Local Equilibrium Approximation in Non-Equilibrium Thermodynamics of Diffusion

Area of Science:

• Non-equilibrium thermodynamics
• Kinetic theory
• Statistical mechanics

Background:

• Local equilibrium approximation (LEA) is fundamental in non-equilibrium thermodynamics for mass, energy, and momentum transport.
• Assessing LEA validity is difficult due to limited tools for non-equilibrium state characterization.

Purpose of the Study:

• Develop a theoretical framework to quantify deviations from LEA.
• Provide tools for analyzing non-equilibrium states beyond LEA.
• Validate the developed theory and assess LEA accuracy under challenging conditions.

Main Methods:

• Developed a nonlinear extension of the telegrapher's equation using kinetic theory.
• Derived a steady-state diffusion equation incorporating thermal energy constraints.
• Performed molecular dynamics simulations on a two-component gas mixture with identical component properties.

Main Results:

• The developed theory enables systematic quantification of deviations from local equilibrium.
• A steady-state diffusion equation was derived, accounting for thermal energy constraints on diffusion flux.
• Molecular dynamics simulations confirmed LEA accuracy even under extreme concentration gradients.

Conclusions:

• The new kinetic theory provides a robust method for analyzing non-equilibrium systems.
• LEA remains a valid assumption for diffusion processes in gas mixtures, even with significant concentration gradients.
• The developed framework advances the characterization of non-equilibrium states.