Critical velocities in ³-⁴He mixtures below 100 mK

Hydrodynamic properties of dilute mixtures of ³He and ⁴He were investigated below 100 mK by measuring the thermodynamic properties of the solution in various flow impedances as functions of the ³He velocity. The ⁴He component in the impedances was practically always macroscopically at rest. If the flow impedances consisted of a bundle of metal or glass capillaries, a distinct critical velocity was observed above which the ³He chemical-potential difference across the impedance was nonzero. The critical velocity of capillaries with diameter d roughly follows a ln(d)/d dependence. In the critical-velocity region, the amplitude of the pressure fluctuations was observed to be relatively large and strongly velocity dependent. The characteristic time for transient effects in the flow system changed abruptly at the critical velocity. There are indications for the existence of a second critical velocity. In flow impedances with an annular cross section, no critical velocities were observed.