Similarity law for Widom lines and coexistence lines

Area of Science:

• Thermodynamics
• Fluid Mechanics
• Physical Chemistry

Background:

• The Widom line delineates liquid-like and gas-like regions in supercritical fluids, crucial for predicting fluid properties.
• Current methods using critical pressures and temperatures fail to universally describe the Widom line across different substances.
• Accurate representation of coexistence and Widom lines is vital for sub- and supercritical applications.

Purpose of the Study:

• To demonstrate that the Widom line adheres to the extended corresponding states principle, not the traditional one.
• To develop a new scaling parameter for the Widom line that universally applies to various fluids.
• To provide a theoretical basis for comparing Widom lines across different chemical species.

Main Methods:

• Derived a Widom line functional using the Clapeyron equation and the Soave-Redlich-Kwong equation of state.
• Developed an analytical expression for a species-specific parameter dependent on the acentric factor.
• Introduced a scaled reduced pressure, p_{r}*, as a replacement for the reduced pressure, p_{r}=p/p_{cr}.

Main Results:

• The derived parameter correlates well with experimental data and depends on the acentric factor.
• The scaled reduced pressure, p_{r}*, collapses both subcritical coexistence and supercritical Widom line data for a wide range of fluids.
• p_{r}* is solely a function of the acentric factor, simplifying its determination from fluid property tables.

Conclusions:

• The extended corresponding states principle, applied via p_{r}*, offers a unified framework for describing fluid phase behavior.
• The new scaling parameter provides a robust method for comparing Widom lines across diverse chemical species.
• This work enhances the predictive accuracy of fluid properties in both subcritical and supercritical regimes.