Hydrodynamics of Oscillating Disks in Viscous Fluids: Density and Viscosity of Normal Fluid in PureHe4from 1.2°K to the Lambda Point

A new study has been made of the viscous component in liquid He II, using the experimental method of Andronikashvili. The hydrodynamic equations for disks oscillating in a viscous medium have been derived from first principles in a form amenable to experimental test of the necessary approximations. Associated studies with several ordinary liquids have yielded an empirical constant for the liquid dragged by the disk corner. The final semiempirical equations of motion appear to provide a significantly better approximation than those previously published. The new formulas have been applied to a combined study of density and viscosity of pure ${\mathrm{He}}^4$ liquid from 1.2°K to the lambda point, 2.1735°K. Refinements in experimental technique include larger oscillating systems, improved temperature regulation and measurement, and precision chronometry. The theoretical roton temperature dependence of Landau and of Feynman provides a good description of the density between 1.2° and 2.0°K. The empirical value of the roton excitation energy is found to be $\frac{\Delta }{k}=10.60\mathrm{}°$K. Detailed investigation in the region of the lambda point shows an accelerated rise in the normal fluid density above 2.0°K; the temperature derivative of density tends toward infinity at $T_{\lambda }$. Our data confirm the measurements made earlier by Andronikashvili over the entire temperature range. At temperatures below 1.5°K the torsion pendulum results lie significantly lower than those derived from second sound and specific heat data. Viscosities of the normal fluid are in substantial agreement with the earlier results of Andronikashvili and with the viscometer values of Heikkila and Hallett down to 1.5°K. Discrepancies between the oscillating disk and viscometer data below 1.5°K have not been resolved. The temperature dependence of the viscosity near the lambda point indicates that $T_{\lambda }$ is a point of strong singularity for both viscosity and normal fluid density.