Current-voltage characteristic of non-stationary 1:1 salt ion transport in the section of desalination channel

The main goal of this work is to derive and analyze different formulas for calculating the current-voltage characteristic (CVC) of non-stationary transport of 1: 1 electrolyte in the cross-section of the desalting channel, including anion-exchange (AEM) and cation-exchange (CEM) membranes, and to establish fundamental regularities of changes in the CVC with time. Modeling is carried out based on the Nernst-Planck-Poisson equations. The transport of ions of strong electrolytes NaCl and KCl through a thin reaction layer of ion-exchange membranes in the section of the desalination channel is considered. For this purpose, a schematic electrical diagram of the current flow in the circuit, including the cross-section of the desalination channel, has been constructed. From the analysis of this circuit, it follows that the total current consists of a conduction current and a displacement current. The conduction current is determined by the flow of salt ions. The displacement current goes to the formation and development of the space charge region. Due to the change in the increase in the potential jump (potentiodynamic mode), the total current in the circuit when calculating the CVC changes over time, and its change can be considered slow. In this case, the displacement current practically does not pass through the cross-section of the desalination channel while the charge distribution density is slowly changing. In the case of a rapid change in the charge distribution density (breakdown phenomenon, as well as before and after breakdown), the displacement current takes on rather large values. The displacement current-voltage characteristic must be taken into account separately. Since the value of the CVC calculated in the study of the transport current is much higher than the value of the CVC at the displacement current, the effect of the electric “breakdown” on the transport current is hardly noticeable. Therefore, the “breakdown” effect must be investigated by the CVC of the displacement current. The proposed formula for calculating the CVC of the conduction current is stable with respect to rounding errors. The effect of nonstationarity is investigated at high growth rates of the potential jump.

1. Pruyn, K.T., Harrington, J.J., Smith, J.D. Mathematical Model of the Electrodialysis Process. Department of the Interior. Federal Water Quality Admin., Cincinnati, Ohio. 1969.

2. Carolin C.F., Kumar P.S., Saravanan A., Joshiba G.J., Naushad M. Efficient techniques for the removal of toxic heavy metals from aquatic environment: a review, J. Environ. Chem. Eng. 2017;5:2782–2799. DOI:10.1016/j.jece.2017.05.029.

3. Sajjad, A.-A., Yunus, M. Y. B. M., Azoddein, A. A. M., Hassell, D. G., Dakhil, I. H., & Hasan, H. A. Electrodialysis Desalination for Water and Wastewater: A Review. Chemical Engineering Journal. 2019;380:122231. DOI:10.1016/j.cej.2019.122231

4. Rajeshwar, K., Ibanez, J. G., & Swain, G. M. Electrochemistry and the environment. Journal of Applied Electrochemistry. 1994;24(11):1077-1091.

5. Bazinet, L., Doyen, A. Antioxidants, mechanisms, and recovery by membrane processes. Crit. Rev. Food Sci. Nutr. 2017, 57:677-700. DOI: 10.1080/10408398.2014.912609

6. Xu, H., Ji, X., Wang, L., Huang, J., Han, J., & Wang, Y. Performance study on a smallscale photovoltaic electrodialysis system for desalination. Renewable Energy. 2020;154:1008-1013. DOI:10.1016/j.renene.2020.03.066

7. Ortiz, J. M., Expósito, E., Gallud, F., García-García, V., Montiel, V., & Aldaz, A. Electrodialysis of brackish water powered by photovoltaic energy without batteries: direct connection behaviour. Desalination. 2007;208(1-3):89-100.

8. Rubinshtein I., Zaltsman B., Prez I., Linder K. Experimental verification of the electroosmotic mechanism of the formation of "beyond" current in a system with a cationexchange electrodialysis membrane. Electrochemistry. 2002,38(8):956.

9. Rubinstein, I.; Shtilman, L. Voltage against current curves of cation exchange membranes. J. Chem. Soc. Faraday Trans. 1979;75:231–246.

10. Rubinstein, I.; Zaltzman, B. Electro-osmotically induced convection at a permselective membrane. Phys. Rev. E. 2000;62:2238–2251.

