Intrinsic critical velocities in superfluid⁴He flow through 12-μm diameter orifices near T_λ: Experiments on the effect of geometry

Abstract

We report super fluid⁴He flow measurements at temperatures from 1.2 K up to T_λ — 3 mK in three orifices of different mesoscopic geometry. Under conditions of our experiments, the flow usually reaches a temperature-dependent intrinsic critical velocity, where dissipation is believed to occur by thermal (or quantum) nucleation of individual quantized vortex rings or loops. The nucleation rate should be sensitive to the wall geometry of the flow channel and to any local velocity enhancement at the most favorable nucleation site. According to the Iordanskii-Langer-Fisher (ILF) theory, the radius of the “critical” vortex ring, the threshold size which can grow freely by extracting energy from the flow, increases inversely as the superfluid density on approach to the superfluid onset temperature, T_λ. Thus sufficiently near T_λ the critical ring should be large enough that the geometry relevant to the nucleation process and local velocity enhancement can be studied by scanning electron microscope (SEM). We examined our three orifices by SEM. One, a standard optical pinhole, has a relatively smooth taper on one side and a sharp lip on the other. The second is similar, but contains a 1-μm flake perpendicular to the flow, which should provide additional velocity enhancement at its edge. In the third, the sharp lip is beveled to reduce the velocity enhancement at that site. Contrary to expectation, the intrinsic critical velocities are the same, within a relative calibration error of 10%, in all three cases. Thus, local sites of enhanced velocity do not appear to be active in nucleating vortices. This raises a question whether the classical two-fluid model which underlies the ILF calculation is adequate to describe the superfluid hydro-dynamics near walls, as it affects the vortex nucleation process.