Motion of tracer particles in He II

Recent experiments have shown that it is possible to implement particle image velocimetry (PIV) in liquid helium. However, to interpret the PIV data in the superfluid phase, it is necessary to understand how the particles are affected by the two components, the viscous normal fluid and the inviscid superfluid, as well as by the quantized vortex lines that may exist in the superfluid component. After setting up the governing equations of motion, we first solve them in some simple cases in order to gain physical insight, and then we formulate semiquantitative general arguments relating to turbulent flow, with the assumption initially that particle trapping by vortex lines does not occur. We find that a number of different but simple regimes can be identified if the particles are neutrally buoyant: in some regimes the particles trace the normal fluid, in others the superfluid, and in others the total mass current. A numerical analysis for a model two-dimensional flow reveals an instability that requires some modification of these conclusions. It is then shown that particle trapping on vortex lines can be important and can lead to serious modification of our conclusions. The results of our analysis are used to discuss what types of superfluid flow can usefully be studied by PIV, and to suggest the most appropriate size and mass of the tracer particles.