Mathematical Simulation of Nanofiltration Process: State of Art Review

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dc.citation.epage199
dc.citation.issue2
dc.citation.journalTitleХімія та хімічна технологія
dc.citation.spage187
dc.citation.volume18
dc.contributor.affiliationNational Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
dc.contributor.affiliationUniversity of Montpellier
dc.contributor.authorHuliienko, Serhii
dc.contributor.authorKornienko, Yaroslav
dc.contributor.authorMuzyka, Svitlana
dc.contributor.authorHolubka, Kateryna
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-09-24T06:47:57Z
dc.date.created2024-02-27
dc.date.issued2024-02-27
dc.description.abstractПроведено огляд публікацій, присвячених математичному моделюванню процесу нанофільтрації, встановлено переваги, обмеження та сфери застосування різних підходів до моделювання. Виявлено, що найефективніші підходи ґрунтуються на розширеному рівняння Нернста-Планка, рівновазі Доннана, а також методах обчислювальної гідродинаміки та молекулярної динаміки. Розглянуто використання програмного забезпечення для вирішення завдань моделювання нанофільтрації.
dc.description.abstractA review of publications devoted to the mathematical simulation of the nanofiltration process was carried out, the advantages, limitations, and areas of application of various modeling approaches were determined. It was found that the most effective approaches are based on the extended Nernst-Planck equation, Donnan equilibrium, as well as methods of computational fluid dynamics and molecular dynamics. The use of software for solving nanofiltration simulation problems was considered.
dc.format.extent187-199
dc.format.pages13
dc.identifier.citationMathematical Simulation of Nanofiltration Process: State of Art Review / Serhii Huliienko, Yaroslav Kornienko, Svitlana Muzyka, Kateryna Holubka // Chemistry & Chemical Technology. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 18. — No 2. — P. 187–199.
dc.identifier.citationenMathematical Simulation of Nanofiltration Process: State of Art Review / Serhii Huliienko, Yaroslav Kornienko, Svitlana Muzyka, Kateryna Holubka // Chemistry & Chemical Technology. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 18. — No 2. — P. 187–199.
dc.identifier.doidoi.org/10.23939/chcht18.02.187
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/111797
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofХімія та хімічна технологія, 2 (18), 2024
dc.relation.ispartofChemistry & Chemical Technology, 2 (18), 2024
dc.relation.references[1] Gumnitsky, J.; Sabadash, V.; Matsuska, O.; Lyuta, O.; Hyvlud, A.; Venger, L. Dynamics of Adsorption of Copper Ions in Fixed-Bed Column and Mathematical Interpretation of the First Stage of the Process. Chem. Chem. Technol. 2022, 16, 267–273. https://doi.org/10.23939/chcht16.02.267
dc.relation.references[2] Semenyshyn, Y.; Atamanyuk, V.; Rymar, T.; Ivashchuk, O.; Hlukhaniuk, A. Mass Transfer in the Solid-Liquid System: Mechanism and Kinetics of the Extraction Process. Chem. Chem. Technol. 2020, 14, 121–128. https://doi.org/10.23939/chcht14.01.121
dc.relation.references[3] Havryshko, M.; Popovych, O.; Yaremko, H.; Tymchuk, I.; Malovanyy, M. Analysis of Prospective Technologies of Food Production Wastewater Treatment. Ecol. Eng. Environ. Technol. 2022, 2, 33–40. https://doi.org/10.12912/27197050/145201
dc.relation.references[4] Ramana, K. V.; Mohan, K. C.; Ravindhranath, K.; Babu, B. H. Bio-Sorbent Derived from Annona Squamosa for the Removal of Methyl Red Dye in Polluted Waters: A Study on Adsorption Potential. Chem. Chem. Technol. 2022, 16, 274–283. https://doi.org/10.23939/chcht16.02.274
dc.relation.references[5] Shon, H. K.; Phuntsho, S.; Chaudhary, D. S.; Vigneswaran, S., Cho, J. Nanofiltration for Water and Wastewater Treatment – A Mini Review. Drink Water Eng Sci. 2013, 6, 47–53. https://doi.org/10.5194/dwes-6-47-2013
dc.relation.references[6] Huliienko, S. V.; Korniienko, Y. M.; Gatilov, K. O. Modern Trends in the Mathematical Simulation of Pressure-Driven Membrane Processes. J. Eng. Sci. 2020, 71, F1–F21. https://doi.org/10.21272/jes.2020.7(1).f1
dc.relation.references[7] Huliienko, S. V.; Korniyenko, Y. M.; Muzyka, S. M.; Holubka K. Simulation of Reverse Osmosis Process: Novel Approaches and Development Trends. J. Eng. Sci. 2022, 92, F6–F36. https://doi.org/10.21272/jes.2022.9(2).f2
dc.relation.references[8] Yaroshchuk, A.; Bruening, M. L.; Zholkovskiy, E. Modelling Nanofiltration of Electrolyte Solutions. Adv. Colloid Interface Sci. 2019, 268, 39–63. https://doi.org/10.1016/j.cis.2019.03.004
dc.relation.references[9] Agboola, O.; Maree J.; Kolesnikov, A.; Mbaya, R.; Sadiku, R. Theoretical Performance of Nanofiltration Membranes for Wastewater Treatment. Environ. Chem. Lett. 2015, 13, 37–47. https://doi.org/10.1007/s10311-014-0486-y
dc.relation.references[10] Marchetti, P.; Livingston, A. G. Predictive Membrane Transport Models for Organic Solvent Nanofiltration: How Complex Do We Need to Be? J. Membr. Sci. 2015, 476, 530–553. https://doi.org/10.1016/j.memsci.2014.10.030
dc.relation.references[11] Schmidt, P.; Lutze, Ph. Characterisation of Organic Solvent Nanofiltration Membranes in Multi-Component Mixtures: Phenomena-based Modelling and Membrane Modelling Maps. J. Membr. Sci. 2013, 445, 183–199. https://doi.org/10.1016/j.memsci.2013.05.062
dc.relation.references[12] Zhang, Sh.; Zhou, J.; Fan, L.; Qiu, Y.; Jiang, L.; Zhao, L. Investigating the Mechanism of Nanofiltration Separation of Glucosamine Hydrochloride and N-acetyl Glucosamine. Bioresour. Bioprocess. 2016, 3, 34. https://doi.org/10.1186/s40643-016-0112-x
dc.relation.references[13] Anand, A.; Unnikrishnan, B.; Mao, J.-Y.; Lin, H.-J.; Huang, Ch.-Ch. Graphene-based Nanofiltration Membranes for Improving Salt Rejection, Water Flux and Antifouling–A review. Desalination 2018, 429, 119–133. https://doi.org/10.1016/j.desal.2017.12.012
dc.relation.references[14] Mohammad, A.W.; Teow, Y.H.; Ang, W.L.; Chung, Y.T.; Oatley-Radcliffe, D.L.; Hilal, N. Nanofiltration Membranes Review: Recent Advances and Future Prospects. Desalination 2015, 356, 226–254. https://doi.org/10.1016/j.desal.2014.10.043
dc.relation.references[15] Ahmed, F. E.; Hashaikeh, R.; Diabat, A.; Hilal, N. Mathematical and Optimization Modelling in Desalination: State-of-the-art and Future Direction. Desalination 2019, 469, 114092. https://doi.org/10.1016/j.desal.2019.114092
dc.relation.references[16] Zhou, D.; Zhu, L.; Fu, Y.; Zhu, M.; Xue, L. Development of Lower Cost Seawater Desalination Processes Using Nanofiltration Technologies — A Review. Desalination 2015, 376, 109–116. https://doi.org/10.1016/j.desal.2015.08.020
dc.relation.references[17] Souza, V. C.; Quadri, M. G. N. Organic-inorganic hybrid membranes in separation processes: a 10-year review. Braz. J. Chem. Eng. 2013, 30, 683–700. https://doi.org/10.1590/S0104-66322013000400001
dc.relation.references[18] Wang, J.; Dlamini, D. S.; Mishra, A. K.; Pendergast, M. Th. M.; Wong, M. C. Y.; Mamba, B. B.; Freger, V.; Verliefd, A. R. D.; Hoek, E. M. V. A Critical Review of Transport through Osmotic Membranes. J. Membr. Sci. 2014, 454, 516–537. https://doi.org/10.1016/j.memsci.2013.12.034
dc.relation.references[19] Keir, G.; Jegatheesan, V. A Review of Computational Fluid Dynamics Applications in Pressure-Driven Membrane Filtration. Rev. Environ. Sci. Biotechnol. 2013, 13, 183–201. https://doi.org/10.1007/s11157-013-9327-x
dc.relation.references[20] Ebro, H.; Kim, Y. M.; Kim, J. H. Molecular Dynamics Simulations in Membrane-Based Water Treatment Processes: A Systematic Overview. J. Membr. Sci. 2013, 438, 112–125. https://doi.org/10.1016/j.memsci.2013.03.027
dc.relation.references[21] Zhang, Y.; Zhu, Y.; Wang, A.; Gao, Q.; Qin, Y.; Chen, Y.; Lu, X. Progress in Molecular-Simulation-Based Research on the Effects of Interface-induced Fluid Microstructures on Flow Resistance. Chin. J. Chem. Eng. 2019, 27, 1403–1415. https://doi.org/10.1016/j.cjche.2019.02.002
dc.relation.references[22] Peshev, D.; Livingston, A. G. OSN Designer, a Tool for Predicting Organic Solvent Nanofiltration Technology Performance Using ASPEN ONE, MATLAB and CAPE OPEN. Chem. Eng. Sci. 2013, 104, 975–987. https://doi.org/10.1016/j.ces.2013.10.033
dc.relation.references[23] Abejon, R.; Garea, A.; Irabien, A. Organic Solvent Recovery and Reuse in Pharmaceutical Purification Processes by Nanofiltration Membrane Cascades. Chem. Eng. Trans. 2015, 43, 1057–1062. https://doi.org/10.3303/CET1543177
dc.relation.references[24] Hidalgo, A. M.; León, G.; Gómez, M.; Murcia, M. D.; Gómez, E.; Macario, J. A. Removal of Different Dye Solutions: A Comparison Study Using a Polyamide NF Membrane. Membranes 2020, 10, 408. https://doi.org/10.3390/membranes10120408
dc.relation.references[25] Yan, Z-Q.; Zeng, L-M.; Li, Q.; Liu, T-Y.; Matsuyama, H.; Wang, X-L. Selective Separation of Chloride and Sulfate by Nanofiltration for High Saline Wastewater Recycling. Sep. Purif. Technol. 2016, 166, 135–141. https://doi.org/10.1016/j.seppur.2016.04.009
dc.relation.references[26] Shahmansouri, A.; Bellona, C. Application of Quantitative Structure–Property Relationships (QSPRs) to Predict the Rejection of Organic Solutes by Nanofiltration. Sep. Purif. Technol. 2013, 118, 627–638. https://doi.org/10.1016/j.seppur.2013.07.050
dc.relation.references[27] Schlackl, K.; Herchl, R.; Samhaber, W. Nanofiltration of Succinic Acid in Strong Alkaline Conditions. Membranes 2019, 9, 147. https://doi.org/10.3390/membranes9110147
dc.relation.references[28] Kim, J. H.; Na, J.-G.; Shim, H. J.; Chang, Y. K. Modeling of Ammonium Lactate Recovery and Impurity Removal from Simulated Fermentation Broth by Nanofiltration. J. Membr. Sci. 2012, 396, 110–118. https://doi.org/10.1016/j.memsci.2012.01.003
dc.relation.references[29] Nair, R. R.; Protasova, E.; Strand, S.; Bilstad, T. Implementation of Spiegler–Kedem and Steric Hindrance Pore Models for Analyzing Nanofiltration Membrane Performance for Smart Water Production. Membranes 2018, 8, 78. https://doi.org/10.3390/membranes8030078
dc.relation.references[30] Peddie, W. L.; van Rensburg, J. N.; Vosloo, H. C. M.; van der Gryp, P. Technological Evaluation of Organic Solvent Nanofiltration for the Recovery of Homogeneous Hydroformylation Catalysts. Chem. Eng. Res. Des. 2017, 121, 219–232. https://doi.org/10.1016/j.cherd.2017.03.015
