An analytical solution of the solution-diffusion-electromigration equations reproduces trends in ion rejections during nanofiltration of mixed electrolytes

Yaroshchuk, Andriy; Bruening, Merlin L.

doi:10.1016/j.memsci.2016.09.046

An analytical solution of the solution-diffusion-electromigration equations reproduces trends in ion rejections during nanofiltration of mixed electrolytes

Journal Article · Wed Sep 28 00:00:00 EDT 2016 · Journal of Membrane Science

DOI:https://doi.org/10.1016/j.memsci.2016.09.046· OSTI ID:1534096

Yaroshchuk, Andriy ^[1]; Bruening, Merlin L. ^[2]

Catalan Institution for Research and Advanced Studies (ICREA), Barcelona (Spain); Polytechnic University of Catalonia, Barcelona (Spain); DOE/OSTI
University of Notre Dame, IN (United States)

Here, this paper develops an analytical solution to the equations governing the solution-diffusion-electromigration transport of the ions from two salts that contain a common ion. The analytical expressions, which rely on constant ion permeances, readily enable simple spreadsheet computations of the permeate ion concentrations in nanofiltration (NF). Despite the model simplicity, calculations of ion rejections as a function of transmembrane volume fluxes, feed-solution compositions, and permeance values reproduce experimental trends, with ion permeances as the only adjustable parameters. For example, with solutions containing dissolved MA and M₂B, when the membrane permeance to B^2– is much lower than the permeances to A^– and M⁺, plots of A^– rejection versus transmembrane volume flux show the negative minimum that is often characteristic of NF. Moreover, B^2– rejection increases with increasing MA in the feed solution, reflecting a decreasing electric field in the membrane. The analytical solution also enables spreadsheet computations of electric fields in membrane separation layers and effectively models experimental data for intrinsic rejections as a function of transmembrane volume flow. Interestingly, the model suggests that with sufficiently high permeances of A^– (relative to M⁺), at certain feed compositions the A^–/B^2– selectivity may increase without bound as a function of volume flow. Otherwise, this selectivity does not vary greatly with feed composition and quickly reaches a limit as the volume flow increases. Despite the simplifying approximation of constant ion permeances, using only a few adjustable parameters this model readily reveals trends in NF ion rejections and may help to identify the desired ion permeances or solution compositions for specific separations.

View Accepted Manuscript (DOE)

Research Organization:: Michigan State Univ., East Lansing, MI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division (CSGB)

Grant/Contract Number:: FG02-98ER14907

OSTI ID:: 1534096

Alternate ID(s):: OSTI ID: 1397962

Journal Information:: Journal of Membrane Science, Journal Name: Journal of Membrane Science Vol. 523; ISSN 0376-7388

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (66)

