Исследование хронограмм тока, строения областей диссоциации, рекомбинации и равновесия в задачах нестационарного переноса 1:1 электролита в мембранных системах с использованием математической модели
Работая с нашим сайтом, вы даете свое согласие на использование файлов cookie. Это необходимо для нормального функционирования сайта, показа целевой рекламы и анализа трафика. Статистика использования сайта отправляется в «Яндекс» и «Google»
Научный журнал Моделирование, оптимизация и информационные технологииThe scientific journal Modeling, Optimization and Information Technology
Online media
issn 2310-6018

Study of current chronograms, structure of dissociation, recombination and equilibrium regions in problems of non-stationary 1:1 electrolyte transfer in membrane systems using a mathematical model

idKovalenko A.V., Gudza V.A.,  idChubyr N.O., Khromykh A.A.,  idUrtenov M.K.

UDC 519.87+004.421
DOI: 10.26102/2310-6018/2022.36.1.028

  • Abstract
  • List of references
  • About authors

The joint research of the dissociation-recombination reaction and space charge along with their effect on the transfer of 1:1 electrolyte ions appears to be a relevant issue. The article is a theoretical study of the dissociation, recombination and equilibrium areas and the features of salt ion transfer in each of these areas using the method of mathematical modeling. In the article, for the first time, on the basis of a mathematical model of non-stationary transfer of 1:1 electrolyte, the main regularities of the influence of the dissociation and recombination non-catalytic reaction on the transfer of 1:1 salt ions and electroconvection are theoretically established. In particular, the chronograms of the current density with and without taking into account the dissociation/recombination reaction of water, the structure of the dissociation regions, recombination and equilibrium were examined, the dependences on the input parameters were determined: the initial concentration, the potential sweep rate. It has been shown that in the boundary layers of ion-exchange membranes, the dissociation reaction prevails over the recombination reaction due to the fact that in these regions the electric field strength takes such high values that the electric field breaks the water molecules and separates the Н+ and ОН- ions, preventing them from recombining. It has been demonstrated for the first time that in the middle part of the desalination channel, a region is formed where the recombination of H+ and OH- ions predominates. This reaction is local in nature, so all H+ and OH- ions cannot recombine at the same time. As a result, in the region of recombination, an excess of H+ ions emerges on the one side and OH- on the other side, in other words, an electric double layer is developed in the middle part of the desalination channel, and the recombination region is rather narrow. The obtained theoretical results and conclusions can be applied to analyze the operation of electrodialysis machine desalination channels.

1. Frilette V.J. Preparation and characterization of bipolar ion exchange membranes. J. Phys. Chem. 1956;60:435–439.

2. Kressman T.R.E., Tye F.L. The effect of current density on the transport of ions through ion-selective membranes. Discuss. Faraday Soc. 1956;21:185–292.

3. Block M., Kitchener J.A. The phenomenon of polarization in an industrial ion-exchange membranes. J. Electrochem. Soc. 1966;113:947.

4. Greben V.P., Pivovarov N.Ya., Kovarskii N.Ya., Nefedova G.Z. The influence of the nature of ionite on the physicochemical properties of bipolar ion-exchange membranes. Zhurnal fizicheskoi khimii = Journal of Physical Chemistry. 1978;52(10):2304–2307. (In Russ.)

5. Zabolotskii V.I., Nikonenko V.V., Korzhenko N.M., Seidov R.R., Urtenov M.Kh. The effect of heterolytic dissociation of water on the mass transfer of salt ions in an electromembrane system with a violation of electroneutrality in the diffusion layer region. Elektrokhimiya = Electrochemistry. 2002;38(8):911–920. Available from: https://elibrary.ru/item.asp?id=44584753 (accessed on: 12.01.2022). (In Russ.)

6. Urtenov M.Kh., Kirillova E.V., Seidova N.M., Nikonenko V.V. Decoupling of the Nernst-Planck and Poisson equations. Application to a membrane system at overlimiting currents. J. Phys. Chem.B. 2008;111(51):14208–14222. Available from: https://www.researchgate.net/publication/5796236_Decoupling_of_the_Nernst-Planck_and_Poisson_Equations_Application_to_a_Membrane_System_at_Overlimiting_Currents (accessed on: 12.01.2022). DOI:10.1021/jp073103d.

7. Simons R. Effect of the electric field on proton transfer between ionized groups and water in ion exchange membranes. Electrochim. Acta. 1984;29(2):151–158. Доступно по: https://www.sciencedirect.com/science/article/abs/pii/0013468684870401?via%3Dihub (accessed on: 12.01.2022). DOI:10.1016/0013-4686(84)87040-1.

8. Rubinstein I., Shtilman L. Voltage against current curves of cation exchange membranes. J. Chem. Soc. Faraday Trans. 1979;75:231–246. Available from: https://pubs.rsc.org/en/content/articlelanding/1979/F2/f29797500231 (accessed on: 12.01.2022).DOI:10.1039/F29797500231.

9. Urtenov M.Kh., Pis'menskii A.V., Nikonenko V.V., Kovalenko A.V. Mathematical modeling of ion transport and dissociation of water at the ion exchange membrane/solution boundary in intensive current modes. Membrany i membrannye tekhnologii = Membranes and membrane technologies. 2018;8(1):24–33. Available from: https://elibrary.ru/item.asp?id=32360057 (accessed on: 12.01.2022). DOI: 10.1134/S2218117218010054. (In Russ.)