dc.relation.references[31] ten Kate, A. J. B.; Schutyser, M.A.I.; Kuzmanovic, B.; Westerink, J.B.; Manuhutu, F.; Bargeman, G. Thermodynamic Perspective on Negative Retention Effects in Nanofiltration of Concentrated Sodium Chloride Solutions. Sep. Purif. Technol. 2020, 250, 117242. https://doi.org/10.1016/j.seppur.2020.117242
dc.relation.references[32] Minelli, M.; Sarti, G. C. Modeling Mass Transport in Dense Polymer Membranes: Cooperative Synergy among Multiple Scale Approaches. Curr. Opin. Chem. Eng. 2020, 28, 43–50. https://doi.org/10.1016/j.coche.2020.01.004
dc.relation.references[33] Qian, J.; Yan, R.; Liu, X.; Li, Ch.; Zhang, X. Modification to Solution-Diffusion Model for Performance Prediction of Nanofiltration of Long-alkyl-chain Ionic Liquids Aqueous Solutions Based on Ion Cluster. Green Energy Environ. 2020, 5, 105–113. https://doi.org/10.1016/j.gee.2018.10.001
dc.relation.references[34] Li, C.; Ma, Y.; Li, H.; Peng, G. Exploring the Nanofiltration Mass Transfer Characteristic and Concentrate Process of Procyanidins from Grape Juice. Food Sci. Nutr. 2019, 7, 1884–1890. https://doi.org/10.1002/fsn3.1045
dc.relation.references[35] Abels, C.; Redepenning, C.; Moll, A.; Melin, T.; Wessling, M. Simple Purification of Ionic Liquid Solvents by Nanofiltration in Biorefining of Lignocellulosic Substrates. J. Membr. Sci. 2012, 405–406, 1–10. https://doi.org/10.1016/j.memsci.2011.12.020
dc.relation.references[36] Shi, B.; Marchetti, P.; Peshev, D.; Zhang, Sh.; Livingston, A. G. Performance of Spiral-Wound Membrane Modules in Organic Solvent Nanofiltration – Fluid Dynamics and Mass Transfer Characteristics. J. Membr. Sci. 2015, 494, 8–24. https://doi.org/10.1016/j.memsci.2015.07.044
dc.relation.references[37] Micovic, J.; Werth, K.; Lutze, Ph. Hybrid Separations Combining Distillation and Organic Solvent Nanofiltration for Separation of Wide Boiling Mixtures. Chem. Eng. Res. Des. 2014, 92, 2131–2147. https://doi.org/10.1016/j.cherd.2014.02.012
dc.relation.references[38] Werhan, H.; Farshori, A.; von Rohr, Ph. R. Separation of Lignin Oxidation Products by Organic Solvent Nanofiltration. J. Membr. Sci. 2012, 423–424, 404–412. https://doi.org/10.1016/j.memsci.2012.08.037
dc.relation.references[39] Werth, K.; Kaupenjohann, P.; Knierbein, M.; Skiborowski, M. Solvent Recovery and Deacidification by Organic Solvent Nanofiltration: Experimental Investigation and Mass Transfer Modelling. J. Membr. Sci. 2017, 528, 369–380. https://doi.org/10.1016/j.memsci.2017.01.021
dc.relation.references[40] Keucken, A.; Wang, Y.; Tng, K. H.; Leslie, G.; Spanjer, T.; Köhler, S. J. Optimizing Hollow Fibre Nanofiltration for Organic Matter Rich Lake Water. Water 2016, 8, 430. https://doi.org/10.3390/w8100430
dc.relation.references[41] Altaee, A.; Hilal, N. High Recovery Rate NF–FO–RO Hybrid System for Inland Brackish Water Treatment. Desalination 2015, 363, 19–25. https://doi.org/10.1016/j.desal.2014.12.017
dc.relation.references[42] Shaaban, A. M. F.; Hafez, A. I.; Abdel-Fatah, M. A.; Abdel-Monem, N. M.; Mahmoud, M. H. Process Engineering Optimization of Nanofiltration Unit for the Treatment of Textile Plant Effluent in View of Solution Diffusion Model. Egypt. J. Pet. 2016, 25, 79–90. https://doi.org/10.1016/j.ejpe.2015.03.018
dc.relation.references[43] Marchetti, P.; Butte, A.; Livingston, A. G. An Improved Phenomenological Model for Prediction of Solvent Permeation Through Ceramic NF and UF Membranes. J. Membr. Sci. 2012, 415–416, 444–458. https://doi.org/10.1016/j.memsci.2012.05.030
dc.relation.references[44] Fierro, D.; Boschetti-de-Fierro, A.; Abetz, V. The Solution-Diffusion with Imperfections Model as a Method to Understand Organic Solvent Nanofiltration of Multicomponent Systems. J. Membr. Sci. 2012, 413–414, 91–101. https://doi.org/10.1016/j.memsci.2012.04.027
dc.relation.references[45] Werth, K.; Kaupenjohann, P.; Skiborowski, M. The Potential of Organic Solvent Nanofiltration Processes for Oleochemical Industry. Sep. Purif. Technol. 2017, 182, 185–196. https://doi.org/10.1016/j.seppur.2017.03.050
dc.relation.references[46] Pérez, L.; Escudero, I.; Arcos-Martínez, M. J.; Benito, J. M. Application of the Solution-Diffusion-Film Model for the Transfer of Electrolytes and Uncharged Compounds in a Nanofiltration Membrane. J Ind Eng Chem. 2017, 47, 368–74. https://doi.org/10.1016/j.jiec.2016.12.007
dc.relation.references[47] Yonge, D.T.; Biscardi, P. G.; Duranceau, S. J. Modeling Ionic Strength Effects on Hollow-Fiber Nanofiltration Membrane Mass Transfer. Membranes 2018, 8, 37. https://doi.org/10.3390/membranes8030037
dc.relation.references[48] Yaroshchuk, A.; Bruening, M. L. An analytical Solution of the Solution-Diffusion-Electromigration Equations Reproduces Trends in ion Rejections During Nanofiltration of Mixed Electrolytes. J. Membr. Sci. 2017, 523, 361–372. https://doi.org/10.1016/j.memsci.2016.09.046
dc.relation.references[49] Madsen, H.T.; Søgaard, E.G. Applicability and Modelling of Nanofiltration and Reverse Osmosis for Remediation of Groundwater Polluted with Pesticides and Pesticide Transformation Products. Sep. Purif. Technol. 2014, 125, 111–119. https://doi.org/10.1016/j.seppur.2014.01.038
dc.relation.references[50] Liu, Y-l.; Wei, W.; Wang, X-m.; Yang, H-w.; Xie, Y.F. Relating the Rejections of Oligomeric Ethylene Glycols and Saccharides by Nanofiltration: Implication for Membrane Pore Size Determination. Sep. Purif. Technol. 2018, 205, 151–158. https://doi.org/10.1016/j.seppur.2018.05.042
dc.relation.references[51] Xu, R.; Zhou, M.; Wang, H.; Wang, X.; Wen, X. Influences of Temperature on the Retention of PPCPs by Nanofiltration Membranes: Experiments and Modeling Assessment. J. Membr. Sci. 2020, 599, 117817. https://doi.org/10.1016/j.memsci.2020.117817
dc.relation.references[52] Kong, F.-x.; Yang, H.-w.; Wang, X.-m.; Xie, Y. F. Assessment of the Hindered Transport Model in Predicting the Rejection of Trace Organic Compounds by Nanofiltration. J. Membr. Sci. 2016, 498, 57–66. https://doi.org/10.1016/j.memsci.2015.09.062
dc.relation.references[53] Aguirre Montesdeoca, V.; Van der Padt, A., Boom, R.M., Janssen, A.E.M. Modelling of Membrane Cascades for the Purification of Oligosaccharides. J. Membr. Sci. 2016, 520, 712–722. https://doi.org/10.1016/j.memsci.2016.08.031
dc.relation.references[54] Darvishmanesh, S.; Van der Bruggen, B. Mass Transport through Nanostructured Membranes: Towards a Predictive Tool. Membranes 2016, 6, 49. https://doi.org/10.3390/membranes6040049
dc.relation.references[55] Labban, O.; Chong, T. H.; Lienhard, V J. H. Design and Modeling of Novel Low-Pressure Nanofiltration Hollow Fiber Modules for Water Softening and Desalination Pretreatment. Desalination 2018, 439, 58–72. https://doi.org/10.1016/j.desal.2018.04.002
dc.relation.references[56] Déon, S.; Escoda, A.; Fievet, P.; Dutournié, P.; Bourseau P. How to Use a Multi-Ionic Transport Model to Fully Predict Rejection of Mineral Salts by Nanofiltration Membranes. Chem. Eng. J. 2012, 189–190, 24–31. https://doi.org/10.1016/j.cej.2012.02.014
dc.relation.references[57] Thibault, K.; Zhu, H.; Szymczyk, A.; Li, G. The Averaged Potential Gradient Approach to Model the Rejection of Electrolyte Solutions Using Nanofiltration: Model Development and Assessment for Highly Concentrated Feed Solutions. Sep. Purif. Technol. 2015, 153, 126–37. https://doi.org/10.1016/j.seppur.2015.08.041
dc.relation.references[58] Blumenschein, S.; Böcking, A.; Kätzel, U.; Postel, S.; Wessling, M. Rejection Modeling of Ceramic Membranes in Organic Solvent Nanofiltration. J. Membr. Sci. 2016, 510, 191–200. https://doi.org/10.1016/j.memsci.2016.02.042
dc.relation.references[59] Fadaei, F.; Shirazian, S.; Ashrafizadeh, S. N. Mass Transfer Modeling of ion Transport through Nanoporous Media. Desalination 2011, 281, 325–333. https://doi.org/10.1016/j.desal.2011.08.025
dc.relation.references[60] Dey, P.; Linnanen, L.; Pal, P. Separation of Lactic Acid from Fermentation Broth by Cross Flow Nanofiltration: Membrane Characterization and Transport Modelling. Desalination 2012, 288, 47–57. https://doi.org/10.1016/j.desal.2011.12.009
dc.relation.references[61] Farsi, A.; Boffa, V.; Qureshi, H. F.; Nijmeijer, A.; Winnubst, L.; Christensen, M. L. Modeling Water Flux and Salt Rejection of Mesoporous γ-Alumina and Microporous Organosilica Membranes. J. Membr. Sci. 2014, 470, 307–315. https://doi.org/10.1016/j.memsci.2014.07.038
dc.relation.references[62] Pal, P.; Das, P.; Chakrabortty, S.; Thakura, R. Dynamic Modelling of a Forward Osmosis-Nanofiltration Integrated Process for Treating Hazardous Wastewater. Environ. Sci. Pollut. Res. 2016, 23, 21604–21618. https://doi.org/10.1007/s11356-016-7392-8
dc.relation.references[63] Silva, V.; Martın, A.; Martınez, F.; Malfeito, J.; Pradanos, P.; Palacio, L.; Hernandez, A. Electrical Characterization of NF Membranes. A Modified Model with Charge Variation along the Pores. Chem. Eng. Sci. 2011, 66, 2898–2911. https://doi.org/10.1016/j.ces.2011.03.025
dc.relation.references[64] Zerafat, M.M.; Shariati-Niassar, M.; Hashemi, S.J.; Sabbaghi, S.; Ismail, A.F.; Matsuura, T. Mathematical Modeling of Nanofiltration for Concentrated Electrolyte Solutions. Desalination 2013, 320, 17–23. https://doi.org/10.1016/j.desal.2013.04.015
dc.relation.references[65] Pal, P.; Sardar, M.; Pal, M.; Chakrabortty, S.; Nayak, J. Modelling Forward Osmosis-Nanofiltration Integrated Process for Treatment and Recirculation of Leather Industry Wastewater. Comput Chem Eng. 2019, 127, 99–110. https://doi.org/10.1016/j.compchemeng.2019.05.018
dc.relation.references[66] Kumar, R.; Chakrabortty, S.; Pal, P. Membrane-Integrated Physico-Chemical Treatment of Coke-Oven Wastewater: Transport Modelling and Economic Evaluation. Environ. Sci. Pollut. Res. 2015, 22, 6010–6023. https://doi.org/10.1007/s11356-014-3787-6
dc.relation.references[67] Luo, J.; Wan, Y. Effect of highly Concentrated Salt on Retention of Organic Solutes by Nanofiltration Polymeric Membranes. J. Membr. Sci. 2011, 372, 145–153. https://doi.org/10.1016/j.memsci.2011.01.066
