Numerical-analytical method for solving boundary value problems for the system of Nernst-Planck and Poisson equations

Authors

UDC

544.638.2:001.891.573

DOI:

https://doi.org/10.31429/vestnik-19-3-6-16

Abstract

Electromembrane systems, are used for desalination at electrolyte solution concentrations ranging from 1 to 100 mol/m3. In a theoretical study of increasing the efficiency of the desalination process, mathematical modeling is used in the form of a boundary value problem for the system of Nernst-Planck and Poisson (NPP) equations, which refers to "hard" problems that are difficult to solve numerically. This is caused by the appearance of a small parameter at the derivative in the Poisson equation in a dimensionless form, and, correspondingly, a boundary layer in ion-exchange membranes, where concentrations and other characteristics of the desalination process change exponentially. It is for this reason that the numerical study of the boundary value problem is currently obtained for initial concentrations of the order of 0.01 mol/m3. The paper proposes a new numerical-analytical method for solving boundary value problems for the system of NPP equations for real initial concentrations, using which the phenomenon of space charge breakdown (SCB) is studied.

Keywords:

system of Nernst-Planck-Poisson equations, electromembrane systems, numerical methods, desalination channel

Acknowledgement

This reported study was funded by RFBR and DFG according to the research project no 20-58-12018 NNIO_a.

Author Infos

Anna V. Kovalenko

д-р техн. наук, доцент, заведующая кафедры анализа данных и искусственного интеллекта Кубанского государственного университета

e-mail: savanna-05@mail.ru

Natalia O. Chubyr

канд. физ.-мат. наук, доцент кафедры прикладной математики Кубанского государственного университета

e-mail: chubyr-natalja@mail.ru

Aminat M. Uzdenova

канд. физ.-мат. наук, доцент кафедры информатики и вычислительной математики Карачаево-Черкесского государственного университета им. А.Д. Алиева

e-mail: uzd_am@mail.ru

Makhamet A. Kh. Urtenov

д-р физ.-мат. наук, профессор, заведующий кафедры прикладной математики Кубанского государственного университета

e-mail: urtenovmax@mail.ru

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Issue

2022. Vol. 19. No. 3

Section

Mathematics

Pages

6-16

Submitted

2022-10-04

Published

2022-10-12

How to Cite

Kovalenko A.V., Chubyr N.O., Uzdenova A.M., Urtenov M.Kh. Numerical-analytical method for solving boundary value problems for the system of Nernst-Planck and Poisson equations. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2022, vol. 19, no. 3, pp. 6-16. DOI: https://doi.org/10.31429/vestnik-19-3-6-16 (In Russian)

Copyright (c) 2022 Kovalenko A.V., Chubyr N.O., Uzdenova A.M., Urtenov M.Kh.

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