Dynamics of solid particles in a tangle of superfluid vortices at low temperatures

Abstract

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 0.7 K, when the normal fluid is practically absent, the moving particle still experiences the damping force caused by the ballistic scattering of quasiparticles ͑phonons and rotons͒ 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 0.5 K. 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.

Toy model for vortex-ring-assisted particle drag in superfluid counterflow

“…Due to inertia, however, the initial particle's backward motion will develop along evolution time scales which are much larger than the ones for the vortex dipole, which, then decouples from the particle. Its worth emphasizing that an analogous connection between small viscous dissipation and the suppression of particle trapping in quantum vortices has been previously noticed from three-dimensional numerical simulations of particle dynamics in vortex tangles [30].…”

“…Our analysis is inspired by superfluid counterflow regimes similar to the ones investigated in experiments [27,28,33] and numerical simulations [30,31]. We mean approximately equal mass densities ρ n and ρ s for the normal and superfluid components of the condensate, respectively, a condition realized at temperatures close to 2 K, and spherical tracking particles with radii around 2.5 µm.…”

“…A theoretical account of the v n /2 velocity peak has been given by Sergeev et al [29], from the assumption that tracking particles could form bound states with vortex rings. In this connection, it has been known that collisions between quantum vortices and particles can produce small vortex rings [30,31], a possible initial stage for the formation of such states.…”

Energy spectra of finite temperature superfluid helium-4 turbulence

“…That the combination of the above reconnection model with the particular α and β values work as expected in practice was shown in Ref. 24. Indeed, in this work, in order to keep a constant tangle length during a T = 0 K computation, thus, to compensate for reconnection induced losses, an energy injection into the system in the form of superfluid vortex rings had to be applied.…”

Spreading of superfluid vorticity clouds in normal-fluid turbulence

“…Since GrossPitaevskii fluid dynamics studies have shown that reconnections transform some of the kinetic flow energy into acoustic energy (Parker et al 2004), one expects that Schwarz surgery would, in effect, be a dissipative process at large incompressible scales. For the particular surgery employed here, this was shown to be the case, since Kivotides, Sergeev & Barenghi (2008b) had to force the superfluid vortex tangle in order to achieve a state with statistically constant length, L, at temperature T = 0 K. Overall, Schwarz surgery is a heuristic model of refined microscopic physics. The same holds for its application in the formulation of the vortex tube model of classical incompressible turbulence, where it models subgrid viscous reconnection physics (Kivotides & Leonard 2003).…”