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Register a new userDensity pattern in supercritical flow of liquid He-4
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Added by
Francesco Ancilotto
Publication date
2004
fields
Physics
and research's language is
English
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A density functional theory is used to investigate the instability arising in superfluid $^4$He as it flows at velocity u just above the Landau critical velocity of rotons v_c. Confirming an early theoretical prediction by one of us [JETP Lett. 39, 511 (1984)], we find that a stationary periodic modulation of the density occurs, with amplitude proportional to (u-v_c)^{1/2} and wave vector equal to the roton wave vector. This density pattern is studied for supercritical flow both in bulk helium and in a channel of nanometer cross-section.
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We show that, at high densities, fully variational solutions of solid-like type can be obtained from a density functional formalism originally designed for liquid 4He. Motivated by this finding, we propose an extension of the method that accurately describes the solid phase and the freezing transition of liquid 4He at zero temperature. The density profile of the interface between liquid and the (0001) surface of the 4He crystal is also investigated, and its surface energy evaluated. The interfacial tension is found to be in semiquantitative agreement with experiments and with other microscopic calculations. This opens the possibility to use unbiased DF methods to study highly non-homogeneous systems, like 4He interacting with strongly attractive impurities/substrates, or the nucleation of the solid phase in the metastable liquid.
We compute the zero-temperature dynamical structure factor of one-dimensional liquid $^4$He by means of state-of-the-art Quantum Monte Carlo and analytic continuation techniques. By increasing the density, the dynamical structure factor reveals a transition from a highly compressible critical liquid to a quasi-solid regime. In the low-energy limit, the dynamical structure factor can be described by the quantum hydrodynamic Luttinger liquid theory, with a Luttinger parameter spanning all possible values by increasing the density. At higher energies, our approach provides quantitative results beyond the Luttinger liquid theory. In particular, as the density increases, the interplay between dimensionality and interaction makes the dynamical structure factor manifest a pseudo {it{particle-hole}} continuum typical of fermionic systems. At the low-energy boundary of such region and moderate densities, we find consistency, within statistical uncertainties, with predictions of a power-law structure by the recently-developed non-linear Luttinger liquid theory. In the quasi-solid regime we observe a novel behavior at intermediate momenta, which can be described by new analytical relations that we derive for the hard-rods model.
Formation of vortex rings around moving spherical objects in superfluid He-4 at 0 K is modeled by time-dependent density functional theory. The simulations provide detailed information of the microscopic events that lead to vortex ring emission through characteristic observables such as liquid current circulation, drag force, and hydrodynamic mass. A series of simulations were performed to determine velocity thresholds for the onset of dissipation as a function of the sphere radius up to 1.8 nm and at external pressures of zero and 1 bar. The threshold was observed to decrease with the sphere radius and increase with pressure thus showing that the onset of dissipation does not involve roton emission events (Landau critical velocity), but rather vortex emission (Feynman critical velocity), which is also confirmed by the observed periodic response of the hydrodynamic observables as well as visualization of the liquid current circulation. An empirical model, which considers the ratio between the boundary layer kinetic and vortex ring formation energies, is presented for extrapolating the current results to larger length scales. The calculated critical velocity value at zero pressure for a sphere that mimics an electron bubble is in good agreement with the previous experimental observations at low temperatures. The stability of the system against symmetry breaking was linked to its ability to excite quantized Kelvin waves around the vortex rings during the vortex shedding process. At high vortex ring emission rates, the downstream dynamics showed complex vortex ring fission and reconnection events that appear similar to those seen in previous Gross-Pitaevskii theory-based calculations, and which mark the onset of turbulent behavior.
We study the response of one-dimensional liquid $^4$He to weak perturbations relying on the dynamical structure factor, $S(q,omega)$, recently obtained via ab-initio techniques [Phys. Rev. Lett. 116, 135302 (2016)]. We evaluate the drag force, $F_v$, experienced by an impurity moving along the system with velocity $v$ and the static response function, $chi(q)$, describing the density modulations induced by a periodic perturbation with wave vector $q$.
The transition to turbulence in the boundary flow of superfluid $^4$He is investigated using a vortex--free vibrating wire. At high wire vibration velocities, we found that stable alternating flow around the wire enters a turbulent phase triggered by free vortex rings. Numerical simulations of vortex dynamics demonstrate that vortex rings can attach to the surface of an oscillating obstacle and expand unstably due to the boundary flow of the superfluid, forming turbulence. Experimental investigations indicate that the turbulent phase continues even after stopping the injection of vortex rings, which is also confirmed by the simulations.
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