CAPILLARY MODEL OF A CHARGED MEMBRANE WITH VARIABLE HYDROPHILICITY AND HYDROPHOBICITY

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Abstract

The paper proposes a capillary model of a charged membrane consisting of a set of separated by impenetrable material plane-parallel slit hydrophilic pores, on the surface of which a zeta potential can be set, or a fixed charge density and a liquid adhesion condition, and hydrophobic pores that differ from hydrophilic ones in size, zeta potential (fixed charge density), and Navier slip condition. The hydrodynamic and electroosmotic permeability of the membrane and its electrical conductivity are derived as functions of relative hydrophilic and hydrophobic porosity, electrolyte concentration, surface charges or potentials, dielectric properties of the solution, ion diffusion coefficients and their charge numbers, and the sizes of both types of pores. In all cases, compliance with the Onsager reciprocity principle for cross coefficients L12 and L21, responsible for the electroosmosis and the streaming current is shown. All boundary value problems for the four types of pores are solved analytically in the Debye-Hückel approximation. It has been established that, under the action of external pressure and electric potential gradients, in the case of aqueous organic mixtures against the background of a weak electrolyte solution, a multidirectional flow of components through the hydrophilic and hydrophobic pores of the membrane is possible. The results obtained make it possible to predict the transport properties of a charged membrane depending on the ratio between the fractions of hydrophilic and hydrophobic pores.

About the authors

A. N. Filippov

Gubkin Russian State University of Oil and Gas (National Research University)

