Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus

Authors

  • Anna V. Kovalenko Kuban State University, 149 Stavropol’skaya Street, Krasnodar 350040, Russia
  • Anna V. Ovsyannikova Financial University under the Government of the Russian Federation, 49/2 Leningradskii Avenue, Moscow 125167, Russia

Keywords:

3D mathematical model of transport, 3D model, three-dimensional model, membrane systems, ion exchange membrane, mathematical modelling, electroconvective vortices, direct numerical simulation
Supporting Agencies
The research was performed with the financial support of the Russian Foundation for Basic Research within the framework of scientific project 20-58-12018 NNIO_a «Study of influence of electroconvection, water dissociation and spacer geometry on electrodialysis desalination in intensive current regimes».

Abstract

A new 3D model of 1:1 salt ion transfer in the desalting channel of an electrodialysis apparatus is presented and investigated in this paper. For the first time a three-dimensional mathematical model of salt ion transfer in the desalting channel taking into account the electroconvection based on the system of Nernst – Planck, Poisson and Navier – Stokes equations with the electric force and the natural boundary conditions is proposed. To solve the boundary value problem, the finite element method is used in the cross-platform numerical analysis software COMSOL Multiphysics in combination with the method of successive approximations, when the electrochemical and hydrodynamic parts of the problem are solved one by one on the current layer. In turn, the electrochemical and hydrodynamic parts of the problem are solved by Newton’s method. As a result of numerical analysis, the fundamental regularities of salt ion transfer in a three-dimensional channel, the emergence and development of electroconvective vortices, including the discovery of new three-dimensional spiral forms of salt ions, are established for the first time. It is shown that electroconvective vortices exist in the form of clusters, within which vortex bifurcations can occur. Thus, the currently existing simplified view of the structure of electroconvective vortices is clarified and developed.

Author Biographies

  • Anna V. Kovalenko, Kuban State University, 149 Stavropol’skaya Street, Krasnodar 350040, Russia

    doctor of science (engineering), docent; head of the department of data analysis and artificial intelligence, faculty of computer technology and applied mathematics

  • Anna V. Ovsyannikova, Financial University under the Government of the Russian Federation, 49/2 Leningradskii Avenue, Moscow 125167, Russia

    PhD (pedagogy), docent; associate professor at the Department of Mathematics

References

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Published

2022-08-03

Issue

No. 2 (2022): Journal of the Belarusian State University. Mathematics and Informatics

Section

Computational Mathematics

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How to Cite

[1]
Kovalenko, A.V. and Ovsyannikova, A.V. 2022. Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Aug. 2022), 70–81. DOI:https://doi.org/10.33581/2520-6508-2022-2-70-81.