Density and Viscosity of Normal Fluid in Dilute Solutions of He-3 in He-4

The torsion pendulum technique has been applied to the study of normal fluid density and viscosity of dilute solutions of ${\mathrm{He}}^{3}$ in ${\mathrm{He}}^{4}$ from 1.3\ifmmode^\circ\else\textdegree\fi{}K to the lambda points. Three isotopic mixtures and pure ${\mathrm{He}}^{4}$ have yielded data which cover the range from 0 to 11 mole percent ${\mathrm{He}}^{3}$ concentration. Lambda temperatures are found to vary as the two-thirds power of the ${\mathrm{He}}^{4}$ mole fraction. Densities at ${T}_{\ensuremath{\lambda}}$ indicate a liquid volume contraction proportional to the concentration of ${\mathrm{He}}^{3}$. Normal fluid densities at lower temperatures are described by a single analytic function for all solutions and temperatures studied. The experimental values may be interpreted in terms of an effective hydrodynamic density of ${\mathrm{He}}^{3}$; empirical behavior of the effective ${\mathrm{He}}^{3}$ density is seen to increase linearly with the density of superfluid, in qualitative agreement with the model suggested by Feynman. Viscosities of all solutions exhibit temperature variations similar to that of pure ${\mathrm{He}}^{4}$. Dependence of the viscosity on ${\mathrm{He}}^{3}$ concentration appears to be markedly nonlinear at all temperatures. Analysis of the data in terms of the Landau-Khalatnikov theory of viscosity, together with additional simple assumptions, yields an empirical estimate of the roton-${\mathrm{He}}^{3}$ atom collision cross section.