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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Statistical mechanical theory for nonequilibrium systems. X. Nonequilibrium phase transitions.

¹School of Chemistry F11, University of Sydney, New South Wales 2006 Australia. attard@chem.usyd.edu.au

The Journal of Chemical Physics

|November 18, 2009

Summary

A new theory explains the stability and coexistence of nonequilibrium phases using entropy maximization. This approach accurately predicts Rayleigh-Bénard convection, a key fluid dynamics phenomenon.

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Area of Science:

Thermodynamics
Fluid Dynamics
Nonlinear Science

Background:

Understanding the stability and coexistence of nonequilibrium phases is crucial in various scientific disciplines.
Existing theories often struggle to provide a unified framework for these complex phenomena.

Purpose of the Study:

To formulate a general theory for the stability and coexistence of nonequilibrium phases.
To develop an integral formulation of the second entropy for this purpose.

Main Methods:

Formulation of a general theory for nonequilibrium phase stability.
Development of an integral formulation for the second entropy.
Functional maximization to derive nonlinear hydrodynamics.
Analysis of Rayleigh-Bénard convection.

Main Results:

An analytic approximation for the second entropy in conduction and convection was obtained.
The theory predicts the coexistence of phases for Rayleigh-Bénard convection.
The predicted Rayleigh number for coexistence is within 5% of the known value.

Conclusions:

The developed theory provides a robust framework for analyzing nonequilibrium phase stability.
The integral formulation of entropy is a powerful tool for deriving hydrodynamic equations.
The model's accuracy in predicting Rayleigh-Bénard convection highlights its potential applicability.