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Closed Formula for Transport across Constrictions.

Paolo Malgaretti1, Jens Harting1,2

  • 1Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, 90429 Erlangen, Germany.

Entropy (Basel, Switzerland)
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The Fick-Jacobs approximation accurately models transport in symmetric channels via its linear response regime. A simple formula derived from this regime aids in designing experiments and simulations for particle transport.

Keywords:
entropic barrierporous materialstransport

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Area of Science:

  • Physics
  • Physical Chemistry
  • Chemical Engineering

Background:

  • The Fick-Jacobs approximation is a key model for understanding particle transport across constrictions.
  • Its application has grown significantly in the last decade for analyzing transport phenomena.

Purpose of the Study:

  • To review the derivation of the Fick-Jacobs equation, focusing on its linear response regime.
  • To provide a simplified formula for predicting transport in symmetric channels.
  • To investigate the behavior of transport in non-symmetric channels.

Main Methods:

  • Review of the Fick-Jacobs equation derivation.
  • Analysis of the linear response regime for transport phenomena.
  • Derivation of a simplified formula for symmetric channels.
  • Examination of higher-order corrections for non-symmetric channels.

Main Results:

  • For fore-aft symmetric channels, the flux of noninteracting systems is entirely described by the linear response regime.
  • A straightforward formula has been derived, accurately reflecting trends for symmetric channels.
  • Higher-order corrections to the flux are observed in non-symmetric channels.

Conclusions:

  • The linear response regime of the Fick-Jacobs approximation is sufficient for modeling transport in symmetric channels.
  • The derived simple formula serves as a practical tool for experimental and simulation design.
  • Non-symmetric channels introduce complexities requiring consideration of higher-order effects.