Viscosity, ion mobility, and theλtransition

A model is presented of the $\lambda$ transition in superfluid helium in which fluctuations near the transition are approximated by distinct regions of normal fluid and superfluid. The macroscopic viscosity of such a medium is computed. The ion mobility is also computed, taking into account a region of normal fluid around the ion induced by electrostriction. The results are, for the viscosity, ${\eta }_{\lambda }-\eta \sim t^{0.67}$ and for the mobility $\mu -{\mu }_{\lambda }\sim t^{0.92}$ both in excellent agreement with recent experiments. The model suggests that the $\lambda$ transition itself is the point at which superfluid regions become macroscopically connected.