Email: filippov.a@gubkin.ru
Moscow, Russia

References

  1. Tseng H.-H., Lau WJ., Al-Ghouti M.A., An L. (editors) 60 Years of the Loeb-Sourirajan membrane. Principles, New Materials, Modelling, Characterization, and Applications. Elsevier. 2022. https://doi.org/10.1016/B978-0-323-89977-2.00030-0
  2. Бункин Н.Ф., Козлов В.А., Кирьянова М.С., Сафроненков Р.С., Болоцкова П.Н., Горелик В.С., Джураев Й., Сабиров Л.М., Применко А.Э., Vu M.T. Исследование эффектов нестационарности при набухании полимерных мембран с помощью Фурье ИК спектроскопии // Оптика и спектроскопия. 2021. Т. 129. № 4. С. 472-482. https://doi.org/10.21883/OS.2021.04.50777.241-20
  3. Голубев Г.С., Соколов С.Е., Рахманка Т.Н., Бахтин Д.С., Борисов И.Л., Волков А.В. Мембраны на основе ПТМСП и сверхсшитого полистирола для газоразделения и термопервапорационного выделения летучих органических соединений из водных сред // Мембраны и мембранные технологии. 2022. Т. 12. № 6. С.459-469. https://doi.org/10.31857/S2218117222060037
  4. Yamauchi Yu., Блонская И.В., Апель П.Ю. Осмос в отрицательно заряженных нанокапиллярах и его усиление анионным поверхностно-активным веществом // Коллоид. журн. 2019. Т. 81. № 1. С. 125-136. https://doi.org/10.1134/S0023291219010166
  5. Meng L., Shi W., Li Y., Li X., Tong X., Wang Z. Janus membranes at the water-energy nexus: A critical review // Advances in Colloid and Interface Science. 2023. V. 318. P. 102937. https://doi.org/10.1016/j.cis.2023.102937
  6. Zou L., Gusnawan P., Zhang G., Yu J. Novel Janus composite hollow fiber membrane-based direct contact membrane distillation (DCMD) process for produced water desalination // Journal of Membrane Science. 2020. V. 597. P. 117756. https://doi.org/10.1016/j.memsci.2019.117756
  7. Zhao S., Tao Z., Han M., Huang Yu-xi., Zhao B., Wang L., Tian X., Meng F. Hierarchical Janus membrane with superior fouling and wetting resistance for efficient water recovery from challenging wastewater via membrane distillation // Journal of Membrane Science. 2021. V. 618. P. 118676. https://doi.org/10.1016/j.memsci.2020.118676
  8. Rodrigues L.N., Sirkar R.R., Weisbrod K.R., Ahern J.C., Beuscher U. Porous hydrophobic-hydrophilic Janus membranes for nondispersive membrane solvent extraction // Journal of Membrane Science. 2021. V. 637. P. 119633. https://doi.org/10.1016/j.memsci.2021.119633
  9. Uragami T., Saito M., Takigawa K. Studies on syntheses and permeabilities of special polymer membranes, 69. Comparison of permeation and separation characteristics for aqueous alcoholic solutions by pervaporation and new evaporation methods through chitosan membranes // Macromol. Chem., Rapid Commun. 1988. V. 9. № 5. P. 361-365. https://doi.org/10.1002/marc.1988.030090513
  10. Виноградов И.И., Дрожжин Н.А., Кравец Л.И., Россоу А., Вершинина Т.Н., Нечаев А.Н. Формирование прямых трендов в водосборах рабочих зон тепловой дестилляции // Коллоид. журн. 2024. Т. 86. № 5. С. 533-548. https://doi.org/10.31857/S0023291224050029
  11. Anamourlis C. The cell membrane // South Afr. J. Anaesth. Analg. 2020. V. 6. № 26. P. S1-7. https://doi.org/10.36303/SAJAA.2020.26.6.S3.2527
  12. Filippov A.N., Kononenko N.A., Loza N.V., Petrova D.A. Modeling asymmetry of a current-voltage curve of a novel MF-4SC/PTMSP bilayer membrane // Membranes MDPI. 2022. V.12. № 1. P. 22. https://doi.org/10.3390/membranes12010022
  13. Zhang R., Sun Y., Guo Z., Liu W. Janus membranes with asymmetric wettability applied in oil/water emulsion separations // Adv. Sustainable Syst. 2021. V. 5. № 5. P. 2000253. https://doi.org/10.1002/adsu.202000253
  14. Zuo J.-H., Gu Y.-H., Wei C., Yan X., Chen Y., Lang W.-Z. Janus polyvinylidene fluoride membranes fabricated with thermally induced phase separation and spray-coating technique for the separations of both W/O and O/W emulsions // Journal of Membrane Science. 2020. V. 595. P. 117475. https://doi.org/10.1016/j.memsci.2019.117475
  15. Main applications of hydrophobic and hydrophilic PTFE membrane filter. https://www.hawachmembrane.com/main-applications-of-hydrophobic-and-hydrophilic-pfte-membrane-filter. (accessed on June 30, 2025).
