Dependence of the Helium-Film Transfer Rate on Pressure Head, Film Height, and Substrate

Helium-film transfer rates \ensuremath{\sigma} have been measured as a function of level difference $z$ and height to the beaker rim $h$ for filling clean glass and neon-coated beakers. Observed transfer rates as a function of level difference or pressure head are described by: $\ensuremath{\sigma}(z)=\frac{1}{[A\ensuremath{-}B\mathrm{ln}z(\mathrm{cm})]}$. For $T=1.65$ K and $h=7$ cm, we find $A=(1.80\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{4}$ sec/${\mathrm{cm}}^{2}$ and $B=(8.9\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}{10}^{2}$ sec/${\mathrm{cm}}^{2}$. For $T=1.28$ K and $h=7$ cm, we find $A=(1.35\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{4}$ sec/${\mathrm{cm}}^{2}$ and $B=(8.3\ifmmode\pm\else\textpm\fi{}1.4)\ifmmode\times\else\texttimes\fi{}{10}^{2}$ sec/${\mathrm{cm}}^{2}$. Dependence of the transfer rate on film height is $\ensuremath{\sigma}(h)=10(\frac{{\ensuremath{\rho}}_{s}}{\ensuremath{\rho}}){h}^{\ensuremath{-}(0.26\ifmmode\pm\else\textpm\fi{}0.05)}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{3}$. For a glass beaker coated with Ne, the transfer rate is 16% less than the transfer rate for the same uncoated beaker. This is in reasonable agreement with our calculated helium-film thickness for a Ne substrate of $2.3 {h}^{\ensuremath{-}\frac{1}{3}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ cm.

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