Surface vibrations of aHe4droplet and the universality of the dispersion relation

Abstract

By applying the liquid-drop model to a 4 He droplet, we derive the universal dispersion relation for the droplet vibrations. Considering the eigenvalue equation for the coupled modes of surface vibrations and inner vibrations, the universality is clarified by using an effective wave number. It is shown that our universal dispersion curve for the surface modes traces well the eigenfrequencies obtained by several workers and provides benchmarks for the various methods of computer simulations.

Energetic study of ultrasonic wettability enhancement

“…This equation describes the resonant frequencies (ω) of a liquid droplet as a function of its surface tension (γ), mass (m) and an integer number (n). With the advance in computational fluid dynamic (CFD) simulation techniques, not only the resonant frequencies but also the modal shape of the droplet has been predicted by authors such as Dong [9] and Tamura [10] . They studied the vibration modes of a sessile water droplet under vibration.…”

Density of states of helium droplets

“…The upper limit, ℓ max , has been set to infinity as before. The actual value is on the order of ℓ max ≈ 2πR/λ min ≈ 2πR/(2d), where λ is the wavelength and d is the interatomic distance [4]. In the liquid drop approximation (R = N 1/3 d/2) one then has ℓ max ≈ πN 1/3 /2.…”

Microcanonical thermodynamic properties of helium nanodroplets

“…Each normal node can be characterized by a wave number k n,L which is determined by k n,L ϭr n,L /R, where r n,L is the nth root of the spherical bessel function j L . 26 For k n,L Ӷ1 Å Ϫ1 ͑i.e., much smaller than the wave number of a roton͒, the excitation angular frequency of each mode is given by n,L ϭuk n,L , where uϭ236 m/s is the speed of sound in helium. 26 We define a reduced energy E p with an energy unit equal to the excitation energy of the lowest (nϭ1,Lϭ0) phonon which is បu…”