WIAS Preprint No. 2396, (2017)

Analysis of improved Nernst--Planck--Poisson models of compressible isothermal electrolytes. Part II: Approximation and a priori estimates



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

  • 82.45Gj, 82.45.Mp, 82.60Lf

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

DOI

10.20347/WIAS.PREPRINT.2396

Abstract

We consider an improved Nernst--Planck--Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non equilibrium. The model takes into account the elastic deformation of the medium that induces 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 of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross--diffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper, which continues the investigation of [DDGG17a], we derive for thermodynamically consistent approximation schemes the natural uniform estimates associated with the dissipations. Our results essentially improve our former study [DDGG16], in particular the a priori estimates concerning the relative chemical potentials.

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