Commercialisation of Kvaerner Chemetics' Sulphate Removal System Maycock, K.; Kotzo, C.; Muret, F. Modern Chlor‐Alkali Technology https://doi.org/10.1002/9780470999479.ch11	book	March 2001
The Application of Generalized Nernst-Planck Equations to the Description of Ion Retention in the Hyperfiltration of Mixed Electrolyte Solutions through a Neutral Membrane Vonk, M. W.; Smit, J. A. M. Berichte der Bunsengesellschaft für physikalische Chemie, Vol. 88, Issue 8 https://doi.org/10.1002/bbpc.19840880811	journal	August 1984
Kreislaufschließung von Metallen und Spülwasser in der Weißblechproduktion Wolters, Ralf; Bettermann, Ines; Rösler, Hans-Werner Chemie Ingenieur Technik, Vol. 84, Issue 10 https://doi.org/10.1002/cite.201200059	journal	September 2012
Thermodynamics of ternary systems in reverse osmosis Vonk, M. W.; Smit, J. A. M. Desalination, Vol. 48, Issue 2 https://doi.org/10.1016/0011-9164(83)80010-1	journal	January 1983
The solution-diffusion model: a review Wijmans, J. G.; Baker, R. W. Journal of Membrane Science, Vol. 107, Issue 1-2 https://doi.org/10.1016/0376-7388(95)00102-I	journal	November 1995
Nanofiltration modeling: the role of dielectric exclusion in membrane characterization Bandini, Serena; Vezzani, Daniele Chemical Engineering Science, Vol. 58, Issue 15 https://doi.org/10.1016/S0009-2509(03)00212-4	journal	August 2003
Modelling the salt rejection of nanofiltration membranes for ternary ion mixtures and for single salts at different pH values Hagmeyer, G.; Gimbel, R. Desalination, Vol. 117, Issue 1-3 https://doi.org/10.1016/S0011-9164(98)00109-X	journal	September 1998
Copper transfer modeling through a nanofiltration membrane in the case of ternary aqueous solution Mehiguene, K.; Taha, S.; Gondrexon, N. Desalination, Vol. 127, Issue 2 https://doi.org/10.1016/S0011-9164(99)00198-8	journal	February 2000
Experimental analysis of negative salt rejection in nanofiltration membranes Gilron, J. Journal of Membrane Science, Vol. 185, Issue 2 https://doi.org/10.1016/S0376-7388(00)00639-6	journal	April 2001
Mass transfer in the membrane concentration polarization layer under turbulent cross flow Gekas, Vassilis; Hallström, Bengt Journal of Membrane Science, Vol. 30, Issue 2 https://doi.org/10.1016/S0376-7388(00)81349-6	journal	February 1987
Can nanofiltration be fully predicted by a model? Straatsma, J.; Bargeman, G.; van der Horst, H. C. Journal of Membrane Science, Vol. 198, Issue 2 https://doi.org/10.1016/S0376-7388(01)00669-X	journal	April 2002
TFC polyamide membranes modified by grafting of hydrophilic polymers: an FT-IR/AFM/TEM study Freger, Viatcheslav; Gilron, Jack; Belfer, Sofia Journal of Membrane Science, Vol. 209, Issue 1 https://doi.org/10.1016/S0376-7388(02)00356-3	journal	November 2002
Characterisation of nanofiltration membranes for predictive purposes — use of salts, uncharged solutes and atomic force microscopy Bowen, W. Richard; Mohammad, A. Wahab; Hilal, Nidal Journal of Membrane Science, Vol. 126, Issue 1 https://doi.org/10.1016/S0376-7388(96)00276-1	journal	April 1997
How to use a multi-ionic transport model to fully predict rejection of mineral salts by nanofiltration membranes Déon, Sébastien; Escoda, Aurélie; Fievet, Patrick Chemical Engineering Journal, Vol. 189-190 https://doi.org/10.1016/j.cej.2012.02.014	journal	May 2012
Rejection of ammonium and nitrate from sodium chloride solutions by nanofiltration: Effect of dominant-salt concentration on the trace-ion rejection Reig, Mònica; Licon, Edxon; Gibert, Oriol Chemical Engineering Journal, Vol. 303 https://doi.org/10.1016/j.cej.2016.06.025	journal	November 2016
Investigating nanofiltration of multi-ionic solutions using the steric, electric and dielectric exclusion model Saliha, Bouranene; Patrick, Fievet; Anthony, Szymczyk Chemical Engineering Science, Vol. 64, Issue 17 https://doi.org/10.1016/j.ces.2009.05.020	journal	September 2009
Rejection of trace ionic solutes in nanofiltration: Influence of aqueous phase composition Pages, Neus; Yaroshchuk, Andriy; Gibert, Oriol Chemical Engineering Science, Vol. 104 https://doi.org/10.1016/j.ces.2013.09.042	journal	December 2013
Negative rejection of ions in pressure-driven membrane processes Yaroshchuk, Andriy E. Advances in Colloid and Interface Science, Vol. 139, Issue 1-2 https://doi.org/10.1016/j.cis.2008.01.004	journal	June 2008
