WIAS Preprint No. 2291, (2016)

Existence of weak solutions for improved Nernst--Planck--Poisson models of compressible reacting electrolytes



Authors

  • Dreyer, Wolfgang
  • Druet, Pierre-Étienne
    ORCID: 0000-0001-5303-0500
  • Gajewski, Paul
  • Guhlke, Clemens

2010 Mathematics Subject Classification

  • 35Q35 76T30 78A57 35Q30 76N10 35M33 35D30 35B45

2008 Physics and Astronomy Classification Scheme

  • 82.45.Gj 82.45.Mp 82.60.Lf

Keywords

  • Electrolyte, electrochemical interface, chemical reaction, compressible fluid, Navier-Stokes equations, advection-diffusion-reaction equations, PDE system of mixed-type, a-priori estimates, weak solution

Abstract

We consider an improved Nernst-Planck-Poisson model for compressible electrolytes first proposed by Dreyer et al. in 2013. The model takes into account the elastic deformation of the medium. In particular, large pressure contributions near electrochemical interfaces induce an inherent coupling of mass and momentum transport. The model consists of convection-diffusion-reaction equations for the constituents of the mixture, of the Navier-Stokes equation for the barycentric velocity and the Poisson equation for the electrical potential. Cross-diffusion phenomena occur due to the principle of mass conservation. Moreover, the diffusion matrix (mobility matrix) has a zero eigenvalue, meaning that the system is degenerate parabolic. In this paper we establish the existence of a global-in- time weak solution for the full model, allowing for cross-diffusion and an arbitrary number of chemical reactions in the bulk and on the active boundary.

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