Superfluids are characterised by being described by an immiscible mixture of two fluids: a normal fluid, that is viscous and a superfluid with no viscosity. When a superfluid is heated on one side of a channel, the normal fluid carries the heat away, and the superfluid flows in the opposite direction to conserve the mass. Such a situation generates an out-of-equilibrium state where the two fluids have a non-zero mean relative velocity, known as counterflow.

Quantum vortices are one of the most important excitations of a superfluid. Such vortices behaves in many aspects as they classical counterpart. They reconnect changing the topology of the flow and transferring energy along scales. We have recently observed that in quantum fluids, there is a manifest irreversibility in the process. Using numerical simulations of the Gross-Pitaevskii model and developing a matching theory we have been able to characterise the momentum and energy exchanges between vortices and density waves.

Particles are used in superfluid to visualise quantum vortices, they get trapped inside vortices, and we can follow their dynamics. Quantum vortices can reconnect, and particles are an essential tool to study the process.

In this paper we study how finite size active particles modify the development of quantum turbulence and how different is their Lagrangian statistics from the classical case.

For more than 10 years, quantum vortices have been visualised in superfluid helium by using hydrogen and deuterium ice particles. Their size is of some micrometers that is much larger than the atomic size of the vortex core. Because particles are big and heavy, they interact with the vortices in a complex and yet not fully understood manner. In this work we study how well such particles sample the movement of quantum vortices.

Particles are today the main tool to study superfluid turbulence and visualize quantum vortices. This work studies the dynamics of inertial particles in finite-temperature quantum turbulence in the framework of the two-fluid Hall-Vinen-Bekarevich-Khalatnikov model. It is revealed that, at low temperatures, when the superfluid mass fraction is dominant, particles cluster on superfluid vortex filaments regardless of their physical properties as it is shown in the figure. Furthermore, under strong counterflow, the flow is dominated by quasi-two-dimensional large-scale structures that govern the spatial distribution of particles.