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

We use a multiscale approach to investigate the dynamics of fluctuations near the critical point of sulfur hexafluoride (SF6) in microgravity. Rather than increasing the fitting model’s complexity during the critical temperature crossing, we used a different approach to finding the thermal diffusivity coefficient (above critical temperature), which can then be distinguished from an effective diffusion coefficient (below critical temperature). We first separate different spatial scales from the original images using the Bidimensional Empirical Mode Decomposition (BEMD) technique. The spatial scale represented by an Intrinsic Mode Function (IMF) image was analyzed using the Dynamic Differential Method (DDM). The Intermediate Scattering Function (ISF) of each IMF was used for computing the structure factor and the relaxation time of fluctuations. We found that the first IMF returns over 90% of the spatial and temporal knowledge contained in the original image, providing thus thermal diffusivity coefficient above the critical temperature and effective diffusion coefficients below the critical temperature very close in magnitude. The relaxation time associated with the distinguishable structures observed in the second IMF could be attributed to the fractal nature of fluctuations. and to light scattering at low wavenumber during the stationary behavior and the transient evolution of the critical fluid cell, which are not easy to detect in the original image. The third order IMF presents no noticeable structure, and the associated relaxation time is not physically significant.