Superfluid helium film below 1 K: Thickness, flow rate, and influence ofHe3

The superfluid helium film flow rate and the film profile (thickness versus height) on polished stainless steel have been measured in the same series of experiments down to 0.03 K. The concentration of ${\mathrm{He}}^3$ was varied from that of nominally "pure" ${\mathrm{He}}^4$ (∼ 0.2 ppm) to 0.44% ${\mathrm{He}}^3$. The film profile was measured below 0.7 K by observing isothermal flow oscillations. Apart from a small hysteresis effect, it agrees with the simple Frenkel-Schiff theory using the van der Waals potential calculated from the Lifshitz equation. In agreement with theory the profile is not changed by small concentrations of ${\mathrm{He}}^3$ (up to a few hundred ppm) which, however, significantly decrease the superfluid flow rate below 1 K. The effect of the ${\mathrm{He}}^3$ on the flow rate is most striking below 0.5 K, where surface-tension measurements have shown that the ${\mathrm{He}}^3$ is partially adsorbed on the surface of the ${\mathrm{He}}^4$, lowering the surface tension. In this region the flow rate is observed to be approximately proportional to the square root of the surface tension, as predicted by Arkhipov. With a larger amount of ${\mathrm{He}}^3$ (0.44%) the flow rate below 0.1 K increases quite rapidly with decreasing temperature. The increase is apparently connected with the beginning of Fermi degeneracy in the ${\mathrm{He}}^3$ dissolved in the film. Some observations of the flow rate for very small level differences are also reported.