Non-equilibrium stratification in supercritical CO₂

Supercritical matter is commonly described as a continuous phase lacking sharp boundaries between liquid-like and gas-like regions. Under non-equilibrium conditions, however, this picture may fail. Here, we experimentally investigate non-equilibrium density fluctuations in supercritical carbon dioxide (CO₂) subjected to a stabilizing temperature gradient. Using shadowgraphy, we observe the spontaneous emergence of fluid stratification into distinct layers separated by transition regions, across which thermodynamic properties vary sharply. These signatures become particularly pronounced as the system crosses the Widom lines, where thermodynamic response functions exhibit extrema in the supercritical regime. Analysis of the structure function of fluctuations reveals Brunt-Väisälä oscillations at multiple frequencies, revealing gravity-driven coupling between thermal and viscous modes and direct evidence of hydrodynamic stratification. Our approach enables systematic exploration of a broad range of thermodynamic states within a single experiment. Altogether, these findings indicate that far from remaining homogeneous, the Widom region develops structured dynamical heterogeneity under non-equilibrium conditions.