We present results of numerical study of motion of micron-size, neutrally buoyant, solid particles in liquid helium at temperatures small enough that the normal fluid is negligible and turbulence manifests itself as a tangle of superfluid line vortices. Based on dynamically self-consistent model of interaction between a solid particle and the quantized vortex, we analyze first an influence of temperature on particle trapping on the vortex core. We find that the particle can be trapped only in the case where the particle experiences the damping force, such as the viscous drag force exerted by the normal fluid. However, at temperature below 0.7K, when the normal fluid is practically absent, the moving particle still experiences the damping force caused by the ballistic scattering of quasiparticles (phonons and rotons) off the particle surface. Using, together with our calculation of close interaction between the particle and the quantized vortex, available experimental data and theoretical results for this force, we show that trapping of micron-size, neutrally buoyant particles on quantized vortices becomes impossible at temperatures below 0.5K. At such temperatures, the particle motion in the vortex tangle can be studied based on the simpler, “one-way coupling” model ignoring the backreaction of the particle on the motion and evolution of quantized vortices. Based on such a model, we present results of numerical calculation of particle trajectories in the vortex tangle and show that, due to instability of trajectories and the mismatch of initial velocities of particles and the fluid, the motion of inertial particles does not reveal the motion of turbulent superfluid. We show that particle trajectories between vortex cores are ballistic. Interaction of particles with moving vortices leads to increase of the average particle velocity until it saturates at the value much larger than the fluid rms velocity. These results prevent the use of small tracer particles to study vortex tangles at low temperatures, but open to investigation a new and remarkably simple model of Lagrangian turbulence. We present the probability density function of the turbulent velocity and show that the particle velocity spectrum obeys a simple scaling law.

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