Transport Properties of Critical Sulfur Hexafluoride From Multiscale Analysis of Density Fluctuations

Abstract

Density fluctuations near critical points have a wide range of sizes limited only by the boundaries of the enclosing container. How would a fluctuating image near the critical point look if we could break it into disjoint spatial scales, like decomposing white light into narrow-band, monochromatic waves? What are the scaling laws governing each spatial scale? How are the relaxation times of fluctuations at each spatial scale related to the dynamics of fluctuations in the original image? Fluctuations near the critical point of pure fluids lead to different patterns of phase separation, which has a significant influence on the materials’ properties. Due to the diverging compressibility of pure fluids near the critical temperature, the critical phase collapses under its weight on Earth. It limits both the spatial extent of fluctuations and their duration. In microgravity, the buoyancy and convection are suppressed, and the critical state can be observed much closer to the critical point for a more extended period. Local density fluctuations induce light intensity fluctuations (the so-called “critical opalescence”), which we recorded for a sulfur hexafluoride (SF6) sample near the critical point in microgravity using the ALI (Alice Like Instrumentation insert) of the DECLIC (Dispositif pour l’Etude de la Croissance et des Liquides Critiques) facility on the International Space Station (ISS). From the very short (approximately 173 s total recording) data set very near, within 200 μK, the critical temperature, we determined the effective diffusion coefficient for fluctuations of different sizes. For transient and non-stationary data recorded very near the critical point immediately after a thermal quench that steps through critical temperature, we separated fluctuations of various sizes from the original images using the Bidimensional Empirical Mode Decomposition (BEMD) technique. Orthogonal and stationary Intrinsic Mode Function (IMF) images were analyzed using the Fourier-based Dynamic Differential Microscopy (DDM) method to extract the correlation time of fluctuations. We found that a single power-law exponent represented each IMF’s structure factor. Additionally, each Intermediate Scattering Function (ISF) was determined by fluctuations’ unique relaxation time constant. We found that the correlation time of fluctuations increases with IMF’s order, which shows that small size fluctuations have the shortest correlation time. Estimating thermophysical properties from short data sets affected by transient phenomena is possible within the BEMD framework