Dynamic structure factor of density fluctuations from direct imaging very near (both above and below) the critical point of SF6

Abstract

Large density fluctuations were observed by illuminating a cylindrical cell filled with sulfur hexafluoride (SF(6)), very near its liquid-gas critical point (|T-T(c)|< 300 μK) and recorded using a microscope with 3 μm spatial resolution. Using a dynamic structure factor algorithm, we determined from the recorded images the structure factor (SF), which measures the spatial distribution of fluctuations at different moments, and the correlation time of fluctuations. This method authorizes local measurements in contrast to the classical scattering techniques that average fluctuations over the illuminating beam. We found that during the very early stages of phase separation the SF scales with the wave vector q according to the Lorentzian q(-2), which shows that the liquid and vapor domains are just emerging. The critical wave number, which is related to the characteristic length of fluctuations, steadily decreases over time, supporting a sustained increase in the spatial scale of the fluctuating domains. The scaled evolution of the critical wave number obeys the universal evolution for the interconnected domains at high volume fraction with an apparent power law exponent of -0.35 ± 0.02. We also determined the correlation time of the fluctuations and inferred values for thermal diffusivity coefficient very near the critical point, above and below. The values were used to pinpoint the crossing of T(c) within 13 μK.

Multiscale empirical mode decomposition of density fluctuation images very near above and below the critical point of SF6

“…The critical temperature resulted somewhere between the upper (UP, i.e., T > T c ) plateau and the lower (DOWN, 100 i.e., T < T c ) one (Fig. 1), and its exact location was previously determined with the histogram method in [17] and by using DDM in [5].…”

“…1A. The full description of this last temperature quench was already presented elsewhere [5,17]. The fluid volume observation during the two hours of the relaxation period following the final 0.3 mK temperature quench revealed unambiguous nonhomogeneous liquid 95 and gas domains within the sample fluid image, which were due to the SF 6 phase separation.…”

“…Hereafter we are only interested in the sample observation recorded during the last, fast 0.3 mK thermal quench, which starts from the homogeneous domain 90 above the critical temperature to finish into the two-phase region below critical temperature [5,17], as shown in the inset of Fig. 1A.…”

“…Dynamic Differential Microscopy (DDM) is an appealing experimental technique to extract the relaxation time of dynamical phenomena [1,2,3,4]. It has recently been applied to critical density fluctuations from light scattering images of systems approaching the liquid-gas critical point of pure fluids from the 5 homogeneous domain [5]. In such experiments, the image processing performed with the dynamic structure factor (DSF) algorithm produces results consistent with the modern theory of critical phenomena.…”

Pattern Evolution during Double Liquid-Vapor Phase Transitions under Weightlessness

“…The focus of this paper is on investigating the phase separation process that takes place after the supercritical SF 6 sample is brought from an initial state, which is already in a liquid-vapor two-phase state slightly below the critical temperature, to a temperature 0.2 mK below its initial temperature by a temperature quench [ 4 , 5 ]. Generally, phase separation could occur in a classical mean-field approach via two mechanisms: nucleation and spinodal decomposition, respectively [ 6 , 7 , 8 , 9 ].…”