Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst–Planck–Poisson Equations in a Diffusion Layer

This article proposes various new approximate analytical solutions of the boundary value problem 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 l...

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Главные авторы:	Chekanov, V. S., Чеканов, В. С.
Формат:	Статья
Язык:	English
Опубликовано:	Multidisciplinary Digital Publishing Institute (MDPI) 2025
Темы:	Asymptotic solution Space charge region Diffusion layer Electromembrane system Galvanodynamic mode Ion-exchange membrane Nernst–Planck–Poisson equations Singularly perturbed boundary value problems
Online-ссылка:	https://dspace.ncfu.ru/handle/123456789/29588
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spelling	ir-123456789-295882025-01-30T12:50:16Z Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst–Planck–Poisson Equations in a Diffusion Layer Chekanov, V. S. Чеканов, В. С. Asymptotic solution Space charge region Diffusion layer Electromembrane system Galvanodynamic mode Ion-exchange membrane Nernst–Planck–Poisson equations Singularly perturbed boundary value problems This article proposes various new approximate analytical solutions of the boundary value problem 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 sufficiently accurate analytical approximation to the solution of the original boundary value problem. The electroneutrality region has a curvilinear boundary with the SCR, and with an unknown boundary condition on it. The article proposes a solution to this problem. The new analytical solution methods developed in the article can be used to study non-stationary boundary value problems of salt ion transfer in membrane systems. The new analytical solution methods developed in the article can be used to study non-stationary boundary value problems of salt ion transport in membrane systems. 2025-01-30T12:49:03Z 2025-01-30T12:49:03Z 2024 Статья 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 // Mathematics. - 2024. - 12 (24). - статья № 4040. - DOI: 10.3390/math12244040 https://dspace.ncfu.ru/handle/123456789/29588 en Mathematics application/pdf application/pdf Multidisciplinary Digital Publishing Institute (MDPI)
institution	СКФУ
collection	Репозиторий
language	English
topic	Asymptotic solution Space charge region Diffusion layer Electromembrane system Galvanodynamic mode Ion-exchange membrane Nernst–Planck–Poisson equations Singularly perturbed boundary value problems
spellingShingle	Asymptotic solution Space charge region Diffusion layer Electromembrane system Galvanodynamic mode Ion-exchange membrane Nernst–Planck–Poisson equations Singularly perturbed boundary value problems Chekanov, V. S. Чеканов, В. С. Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst–Planck–Poisson Equations in a Diffusion Layer
description	This article proposes various new approximate analytical solutions of the boundary value problem 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 sufficiently accurate analytical approximation to the solution of the original boundary value problem. The electroneutrality region has a curvilinear boundary with the SCR, and with an unknown boundary condition on it. The article proposes a solution to this problem. The new analytical solution methods developed in the article can be used to study non-stationary boundary value problems of salt ion transfer in membrane systems. The new analytical solution methods developed in the article can be used to study non-stationary boundary value problems of salt ion transport in membrane systems.
format	Статья
author	Chekanov, V. S. Чеканов, В. С.
author_facet	Chekanov, V. S. Чеканов, В. С.
author_sort	Chekanov, V. S.
title	Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst–Planck–Poisson Equations in a Diffusion Layer
title_short	Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst–Planck–Poisson Equations in a Diffusion Layer
title_full	Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst–Planck–Poisson Equations in a Diffusion Layer
title_fullStr	Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst–Planck–Poisson Equations in a Diffusion Layer
title_full_unstemmed	Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst–Planck–Poisson Equations in a Diffusion Layer
title_sort	analytical solutions and computer modeling of a boundary value problem for a nonstationary system of nernst–planck–poisson equations in a diffusion layer
publisher	Multidisciplinary Digital Publishing Institute (MDPI)
publishDate	2025
url	https://dspace.ncfu.ru/handle/123456789/29588
work_keys_str_mv	AT chekanovvs analyticalsolutionsandcomputermodelingofaboundaryvalueproblemforanonstationarysystemofnernstplanckpoissonequationsinadiffusionlayer AT čekanovvs analyticalsolutionsandcomputermodelingofaboundaryvalueproblemforanonstationarysystemofnernstplanckpoissonequationsinadiffusionlayer
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Analytical Solutions and Computer Modeling of a Boundary Value Problem for a Nonstationary System of Nernst–Planck–Poisson Equations in a Diffusion Layer

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