Theoretical analysis of the current-voltage characteristic of the unsteady 1:1 transfer of an electrolyte in membrane systems, taking into account electroconvection and the dissociation/recombination reaction of water

The current-voltage characteristic (CVC) is an important integral characteristic of the salt ion transfer process in electromembrane systems, which are considered as the desalination channel of the electrodialysis apparatus. The article examines the theoretical current-voltage characteristic, for the calculation of which a new 2D mathematical model of non-stationary 1:1 transfer of an electrolyte in a potentiodynamic mode is formulated and numerically solved, taking into account the electroconvection and non-catalytic reaction of dissociation and recombination of water molecules. The main regularities of changes in the current-voltage characteristic and their connection with the electroconvection and non-catalytic reaction of dissociation and recombination of water molecules are established. It is shown that before the occurrence of electroconvection, the values of CVC, taking into account the dissociation/recombination reaction of water molecules, are higher than the values of CVC without taking into account this reaction. This difference is caused by the effect on the electric field strength of the products of water dissociation, i.e., the exaltation of the limiting current. Electroconvection begins later, taking into account the dissociation/recombination reaction of water molecules, than without taking into account this reaction. At higher values of the potential jump, the values of the VAC taking into account the dissociation/recombination reaction of water molecules are lower than the values of the CVC without taking into account this reaction. It is established that the non-solenoidal part of the current is small, so the total current and the solenoid part of the current coincide with good accuracy, both in the case of taking into account and in the case without taking into account the dissociation/recombination reaction of water molecules. Thus, in the first approximation, the total current can be considered as the solenoid part of the current, which is calculated using a double integral that is resistant to rounding errors in spatial variables, but retains all the features of the change in current density over time.

1. Budnikov, E. Y. Analysis of fluctuation phenomena in the field of extreme currents in an electromembrane system. Dissertation for the degree of Candidate of Physical and Mathematical Sciences. Moscow. 2000;115. (In Russ)

2. Budnikov, E. Yu., Kukoev I. Yu., Maksimychev A.V., Miroshnikova I. N., Timashev S. F., Gulyaev A.M.. Wavelet and Fourier analysis of electrical fluctuations in polyconducting and electrochemical systems. Measuring Equipment. 1999;11:40-44. (In Russ)

3. Shkorkina I., Chubyr N., Gudza V., Urtenov M.A.Kh. Analysis of theoretical current-voltage characteristic of non-stationary transport in the cross-section of the desalination channel. E3S Web of Conferences. Сер. "Topical Problems of Agriculture, Civil and Environmental Engineering, TPACEE 2020". 2020; 02015. Available at: https://www.e3s-conferences.org/articles/e3sconf/abs/2020/84/e3sconf_TPACEE2020_02015/e3sconf_TPACEE2020_02015.html. DOI: 10.1051/e3sconf/202022402015

4. 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. IOP Conference Series: Materials Science and Engineering. Collection of materials of the XV International Scientific - Technical Conference. Don State Technical University. 2019;012030. Available at: https://www.researchgate.net/publication/337743733_Model_and_numerical_experiment_for_calculating_the_theoretical_current-voltage_characteristic_in_electro-membrane_systems. DOI: 10.1088/1757-899X/680/1/012030. (accessed 28.06.2021).

5. Kressman T.R.E., Туе F.L. The effect of current density on the transport of ions through ion selective membranes. Disc. Far. Soc. 1956;21:183-192.

6. Greben V.P., Pivovarov N.Y., Kovarskii N.Y., Nefedova, G.V. Influence of ion-exchange resin nature on physic-chemical properties of bipolar membranes. Sov. J. Phys. Chem. 1978; 52: 2641-2645.

7. Simons R., Water splitting in ion exchange membranes. Electrochim. 1985;30(3):275 - 282.

8. Choi J.-H., Lee H.-J., Moon S.-H., J. Colloid Interface Sci, 2001;1:188-195.

9. Urtenov M. Kh., Pismenskiy A.V., Nikonenko V. V., Kovalenko A.V. Mathematical modeling of ion transfer and water dissociation at the ion exchange membrane / solution boundary in intensive current modes. Membranes and membrane technologies. 2018;8(1): 24-33. Available at: https://elibrary.ru/item.asp?id=32360057. DOI: 10.1134/S2218117218010054. (In Russ) (accessed 28.06.2021).

10. Kovalenko A.V., Urtenov M. Kh., Chubyr N. O., Uzdenova A.M., Gudza V. A. The influence of temperature effects related with dissociation/recombination of water molecules and Joule heating of solution on stationary transport of salt ions in diffusion layer. Ecological Bulletin of the Scientific Centers of the Black Sea Economic Cooperation. 2018;15 (4):67-84. Available at: https://elibrary.ru/item.asp?id=36642511. DOI: 10.31429/vestnik-15-4-67-84. (In Russ) (accessed 28.06.2021).

11. Chubyr N. O., Kovalenko A.V., Urtenov M. Kh. Two-dimensional mathematical models of binary electrolyte transfer in membrane systems (Numerical and asymptotic analysis). Krasnodar.: Publishing house of KubSTU. 2012:132. ISBN: 978-5-8333-0417-4 (In Russ)

12. Rubinstein I., Maletzki F. Electroconvection at an electrically inhomoheneous permselective membrane surface. Trans. Faraday Soc. 1991;87(13):2079-2087.

13. Urtenov, M. Kh.; 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. Available at: https://www.researchgate.net/publication/259460278_Basic_mathematical_model_of_overlimiting_transfer_enhanced_by_electroconvection_in_flow-through_electrodialysis_membrane_cells. DOI:10.1016/j.memsci.2013.07.033. (accessed 28.06.2021).

14. Kim B, Choi S, Pham V, Kwak R, Han J., Energy efficiency enhancement of electromembrane desalination systems by local flow redistribution optimized for the asymmetry of cation/anion diffusivity. Journal of Membrane Science. 2017;524:280-287. Available at: https://www.researchgate.net/publication/310661107_Energy_Efficiency_Enhancement_of_Electromembrane_Desalination_Systems_by_Local_Flow_Redistribution_Optimized_for_the_Asymmetry_of_CationAnion_Diffusivity. DOI:10.1016/j.memsci.2016.11.046. (accessed 28.06.2021).

15. Newman, J.; Thomas-Alyea, K.E. Electrochemical systems, 3rd ed.; John Wiley & Sons, Inc.: Honoken, NJ, USA, 2004;647. ISBN 0-471-47756-7.

16. Kharkats Yu. I. On the theory of the migration current exaltation effect. Electrochemistry. 1978;12(14):1840-1844. (In Russ)

17. Kharkats Yu. I. The effect of correlation exaltation of currents during parallel electrochemical processes in the absence of a background electrolyte. Electrochemistry. 1978;11(14):1716-1720. (In Russ)