Discrete potential fluids in the supercritical region

Competing interactions near the liquid-liquid phase transition of core-softened water/methanol mixtures

“…From a practical point of view, one can investigate the location of a critical point through an analysis of the the thermodynamic response functions in region above the LLCP. For instance, the isothermal compressibility and hence the correlation length, display a line of maxima in the P-T plane (Widom's line) that typically ends at a critical point with where the maximum evolves into a divergence in the thermodynamic limit [29,30,31,32,33,34]. Correspondingly, for water in addition to a Widom line ending at the vapor-liquid critical point, there is evidence of a second one that should end at the LLCP [35,36,37,38,39,40,41].…”

Widom and extrema lines as criteria for optimizing operating conditions in supercritical processes

“…These end point coordinates are estimated using a quantitative criterion which involves the difference between the temperature maxima of isothermal compressibility (Tb max) and the temperature maxima of isobaric heat capacity (TCp max): DT = Tb max -TCp max. Moving along the Widom line of carbon dioxide, the end point locus corresponds to DT = 0.001T c according to Zeron et al [14] or to DT = 0.005T c according to De Jesus et al [13], where Tc is the critical temperature of the compound.…”