dc.relation.references[68] Chakrabortty, S.; Sen, M.; Pal, P. Arsenic Removal from Contaminated Groundwater by Membrane-Integrated Hybrid Plant: Optimization and Control Using Visual Basic Platform. Environ. Sci. Pollut. Res. 2014, 21, 3840–3857. https://doi.org/10.1007/s11356-013-2382-6
dc.relation.references[69] Chakrabortty, S.; Roy, M.; Pal, P. Removal of Fluoride from Contaminated Groundwater by Cross Flow Nanofiltration: Transport Modeling and Economic Evaluation. Desalination 2013, 313, 115–124. https://doi.org/10.1016/j.desal.2012.12.021
dc.relation.references[70] Oatley-Radcliffe, D. L.; Williams, S. R.; Barrow, M. S.; Williams, P. M. Critical Appraisal of Current Nanofiltration Modelling Strategies for Seawater Desalination and Further Insights on Dielectric Exclusion. Desalination 2014, 343, 154–161. https://doi.org/10.1016/j.desal.2013.10.001
dc.relation.references[71] Roy, Y.; Sharqawy, M. H.; Lienhard, J. H. Modeling of Flat-Sheet and Spiral-Wound Nanofiltration Configurations and its Application in Seawater Nanofiltration. J. Membr. Sci. 2015, 493, 360–372. https://doi.org/10.1016/j.memsci.2015.06.030
dc.relation.references[72] Bonner, R.; Germishuizen, Ch.; Franzsen, S. Prediction of Nanofiltration Rejection Performance in Brackish Water Reverse Osmosis Brine Treatment Processes. J. Water Process. Eng. 2019, 32, 100900. https://doi.org/10.1016/j.jwpe.2019.100900
dc.relation.references[73] Labban, O.; Liu, Ch.; Chong, T. H.; Lienhard, J. H. Fundamentals of Low-Pressure Nanofiltration: Membrane Characterization, Modeling, and Understanding the Multi-Ionic Interactions in Water Softening. J. Membr. Sci. 2017, 521, 18–32. https://doi.org/10.1016/j.memsci.2016.08.062
dc.relation.references[74] Chakrabortty, S.; Nayak, J.; Pal, P.; Kumar, R.; Chakraborty, P. Separation of COD, Sulphate and Chloride from Pharmaceutical Wastewater Using Membrane Integrated System: Transport Modeling Towards Scale-Up. J. Environ. Chem. Eng. 2020, 8, 104275. https://doi.org/10.1016/j.jece.2020.104275
dc.relation.references[75] Pal, P.; Thakura, R., Chakrabortty S. Performance Analysis and Optimization of an Advanced Pharmaceutical Wastewater Treatment Plant Through a Visual Basic Software Tool (PWWT.VB). Environ. Sci. Pollut. Res. 2016, 23, 9901–9917. https://doi.org/10.1007/s11356-016-6238-8
dc.relation.references[76] Roy, Y.; Warsinger, D. M.; Lienhard, J. H. Effect of Temperature on Ion Transport in Nanofiltration Membranes: Diffusion, Convection and Electromigration. Desalination 2017, 420, 241–257. https://doi.org/10.1016/j.desal.2017.07.020
dc.relation.references[77] Déon, S.; Escoda, A.; Fievet, P. A Transport Model Considering Charge Adsorption Inside Pores to Describe Salts Rejection by Nanofiltration Membranes. Chem. Eng. Sci. 2011, 66, 2823–2832. https://doi.org/10.1016/j.ces.2011.03.043
dc.relation.references[78] Bajpai, Sh.; Rajendran, R. M.; Hooda, S. Modeling the Performance of HPA Membrane for Sulfate Ion Removal from Ternary Ion System. Korean J. Chem. Eng. 2019, 36, 1648–1656. https://doi.org/10.1007/s11814-019-0357-0
dc.relation.references[79] Fang, J.; Deng, B. Rejection and Modeling of Arsenate by Nanofiltration: Contributions of Convection, Diffusion and Electromigration to Arsenic Transport. J. Membr. Sci. 2014, 453, 42–51. https://doi.org/10.1016/j.memsci.2013.10.056
dc.relation.references[80] Cathie Lee, W.P.; Mah, Sh.-K.; Leo, C.P.; Wu, T. Y.; Chai, S.-P. Phosphorus Removal by NF90 Membrane: Optimisation Using Central Composite Design. J. Taiwan Inst. Chem. Eng. 2014, 45, 1260–1269. https://doi.org/10.1016/j.jtice.2014.02.011
dc.relation.references[81] Bandini, S.; Morelli, V. Effect of Temperature, pH and Composition on Nanofiltration of Mono/Disaccharides: Experiments and Modeling Assessment. J. Membr. Sci. 2017, 533, 57–74. https://doi.org/10.1016/j.memsci.2017.03.021
dc.relation.references[82] Liu, H.; Zhao, L.; Fan, L.; Jiang, L.; Qiu, Y.; Xia, Q.; Zhou J. Establishment of a Nanofiltration Rejection Sequence and Calculated Rejections of Available Monosaccharides. Sep. Purif. Technol. 2016, 163, 319–330. https://doi.org/10.1016/j.seppur.2016.03.016
dc.relation.references[83] Shah, A. D.; Huang, Ch.-H.; Kim, J.-H. Mechanisms of Antibiotic Removal by Nanofiltration Membranes: Model Development and Application. J. Membr. Sci. 2012, 389, 234–244. https://doi.org/10.1016/j.memsci.2011.10.034
dc.relation.references[84] Balannec, B.; Ghoufi, A.; Szymczyk, A. Nanofiltration Performance of Conical and Hourglass Nanopores. J. Membr. Sci. 2018, 552, 336–340. https://doi.org/10.1016/j.memsci.2018.02.026
dc.relation.references[85] Fadaei, F.; Hoshyargar, V.; Shirazian, S.; Ashrafizadeh S. Mass Transfer Simulation of Ion Separation by Nanofiltration Considering Electrical and Dielectrical Effects. Desalination 2012, 284, 316–323. https://doi.org/10.1016/j.desal.2011.09.018
dc.relation.references[86] Fridman-Bishop, N.; Tankus, K. A.; Freger, V. Permeation Mechanism and Interplay between Ions in Nanofiltration. J. Membr. Sci. 2018, 548, 449–458. https://doi.org/10.1016/j.memsci.2017.11.050
dc.relation.references[87] Zhu, Y.; Zhu, H.; Li, G.; Mai, Zh.; Gu, Y. The Effect of Dielectric Exclusion on the Rejection Performance of Inhomogeneously Charged Polyamide Nanofiltration Membranes. J Nanopart Res. 2019, 21, 217. https://doi.org/10.1007/s11051-019-4665-4
dc.relation.references[88] Marecka-Migacz, A.; Mitkowski, P. T.; Nedzarek, A., Rózanski, J.; Szaferski, W. Effect of pH on Total Volume Membrane Charge Density in the Nanofiltration of Aqueous Solutions of Nitrate Salts of Heavy Metals. Membranes 2020, 10, 235. https://doi.org/10.3390/membranes10090235
dc.relation.references[89] Ortiz-Albo, P.; Ibañez R.; Urtiaga A.; Ortiz I. Phenomenological Prediction of Desalination Brines Nanofiltration through the Indirect Determination of Zeta Potential. Sep. Purif. Technol. 2019, 210, 746–753. https://doi.org/10.1016/j.seppur.2018.08.066
dc.relation.references[90] Marecka-Migacz, A.; Mitkowski, P. T.; Antczak, J.; Rózanski, J.; Prochaska K. Assessment of the Total Volume Membrane Charge Density through Mathematical Modeling for Separation of Succinic Acid Aqueous Solutions on Ceramic Nanofiltration Membrane. Processes 2019, 7, 559. https://doi.org/10.3390/pr7090559
dc.relation.references[91] Micari, M.; Diamantidou, D.; Heijman, B.; Moser, M.; Haidari A., Spanjers, H.; Bertsch V. Experimental and Theoretical Characterization of Commercial Nanofiltration Membranes for the Treatment of Ion Exchange Spent Regenerant. J. Membr. Sci. 2020, 606, 118117. https://doi.org/10.1016/j.memsci.2020.118117
dc.relation.references[92] Wang, X.; Li B.; Zhang, T.; Li, X. Performance of Nanofiltration Membrane in Rejecting Trace Organic Compounds: Experiment and Model Prediction. Desalination 2015, 370, 7–16. https://doi.org/10.1016/j.desal.2015.05.010
dc.relation.references[93] Kumar, V. S.; Hariharan, K. S.; Mayya, K. S.; Han, S. Volume Averaged Reduced Order Donnan Steric Pore Model for Nanofiltration Membranes. Desalination 2013, 322, 21–28. https://doi.org/10.1016/j.desal.2013.04.030
dc.relation.references[94] Wang, Zh.; Xiao, K.; Wang, X. Role of Coexistence of Negative and Positive Membrane Surface Charges in Electrostatic Effect for Salt Rejection by Nanofiltration. Desalination 2018, 444, 75–83. https://doi.org/10.1016/j.desal.2018.07.010
dc.relation.references[95] Escoda, A.; Déon, S.; Fievet, P. Assessment of Dielectric Contribution in the Modeling of Multi-Ionic Transport Through Nanofiltration Membranes. J. Membr. Sci. 2011, 378, 214–223. https://doi.org/10.1016/j.memsci.2011.05.004
dc.relation.references[96] Karakhim, S. O.; Zhuk, P. F.; Kosterin, S. O. Kinetics Simulation of Transmembrane Transport of Ions and Molecules Through a Semipermeable Membrane. J. Bioenerg. Biomembr. 2020, 52, 47–60. https://doi.org/10.1007/s10863-019-09821-8
dc.relation.references[97] Hoshyargar, V.; Fadaei, F.; Ashrafizadeh, S. N. Mass Transfer Simulation of Nanofiltration Membranes for Electrolyte Solutions through Generalized Maxwell-Stefan Approach. Korean J. Chem. Eng. 2015, 32, 1388–1404. https://doi.org/10.1007/s11814-014-0329-3
dc.relation.references[98] Saeed, A.; Vuthaluru, R.; Vuthaluru, H. B. Investigations into the Effects of Mass Transport and Flow Dynamics of Spacer Filled Membrane Modules Using CFD. Chem. Eng. Res. Des. 2015, 93, 79–99. https://doi.org/10.1016/j.cherd.2014.07.002
dc.relation.references[99] Kaufman, Y.; Kasher, R.; Lammertink, R. G. H.; Freger, V. Microfluidic NF/RO Separation: Cell Design, Performance and Application. J. Membr. Sci. 2012, 396, 67–73. https://doi.org/10.1016/j.memsci.2011.12.052
dc.relation.references[100] Asefi, H.; Alighardashi, A.; Fazeli, M., Fouladitajar A. CFD Modeling and Simulation of Concentration Polarization Reduction by Gas Sparging Cross-flow Nanofiltration. J. Environ. Chem. Eng. 2019, 7, 103275. https://doi.org/10.1016/j.jece.2019.103275
dc.relation.references[101] Cao, H.; O'Rourke, M.; Habimana, O.; Casey, E. Analysis of Surrogate Bacterial Cell Transport to Nanofiltration Membranes: Effect of Salt Concentration and Hydrodynamics. Sep. Purif. Technol. 2018, 207, 498–505. https://doi.org/10.1016/j.seppur.2018.06.072
dc.relation.references[102] Onorato, C.; Gaedtke, M.; Kespe, M.; Nirschl, H.; Schäfer, A. I. Renewable Energy Powered Membrane Technology: Computational Fluid Dynamics Evaluation of System Performance with Variable Module Size and Fluctuating Energy. Sep. Purif. Technol. 2019, 220, 206–216. https://doi.org/10.1016/j.seppur.2019.02.041
dc.relation.references[103] Kostoglou, M.; Karabelas, A. J. Comprehensive Simulation of Flat-Sheet Membrane Element Performance in Steady State Desalination. Desalination 2013, 316, 91–102. https://doi.org/10.1016/j.desal.2013.01.033
dc.relation.references[104] Naskar, M.; Rana, K.; Chatterjee, D.; Dhara, T.; Sultana, R.; Sarkar, D. Design, Performance Characterization and Hydrodynamic Modeling of Intermeshed Spinning Basket Membrane (ISBM) Module. Chem. Eng. Sci. 2019, 206, 446–462. https://doi.org/10.1016/j.ces.2019.05.049
dc.relation.references[105] Dzhonova-Atanasova, D. B.; Tsibranska, I. H.; Paniovska, S. P. CFD Simulation of Cross-Flow Filtration. Chem. Eng. Trans. 2018, 70, 2041–2046. https://doi.org/10.3303/CET1870341
