Interaction between active particles and quantum vortices leading to Kelvin wave generation

Abstract

One of the main features of superfluids is the presence of topological defects with quantised circulation. These objects are known as quantum vortices and exhibit a hydrodynamic behaviour. Nowadays, particles are the main experimental tool used to visualise quantum vortices and to study their dynamics. We use a self-consistent model based on the three-dimensional Gross-Pitaevskii (GP) equation to explore theoretically and numerically the attractive interaction between particles and quantized vortices at very low temperature. Particles are described as localised potentials depleting the superfluid and following Newtonian dynamics. We are able to derive analytically a reduced central-force model that only depends on the classical degrees of freedom of the particle. Such model is found to be consistent with the GP simulations. We then generalised the model to include deformations of the vortex filament. The resulting long-range mutual interaction qualitatively reproduces the observed generation of a cusp on the vortex filament during the particle approach. Moreover, we show that particles can excite Kelvin waves on the vortex filament through a resonance mechanism even if they are still far from it.

How trapped particles interact with and sample superfluid vortex excitations

“…See Refs. [20,22] and the next section for further details about the model. The equations of motion for the superfluid field ψ and the particle positions…”

“…In the same context, an alternative possibility is to assume classical degrees of freedom for the particles, while the superfluid is still a complex field obeying the Gross-Pitaevskii equation. This idea of modeling particles as simple classical hard spheres has been shown to be both numerically and analytically very powerful [19][20][21][22]. In particular, such minimal and self-consistent model allows for simulating a relatively large number of particles, and describes well the particle-vortex interaction [22].…”

“…This idea of modeling particles as simple classical hard spheres has been shown to be both numerically and analytically very powerful [19][20][21][22]. In particular, such minimal and self-consistent model allows for simulating a relatively large number of particles, and describes well the particle-vortex interaction [22]. Although formally valid for weakly interacting BECs, it is expected to give a good qualitative description of superfluid helium.…”

Validation of Nanoparticle Response to the Sound Pressure Effect during the Drug-Delivery Process

“…The impact of acoustic field settings and assembling process parameters on the design was described [5]. Moreover, particles can energize Kelvin waves on the vortex fiber through a reverberation instrument regardless of their distance [6]. The arrangement of the Navier-Stirs condition for an incompressible liquid based on the following two numerical strategies was proposed: a direct numerical simulation (DNS) in the light of a ghastly component strategy; and a pitifully non-straight plan (WNF) in the light of a limited component technique [7].…”

Inhomogeneous distribution of particles in coflow and counterflow quantum turbulence

“…In a superfluid, the situation is more complex as particles interact in a non trivial manner with both components of the superfluid [15]. For instance, at low temperatures when the fraction of normal fluid is negligible, particle dynamics is dominated by pressure gradients leading to their trapping by quantum vortices [3,16,17]. At temperatures where the normal and superfluid densities are comparable, particles experience a competition of different physical effects, as they also respond to a viscous Stokes drag from the normal component.…”