. Torques of order ${10}^{-6\mathrm{}}$ to ${10}^{-7\mathrm{}}$ dyn cm are observed at 1.30°K for power inputs of a few milliwatts and for cylinders 2 mm in diameter and 1 cm long. If the superfluid circulation is quantized, as first suggested by Onsager and Feynman, the torque should also be quantized. The torque values measured in the present experiment correspond to those expected for a few quanta of circulation about the cylinder, but the present experimental noise levels do not permit clear resolution of individual quantum levels.