Mutual friction force in rotating helium II at low temperatures and near the λ-point

Mutual friction parameters in rotating He II are derived for the case of vortices kept at rest by external forces (surface pinning forces). They are different from those obtained in the theory of Hall and Vinen for the case of free vortices with the total momentum of the fluid being conserved. The difference increases if the temperature increases. In the critical region Hall and Vinen 's theory fails and the mutual friction problem is solved with the help of the phenomenological theory of superfluidity fitted to the critical behavior of known physical quantities. The theory is in satisfactory quantitative agreement with experimental data on the critical behavior of the mutual friction parameters B and B′. The theory predicts a strong effect of the vortex pinning on the thermal counterflow in the critical region.