  16. Tian X., Li J., Wang X. Anisotropic liquid penetration arising from a cross-sectional wettability gradient // Soft Matter. 2012. V. 8. № 9. P. 2633-2637. https://doi.org/10.1039/c2sm07111h
  17. Филиппов А.Н., Иванов В.И., Юшкин А.А., Волков В.В., Богданова Ю.Г., Должикова В.Д. Моделирование возникновения течения водно-этанольной смеси через полимерную мембрану на основе ПТМСП при нанофильтрации // Мембраны и мембранные технологии. 2015. Т. 5. № 2. С. 103-119. https://doi.org/10.1134/S2218117215020054
  18. Chamani A., Rana D., Matsuura T., Lan Ch. Directional water transport of Janus membrane - theoretical approach // Desalination. 2025. V. 601. P. 118577. https://doi.org/10.1016/j.desal.2025.118577
  19. Tseng S., Kao C.-Y., Hsu J.-P. Electrokinetic flow in a planar slit covered by an ion-penetrable charged membrane // Electrophoresis. 2000. V. 21. № 17. P. 3541-3551. https://doi.org/10.1002/1522-2683(200011)21:17%3C3541::aid-elps3541%3E3.0.co;2-9
  20. Ryzhkov I. I., Minakov A.V. Theoretical study of electrolyte transport in nanofiltration membranes with constant surface potential/charge density // J. Membr. Sci. 2016. V. 520. P. 515-528. https://doi.org/10.1016/j.memsci.2016.08.004
  21. Ramos E.A., Bautista O., Lizardi J.J., Mendez F.A perturbative thermal analysis for an electro-osmotic flow in a slit microchannel based on a lubrication theory // Int. J. Therm. Sci. 2017. V. 111. P. 499-510. https://doi.org/10.1016/j.ijthermalsci.2016.09.028
  22. Malick A., Barman B. Electroosmotic flow modulation through soft nanochannel filled with power-law fluid under impacts of ion steric and ion partitioning effects // Colloid J. 2024. V. 86. № 4. P. 610-626. https://doi.org/10.1134/S1061933X24600222
  23. Silikina E.F., Asmolov E.S., Vinogradova O.I. Electro-osmotic flow in hydrophobic nanochannels // Phys. Chem. Chem. Phys. 2019. V. 21. № 41. P. 23036. https://doi.org/10.1039/c9cp04259h
  24. Vinogradova O.I., Silikina E.F., Asmolov E.S. Transport of ions in hydrophobic nanotubes // Phys. Fluids. 2022. V. 34 № 12. P. 122003. https://doi.org/10.1063/5.0131440
  25. Фалина И.В., Кононенко Н.А., Шкирская С.А., Демина О.А., Вольфкович Ю.М., Сосенкин В.Е., Грицкий М.В. Экспериментальное и теоретическое исследование влияния природы противоиона на на электроосмотический перенос воды в сульфокатионитовых мембранах // Мембраны и мембранные технологии. 2022. Т. 12. № 5. С. 323-332. https://doi.org/10.31857/S2218117222050042
  26. Филиппов А.Н., Ханукаева Д.Ю., Васин С.И., Соболев В.Д., Старов В.М. Течение жидкости внутри цилиндрического капилляра, стенки которого покрыты пористым слоем (гелем) // Коллоид. журн. 2013. Т. 75. № 2. С. 237–249. https://doi.org/10.7868/S0023291213020055
  27. Li A., He X., Wu J., et al Ultrathin silicon nitride membrane with slit-shaped pores for high-performance separation of circulating tumor cells // Lab Chip. 2022. V. 22. № 19. P. 3676–3686. https://doi.org/10.1039/D2LC00703G
  28. van der Heyden F.H.J., Stein D., and Dekker C. Streaming currents in a single nanofluidic channel // Phys. Rev. Lett. 2005. V. 95. P. 116104. https://doi.org/10.1103/PhysRevLett.95.116104
  29. Filippov A.N., Ermakova L.E., Philippova T.S. Hydrodynamic permeability of charged porous glass-like membranes. Conference Proceeding "Ion Transport in Organic and Inorganic Membranes". I.T.I.M. 2024, Sochi, Russia. 2024. P. 80–82.
  30. Deo S., Filippov A., Tiwari A., Vasin S., Starov V. Hydrodynamic permeability of aggregates of porous particles with an impermeable core // Advances in Colloid and Interface Science. 2011. V. 164. № 1–2. P. 21–37. https://doi.org/10.1016/j.cis.2010.08.004
  31. https://neftegaz.ru/science/development/331612-geologicheskie-faktory-smachivaemosti-porod-kollektorov-nefti-i-gaza/?ysclid=mefjzesknq360987694
  32. Breslau B.R., Miller I.F. A hydrodynamic model for electrophoresis // Industrial and Engineering Chemistry Fundamentals. 1971. V. 10. № 4. P. 554–565.
  33. Фалина И.В., Демина О.А., Заболоцкий В.И. Верификация капиллярной модели электроосмотического переноса свободного растворителя в ионообменных мембранах различной природы // Коллоидный журнал. 2017. Т. 79. № 6. С. 792–801. https://doi.org/10.7868/S002329121706012X

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