10. Kovalenko A.V., Urtenov M.Kh., Chubyr N.O., Uzdenova A.M., Gudza V.A. The effect of temperature effects associated with the dissociation/recombination reaction of water molecules and Joule heating of the solution on the stationary transport of salt ions in the diffusion layer. Ekologicheskii vestnik nauchnykh tsentrov ChES = Ecological Bulletin of the ChES Scientific Centers. Available from: https://elibrary.ru/item.asp?id=36642511 (accessed on: 12.01.2022). DOI: 10.31429/vestnik-15-4-67-84. (In Russ.)

11. Xu H., Ji X., Wang L., Huang J., Han J., Wang Y. Performance study on a small-scale photovoltaic electrodialysis system for desalination. Renewable Energy. 2020;154(11):1008–1013. Available from: https://www.researchgate.net/publication/339949517_Performance_study_on_a_small-scale_photovoltaic_electrodialysis_system_for_desalination (accessed on: 12.01.2022). DOI:10.1016/j.renene.2020.03.066.

12. Chubyr N.O., Kovalenko A.V., Urtenov M.Kh., Sukhinov A.I., Gudza V.A. Modeling and numerical analysis of the effect of the dissociation reaction (recombination) of water molecules on the transport of salt ions in the diffusion layer. Vestnik Donskogo gosudarstvennogo tekhnicheskogo universiteta = Bulletin of the Don State Technical University. 2019;19(3):268–280. Available from: https://elibrary.ru/item.asp?id=40962593 (accessed on: 12.01.2022). DOI: 10.23947/1992-5980-2019-19-3-268-280. (In Russ.)

13. Urtenov M., Gudza V., Chubyr N., Shkorkina I. Theoretical analysis of the stationary transport of 1:1 salt ions in a cross-section of a desalination channel, taking into account the non-catalytic dissociation/recombination reaction of water molecules. Membranes. 2020;10(11):342. Available from: https://elibrary.ru/item.asp?id=45153303 (accessed on: 12.01.2022). DOI: 10.3390/membranes10110342.

14. Urtenov M.Kh., Kovalenko A.V., Sharafan M.V., Gudza V.A., Chubyr' N.O. Mathematical modeling of unsteady 1:1 electrolyte transfer and investigation of the spatial charge region in membrane systems taking into account electroconvection and dissociation/recombination reaction of water. Ekologicheskii vestnik nauchnykh tsentrov ChES = Ecological Bulletin of the ChES Scientific Centers. Available from: https://elibrary.ru/item.asp?id=46200217 (accessed on: 12.01.2022). DOI: 10.31429/vestnik-18-2-62-71. (In Russ.)

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

16. Kovalenko A.V., Gudza I.V., Pismenskiy A.V., Chubyr N.O., Urtenov M.Kh. 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. Modelirovanie, optimizatsia i informatsionnyie tekhnologii = Modeling, Optimization and Information Technology. 2021;9(3). Available from: https://moitvivt.ru/ru/journal/pdf?id=1014 (accessed on: 12.01.2022). DOI: 10.26102/2310-6018/2021.34.3.011. (In Russ.)

17. Urtenov M.Kh. Chubyr N.O., Gudza V.A. Reasons for the formation and properties of soliton-like charge waves in membrane systems when using overlimiting current modes. Membranes. 2020;10(8):189. Available from:https://www.researchgate.net/publication/343693372_Reasons_for_the_Formation_and_Properties_of_Soliton-Like_Charge_Waves_in_Membrane_Systems_When_Using_Overlimiting_Current_Modes (accessed on: 12.01.2022). DOI:10.3390/membranes10080189.

Kovalenko Anna Vladimirovna
Dr. Sci, associate professor

ORCID |

Kuban State University

Krasnodar, Russian Federation

Gudza Vitaly Alexandrovich

Kuban State University

Krasnodar, Russian Federation

Chubyr Natalia Olegovna
Cand.Sci. (Phys.–Math.), associate professor

ORCID |

Kuban State Technological University

Krasnodar, Russian Federation

Khromykh Anna Alekseyevna
Cand.Sci. (Phys.–Math.)

Krasnodar University of the Ministry of the Internal of Russia

Krasnodar, Russian Federation

Urtenov Makhamet Khuseevich
Dr. Sci. (Phys.–Math.), Professor

ORCID |

Kuban State University

Krasnodar, Russian Federation

Keywords: electrolyte, membrane, dissociation, recombination, electroconvection, desalination channel

For citation: Kovalenko A.V., Gudza V.A., Chubyr N.O., Khromykh A.A., Urtenov M.K. Study of current chronograms, structure of dissociation, recombination and equilibrium regions in problems of non-stationary 1:1 electrolyte transfer in membrane systems using a mathematical model. Modeling, Optimization and Information Technology. 2022;10(1). URL: https://moitvivt.ru/ru/journal/pdf?id=1131 DOI: 10.26102/2310-6018/2022.36.1.028 (In Russ).

420

Full text in PDF

Received 15.01.2022

Revised 10.03.2022

Accepted 30.03.2022

Published 31.03.2022