Flow of Superfluid Helium through a Bed of Large Angular Particles

In several different theoretical models, the critical velocity for onset of dissipation in superfluid flow through a packed bed of particles appears as a condition for escape of segments of quantized vortex line pinned between particles. This condition has essentially the form of the Feynman critical velocity based on particle diameter $d$; thus the predicted critical velocity is of order $\frac{h}{\mathrm{md}}$ and is independent of temperature. This is in accord with the well-known increase in critical velocity when a tube is packed with fine powder, but predicts a decrease for coarse powder. Measurements of superfluid flow through a glass tube constricted to 390-μm diam and packed with 35-μm silicon-carbide grains give a critical velocity of 1.6 cm ${\sec }^{-1\mathrm{}}$, nearly constant over the temperature range $1.35<T<\mathrm{}2.13\mathrm{}$ K. This is considerably slower than the flow observed in the empty tube (at least for $\Delta p\gtrsim 0.1$ dyne ${\mathrm{cm}}^{-2\mathrm{}}$). The results are not sensitive to the vortex nucleation or regeneration processes, which would distinguish between theoretical models.