dc.relation.references[106] Trojanowska, A.; Tsibranska, I.; Dzhonova, D.; Wroblewska, M.; Haponska, M.; Jovancic, P.; Marturano, V.; Tylkowski, B. Ultrasound-Assisted Extraction of Biologically Active Compounds and Their Successive Concentration by Using Membrane Processes. Chem. Eng. Res. Des. 2019, 147, 378–389. https://doi.org/10.1016/j.cherd.2019.05.018
dc.relation.references[107] Kerdi, S.; Qamar, A.; Alpatova, A.; Vrouwenvelder, J. S.; Ghaffour, N. Membrane Filtration Performance Enhancement and Biofouling Mitigation Using Symmetric Spacers with Helical Filaments. Desalination 2020, 484, 114454. https://doi.org/10.1016/j.desal.2020.114454
dc.relation.references[108] Koutsou, C. P.; Karabelas, A. J. A Novel Retentate Spacer Geometry for Improved Spiral Wound Membrane (SWM) Module Performance. J. Membr. Sci. 2015, 488, 129–142. https://doi.org/10.1016/j.memsci.2015.03.064
dc.relation.references[109] Lim, K. B.; Wang, P. Ch.; An, H.; Yu, S. C. M. Computational Studies for the Design Parameters of Hollow Fibre Membrane Modules. J. Membr. Sci. 2017, 529, 263–273. https://doi.org/10.1016/j.memsci.2017.01.053
dc.relation.references[110] Min, J.; Zhang, B. Convective Mass Transfer Enhancement in a Membrane Channel by Delta Winglets and Their Comparison with Rectangular Winglets. Chin. J. Chem. Eng. 2015, 23, 1755–1762. https://doi.org/10.1016/j.cjche.2015.09.006
dc.relation.references[111] Qamar, A.; Bucs, S.; Picioreanu, C.; Vrouwenvelder, J.; Ghaffour, N. Hydrodynamic Flow Transition Dynamics in a Spacer Filled Filtration Channel Using Direct Numerical Simulation. J. Membr. Sci. 2019, 590, 117264. https://doi.org/10.1016/j.memsci.2019.117264
dc.relation.references[112] Tonova, K.; Lazarova, M.; Dencheva-Zarkova, M.; Paniovska, S.; Tsibranska, I.; Stanoev, V.; Dzhonova, D.; Genova, J. Separation of Glucose, other Reducing Sugars and Phenolics from Natural Extract by Nanofiltration: Effect of Pressure and Cross-Flow Velocity. Chem. Eng. Res. Des. 2020, 162, 107–116. https://doi.org/10.1016/j.cherd.2020.07.030
dc.relation.references[113] Yang, Zh.; Cheng, J.; Yang, Ch.; Liang, B. CFD-based Optimization and Design of Multi-Channel Inorganic Membrane Tubes. Chin. J. Chem. Eng. 2016, 24, 1375–1385. https://doi.org/10.1016/j.cjche.2016.05.044
dc.relation.references[114] Al-Rudainy, B.; Galbe, M.; Wallberg O. From Lab-Scale to On-Site Pilot Trials for the Recovery of Hemicellulose by Ultrafiltration: Experimental and Theoretical Evaluations. Sep. Purif. Technol. 2020, 250, 117187. https://doi.org/10.1016/j.seppur.2020.117187
dc.relation.references[115] Cortés-Juan, F.; Balannec, B.; Renouard, T. CFD-assisted Design Improvement of a Bench-Scale Nanofiltration Cell. Sep. Purif. Technol. 2011, 82, 177–184. https://doi.org/10.1016/j.seppur.2011.09.010
dc.relation.references[116] Lee, Y. K.; Won, Y.-J.; Yoo, J. H.; Ahn, K. H.; Lee, Ch.-H. Flow Analysis and Fouling on the Patterned Membrane Surface. J. Membr. Sci. 2013, 427, 320–325. https://doi.org/10.1016/j.memsci.2012.10.010
dc.relation.references[117] Ronen, A.; Lerman, S.; Ramon, G. Z.; Dosoretz, C. G. Experimental Characterization and Numerical Simulation of the Anti-Biofuling Activity of Nanosilver-Modified Feed Spacers in Membrane Filtration. J. Membr. Sci. 2015, 475, 320–329. https://doi.org/10.1016/j.memsci.2014.10.042
dc.relation.references[118] Koutsou, C.P.; Karabelas, A.J.; Kostoglou, M. Membrane Desalination under Constant Water Recovery – The Effect of Module Design Parameters on System Performance. Sep. Purif. Technol. 2015, 147, 90–113. https://doi.org/10.1016/j.seppur.2015.04.012
dc.relation.references[119] Yao, L.; Qin, Zh.; Chen, Q.; Zhao, M.; Zhao, H.; Ahmad, W.; Fan, L.; Zhao, L. Insights Into the Nanofiltration Separation Mechanism of Monosaccharides by Molecular Dynamics Simulation. Sep. Purif. Technol. 2018, 205, 48–57. https://doi.org/10.1016/j.seppur.2018.04.056
dc.relation.references[120] Suk, M. E. Single-File Water Flux Through Two-Dimensional Nanoporous Membranes. Nanoscale Res. Lett. 2020, 15, 204. https://doi.org/10.1186/s11671-020-03436-4
dc.relation.references[121] Liu, J.; Xu, Q.; Jiang, J. A Molecular Simulation Protocol for Swelling and Organic Solvent Nanofiltration of Polymer Membranes. J. Membr. Sci. 2019, 573, 639–646. https://doi.org/10.1016/j.memsci.2018.12.035
dc.relation.references[122] Teng, X.; Fang, W.; Liang, Y.; Lin, Sh.; Lin, H.; Liu, Sh.; Wang, Zh.; Zhu, Y.; Jin, J. High-Performance Polyamide Nanofiltration Membrane with Arch-Bridge Structure on a Highly Hydrated Cellulose Nanofiber Support. Sci. China Mater. 2020, 63, 2570–2581. https://doi.org/10.1007/s40843-020-1335-x
dc.relation.references[123] Xu, Q.; Jiang, J. Effects of Functionalization on the Nanofiltration Performance of PIM-1: Molecular Simulation Investigation. J. Membr. Sci. 2019, 591, 117357. https://doi.org/10.1016/j.memsci.2019.117357
dc.relation.references[124] Liu, J.; Kong, X.; Jiang, J. Solvent Nanofiltration through Polybenzimidazole Membranes: Unravelling the Role of Pore Size from Molecular Simulations. J. Membr. Sci. 2018, 564, 782–787. https://doi.org/10.1016/j.memsci.2018.07.086
dc.relation.references[125] Azamat, J.; Baghbani, N. B.; Erfan-Niya, H. Atomistic Understanding of Functionalized γ-graphyne-1 Nanosheet Membranes for Water Desalination. J. Membr. Sci. 2020, 604, 118079. https://doi.org/10.1016/j.memsci.2020.118079
dc.relation.references[126] Cong, W.; Gao, W.; Garvey, Ch. J.; Dumée, L. F.; Zhang, J.; Kent, B.; Wang, G.; She, F.; Kong, L. In Situ SAXS Measurement and Molecular Dynamics Simulation of Magnetic Alignment of Hexagonal LLC Nanostructures. Membranes 2018, 8, 123. https://doi.org/10.3390/membranes8040123
dc.relation.references[127] Zhang, X.; Liu, Ch.; Yang, J.; Zhu, Ch.-Y.; Zhang, L.; Xu, Zh.-K. Nanofiltration Membranes with Hydrophobic Microfiltration Substrates for Robust Structure Stability and High Water Permeation Flux. J. Membr. Sci. 2020, 593, 117444. https://doi.org/10.1016/j.memsci.2019.117444
dc.relation.references[128] Calabrò, F. Modeling the Effects of Material Chemistry on Water Flow Enhancement in Nanotube Membranes. MRS Bull. 2017, 42, 289–293. https://doi.org/10.1557/mrs.2017.58
dc.relation.references[129] da Silva Arouche, T.; dos Santos Cavaleiro, R. M.; Tanoue, P. S. M.; Sousa de Sa Pereira, T.; Filho, T. A.; de Jesus Chaves Neto, A. M. Heavy Metals Nanofiltration Using Nanotube and Electric Field by Molecular Dynamics. J. Nanomater. 2020, 2020, 4063201. https://doi.org/10.1155/2020/4063201
dc.relation.references[130] Calo, V. M.; Iliev, O.; Lakdawala, Z.; Leonard, K. H. L.; Printsypar, G. Pore-Scale Modeling and Simulation of Flow, Transport, and Adsorptive or Osmotic Effects in Membranes: The Influence of Membrane Microstructure. Int J Adv Eng Sci Appl Math. 2015, 7, 2–13. https://doi.org/10.1007/s12572-015-0132-3
dc.relation.references[131] Sofos, F.; Karakasidis, Th. E.; Giannakopoulos, A. E.; Liakopoulos, A. Molecular Dynamics Simulation on Flows in Nano-Ribbed and Nano-Grooved Channels. Heat Mass Transf. 2016, 52, 153–162. https://doi.org/10.1007/s00231-015-1601-8
dc.relation.references[132] Xu, Q.; Jiang, J. Molecular Simulations of Liquid Separations in Polymer Membranes. Curr. Opin. Chem. Eng. 2020, 28, 66–74. https://doi.org/10.1016/j.coche.2020.02.001
dc.relation.referencesen[1] Gumnitsky, J.; Sabadash, V.; Matsuska, O.; Lyuta, O.; Hyvlud, A.; Venger, L. Dynamics of Adsorption of Copper Ions in Fixed-Bed Column and Mathematical Interpretation of the First Stage of the Process. Chem. Chem. Technol. 2022, 16, 267–273. https://doi.org/10.23939/chcht16.02.267
dc.relation.referencesen[2] Semenyshyn, Y.; Atamanyuk, V.; Rymar, T.; Ivashchuk, O.; Hlukhaniuk, A. Mass Transfer in the Solid-Liquid System: Mechanism and Kinetics of the Extraction Process. Chem. Chem. Technol. 2020, 14, 121–128. https://doi.org/10.23939/chcht14.01.121
dc.relation.referencesen[3] Havryshko, M.; Popovych, O.; Yaremko, H.; Tymchuk, I.; Malovanyy, M. Analysis of Prospective Technologies of Food Production Wastewater Treatment. Ecol. Eng. Environ. Technol. 2022, 2, 33–40. https://doi.org/10.12912/27197050/145201
dc.relation.referencesen[4] Ramana, K. V.; Mohan, K. C.; Ravindhranath, K.; Babu, B. H. Bio-Sorbent Derived from Annona Squamosa for the Removal of Methyl Red Dye in Polluted Waters: A Study on Adsorption Potential. Chem. Chem. Technol. 2022, 16, 274–283. https://doi.org/10.23939/chcht16.02.274
dc.relation.referencesen[5] Shon, H. K.; Phuntsho, S.; Chaudhary, D. S.; Vigneswaran, S., Cho, J. Nanofiltration for Water and Wastewater Treatment – A Mini Review. Drink Water Eng Sci. 2013, 6, 47–53. https://doi.org/10.5194/dwes-6-47-2013
dc.relation.referencesen[6] Huliienko, S. V.; Korniienko, Y. M.; Gatilov, K. O. Modern Trends in the Mathematical Simulation of Pressure-Driven Membrane Processes. J. Eng. Sci. 2020, 71, F1–F21. https://doi.org/10.21272/jes.2020.7(1).f1
dc.relation.referencesen[7] Huliienko, S. V.; Korniyenko, Y. M.; Muzyka, S. M.; Holubka K. Simulation of Reverse Osmosis Process: Novel Approaches and Development Trends. J. Eng. Sci. 2022, 92, F6–F36. https://doi.org/10.21272/jes.2022.9(2).f2
dc.relation.referencesen[8] Yaroshchuk, A.; Bruening, M. L.; Zholkovskiy, E. Modelling Nanofiltration of Electrolyte Solutions. Adv. Colloid Interface Sci. 2019, 268, 39–63. https://doi.org/10.1016/j.cis.2019.03.004
dc.relation.referencesen[9] Agboola, O.; Maree J.; Kolesnikov, A.; Mbaya, R.; Sadiku, R. Theoretical Performance of Nanofiltration Membranes for Wastewater Treatment. Environ. Chem. Lett. 2015, 13, 37–47. https://doi.org/10.1007/s10311-014-0486-y
dc.relation.referencesen[10] Marchetti, P.; Livingston, A. G. Predictive Membrane Transport Models for Organic Solvent Nanofiltration: How Complex Do We Need to Be? J. Membr. Sci. 2015, 476, 530–553. https://doi.org/10.1016/j.memsci.2014.10.030
dc.relation.referencesen[11] Schmidt, P.; Lutze, Ph. Characterisation of Organic Solvent Nanofiltration Membranes in Multi-Component Mixtures: Phenomena-based Modelling and Membrane Modelling Maps. J. Membr. Sci. 2013, 445, 183–199. https://doi.org/10.1016/j.memsci.2013.05.062
dc.relation.referencesen[12] Zhang, Sh.; Zhou, J.; Fan, L.; Qiu, Y.; Jiang, L.; Zhao, L. Investigating the Mechanism of Nanofiltration Separation of Glucosamine Hydrochloride and N-acetyl Glucosamine. Bioresour. Bioprocess. 2016, 3, 34. https://doi.org/10.1186/s40643-016-0112-x
