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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
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Local Equilibrium Approximation in Non-Equilibrium Thermodynamics of Diffusion.

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Summary
This summary is machine-generated.

We developed a new theory to quantify deviations from local equilibrium approximation (LEA) in non-equilibrium thermodynamics. Our findings confirm LEA remains accurate even with extreme concentration gradients in gas mixtures.

Keywords:
diffusionkinetic theorylocal equilibrium approximationmolecular dynamicsnon-equilibrium entropytelegrapher equation

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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.