Critical Velocities and Boundary Interactions in the Isothermal Flow of Superfluid Helium

Abstract

The pressure gradient as a function of the superfluid velocity in a 1.1-mm-diam capillary has been measured at four temperatures between 1.26 and 1.57\ifmmode^\circ\else\textdegree\fi{}K. In the flow tube the normal fluid was held at rest by ultrafine porosity filters, while the superfluid flowed isothermally. Superconducting microwave cavities were used as level indicators, making it possible to detect pressure gradients as small as 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ dyn/${\mathrm{cm}}^{3}$. A critical superfluid velocity, below which no pressure gradient could be detected, was observed directly. The critical velocity decreased linearly with temperature, being 1.25 mm/sec at 1.26\ifmmode^\circ\else\textdegree\fi{}K, and 0.85 mm/sec at 1.57\ifmmode^\circ\else\textdegree\fi{}K. For a superfluid velocity ${v}_{s}$ greater than the critical velocity ${v}_{c}$, the variation of the pressure gradient with velocity could be described by ${\ensuremath{\alpha}}_{2}{v}_{s}({v}_{s}\ensuremath{-}{v}_{c})$ or ${\ensuremath{\alpha}}_{1}{({v}_{s}\ensuremath{-}{v}_{c})}^{1.7}$, where ${\ensuremath{\alpha}}_{1}$ and ${\ensuremath{\alpha}}_{2}$ are constants that vary with temperature. It is believed that this represents an interaction between vorticity in the superfluid and the wall of the flow tube.