WIAS Preprint No. 1860, (2013)

Rational modeling of electrochemical double-layers and derivation of Butler--Volmer equations


  • Dreyer, Wolfgang
  • Guhlke, Clemens
  • Müller, Rüdiger
    ORCID: 0000-0003-2643-722X

2010 Mathematics Subject Classification

  • 35Q35 76T30 35C20

2008 Physics and Astronomy Classification Scheme

  • 82.45.Gj, 82.45.Fk


  • electrolyte, double-layer, Butler-Volmer, thermodynamics, asymptotic analysis


We derive the boundary conditions for the contact between an electrolyte and a solid electrode. At first we revisit the thermodynamic consistent complete model that resolves the actual electrode--electrolyte interface and its adjacent boundary layers. The width of these layers is controlled by the Debye length that is typically very small, leading to strongly different length scales in the system. We apply the method of asymptotic analysis to derive a simpler reduced model that does not resolve the boundary layers but instead incorporates the electrochemical properties of the layers into a set of new boundary conditions. This approach fully determines the relation of bulk quantities to the boundary conditions of the reduced model. In particular, the Butler-Volmer equations for electrochemical reactions, which are still under discussion in the literature, are rational consequences of our approach. For illustration and to compare with the literature, we consider a simple generic reaction.

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