Quantum Crystal Oscillations in a Superfluid Liquid

Abstract

We study the hydrodynamics of quantum 4 He crystal oscillations in a superfluid liquid with involving the dynamics of atomically rough surfaces. It is shown that, due to enhancement of the kinetic growth coefficient as the temperature lowers, the reaction force of the liquid applied to the 4 He crystal changes its character from the inertial to viscous one vanishing as T → 0. The model is confirmed by the experiments on the oscillations of the 4 He crystal within the temperature range 0.54-1.43 K at frequencies 484 and 211 Hz. A new type of hydrodynamic instability is found. The instability occurs provided that the oscillation amplitude of the velocity becomes higher than ∼ 3 cm/sec.

The Effect of the Interphase Kinetics on the Motion of a Quantum Crystal in Superfluid Liquid

“…In experiments [5] the crystal oscillations occur with the amplitude much smaller than the crystal size. In this case the quadratic terms in Eqs.…”

“…In this approximation the shape of the crystal during its growth under influence of the fluid flow will evolve, tracking only the phase nonequilibrium at the liquid-crystal interface. The initial shape of the crystal is approximated as spherical, this shape being above the roughening transitions [4]. At ∼ 0.1K the concentration of the normal component of liquid helium is negligible.…”

“…(4) Here − → v is the velocity of the liquid, ϕ is the velocity potential and z is the coordinate axis directed vertically upwards. The boundary conditions read [5,18]…”

“…In paper [5] the crystal is placed on the crossbar of the U-shaped superconducting loop. The crystal is either pierced by the crossbar or placed on the platform mounted on the crossbar.…”

Falling4He crystals in superfluid

“…A few experiments have been performed to investigate the effect of superflow [12,13], however, it is not easy to induce a uniform and stable superflow experimentally. It is intriguing to see how the crystal shape of 4 He is changed by crystallization and melting when subjected to a superflow, responding almost instantaneously to the surrounding superflow due to the high crystal growth rate.…”