dc.relation.referencesen[13] Anand, A.; Unnikrishnan, B.; Mao, J.-Y.; Lin, H.-J.; Huang, Ch.-Ch. Graphene-based Nanofiltration Membranes for Improving Salt Rejection, Water Flux and Antifouling–A review. Desalination 2018, 429, 119–133. https://doi.org/10.1016/j.desal.2017.12.012
dc.relation.referencesen[14] Mohammad, A.W.; Teow, Y.H.; Ang, W.L.; Chung, Y.T.; Oatley-Radcliffe, D.L.; Hilal, N. Nanofiltration Membranes Review: Recent Advances and Future Prospects. Desalination 2015, 356, 226–254. https://doi.org/10.1016/j.desal.2014.10.043
dc.relation.referencesen[15] Ahmed, F. E.; Hashaikeh, R.; Diabat, A.; Hilal, N. Mathematical and Optimization Modelling in Desalination: State-of-the-art and Future Direction. Desalination 2019, 469, 114092. https://doi.org/10.1016/j.desal.2019.114092
dc.relation.referencesen[16] Zhou, D.; Zhu, L.; Fu, Y.; Zhu, M.; Xue, L. Development of Lower Cost Seawater Desalination Processes Using Nanofiltration Technologies - A Review. Desalination 2015, 376, 109–116. https://doi.org/10.1016/j.desal.2015.08.020
dc.relation.referencesen[17] Souza, V. C.; Quadri, M. G. N. Organic-inorganic hybrid membranes in separation processes: a 10-year review. Braz. J. Chem. Eng. 2013, 30, 683–700. https://doi.org/10.1590/S0104-66322013000400001
dc.relation.referencesen[18] Wang, J.; Dlamini, D. S.; Mishra, A. K.; Pendergast, M. Th. M.; Wong, M. C. Y.; Mamba, B. B.; Freger, V.; Verliefd, A. R. D.; Hoek, E. M. V. A Critical Review of Transport through Osmotic Membranes. J. Membr. Sci. 2014, 454, 516–537. https://doi.org/10.1016/j.memsci.2013.12.034
dc.relation.referencesen[19] Keir, G.; Jegatheesan, V. A Review of Computational Fluid Dynamics Applications in Pressure-Driven Membrane Filtration. Rev. Environ. Sci. Biotechnol. 2013, 13, 183–201. https://doi.org/10.1007/s11157-013-9327-x
dc.relation.referencesen[20] Ebro, H.; Kim, Y. M.; Kim, J. H. Molecular Dynamics Simulations in Membrane-Based Water Treatment Processes: A Systematic Overview. J. Membr. Sci. 2013, 438, 112–125. https://doi.org/10.1016/j.memsci.2013.03.027
dc.relation.referencesen[21] Zhang, Y.; Zhu, Y.; Wang, A.; Gao, Q.; Qin, Y.; Chen, Y.; Lu, X. Progress in Molecular-Simulation-Based Research on the Effects of Interface-induced Fluid Microstructures on Flow Resistance. Chin. J. Chem. Eng. 2019, 27, 1403–1415. https://doi.org/10.1016/j.cjche.2019.02.002
dc.relation.referencesen[22] Peshev, D.; Livingston, A. G. OSN Designer, a Tool for Predicting Organic Solvent Nanofiltration Technology Performance Using ASPEN ONE, MATLAB and CAPE OPEN. Chem. Eng. Sci. 2013, 104, 975–987. https://doi.org/10.1016/j.ces.2013.10.033
dc.relation.referencesen[23] Abejon, R.; Garea, A.; Irabien, A. Organic Solvent Recovery and Reuse in Pharmaceutical Purification Processes by Nanofiltration Membrane Cascades. Chem. Eng. Trans. 2015, 43, 1057–1062. https://doi.org/10.3303/CET1543177
dc.relation.referencesen[24] Hidalgo, A. M.; León, G.; Gómez, M.; Murcia, M. D.; Gómez, E.; Macario, J. A. Removal of Different Dye Solutions: A Comparison Study Using a Polyamide NF Membrane. Membranes 2020, 10, 408. https://doi.org/10.3390/membranes10120408
dc.relation.referencesen[25] Yan, Z-Q.; Zeng, L-M.; Li, Q.; Liu, T-Y.; Matsuyama, H.; Wang, X-L. Selective Separation of Chloride and Sulfate by Nanofiltration for High Saline Wastewater Recycling. Sep. Purif. Technol. 2016, 166, 135–141. https://doi.org/10.1016/j.seppur.2016.04.009
dc.relation.referencesen[26] Shahmansouri, A.; Bellona, C. Application of Quantitative Structure–Property Relationships (QSPRs) to Predict the Rejection of Organic Solutes by Nanofiltration. Sep. Purif. Technol. 2013, 118, 627–638. https://doi.org/10.1016/j.seppur.2013.07.050
dc.relation.referencesen[27] Schlackl, K.; Herchl, R.; Samhaber, W. Nanofiltration of Succinic Acid in Strong Alkaline Conditions. Membranes 2019, 9, 147. https://doi.org/10.3390/membranes9110147
dc.relation.referencesen[28] Kim, J. H.; Na, J.-G.; Shim, H. J.; Chang, Y. K. Modeling of Ammonium Lactate Recovery and Impurity Removal from Simulated Fermentation Broth by Nanofiltration. J. Membr. Sci. 2012, 396, 110–118. https://doi.org/10.1016/j.memsci.2012.01.003
dc.relation.referencesen[29] Nair, R. R.; Protasova, E.; Strand, S.; Bilstad, T. Implementation of Spiegler–Kedem and Steric Hindrance Pore Models for Analyzing Nanofiltration Membrane Performance for Smart Water Production. Membranes 2018, 8, 78. https://doi.org/10.3390/membranes8030078
dc.relation.referencesen[30] Peddie, W. L.; van Rensburg, J. N.; Vosloo, H. C. M.; van der Gryp, P. Technological Evaluation of Organic Solvent Nanofiltration for the Recovery of Homogeneous Hydroformylation Catalysts. Chem. Eng. Res. Des. 2017, 121, 219–232. https://doi.org/10.1016/j.cherd.2017.03.015
dc.relation.referencesen[31] ten Kate, A. J. B.; Schutyser, M.A.I.; Kuzmanovic, B.; Westerink, J.B.; Manuhutu, F.; Bargeman, G. Thermodynamic Perspective on Negative Retention Effects in Nanofiltration of Concentrated Sodium Chloride Solutions. Sep. Purif. Technol. 2020, 250, 117242. https://doi.org/10.1016/j.seppur.2020.117242
dc.relation.referencesen[32] Minelli, M.; Sarti, G. C. Modeling Mass Transport in Dense Polymer Membranes: Cooperative Synergy among Multiple Scale Approaches. Curr. Opin. Chem. Eng. 2020, 28, 43–50. https://doi.org/10.1016/j.coche.2020.01.004
dc.relation.referencesen[33] Qian, J.; Yan, R.; Liu, X.; Li, Ch.; Zhang, X. Modification to Solution-Diffusion Model for Performance Prediction of Nanofiltration of Long-alkyl-chain Ionic Liquids Aqueous Solutions Based on Ion Cluster. Green Energy Environ. 2020, 5, 105–113. https://doi.org/10.1016/j.gee.2018.10.001
dc.relation.referencesen[34] Li, C.; Ma, Y.; Li, H.; Peng, G. Exploring the Nanofiltration Mass Transfer Characteristic and Concentrate Process of Procyanidins from Grape Juice. Food Sci. Nutr. 2019, 7, 1884–1890. https://doi.org/10.1002/fsn3.1045
dc.relation.referencesen[35] Abels, C.; Redepenning, C.; Moll, A.; Melin, T.; Wessling, M. Simple Purification of Ionic Liquid Solvents by Nanofiltration in Biorefining of Lignocellulosic Substrates. J. Membr. Sci. 2012, 405–406, 1–10. https://doi.org/10.1016/j.memsci.2011.12.020
dc.relation.referencesen[36] Shi, B.; Marchetti, P.; Peshev, D.; Zhang, Sh.; Livingston, A. G. Performance of Spiral-Wound Membrane Modules in Organic Solvent Nanofiltration – Fluid Dynamics and Mass Transfer Characteristics. J. Membr. Sci. 2015, 494, 8–24. https://doi.org/10.1016/j.memsci.2015.07.044
dc.relation.referencesen[37] Micovic, J.; Werth, K.; Lutze, Ph. Hybrid Separations Combining Distillation and Organic Solvent Nanofiltration for Separation of Wide Boiling Mixtures. Chem. Eng. Res. Des. 2014, 92, 2131–2147. https://doi.org/10.1016/j.cherd.2014.02.012
dc.relation.referencesen[38] Werhan, H.; Farshori, A.; von Rohr, Ph. R. Separation of Lignin Oxidation Products by Organic Solvent Nanofiltration. J. Membr. Sci. 2012, 423–424, 404–412. https://doi.org/10.1016/j.memsci.2012.08.037
dc.relation.referencesen[39] Werth, K.; Kaupenjohann, P.; Knierbein, M.; Skiborowski, M. Solvent Recovery and Deacidification by Organic Solvent Nanofiltration: Experimental Investigation and Mass Transfer Modelling. J. Membr. Sci. 2017, 528, 369–380. https://doi.org/10.1016/j.memsci.2017.01.021
dc.relation.referencesen[40] Keucken, A.; Wang, Y.; Tng, K. H.; Leslie, G.; Spanjer, T.; Köhler, S. J. Optimizing Hollow Fibre Nanofiltration for Organic Matter Rich Lake Water. Water 2016, 8, 430. https://doi.org/10.3390/w8100430
dc.relation.referencesen[41] Altaee, A.; Hilal, N. High Recovery Rate NF–FO–RO Hybrid System for Inland Brackish Water Treatment. Desalination 2015, 363, 19–25. https://doi.org/10.1016/j.desal.2014.12.017
dc.relation.referencesen[42] Shaaban, A. M. F.; Hafez, A. I.; Abdel-Fatah, M. A.; Abdel-Monem, N. M.; Mahmoud, M. H. Process Engineering Optimization of Nanofiltration Unit for the Treatment of Textile Plant Effluent in View of Solution Diffusion Model. Egypt. J. Pet. 2016, 25, 79–90. https://doi.org/10.1016/j.ejpe.2015.03.018
dc.relation.referencesen[43] Marchetti, P.; Butte, A.; Livingston, A. G. An Improved Phenomenological Model for Prediction of Solvent Permeation Through Ceramic NF and UF Membranes. J. Membr. Sci. 2012, 415–416, 444–458. https://doi.org/10.1016/j.memsci.2012.05.030
dc.relation.referencesen[44] Fierro, D.; Boschetti-de-Fierro, A.; Abetz, V. The Solution-Diffusion with Imperfections Model as a Method to Understand Organic Solvent Nanofiltration of Multicomponent Systems. J. Membr. Sci. 2012, 413–414, 91–101. https://doi.org/10.1016/j.memsci.2012.04.027
dc.relation.referencesen[45] Werth, K.; Kaupenjohann, P.; Skiborowski, M. The Potential of Organic Solvent Nanofiltration Processes for Oleochemical Industry. Sep. Purif. Technol. 2017, 182, 185–196. https://doi.org/10.1016/j.seppur.2017.03.050
dc.relation.referencesen[46] Pérez, L.; Escudero, I.; Arcos-Martínez, M. J.; Benito, J. M. Application of the Solution-Diffusion-Film Model for the Transfer of Electrolytes and Uncharged Compounds in a Nanofiltration Membrane. J Ind Eng Chem. 2017, 47, 368–74. https://doi.org/10.1016/j.jiec.2016.12.007
dc.relation.referencesen[47] Yonge, D.T.; Biscardi, P. G.; Duranceau, S. J. Modeling Ionic Strength Effects on Hollow-Fiber Nanofiltration Membrane Mass Transfer. Membranes 2018, 8, 37. https://doi.org/10.3390/membranes8030037
dc.relation.referencesen[48] Yaroshchuk, A.; Bruening, M. L. An analytical Solution of the Solution-Diffusion-Electromigration Equations Reproduces Trends in ion Rejections During Nanofiltration of Mixed Electrolytes. J. Membr. Sci. 2017, 523, 361–372. https://doi.org/10.1016/j.memsci.2016.09.046
dc.relation.referencesen[49] Madsen, H.T.; Søgaard, E.G. Applicability and Modelling of Nanofiltration and Reverse Osmosis for Remediation of Groundwater Polluted with Pesticides and Pesticide Transformation Products. Sep. Purif. Technol. 2014, 125, 111–119. https://doi.org/10.1016/j.seppur.2014.01.038
dc.relation.referencesen[50] Liu, Y-l.; Wei, W.; Wang, X-m.; Yang, H-w.; Xie, Y.F. Relating the Rejections of Oligomeric Ethylene Glycols and Saccharides by Nanofiltration: Implication for Membrane Pore Size Determination. Sep. Purif. Technol. 2018, 205, 151–158. https://doi.org/10.1016/j.seppur.2018.05.042