Salt rejection in nanofiltration for single and binary salt mixtures in view of sulphate removal Krieg, H. M.; Modise, S. J.; Keizer, K. Desalination, Vol. 171, Issue 2 https://doi.org/10.1016/j.desal.2004.05.005	journal	January 2005
Separation performance of a nanofiltration membrane influenced by species and concentration of ions Wang, Da-Xin; Su, Meng; Yu, Zhao-Yang Desalination, Vol. 175, Issue 2 https://doi.org/10.1016/j.desal.2004.10.009	journal	May 2005
Rejection of ions by NF membranes for binary electrolyte solutions of NaCl, NaNO3, CaCl2 and Ca(NO3)2 Su, Meng; Wang, Da-Xin; Wang, Xiao-Lin Desalination, Vol. 191, Issue 1-3 https://doi.org/10.1016/j.desal.2005.06.041	journal	May 2006
Rejection and modelling of sulphate and potassium salts by nanofiltration membranes: neural network and Spiegler–Kedem model Al-Zoubi, H.; Hilal, N.; Darwish, N. A. Desalination, Vol. 206, Issue 1-3 https://doi.org/10.1016/j.desal.2006.02.060	journal	February 2007
Characterization of nanofiltration and reverse osmosis membrane performance for aqueous salt solutions using irreversible thermodynamics Gupta, Vineet K.; Hwang, Sun-Tak; Krantz, William B. Desalination, Vol. 208, Issue 1-3 https://doi.org/10.1016/j.desal.2006.05.023	journal	April 2007
Nanofiltration as energy-efficient solution for sulfate waste in vacuum salt production Bargeman, G.; Steensma, M.; ten Kate, A. Desalination, Vol. 245, Issue 1-3 https://doi.org/10.1016/j.desal.2009.02.009	journal	September 2009
Multi-ionic nanofiltration of highly concentrated salt mixtures in the seawater range Silva, V.; Geraldes, V.; Brites Alves, A. M. Desalination, Vol. 277, Issue 1-3 https://doi.org/10.1016/j.desal.2011.03.088	journal	August 2011
Nanofiltration membranes review: Recent advances and future prospects Mohammad, A. W.; Teow, Y. H.; Ang, W. L. Desalination, Vol. 356 https://doi.org/10.1016/j.desal.2014.10.043	journal	January 2015
Solute hindrance in non-porous membranes: An ATR-FTIR study Dlamini, Derrick S.; Levchenko, Stanislav; Bass, Maria Desalination, Vol. 368 https://doi.org/10.1016/j.desal.2015.03.009	journal	July 2015
Permeation of mixed-salt solutions with commercial and pore-filled nanofiltration membranes: membrane charge inversion phenomena Garcia-Aleman, Jesus; Dickson, James M. Journal of Membrane Science, Vol. 239, Issue 2 https://doi.org/10.1016/j.memsci.2004.02.036	journal	August 2004
Reformulation of the solution-diffusion theory of reverse osmosis Paul, D. Journal of Membrane Science, Vol. 241, Issue 2 https://doi.org/10.1016/j.memsci.2004.05.026	journal	October 2004
Identification of dielectric effects in nanofiltration of metallic salts Szymczyk, A.; Fatinrouge, N.; Fievet, P. Journal of Membrane Science, Vol. 287, Issue 1 https://doi.org/10.1016/j.memsci.2006.10.025	journal	January 2007
Characterization of ion transport in thin films using electrochemical impedance spectroscopyII: Examination of the polyamide layer of RO membranes Bason, S.; Oren, Y.; Freger, V. Journal of Membrane Science, Vol. 302, Issue 1-2 https://doi.org/10.1016/j.memsci.2007.05.007	journal	September 2007
Phenomenological analysis of transport of mono- and divalent ions in nanofiltration Bason, Sarit; Freger, Viatcheslav Journal of Membrane Science, Vol. 360, Issue 1-2 https://doi.org/10.1016/j.memsci.2010.05.037	journal	September 2010
Solution-diffusion-film model for the description of pressure-driven trans-membrane transfer of electrolyte mixtures: One dominant salt and trace ions Yaroshchuk, Andriy; Martínez-Lladó, Xavier; Llenas, Laia Journal of Membrane Science, Vol. 368, Issue 1-2 https://doi.org/10.1016/j.memsci.2010.11.037	journal	February 2011
Assessment of dielectric contribution in the modeling of multi-ionic transport through nanofiltration membranes Escoda, Aurélie; Déon, Sébastien; Fievet, Patrick Journal of Membrane Science, Vol. 378, Issue 1-2 https://doi.org/10.1016/j.memsci.2011.05.004	journal	August 2011
Sodium chloride sorption in sulfonated polymers for membrane applications Geise, Geoffrey M.; Falcon, Linda P.; Freeman, Benny D. Journal of Membrane Science, Vol. 423-424 https://doi.org/10.1016/j.memsci.2012.08.014	journal	December 2012
Sodium chloride diffusion in sulfonated polymers for membrane applications Geise, Geoffrey M.; Freeman, Benny D.; Paul, Donald R. Journal of Membrane Science, Vol. 427 https://doi.org/10.1016/j.memsci.2012.09.029	journal	January 2013
