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Stability of Equilibrium Configuration

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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
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Related Experiment Video

Updated: Feb 26, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Local Equilibrium and Retardation Revisited.

Scott K Hansen, Velimir V Vesselinov1

  • 1Computational Earth Science Group, Los Alamos National Laboratory, Los Alamos, NM, 87545.

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|July 20, 2017
PubMed
Summary

The common retarded ADE model for solute transport with mobile-immobile mass transfer (MIMT) incorrectly assumes all particles spend equal time immobile. A Lagrangian approach reveals this ignores dispersion, even near local equilibrium.

Area of Science:

  • Environmental Science
  • Hydrogeology
  • Chemical Engineering

Background:

  • Solute transport modeling often uses the advection-dispersion equation (ADE) with a retardation factor, assuming local equilibrium (LEA).
  • Rigorous derivations show MIMT introduces dispersion, even with rapid mass transfer, contradicting some Eulerian ADE derivations.

Purpose of the Study:

  • To resolve the discrepancy between Eulerian and Lagrangian models of solute transport with MIMT.
  • To demonstrate the limitations of the retarded ADE, particularly under near-local equilibrium conditions.

Main Methods:

  • Adopting a Lagrangian perspective to analyze MIMT effects on solute transport.
  • Comparing Eulerian derivations with rigorous mathematical treatments.
  • Utilizing particle tracking simulations to illustrate the retarded ADE's approximation accuracy.

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Main Results:

  • The retarded ADE imposes a nonphysical constraint that all particles spend identical time immobile.
  • Eulerian derivations of the retarded ADE neglect dispersion arising from MIMT.
  • Particle tracking simulations show the retarded ADE can be a poor approximation, even when near local equilibrium.

Conclusions:

  • The common "local equilibrium assumption" criteria for retarded ADE validity actually assess the insignificance of MIMT-driven dispersion relative to hydrodynamic dispersion.
  • A Lagrangian viewpoint provides a more accurate representation of solute transport with MIMT, accounting for dispersion missed by the retarded ADE.