dc.relation.referencesen[51] Xu, R.; Zhou, M.; Wang, H.; Wang, X.; Wen, X. Influences of Temperature on the Retention of PPCPs by Nanofiltration Membranes: Experiments and Modeling Assessment. J. Membr. Sci. 2020, 599, 117817. https://doi.org/10.1016/j.memsci.2020.117817
dc.relation.referencesen[52] Kong, F.-x.; Yang, H.-w.; Wang, X.-m.; Xie, Y. F. Assessment of the Hindered Transport Model in Predicting the Rejection of Trace Organic Compounds by Nanofiltration. J. Membr. Sci. 2016, 498, 57–66. https://doi.org/10.1016/j.memsci.2015.09.062
dc.relation.referencesen[53] Aguirre Montesdeoca, V.; Van der Padt, A., Boom, R.M., Janssen, A.E.M. Modelling of Membrane Cascades for the Purification of Oligosaccharides. J. Membr. Sci. 2016, 520, 712–722. https://doi.org/10.1016/j.memsci.2016.08.031
dc.relation.referencesen[54] Darvishmanesh, S.; Van der Bruggen, B. Mass Transport through Nanostructured Membranes: Towards a Predictive Tool. Membranes 2016, 6, 49. https://doi.org/10.3390/membranes6040049
dc.relation.referencesen[55] Labban, O.; Chong, T. H.; Lienhard, V J. H. Design and Modeling of Novel Low-Pressure Nanofiltration Hollow Fiber Modules for Water Softening and Desalination Pretreatment. Desalination 2018, 439, 58–72. https://doi.org/10.1016/j.desal.2018.04.002
dc.relation.referencesen[56] Déon, S.; Escoda, A.; Fievet, P.; Dutournié, P.; Bourseau P. How to Use a Multi-Ionic Transport Model to Fully Predict Rejection of Mineral Salts by Nanofiltration Membranes. Chem. Eng. J. 2012, 189–190, 24–31. https://doi.org/10.1016/j.cej.2012.02.014
dc.relation.referencesen[57] Thibault, K.; Zhu, H.; Szymczyk, A.; Li, G. The Averaged Potential Gradient Approach to Model the Rejection of Electrolyte Solutions Using Nanofiltration: Model Development and Assessment for Highly Concentrated Feed Solutions. Sep. Purif. Technol. 2015, 153, 126–37. https://doi.org/10.1016/j.seppur.2015.08.041
dc.relation.referencesen[58] Blumenschein, S.; Böcking, A.; Kätzel, U.; Postel, S.; Wessling, M. Rejection Modeling of Ceramic Membranes in Organic Solvent Nanofiltration. J. Membr. Sci. 2016, 510, 191–200. https://doi.org/10.1016/j.memsci.2016.02.042
dc.relation.referencesen[59] Fadaei, F.; Shirazian, S.; Ashrafizadeh, S. N. Mass Transfer Modeling of ion Transport through Nanoporous Media. Desalination 2011, 281, 325–333. https://doi.org/10.1016/j.desal.2011.08.025
dc.relation.referencesen[60] Dey, P.; Linnanen, L.; Pal, P. Separation of Lactic Acid from Fermentation Broth by Cross Flow Nanofiltration: Membrane Characterization and Transport Modelling. Desalination 2012, 288, 47–57. https://doi.org/10.1016/j.desal.2011.12.009
dc.relation.referencesen[61] Farsi, A.; Boffa, V.; Qureshi, H. F.; Nijmeijer, A.; Winnubst, L.; Christensen, M. L. Modeling Water Flux and Salt Rejection of Mesoporous g-Alumina and Microporous Organosilica Membranes. J. Membr. Sci. 2014, 470, 307–315. https://doi.org/10.1016/j.memsci.2014.07.038
dc.relation.referencesen[62] Pal, P.; Das, P.; Chakrabortty, S.; Thakura, R. Dynamic Modelling of a Forward Osmosis-Nanofiltration Integrated Process for Treating Hazardous Wastewater. Environ. Sci. Pollut. Res. 2016, 23, 21604–21618. https://doi.org/10.1007/s11356-016-7392-8
dc.relation.referencesen[63] Silva, V.; Martın, A.; Martınez, F.; Malfeito, J.; Pradanos, P.; Palacio, L.; Hernandez, A. Electrical Characterization of NF Membranes. A Modified Model with Charge Variation along the Pores. Chem. Eng. Sci. 2011, 66, 2898–2911. https://doi.org/10.1016/j.ces.2011.03.025
dc.relation.referencesen[64] Zerafat, M.M.; Shariati-Niassar, M.; Hashemi, S.J.; Sabbaghi, S.; Ismail, A.F.; Matsuura, T. Mathematical Modeling of Nanofiltration for Concentrated Electrolyte Solutions. Desalination 2013, 320, 17–23. https://doi.org/10.1016/j.desal.2013.04.015
dc.relation.referencesen[65] Pal, P.; Sardar, M.; Pal, M.; Chakrabortty, S.; Nayak, J. Modelling Forward Osmosis-Nanofiltration Integrated Process for Treatment and Recirculation of Leather Industry Wastewater. Comput Chem Eng. 2019, 127, 99–110. https://doi.org/10.1016/j.compchemeng.2019.05.018
dc.relation.referencesen[66] Kumar, R.; Chakrabortty, S.; Pal, P. Membrane-Integrated Physico-Chemical Treatment of Coke-Oven Wastewater: Transport Modelling and Economic Evaluation. Environ. Sci. Pollut. Res. 2015, 22, 6010–6023. https://doi.org/10.1007/s11356-014-3787-6
dc.relation.referencesen[67] Luo, J.; Wan, Y. Effect of highly Concentrated Salt on Retention of Organic Solutes by Nanofiltration Polymeric Membranes. J. Membr. Sci. 2011, 372, 145–153. https://doi.org/10.1016/j.memsci.2011.01.066
dc.relation.referencesen[68] Chakrabortty, S.; Sen, M.; Pal, P. Arsenic Removal from Contaminated Groundwater by Membrane-Integrated Hybrid Plant: Optimization and Control Using Visual Basic Platform. Environ. Sci. Pollut. Res. 2014, 21, 3840–3857. https://doi.org/10.1007/s11356-013-2382-6
dc.relation.referencesen[69] Chakrabortty, S.; Roy, M.; Pal, P. Removal of Fluoride from Contaminated Groundwater by Cross Flow Nanofiltration: Transport Modeling and Economic Evaluation. Desalination 2013, 313, 115–124. https://doi.org/10.1016/j.desal.2012.12.021
dc.relation.referencesen[70] Oatley-Radcliffe, D. L.; Williams, S. R.; Barrow, M. S.; Williams, P. M. Critical Appraisal of Current Nanofiltration Modelling Strategies for Seawater Desalination and Further Insights on Dielectric Exclusion. Desalination 2014, 343, 154–161. https://doi.org/10.1016/j.desal.2013.10.001
dc.relation.referencesen[71] Roy, Y.; Sharqawy, M. H.; Lienhard, J. H. Modeling of Flat-Sheet and Spiral-Wound Nanofiltration Configurations and its Application in Seawater Nanofiltration. J. Membr. Sci. 2015, 493, 360–372. https://doi.org/10.1016/j.memsci.2015.06.030
dc.relation.referencesen[72] Bonner, R.; Germishuizen, Ch.; Franzsen, S. Prediction of Nanofiltration Rejection Performance in Brackish Water Reverse Osmosis Brine Treatment Processes. J. Water Process. Eng. 2019, 32, 100900. https://doi.org/10.1016/j.jwpe.2019.100900
dc.relation.referencesen[73] Labban, O.; Liu, Ch.; Chong, T. H.; Lienhard, J. H. Fundamentals of Low-Pressure Nanofiltration: Membrane Characterization, Modeling, and Understanding the Multi-Ionic Interactions in Water Softening. J. Membr. Sci. 2017, 521, 18–32. https://doi.org/10.1016/j.memsci.2016.08.062
dc.relation.referencesen[74] Chakrabortty, S.; Nayak, J.; Pal, P.; Kumar, R.; Chakraborty, P. Separation of COD, Sulphate and Chloride from Pharmaceutical Wastewater Using Membrane Integrated System: Transport Modeling Towards Scale-Up. J. Environ. Chem. Eng. 2020, 8, 104275. https://doi.org/10.1016/j.jece.2020.104275
dc.relation.referencesen[75] Pal, P.; Thakura, R., Chakrabortty S. Performance Analysis and Optimization of an Advanced Pharmaceutical Wastewater Treatment Plant Through a Visual Basic Software Tool (PWWT.VB). Environ. Sci. Pollut. Res. 2016, 23, 9901–9917. https://doi.org/10.1007/s11356-016-6238-8
dc.relation.referencesen[76] Roy, Y.; Warsinger, D. M.; Lienhard, J. H. Effect of Temperature on Ion Transport in Nanofiltration Membranes: Diffusion, Convection and Electromigration. Desalination 2017, 420, 241–257. https://doi.org/10.1016/j.desal.2017.07.020
dc.relation.referencesen[77] Déon, S.; Escoda, A.; Fievet, P. A Transport Model Considering Charge Adsorption Inside Pores to Describe Salts Rejection by Nanofiltration Membranes. Chem. Eng. Sci. 2011, 66, 2823–2832. https://doi.org/10.1016/j.ces.2011.03.043
dc.relation.referencesen[78] Bajpai, Sh.; Rajendran, R. M.; Hooda, S. Modeling the Performance of HPA Membrane for Sulfate Ion Removal from Ternary Ion System. Korean J. Chem. Eng. 2019, 36, 1648–1656. https://doi.org/10.1007/s11814-019-0357-0
dc.relation.referencesen[79] Fang, J.; Deng, B. Rejection and Modeling of Arsenate by Nanofiltration: Contributions of Convection, Diffusion and Electromigration to Arsenic Transport. J. Membr. Sci. 2014, 453, 42–51. https://doi.org/10.1016/j.memsci.2013.10.056
dc.relation.referencesen[80] Cathie Lee, W.P.; Mah, Sh.-K.; Leo, C.P.; Wu, T. Y.; Chai, S.-P. Phosphorus Removal by NF90 Membrane: Optimisation Using Central Composite Design. J. Taiwan Inst. Chem. Eng. 2014, 45, 1260–1269. https://doi.org/10.1016/j.jtice.2014.02.011
dc.relation.referencesen[81] Bandini, S.; Morelli, V. Effect of Temperature, pH and Composition on Nanofiltration of Mono/Disaccharides: Experiments and Modeling Assessment. J. Membr. Sci. 2017, 533, 57–74. https://doi.org/10.1016/j.memsci.2017.03.021
dc.relation.referencesen[82] Liu, H.; Zhao, L.; Fan, L.; Jiang, L.; Qiu, Y.; Xia, Q.; Zhou J. Establishment of a Nanofiltration Rejection Sequence and Calculated Rejections of Available Monosaccharides. Sep. Purif. Technol. 2016, 163, 319–330. https://doi.org/10.1016/j.seppur.2016.03.016
dc.relation.referencesen[83] Shah, A. D.; Huang, Ch.-H.; Kim, J.-H. Mechanisms of Antibiotic Removal by Nanofiltration Membranes: Model Development and Application. J. Membr. Sci. 2012, 389, 234–244. https://doi.org/10.1016/j.memsci.2011.10.034
dc.relation.referencesen[84] Balannec, B.; Ghoufi, A.; Szymczyk, A. Nanofiltration Performance of Conical and Hourglass Nanopores. J. Membr. Sci. 2018, 552, 336–340. https://doi.org/10.1016/j.memsci.2018.02.026
dc.relation.referencesen[85] Fadaei, F.; Hoshyargar, V.; Shirazian, S.; Ashrafizadeh S. Mass Transfer Simulation of Ion Separation by Nanofiltration Considering Electrical and Dielectrical Effects. Desalination 2012, 284, 316–323. https://doi.org/10.1016/j.desal.2011.09.018
dc.relation.referencesen[86] Fridman-Bishop, N.; Tankus, K. A.; Freger, V. Permeation Mechanism and Interplay between Ions in Nanofiltration. J. Membr. Sci. 2018, 548, 449–458. https://doi.org/10.1016/j.memsci.2017.11.050
dc.relation.referencesen[87] Zhu, Y.; Zhu, H.; Li, G.; Mai, Zh.; Gu, Y. The Effect of Dielectric Exclusion on the Rejection Performance of Inhomogeneously Charged Polyamide Nanofiltration Membranes. J Nanopart Res. 2019, 21, 217. https://doi.org/10.1007/s11051-019-4665-4
dc.relation.referencesen[88] Marecka-Migacz, A.; Mitkowski, P. T.; Nedzarek, A., Rózanski, J.; Szaferski, W. Effect of pH on Total Volume Membrane Charge Density in the Nanofiltration of Aqueous Solutions of Nitrate Salts of Heavy Metals. Membranes 2020, 10, 235. https://doi.org/10.3390/membranes10090235
