Next Article in Journal
Purification of Methylsulfonylmethane from Mixtures Containing Salt by Conventional Electrodialysis
Previous Article in Journal
Mitigation of Membrane Fouling Using an Electroactive Polyether Sulfone Membrane
Open AccessArticle

Mathematical Modeling of the Effect of Water Splitting on Ion Transfer in the Depleted Diffusion Layer Near an Ion-Exchange Membrane

1
Department/school, Kuban State University, 149 Stavropolskaya St., 350040 Krasnodar, Russia
2
Institut Européen des Membranes, UMR 5635 (CNRS-ENSCM-UM), Université Montpellier, Place E. Bataillon, F-34095 Montpellier, France
*
Author to whom correspondence should be addressed.
Membranes 2020, 10(2), 22; https://doi.org/10.3390/membranes10020022
Received: 4 January 2020 / Revised: 30 January 2020 / Accepted: 30 January 2020 / Published: 31 January 2020
(This article belongs to the Special Issue Membrane-Assisted (Bio)Chemical Process and Technology)
Water splitting (WS) and electroconvection (EC) are the main phenomena affecting ion transfer through ion-exchange membranes in intensive current regimes of electrodialysis. While EC enhances ion transport, WS, in most cases, is an undesirable effect reducing current efficiency and causing precipitation of sparingly soluble compounds. A mathematical description of the transfer of salt ions and H+ (OH) ions generated in WS is presented. The model is based on the Nernst–Planck and Poisson equations; it takes into account deviation from local electroneutrality in the depleted diffusion boundary layer (DBL). The current transported by water ions is given as a parameter. Numerical and semi-analytical solutions are developed. The analytical solution is found by dividing the depleted DBL into three zones: the electroneutral region, the extended space charge region (SCR), and the quasi-equilibrium zone near the membrane surface. There is an excellent agreement between two solutions when calculating the concentration of all four ions, electric field, and potential drop across the depleted DBL. The treatment of experimental partial current–voltage curves shows that under the same current density, the surface space charge density at the anion-exchange membrane is lower than that at the cation-exchange membrane. This explains the negative effect of WS, which partially suppresses EC and reduces salt ion transfer. The restrictions of the analytical solution, namely, the local chemical equilibrium assumption, are discussed.
Keywords: ion exchange membranes; concentration polarization; overlimiting current; ion transfer; mathematical modeling. ion exchange membranes; concentration polarization; overlimiting current; ion transfer; mathematical modeling.
Show Figures

Graphical abstract

MDPI and ACS Style

Nikonenko, V.; Urtenov, M.; Mareev, S.; Pourcelly, G. Mathematical Modeling of the Effect of Water Splitting on Ion Transfer in the Depleted Diffusion Layer Near an Ion-Exchange Membrane. Membranes 2020, 10, 22.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop