Comprehensive Theory of Flow Properties of He3 Moving through Superfluid He4 in Capillaries

We propose a new set of hydrodynamic equations for flow of $^{3}\mathrm{He}$ through superfluid $^{4}\mathrm{He}$. They differ from earlier work by including both a mutual friction force between $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ and a viscous force. Both the mechanical vacuum model, in which mutual friction is neglected, and an earlier model by the authors, without viscous force, are limiting cases of this new description. An experimental setup is devised in which both forces play a significant role. The results of this experiment are in agreement with the theory.