Enhanced desalination performance of polyamide bi-layer membranes prepared by sequential interfacial polymerization La, Young-Hye; Diep, Jacquana; Al-Rasheed, Radwan Journal of Membrane Science, Vol. 437 https://doi.org/10.1016/j.memsci.2013.02.044	journal	June 2013
Solution-Diffusion–Electro-Migration model and its uses for analysis of nanofiltration, pressure-retarded osmosis and forward osmosis in multi-ionic solutions Yaroshchuk, Andriy; Bruening, Merlin L.; Licón Bernal, Edxon Eduardo Journal of Membrane Science, Vol. 447 https://doi.org/10.1016/j.memsci.2013.07.047	journal	November 2013
A critical review of transport through osmotic membranes Wang, Jinwen; Dlamini, Derrick S.; Mishra, Ajay K. Journal of Membrane Science, Vol. 454 https://doi.org/10.1016/j.memsci.2013.12.034	journal	March 2014
Mixed polyamide-based composite nanofiltration hollow fiber membranes with improved low-pressure water softening capability Fang, Wangxi; Shi, Lei; Wang, Rong Journal of Membrane Science, Vol. 468 https://doi.org/10.1016/j.memsci.2014.05.047	journal	October 2014
Nanofiltration separation of polyvalent and monovalent anions in desalination brines Pérez-González, A.; Ibáñez, R.; Gómez, P. Journal of Membrane Science, Vol. 473 https://doi.org/10.1016/j.memsci.2014.08.045	journal	January 2015
The porous structure of the fully-aromatic polyamide film in reverse osmosis membranes Yan, Hao; Miao, Xiaopei; Xu, Jian Journal of Membrane Science, Vol. 475 https://doi.org/10.1016/j.memsci.2014.10.052	journal	February 2015
Specific ion effects on the permselectivity of sulfonated poly(ether sulfone) cation exchange membranes Cassady, Harrison J.; Cimino, Emily C.; Kumar, Manish Journal of Membrane Science, Vol. 508 https://doi.org/10.1016/j.memsci.2016.02.048	journal	June 2016
Cation separations in electrodialysis through membranes coated with polyelectrolyte multilayers Cheng, Chao; White, Nicholas; Shi, Hang Polymer, Vol. 55, Issue 6 https://doi.org/10.1016/j.polymer.2013.12.002	journal	March 2014
Highly selective separations of multivalent and monovalent cations in electrodialysis through Nafion membranes coated with polyelectrolyte multilayers White, Nicholas; Misovich, Maria; Alemayehu, Elena Polymer, Vol. 103 https://doi.org/10.1016/j.polymer.2015.12.019	journal	October 2016
Fundamental water and salt transport properties of polymeric materials Geise, Geoffrey M.; Paul, Donald R.; Freeman, Benny D. Progress in Polymer Science, Vol. 39, Issue 1 https://doi.org/10.1016/j.progpolymsci.2013.07.001	journal	January 2014
Study of synthesis parameters and active layer morphology of interfacially polymerized polyamide–polysulfone membranes Hermans, Sanne; Bernstein, Roy; Volodin, Alexander Reactive and Functional Polymers, Vol. 86 https://doi.org/10.1016/j.reactfunctpolym.2014.09.013	journal	January 2015
On nanofiltration Desal-5 DK performances with calcium chloride–water solutions Mazzoni, Carolina; Bandini, Serena Separation and Purification Technology, Vol. 52, Issue 2 https://doi.org/10.1016/j.seppur.2006.04.004	journal	December 2006
Drawbacks of applying nanofiltration and how to avoid them: A review Van der Bruggen, B.; Mänttäri, M.; Nyström, M. Separation and Purification Technology, Vol. 63, Issue 2 https://doi.org/10.1016/j.seppur.2008.05.010	journal	October 2008
Predicting the Rejection of Major Seawater Ions by Spiral-Wound Nanofiltration Membranes Fridman-Bishop, Noga; Nir, Oded; Lahav, Ori Environmental Science & Technology, Vol. 49, Issue 14 https://doi.org/10.1021/acs.est.5b00336	journal	July 2015
Deviations from Electroneutrality in Membrane Barrier Layers: A Possible Mechanism Underlying High Salt Rejections Yaroshchuk, Andriy; Zhu, Yan; Bondarenko, Mykola Langmuir, Vol. 32, Issue 11 https://doi.org/10.1021/acs.langmuir.5b04588	journal	March 2016
Coating of Nafion Membranes with Polyelectrolyte Multilayers to Achieve High Monovalent/Divalent Cation Electrodialysis Selectivities White, Nicholas; Misovich, Maria; Yaroshchuk, Andriy ACS Applied Materials & Interfaces, Vol. 7, Issue 12 https://doi.org/10.1021/am508945p	journal	March 2015
Ion Selective Permeation Through Cellulose Acetate Membranes in Forward Osmosis Irvine, Gavin J.; Rajesh, Sahadevan; Georgiadis, Michael Environmental Science & Technology, Vol. 47, Issue 23 https://doi.org/10.1021/es403581t	journal	November 2013
Does Hindered Transport Theory Apply to Desalination Membranes? Dražević, Emil; Košutić, Krešimir; Kolev, Vesselin Environmental Science & Technology, Vol. 48, Issue 19 https://doi.org/10.1021/es502085p	journal	September 2014
Nanofiltration: Role of the Electrolyte and pH on Desal DK Performances Mazzoni, Carolina; Bruni, Luigi; Bandini, Serena Industrial & Engineering Chemistry Research, Vol. 46, Issue 8 https://doi.org/10.1021/ie060974l	journal	January 2007
Nanofiltration Theory: An Analytic Approach for Single Salts Lefebvre, Xavier; Palmeri, John; David, Patrice The Journal of Physical Chemistry B, Vol. 108, Issue 43 https://doi.org/10.1021/jp048631t	journal	October 2004
Analysis of Ion Transport in Nanofiltration Using Phenomenological Coefficients and Structural Characteristics Bason, Sarit; Kaufman, Yair; Freger, Viatcheslav The Journal of Physical Chemistry B, Vol. 114, Issue 10 https://doi.org/10.1021/jp911615n	journal	February 2010
Ultrathin, Multilayered Polyelectrolyte Films as Nanofiltration Membranes Stanton, Brian W.; Harris, Jeremy J.; Miller, Matthew D. Langmuir, Vol. 19, Issue 17 https://doi.org/10.1021/la034603a	journal	August 2003
Selective Ion Transport across Self-Assembled Alternating Multilayers of Cationic and Anionic Polyelectrolytes Krasemann, Lutz; Tieke, Bernd Langmuir, Vol. 16, Issue 2 https://doi.org/10.1021/la991240z	journal	January 2000
Specific ion effects on membrane potential and the permselectivity of ion exchange membranes Geise, Geoffrey M.; Cassady, Harrison J.; Paul, Donald R. Phys. Chem. Chem. Phys., Vol. 16, Issue 39 https://doi.org/10.1039/C4CP03076A	journal	January 2014
Ion Rejection in Single and Binary Mixed Electrolyte Systems by Nanofiltration: Effect of Feed Concentration Ko, Ya‐Wen; Chen, Rou‐Min Separation Science and Technology, Vol. 42, Issue 14 https://doi.org/10.1080/01496390701588919	journal	October 2007
Bulk-Phase Criteria for Negative Ion Rejection in Nanofiltration of Multicomponent Salt Solutions Nielsen∗, Dennis W.; Jonsson, Gunnar Separation Science and Technology, Vol. 29, Issue 9 https://doi.org/10.1080/01496399408005623	journal	June 1994
Effect of concentration polarization on permselectivity abu-Rjal, Ramadan; Chinaryan, Vahe; Bazant, Martin Z. Physical Review E, Vol. 89, Issue 1 https://doi.org/10.1103/PhysRevE.89.012302	journal	January 2014
Comparison of the Behavior of Two Nanofiltration Membranes for Sweet Whey Demineralization Cuartas-Uribe, B.; Alcaina-Miranda, M. I.; Soriano-Costa, E. Journal of Dairy Science, Vol. 90, Issue 3 https://doi.org/10.3168/jds.S0022-0302(07)71596-5	journal	March 2007
Mechanisms of transfer of ionic solutes through composite polymer nano-filtration membranes in view of their high sulfate/chloride selectivities Yaroshchuk, Andriy; Martínez-Lladó, Xavier; Llenas, Laia Desalination and Water Treatment, Vol. 6, Issue 1-3 https://doi.org/10.5004/dwt.2009.642	journal	June 2009
Mass transport modelling to estimate the efficiency of nanofiltration application for the recovery of phosphorus from sewage sludge Niewersch, Claudia; Abels, Christian; Li, Ran Desalination and Water Treatment, Vol. 6, Issue 1-3 https://doi.org/10.5004/dwt.2009.651	journal	June 2009

Similar Records

Modelling nanofiltration of electrolyte solutions

Journal Article · Mon Mar 18 20:00:00 EDT 2019 · Advances in Colloid and Interface Science · OSTI ID:1597632

Performance characterization of nanofiltration, reverse osmosis, and ion exchange technologies for acetic acid separation

Journal Article · Thu Nov 25 19:00:00 EST 2021 · Separation and Purification Technology · OSTI ID:1798306

Application of electrodialysis pretreatment to enhance boron removal and reduce fouling during desalination by nanofiltration/reverse osmosis

Journal Article · Mon Jun 29 20:00:00 EDT 2020 · Desalination · OSTI ID:1852965

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Electromigration
Ion permeance
Nanofiltration
Negative rejection
Solution-diffusion

An analytical solution of the solution-diffusion-electromigration equations reproduces trends in ion rejections during nanofiltration of mixed electrolytes

Citation Formats

References (66)

Similar Records

Related Subjects