dc.relation.referencesen[89] Ortiz-Albo, P.; Ibañez R.; Urtiaga A.; Ortiz I. Phenomenological Prediction of Desalination Brines Nanofiltration through the Indirect Determination of Zeta Potential. Sep. Purif. Technol. 2019, 210, 746–753. https://doi.org/10.1016/j.seppur.2018.08.066
dc.relation.referencesen[90] Marecka-Migacz, A.; Mitkowski, P. T.; Antczak, J.; Rózanski, J.; Prochaska K. Assessment of the Total Volume Membrane Charge Density through Mathematical Modeling for Separation of Succinic Acid Aqueous Solutions on Ceramic Nanofiltration Membrane. Processes 2019, 7, 559. https://doi.org/10.3390/pr7090559
dc.relation.referencesen[91] Micari, M.; Diamantidou, D.; Heijman, B.; Moser, M.; Haidari A., Spanjers, H.; Bertsch V. Experimental and Theoretical Characterization of Commercial Nanofiltration Membranes for the Treatment of Ion Exchange Spent Regenerant. J. Membr. Sci. 2020, 606, 118117. https://doi.org/10.1016/j.memsci.2020.118117
dc.relation.referencesen[92] Wang, X.; Li B.; Zhang, T.; Li, X. Performance of Nanofiltration Membrane in Rejecting Trace Organic Compounds: Experiment and Model Prediction. Desalination 2015, 370, 7–16. https://doi.org/10.1016/j.desal.2015.05.010
dc.relation.referencesen[93] Kumar, V. S.; Hariharan, K. S.; Mayya, K. S.; Han, S. Volume Averaged Reduced Order Donnan Steric Pore Model for Nanofiltration Membranes. Desalination 2013, 322, 21–28. https://doi.org/10.1016/j.desal.2013.04.030
dc.relation.referencesen[94] Wang, Zh.; Xiao, K.; Wang, X. Role of Coexistence of Negative and Positive Membrane Surface Charges in Electrostatic Effect for Salt Rejection by Nanofiltration. Desalination 2018, 444, 75–83. https://doi.org/10.1016/j.desal.2018.07.010
dc.relation.referencesen[95] Escoda, A.; Déon, S.; Fievet, P. Assessment of Dielectric Contribution in the Modeling of Multi-Ionic Transport Through Nanofiltration Membranes. J. Membr. Sci. 2011, 378, 214–223. https://doi.org/10.1016/j.memsci.2011.05.004
dc.relation.referencesen[96] Karakhim, S. O.; Zhuk, P. F.; Kosterin, S. O. Kinetics Simulation of Transmembrane Transport of Ions and Molecules Through a Semipermeable Membrane. J. Bioenerg. Biomembr. 2020, 52, 47–60. https://doi.org/10.1007/s10863-019-09821-8
dc.relation.referencesen[97] Hoshyargar, V.; Fadaei, F.; Ashrafizadeh, S. N. Mass Transfer Simulation of Nanofiltration Membranes for Electrolyte Solutions through Generalized Maxwell-Stefan Approach. Korean J. Chem. Eng. 2015, 32, 1388–1404. https://doi.org/10.1007/s11814-014-0329-3
dc.relation.referencesen[98] Saeed, A.; Vuthaluru, R.; Vuthaluru, H. B. Investigations into the Effects of Mass Transport and Flow Dynamics of Spacer Filled Membrane Modules Using CFD. Chem. Eng. Res. Des. 2015, 93, 79–99. https://doi.org/10.1016/j.cherd.2014.07.002
dc.relation.referencesen[99] Kaufman, Y.; Kasher, R.; Lammertink, R. G. H.; Freger, V. Microfluidic NF/RO Separation: Cell Design, Performance and Application. J. Membr. Sci. 2012, 396, 67–73. https://doi.org/10.1016/j.memsci.2011.12.052
dc.relation.referencesen[100] Asefi, H.; Alighardashi, A.; Fazeli, M., Fouladitajar A. CFD Modeling and Simulation of Concentration Polarization Reduction by Gas Sparging Cross-flow Nanofiltration. J. Environ. Chem. Eng. 2019, 7, 103275. https://doi.org/10.1016/j.jece.2019.103275
dc.relation.referencesen[101] Cao, H.; O'Rourke, M.; Habimana, O.; Casey, E. Analysis of Surrogate Bacterial Cell Transport to Nanofiltration Membranes: Effect of Salt Concentration and Hydrodynamics. Sep. Purif. Technol. 2018, 207, 498–505. https://doi.org/10.1016/j.seppur.2018.06.072
dc.relation.referencesen[102] Onorato, C.; Gaedtke, M.; Kespe, M.; Nirschl, H.; Schäfer, A. I. Renewable Energy Powered Membrane Technology: Computational Fluid Dynamics Evaluation of System Performance with Variable Module Size and Fluctuating Energy. Sep. Purif. Technol. 2019, 220, 206–216. https://doi.org/10.1016/j.seppur.2019.02.041
dc.relation.referencesen[103] Kostoglou, M.; Karabelas, A. J. Comprehensive Simulation of Flat-Sheet Membrane Element Performance in Steady State Desalination. Desalination 2013, 316, 91–102. https://doi.org/10.1016/j.desal.2013.01.033
dc.relation.referencesen[104] Naskar, M.; Rana, K.; Chatterjee, D.; Dhara, T.; Sultana, R.; Sarkar, D. Design, Performance Characterization and Hydrodynamic Modeling of Intermeshed Spinning Basket Membrane (ISBM) Module. Chem. Eng. Sci. 2019, 206, 446–462. https://doi.org/10.1016/j.ces.2019.05.049
dc.relation.referencesen[105] Dzhonova-Atanasova, D. B.; Tsibranska, I. H.; Paniovska, S. P. CFD Simulation of Cross-Flow Filtration. Chem. Eng. Trans. 2018, 70, 2041–2046. https://doi.org/10.3303/CET1870341
dc.relation.referencesen[106] Trojanowska, A.; Tsibranska, I.; Dzhonova, D.; Wroblewska, M.; Haponska, M.; Jovancic, P.; Marturano, V.; Tylkowski, B. Ultrasound-Assisted Extraction of Biologically Active Compounds and Their Successive Concentration by Using Membrane Processes. Chem. Eng. Res. Des. 2019, 147, 378–389. https://doi.org/10.1016/j.cherd.2019.05.018
dc.relation.referencesen[107] Kerdi, S.; Qamar, A.; Alpatova, A.; Vrouwenvelder, J. S.; Ghaffour, N. Membrane Filtration Performance Enhancement and Biofouling Mitigation Using Symmetric Spacers with Helical Filaments. Desalination 2020, 484, 114454. https://doi.org/10.1016/j.desal.2020.114454
dc.relation.referencesen[108] Koutsou, C. P.; Karabelas, A. J. A Novel Retentate Spacer Geometry for Improved Spiral Wound Membrane (SWM) Module Performance. J. Membr. Sci. 2015, 488, 129–142. https://doi.org/10.1016/j.memsci.2015.03.064
dc.relation.referencesen[109] Lim, K. B.; Wang, P. Ch.; An, H.; Yu, S. C. M. Computational Studies for the Design Parameters of Hollow Fibre Membrane Modules. J. Membr. Sci. 2017, 529, 263–273. https://doi.org/10.1016/j.memsci.2017.01.053
dc.relation.referencesen[110] Min, J.; Zhang, B. Convective Mass Transfer Enhancement in a Membrane Channel by Delta Winglets and Their Comparison with Rectangular Winglets. Chin. J. Chem. Eng. 2015, 23, 1755–1762. https://doi.org/10.1016/j.cjche.2015.09.006
dc.relation.referencesen[111] Qamar, A.; Bucs, S.; Picioreanu, C.; Vrouwenvelder, J.; Ghaffour, N. Hydrodynamic Flow Transition Dynamics in a Spacer Filled Filtration Channel Using Direct Numerical Simulation. J. Membr. Sci. 2019, 590, 117264. https://doi.org/10.1016/j.memsci.2019.117264
dc.relation.referencesen[112] Tonova, K.; Lazarova, M.; Dencheva-Zarkova, M.; Paniovska, S.; Tsibranska, I.; Stanoev, V.; Dzhonova, D.; Genova, J. Separation of Glucose, other Reducing Sugars and Phenolics from Natural Extract by Nanofiltration: Effect of Pressure and Cross-Flow Velocity. Chem. Eng. Res. Des. 2020, 162, 107–116. https://doi.org/10.1016/j.cherd.2020.07.030
dc.relation.referencesen[113] Yang, Zh.; Cheng, J.; Yang, Ch.; Liang, B. CFD-based Optimization and Design of Multi-Channel Inorganic Membrane Tubes. Chin. J. Chem. Eng. 2016, 24, 1375–1385. https://doi.org/10.1016/j.cjche.2016.05.044
dc.relation.referencesen[114] Al-Rudainy, B.; Galbe, M.; Wallberg O. From Lab-Scale to On-Site Pilot Trials for the Recovery of Hemicellulose by Ultrafiltration: Experimental and Theoretical Evaluations. Sep. Purif. Technol. 2020, 250, 117187. https://doi.org/10.1016/j.seppur.2020.117187
dc.relation.referencesen[115] Cortés-Juan, F.; Balannec, B.; Renouard, T. CFD-assisted Design Improvement of a Bench-Scale Nanofiltration Cell. Sep. Purif. Technol. 2011, 82, 177–184. https://doi.org/10.1016/j.seppur.2011.09.010
dc.relation.referencesen[116] Lee, Y. K.; Won, Y.-J.; Yoo, J. H.; Ahn, K. H.; Lee, Ch.-H. Flow Analysis and Fouling on the Patterned Membrane Surface. J. Membr. Sci. 2013, 427, 320–325. https://doi.org/10.1016/j.memsci.2012.10.010
dc.relation.referencesen[117] Ronen, A.; Lerman, S.; Ramon, G. Z.; Dosoretz, C. G. Experimental Characterization and Numerical Simulation of the Anti-Biofuling Activity of Nanosilver-Modified Feed Spacers in Membrane Filtration. J. Membr. Sci. 2015, 475, 320–329. https://doi.org/10.1016/j.memsci.2014.10.042
dc.relation.referencesen[118] Koutsou, C.P.; Karabelas, A.J.; Kostoglou, M. Membrane Desalination under Constant Water Recovery – The Effect of Module Design Parameters on System Performance. Sep. Purif. Technol. 2015, 147, 90–113. https://doi.org/10.1016/j.seppur.2015.04.012
dc.relation.referencesen[119] Yao, L.; Qin, Zh.; Chen, Q.; Zhao, M.; Zhao, H.; Ahmad, W.; Fan, L.; Zhao, L. Insights Into the Nanofiltration Separation Mechanism of Monosaccharides by Molecular Dynamics Simulation. Sep. Purif. Technol. 2018, 205, 48–57. https://doi.org/10.1016/j.seppur.2018.04.056
dc.relation.referencesen[120] Suk, M. E. Single-File Water Flux Through Two-Dimensional Nanoporous Membranes. Nanoscale Res. Lett. 2020, 15, 204. https://doi.org/10.1186/s11671-020-03436-4
dc.relation.referencesen[121] Liu, J.; Xu, Q.; Jiang, J. A Molecular Simulation Protocol for Swelling and Organic Solvent Nanofiltration of Polymer Membranes. J. Membr. Sci. 2019, 573, 639–646. https://doi.org/10.1016/j.memsci.2018.12.035
dc.relation.referencesen[122] Teng, X.; Fang, W.; Liang, Y.; Lin, Sh.; Lin, H.; Liu, Sh.; Wang, Zh.; Zhu, Y.; Jin, J. High-Performance Polyamide Nanofiltration Membrane with Arch-Bridge Structure on a Highly Hydrated Cellulose Nanofiber Support. Sci. China Mater. 2020, 63, 2570–2581. https://doi.org/10.1007/s40843-020-1335-x
dc.relation.referencesen[123] Xu, Q.; Jiang, J. Effects of Functionalization on the Nanofiltration Performance of PIM-1: Molecular Simulation Investigation. J. Membr. Sci. 2019, 591, 117357. https://doi.org/10.1016/j.memsci.2019.117357
dc.relation.referencesen[124] Liu, J.; Kong, X.; Jiang, J. Solvent Nanofiltration through Polybenzimidazole Membranes: Unravelling the Role of Pore Size from Molecular Simulations. J. Membr. Sci. 2018, 564, 782–787. https://doi.org/10.1016/j.memsci.2018.07.086
dc.relation.referencesen[125] Azamat, J.; Baghbani, N. B.; Erfan-Niya, H. Atomistic Understanding of Functionalized g-graphyne-1 Nanosheet Membranes for Water Desalination. J. Membr. Sci. 2020, 604, 118079. https://doi.org/10.1016/j.memsci.2020.118079
