Critical asymmetry in renormalization group theory for fluids

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Fluid Dynamics

Background:

• Vapor-liquid equilibrium (VLE) critical asymmetry is a key phenomenon in fluid thermodynamics.
• Renormalization-group (RG) theory provides a powerful framework for studying critical phenomena in fluids.
• Understanding VLE critical asymmetry is crucial for accurate fluid modeling and phase behavior prediction.

Purpose of the Study:

• To investigate the critical asymmetry of vapor-liquid equilibrium (VLE) in fluids using renormalization-group (RG) approaches.
• To review and compare three different RG approaches for fluid systems.
• To assess the capability of RG theory in describing VLE critical asymmetry for various fluid models and n-alkanes.

Main Methods:

• Application of three distinct RG approaches to model fluid systems.
• Analysis of phase diagrams for hard-core square-well fluids, hard-core Yukawa fluids, and square-well dimer fluids.
• Modeling VLE of n-alkane molecules using RG theory.
• Comparison of RG results with simulation and experimental data.

Main Results:

• RG approaches successfully describe thermodynamic properties and VLE critical asymmetry for several fluid systems, showing agreement with experimental and simulation data.
• Coexistence diameters smaller than critical densities were observed in RG descriptions of critical asymmetries.
• An RG approach coupling local free energy with White's RG iteration was found inadequate for VLE critical asymmetry.

Conclusions:

• RG theory is a valuable tool for investigating VLE critical asymmetry in fluids.
• The choice of order parameter and local free energy functional is critical for the success of RG approaches in describing VLE critical asymmetry.
• Further refinement of RG methods is needed to accurately capture VLE critical asymmetry in all fluid systems.