Instability of trajectories of solid particles around vortex lines

Progress in implementing the particle image velocimetry visualization technique in liquid helium has stimulated interest in understanding the dynamics of micron-size solid particles in a superfluid. We show that at sufficiently low temperatures, in the limit of a pure superfluid, the trajectories of small, neutrally buoyant, solid particles are unstable and deviate from the trajectories of superfluid particles, even in the simplest case of the motion around a single stationary straight vortex line. The result also applies to classical Euler flows. The implications of this result for the visualization of turbulent superflow at very low temperatures are discussed.