dc.relation.referencesen[126] Cong, W.; Gao, W.; Garvey, Ch. J.; Dumée, L. F.; Zhang, J.; Kent, B.; Wang, G.; She, F.; Kong, L. In Situ SAXS Measurement and Molecular Dynamics Simulation of Magnetic Alignment of Hexagonal LLC Nanostructures. Membranes 2018, 8, 123. https://doi.org/10.3390/membranes8040123
dc.relation.referencesen[127] Zhang, X.; Liu, Ch.; Yang, J.; Zhu, Ch.-Y.; Zhang, L.; Xu, Zh.-K. Nanofiltration Membranes with Hydrophobic Microfiltration Substrates for Robust Structure Stability and High Water Permeation Flux. J. Membr. Sci. 2020, 593, 117444. https://doi.org/10.1016/j.memsci.2019.117444
dc.relation.referencesen[128] Calabrò, F. Modeling the Effects of Material Chemistry on Water Flow Enhancement in Nanotube Membranes. MRS Bull. 2017, 42, 289–293. https://doi.org/10.1557/mrs.2017.58
dc.relation.referencesen[129] da Silva Arouche, T.; dos Santos Cavaleiro, R. M.; Tanoue, P. S. M.; Sousa de Sa Pereira, T.; Filho, T. A.; de Jesus Chaves Neto, A. M. Heavy Metals Nanofiltration Using Nanotube and Electric Field by Molecular Dynamics. J. Nanomater. 2020, 2020, 4063201. https://doi.org/10.1155/2020/4063201
dc.relation.referencesen[130] Calo, V. M.; Iliev, O.; Lakdawala, Z.; Leonard, K. H. L.; Printsypar, G. Pore-Scale Modeling and Simulation of Flow, Transport, and Adsorptive or Osmotic Effects in Membranes: The Influence of Membrane Microstructure. Int J Adv Eng Sci Appl Math. 2015, 7, 2–13. https://doi.org/10.1007/s12572-015-0132-3
dc.relation.referencesen[131] Sofos, F.; Karakasidis, Th. E.; Giannakopoulos, A. E.; Liakopoulos, A. Molecular Dynamics Simulation on Flows in Nano-Ribbed and Nano-Grooved Channels. Heat Mass Transf. 2016, 52, 153–162. https://doi.org/10.1007/s00231-015-1601-8
dc.relation.referencesen[132] Xu, Q.; Jiang, J. Molecular Simulations of Liquid Separations in Polymer Membranes. Curr. Opin. Chem. Eng. 2020, 28, 66–74. https://doi.org/10.1016/j.coche.2020.02.001
dc.relation.urihttps://doi.org/10.23939/chcht16.02.267
dc.relation.urihttps://doi.org/10.23939/chcht14.01.121
dc.relation.urihttps://doi.org/10.12912/27197050/145201
dc.relation.urihttps://doi.org/10.23939/chcht16.02.274
dc.relation.urihttps://doi.org/10.5194/dwes-6-47-2013
dc.relation.urihttps://doi.org/10.21272/jes.2020.7(1).f1
dc.relation.urihttps://doi.org/10.21272/jes.2022.9(2).f2
dc.relation.urihttps://doi.org/10.1016/j.cis.2019.03.004
dc.relation.urihttps://doi.org/10.1007/s10311-014-0486-y
dc.relation.urihttps://doi.org/10.1016/j.memsci.2014.10.030
dc.relation.urihttps://doi.org/10.1016/j.memsci.2013.05.062
dc.relation.urihttps://doi.org/10.1186/s40643-016-0112-x
dc.relation.urihttps://doi.org/10.1016/j.desal.2017.12.012
dc.relation.urihttps://doi.org/10.1016/j.desal.2014.10.043
dc.relation.urihttps://doi.org/10.1016/j.desal.2019.114092
dc.relation.urihttps://doi.org/10.1016/j.desal.2015.08.020
dc.relation.urihttps://doi.org/10.1590/S0104-66322013000400001
dc.relation.urihttps://doi.org/10.1016/j.memsci.2013.12.034
dc.relation.urihttps://doi.org/10.1007/s11157-013-9327-x
dc.relation.urihttps://doi.org/10.1016/j.memsci.2013.03.027
dc.relation.urihttps://doi.org/10.1016/j.cjche.2019.02.002
dc.relation.urihttps://doi.org/10.1016/j.ces.2013.10.033
dc.relation.urihttps://doi.org/10.3303/CET1543177
dc.relation.urihttps://doi.org/10.3390/membranes10120408
dc.relation.urihttps://doi.org/10.1016/j.seppur.2016.04.009
dc.relation.urihttps://doi.org/10.1016/j.seppur.2013.07.050
dc.relation.urihttps://doi.org/10.3390/membranes9110147
dc.relation.urihttps://doi.org/10.1016/j.memsci.2012.01.003
dc.relation.urihttps://doi.org/10.3390/membranes8030078
dc.relation.urihttps://doi.org/10.1016/j.cherd.2017.03.015
dc.relation.urihttps://doi.org/10.1016/j.seppur.2020.117242
dc.relation.urihttps://doi.org/10.1016/j.coche.2020.01.004
dc.relation.urihttps://doi.org/10.1016/j.gee.2018.10.001
dc.relation.urihttps://doi.org/10.1002/fsn3.1045
dc.relation.urihttps://doi.org/10.1016/j.memsci.2011.12.020
dc.relation.urihttps://doi.org/10.1016/j.memsci.2015.07.044
dc.relation.urihttps://doi.org/10.1016/j.cherd.2014.02.012
dc.relation.urihttps://doi.org/10.1016/j.memsci.2012.08.037
dc.relation.urihttps://doi.org/10.1016/j.memsci.2017.01.021
dc.relation.urihttps://doi.org/10.3390/w8100430
dc.relation.urihttps://doi.org/10.1016/j.desal.2014.12.017
dc.relation.urihttps://doi.org/10.1016/j.ejpe.2015.03.018
dc.relation.urihttps://doi.org/10.1016/j.memsci.2012.05.030
dc.relation.urihttps://doi.org/10.1016/j.memsci.2012.04.027
dc.relation.urihttps://doi.org/10.1016/j.seppur.2017.03.050
dc.relation.urihttps://doi.org/10.1016/j.jiec.2016.12.007
dc.relation.urihttps://doi.org/10.3390/membranes8030037
dc.relation.urihttps://doi.org/10.1016/j.memsci.2016.09.046
dc.relation.urihttps://doi.org/10.1016/j.seppur.2014.01.038
dc.relation.urihttps://doi.org/10.1016/j.seppur.2018.05.042
dc.relation.urihttps://doi.org/10.1016/j.memsci.2020.117817
dc.relation.urihttps://doi.org/10.1016/j.memsci.2015.09.062
dc.relation.urihttps://doi.org/10.1016/j.memsci.2016.08.031
dc.relation.urihttps://doi.org/10.3390/membranes6040049
dc.relation.urihttps://doi.org/10.1016/j.desal.2018.04.002
dc.relation.urihttps://doi.org/10.1016/j.cej.2012.02.014
dc.relation.urihttps://doi.org/10.1016/j.seppur.2015.08.041
dc.relation.urihttps://doi.org/10.1016/j.memsci.2016.02.042
dc.relation.urihttps://doi.org/10.1016/j.desal.2011.08.025
dc.relation.urihttps://doi.org/10.1016/j.desal.2011.12.009
dc.relation.urihttps://doi.org/10.1016/j.memsci.2014.07.038
dc.relation.urihttps://doi.org/10.1007/s11356-016-7392-8
dc.relation.urihttps://doi.org/10.1016/j.ces.2011.03.025
dc.relation.urihttps://doi.org/10.1016/j.desal.2013.04.015
dc.relation.urihttps://doi.org/10.1016/j.compchemeng.2019.05.018
dc.relation.urihttps://doi.org/10.1007/s11356-014-3787-6
dc.relation.urihttps://doi.org/10.1016/j.memsci.2011.01.066
dc.relation.urihttps://doi.org/10.1007/s11356-013-2382-6
dc.relation.urihttps://doi.org/10.1016/j.desal.2012.12.021
dc.relation.urihttps://doi.org/10.1016/j.desal.2013.10.001
dc.relation.urihttps://doi.org/10.1016/j.memsci.2015.06.030
dc.relation.urihttps://doi.org/10.1016/j.jwpe.2019.100900
dc.relation.urihttps://doi.org/10.1016/j.memsci.2016.08.062
dc.relation.urihttps://doi.org/10.1016/j.jece.2020.104275
dc.relation.urihttps://doi.org/10.1007/s11356-016-6238-8
dc.relation.urihttps://doi.org/10.1016/j.desal.2017.07.020
dc.relation.urihttps://doi.org/10.1016/j.ces.2011.03.043
dc.relation.urihttps://doi.org/10.1007/s11814-019-0357-0
dc.relation.urihttps://doi.org/10.1016/j.memsci.2013.10.056
dc.relation.urihttps://doi.org/10.1016/j.jtice.2014.02.011
dc.relation.urihttps://doi.org/10.1016/j.memsci.2017.03.021
dc.relation.urihttps://doi.org/10.1016/j.seppur.2016.03.016
dc.relation.urihttps://doi.org/10.1016/j.memsci.2011.10.034
dc.relation.urihttps://doi.org/10.1016/j.memsci.2018.02.026
dc.relation.urihttps://doi.org/10.1016/j.desal.2011.09.018
dc.relation.urihttps://doi.org/10.1016/j.memsci.2017.11.050
dc.relation.urihttps://doi.org/10.1007/s11051-019-4665-4
dc.relation.urihttps://doi.org/10.3390/membranes10090235
dc.relation.urihttps://doi.org/10.1016/j.seppur.2018.08.066
dc.relation.urihttps://doi.org/10.3390/pr7090559
dc.relation.urihttps://doi.org/10.1016/j.memsci.2020.118117
dc.relation.urihttps://doi.org/10.1016/j.desal.2015.05.010
dc.relation.urihttps://doi.org/10.1016/j.desal.2013.04.030
dc.relation.urihttps://doi.org/10.1016/j.desal.2018.07.010
dc.relation.urihttps://doi.org/10.1016/j.memsci.2011.05.004
dc.relation.urihttps://doi.org/10.1007/s10863-019-09821-8
dc.relation.urihttps://doi.org/10.1007/s11814-014-0329-3
dc.relation.urihttps://doi.org/10.1016/j.cherd.2014.07.002
dc.relation.urihttps://doi.org/10.1016/j.memsci.2011.12.052
dc.relation.urihttps://doi.org/10.1016/j.jece.2019.103275
dc.relation.urihttps://doi.org/10.1016/j.seppur.2018.06.072
dc.relation.urihttps://doi.org/10.1016/j.seppur.2019.02.041
dc.relation.urihttps://doi.org/10.1016/j.desal.2013.01.033
dc.relation.urihttps://doi.org/10.1016/j.ces.2019.05.049
dc.relation.urihttps://doi.org/10.3303/CET1870341
dc.relation.urihttps://doi.org/10.1016/j.cherd.2019.05.018
dc.relation.urihttps://doi.org/10.1016/j.desal.2020.114454
dc.relation.urihttps://doi.org/10.1016/j.memsci.2015.03.064
dc.relation.urihttps://doi.org/10.1016/j.memsci.2017.01.053
dc.relation.urihttps://doi.org/10.1016/j.cjche.2015.09.006
dc.relation.urihttps://doi.org/10.1016/j.memsci.2019.117264
dc.relation.urihttps://doi.org/10.1016/j.cherd.2020.07.030
dc.relation.urihttps://doi.org/10.1016/j.cjche.2016.05.044
dc.relation.urihttps://doi.org/10.1016/j.seppur.2020.117187
dc.relation.urihttps://doi.org/10.1016/j.seppur.2011.09.010
dc.relation.urihttps://doi.org/10.1016/j.memsci.2012.10.010
dc.relation.urihttps://doi.org/10.1016/j.memsci.2014.10.042
dc.relation.urihttps://doi.org/10.1016/j.seppur.2015.04.012
dc.relation.urihttps://doi.org/10.1016/j.seppur.2018.04.056
dc.relation.urihttps://doi.org/10.1186/s11671-020-03436-4
dc.relation.urihttps://doi.org/10.1016/j.memsci.2018.12.035
dc.relation.urihttps://doi.org/10.1007/s40843-020-1335-x
dc.relation.urihttps://doi.org/10.1016/j.memsci.2019.117357
dc.relation.urihttps://doi.org/10.1016/j.memsci.2018.07.086
dc.relation.urihttps://doi.org/10.1016/j.memsci.2020.118079
dc.relation.urihttps://doi.org/10.3390/membranes8040123
dc.relation.urihttps://doi.org/10.1016/j.memsci.2019.117444
dc.relation.urihttps://doi.org/10.1557/mrs.2017.58
dc.relation.urihttps://doi.org/10.1155/2020/4063201
dc.relation.urihttps://doi.org/10.1007/s12572-015-0132-3
dc.relation.urihttps://doi.org/10.1007/s00231-015-1601-8
dc.relation.urihttps://doi.org/10.1016/j.coche.2020.02.001
dc.rights.holder© Національний університет “Львівська політехніка”, 2024
dc.rights.holder© Huliienko S., Korniyenko Y., Muzyka S., Holubka K., 2024
dc.subjectмембрана
dc.subjectнанофільтрація
dc.subjectматематична модель
dc.subjectоптимізація
dc.subjectпрограмне забезпечення
dc.subjectmembrane
dc.subjectnanofiltration
dc.subjectmathematical model
dc.subjectoptimization
dc.subjectsoftware
dc.titleMathematical Simulation of Nanofiltration Process: State of Art Review
dc.title.alternativeМатематичне моделювання процесу нанофільтрації: аналітичний огляд
dc.typeArticle

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Chemistry & Chemical Technology. – 2024. – Vol. 18, No. 2