PreprintArticleVersion 1This version is not peer-reviewed
Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst-Planck-Poisson Equations in a Diffusion Layer
Version 1
: Received: 27 October 2024 / Approved: 28 October 2024 / Online: 28 October 2024 (13:24:39 CET)
How to cite:
Kovalenko, S.; Kirillova, E.; Chekanov, V.; Uzdenova, A.; Urtenov, M. Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst-Planck-Poisson Equations in a Diffusion Layer. Preprints2024, 2024102136. https://doi.org/10.20944/preprints202410.2136.v1
Kovalenko, S.; Kirillova, E.; Chekanov, V.; Uzdenova, A.; Urtenov, M. Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst-Planck-Poisson Equations in a Diffusion Layer. Preprints 2024, 2024102136. https://doi.org/10.20944/preprints202410.2136.v1
Kovalenko, S.; Kirillova, E.; Chekanov, V.; Uzdenova, A.; Urtenov, M. Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst-Planck-Poisson Equations in a Diffusion Layer. Preprints2024, 2024102136. https://doi.org/10.20944/preprints202410.2136.v1
APA Style
Kovalenko, S., Kirillova, E., Chekanov, V., Uzdenova, A., & Urtenov, M. (2024). Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst-Planck-Poisson Equations in a Diffusion Layer. Preprints. https://doi.org/10.20944/preprints202410.2136.v1
Chicago/Turabian Style
Kovalenko, S., Aminat Uzdenova and Mahamet Urtenov. 2024 "Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst-Planck-Poisson Equations in a Diffusion Layer" Preprints. https://doi.org/10.20944/preprints202410.2136.v1
Abstract
The article proposes various new approximate analytical solutions of the boundary value prob-lem for the non-stationary system of Nernst-Planck-Poisson (NPP) equations in the diffusion layer of an ideally selective ion-exchange membrane at overlimiting current densities. As is known, the diffusion layer in the general case consists of a space charge region and a region of local electroneutrality. The proposed analytical solutions of the boundary value problems for the non-stationary system of Nernst-Planck-Poisson equations are based on the derivation of a new singularly perturbed nonlinear partial differential equation for the potential in the space charge region (SCR). This equation can be reduced to a singularly perturbed inhomogeneous Burgers equation, which, by the Hopf-Cole transformation, is reduced to an inhomogeneous singularly perturbed linear equation of parabolic type. Inside the extended SCR, there is a suffi-ciently accurate analytical approximation to the solution of the original boundary value prob-lem. The electroneutrality region has a curvilinear boundary with the SCR, and with an un-known boundary condition on it. The article proposes a solution to this problem. The new ana-lytical solution methods developed in the article can be used to study non-stationary boundary value problems of salt ion transfer in membrane systems.
Keywords
Nernst-Planck-Poisson equations; asymptotic solution; singularly perturbed boundary value problems; galvanodynamic mode; electromembrane system; diffusion layer; ion-exchange membrane; space charge region
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