11. Pham, S.V.; Li, Z.; Lim, K.M.; White, J.K.; Han, J. Direct numerical simulation of electroconvective instability and hysteretic current-voltage response of a permselective membrane. Phys. Rev. E. 2012;86:046310. DOI: 10.1103/PhysRevE.86.046310

12. Uzdenova A., Kovalenko A., Urtenov M. Nikonenko V. 1D mathematical modelling of non-stationary ion transfer in the diffusion layer adjacent to an ion-exchange membrane in galvanostatic mode. Membranes. 2018;8(3):84. DOI:10.3390/membranes8030084

13. Ganchenko, G.S.; Kalaydin, E.N.; Schiffbauer, J.; Demekhin, E.A. Modes of electrokinetic instability for imperfect electric membranes. Phys. Rev. E. 2016;94:063106. DOI:10.1103/PhysRevE.94.063106

14. Urtenov, M.K.; Uzdenova, A.M.; Kovalenko, A.V.; Nikonenko, V.V.; Pismenskaya, N.D.; Vasil’eva, V.I.; Sistat, P.; Pourcelly, G. Basic mathematical model of overlimiting transfer enhanced by electroconvection in flow-through electrodialysis membrane cells. J. Membr. Sci. 2013;447:190–202. DOI:10.1016/j.memsci.2013.07.033

15. Karatay, E.; Druzgalski, C.L.; Mani, A. Simulation of Chaotic Electrokinetic Transport: Performance of Commercial Software versus Custom-built Direct Numerical Simulation Codes. J. Colloid Interface Sci. 2015;446:67–76

16. Druzgalski, C.; Mani, A. Statistical analysis of electroconvection near an ion-selective membrane in the highly chaotic regime. Phys. Rev. Fluids. 2016, 1, 073601.

17. Davidson, S.M.;Wessling, M.; Mani, A. On the Dynamical Regimes of Pattern-Accelerated Electroconvection. Sci. Rep. 2016;6,22505.

18. Urtenov M.Kh., Kovalenko A.V., Sukhinov A.I., Chubyr N.O., Gudza V.A. Model and numerical experiment for calculating the theoretical current-voltage characteristic in electro-membrane systems. В сборнике: IOP Conference Series: Materials Science and Engineering Collection of materials of the XV International Scientific - Technical Conference. Don State Technical University. 2019;012030.

19. Pham, S.V.; Kwon, H.; Kim, B.; White, J.K.; Lim, G.; Han, J. Helical vortex formation in three-dimensional electrochemical systems with ion-selective membranes. Phys. Rev. E. 2016;93:033114.

20. Andersen, M.; Wang, K.; Schiffbauer, J.; Mani, A. Confinement effects on electroconvective instability. Electrophoresis. 2017;38:702–711.

21. Femmer, R.; Mani, A.; Wessling, M. Ion transport through electrolyte/polyelectrolyte multi-layers. Sci. Rep. 2015;5,11583.

22. Moya, A.A. Electrochemical Impedance of Ion-Exchange Membranes with Interfacial Charge Transfer Resistances. J. Phys. Chem. C. 2016; 120;6543–6552.

23. Chubyr N.O., Urtenov M.Kh., Kovalenko A.V., Numerical and asymptotic methods for analyzing the transfer of 1: 1 electrolyte in membrane systems. Krasnodar. 2018;106 pp.

24. Kodým, R.; Fíla, V.; Šnita, D.; Bouzek, K. Poisson-Nernst-Planck model of multiple ion transport across an ion-selective membrane under conditions close to chlor-alkali electrolysis. J. Appl. Electrochem. 2016;46:679–694.

25. Chubyr N. O., Urtenov M. Kh., Kovalenko A. V., Uzdenova A. M. Algorithm for calculating the current-voltage characteristic in the diffusion layer for membrane systems in the galvanodynamic mode. Modern high technologies. 2019;10:92-96.

26. Suzuki, Y.; Seki, K. Possible influence of the Kuramoto length in a photo-catalytic water splitting reaction revealed by Poisson–Nernst–Planck equations involving ionization in a weak electrolyte. Chem. Phys. 2018;502:39–49.

27. Urtenov, M.; Chubyr, N.; Gudza, V. Reasons for the formation and properties of solitonlike charge waves in membrane systems when using overlimiting current modes. Membranes 2020;10(8):189. DOI:10.3390/membranes10080189