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Generalized approach to global renormalization-group theory for fluids.

A Sai Venkata Ramana¹, S V G Menon

¹Theoretical Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India. asaivenk@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 12, 2012

Summary

A new global renormalization-group theory (GRGT) for fluids accurately models density fluctuations. This advanced GRGT approach avoids Maxwell

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Area of Science:

Statistical Mechanics
Physical Chemistry
Computational Fluid Dynamics

Background:

Traditional fluid theories often rely on approximations for density fluctuations.
Existing global renormalization-group theory (GRGT) models have limitations, such as assuming cosine variation of density fluctuations.
Accurate modeling of fluid behavior across all length scales is crucial for understanding phase transitions.

Purpose of the Study:

To derive a more general global renormalization-group theory (GRGT) for fluids.
To relax assumptions made in previous GRGT formulations regarding density fluctuations.
To develop a theory that inherently accounts for fluctuations and avoids empirical constructions like Maxwell's.

Main Methods:

Derivation of GRGT using the square-gradient approximation for the Helmholtz free energy functional.
Utilization of Wilson's functions to represent density fluctuations, removing the cosine variation constraint.
Application of the derived GRGT to model square-well and Lennard-Jones fluids.

Main Results:

The new GRGT formulation successfully produces a flat isotherm in the two-phase region, indicating accurate fluctuation modeling.
The theory naturally incorporates fluctuations across all length scales, eliminating the need for Maxwell's construction.
Analysis of phase diagrams and critical constants for various potentials shows good agreement with simulation and experimental data.

Conclusions:

The generalized GRGT provides a robust framework for fluid behavior, accurately capturing critical phenomena.
By incorporating fluctuations and avoiding empirical constructions, this theory offers improved predictive power for fluid properties.
The developed GRGT, when combined with appropriate mean-field approximations and coarse-graining lengths, aligns well with empirical and simulated fluid data.