Dynamic equilibrium under vibrations of H₂ liquid-vapor interface at various gravity levels

Turbidity data obtained from image analysis in near critical hydrogen

Video images are being used with increased frequency in science, supplanting current methods such as light scattering by statistical evaluation of the images. In this study we use light turbidity data due to density-induced refractive index fluctuations to obtain critical amplitudes from image analysis. In order to bring hydrogen (H_{2}) very close to its critical point, we place the sample cell under weightlessness using a magnetic levitation device. Images of an H_{2}-filled cell are taken near its critical temperature of 33 K by illuminating the cell with three different filters. We fit the turbidity data to a theoretical expression that allows us to estimate the critical amplitudes of isothermal compressibility and fluctuation correlation length. The values of isothermal compressibility and correlation length obtained from turbidity fitting are compared against literature values. Our data analysis shows a large sensitivity of the fitting parameters to the refractive index value and to even minute density deviations from criticality.

Interfacial fluid instabilities and Kapitsa pendula

The onset and development of instabilities is one of the central problems in fluid mechanics. Here we develop a connection between instabilities of free fluid interfaces and inverted pendula. When acted upon solely by the gravitational force, the inverted pendulum is unstable. This position can be stabilized by the Kapitsa phenomenon, in which high-frequency low-amplitude vertical vibrations of the base creates a fictitious force which opposes the gravitational force. By transforming the dynamical equations governing a fluid interface into an appropriate pendulum-type equation, we demonstrate how stability can be induced in fluid systems by properly tuned vibrations. We construct a "dictionary"-type relationship between various pendula and the classical Rayleigh-Taylor, Kelvin-Helmholtz, Rayleigh-Plateau and the self-gravitational instabilities. This makes several results in control theory and dynamical systems directly applicable to the study of tunable fluid instabilities, where the critical wavelength depends on the external forces or the instability is suppressed entirely. We suggest some applications and instances of the effect ranging in scale from microns to the radius of a galaxy.