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Time-dependent modelling and asymptotic analysis of electrochemical cells

By Giles Richardson and J.R. King

Abstract

A (time-dependent) model for an electrochemical cell, comprising a dilute binary electrolytic solution between two flat electrodes, is formulated. The method of matched asymptotic expansions (taking the ratio of the Debye length to the cell width as the small asymptotic parameter) is used to derive simplified models of the cell in two distinguished limits and to systematically derive the Butler–Volmer boundary conditions. The first limit corresponds to a diffusion-limited reaction and the second to a capacitance-limited reaction. Additionally, for sufficiently small current flow/large diffusion, a simplified (lumped-parameter) model is derived which describes the long-time behaviour of the cell as the electrolyte is depleted. The limitations of the dilute model are identified, namely that for sufficiently large half-electrode potentials it predicts unfeasibly large concentrations of the ion species in the immediate vicinity of the electrodes. This motivates the formulation of a second model, for a concentrated electrolyte. Matched asymptotic analyses of this new model are conducted, in distinguished limits corresponding to a diffusion-limited reaction and a capacitance-limited reaction. These lead to simplified models in both of which a system of PDEs, in the outer region (the bulk of the electrolyte), matches to systems of ODEs, in inner regions about the electrodes. Example (steady-state) numerical solutions of the inner equations are presented

Year: 2007
OAI identifier: oai:eprints.soton.ac.uk:156353
Provided by: e-Prints Soton

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Citations

  1. (1913). A contribution to the theory of electrocapillarity. doi
  2. (2004). Ajdari A doi
  3. (2001). Analysis of diffuse-layer effects on time-dependent interfacial kinetics. doi
  4. (1998). Analysis of transport phenomena.
  5. (2001). Atkins’ physical chemistry, 7th edn.
  6. (2002). Coupling Poisson-Nernst-Planck and density functional theory to calculate ion flux. doi
  7. (2005). Current voltage relations for electrochemical thin films. doi
  8. (1993). Electrochemistry, principles, methods and applications.
  9. (1993). Free energy models for inhomogeneous fluid mixture: Yukawa-charged hard-spheres, general interactions and plasmas. doi
  10. (1996). Iglic A doi
  11. (1996). Interfacial electrochemistry. doi
  12. (1983). Mathematical modelling of two-phase flow.
  13. (1968). Nernst-Planck equations and the electroneutrality and Donnan equilibrium assumptions. doi
  14. (2000). Primary alkaline battery cathodes a three-scale model. doi
  15. (1997). Steric effects in electrolytes: a modified Poisson-Boltzmann equation. doi
  16. (1910). Sur la compression de la charge électrique a la surface d’un électrolyte. doi
  17. (1947). The electrical double layer and the theory of electrocapillarity. doi
  18. (1975). The mathematics of diffusion, 2nd edn.
  19. (1966). The polarized diffuse double layer. Trans Faraday Soc 61:2229–2237 doi
  20. (1997). The role of charge separation in the response of electrochemical systems.
  21. (1962). The theory of the passage of a direct current through a solution of binary electrolyte.
  22. (1924). Zur Theorie der electrolytischen Doppelschist.

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