{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:50:05Z","timestamp":1760241005974,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T00:00:00Z","timestamp":1573171200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["685579"],"award-info":[{"award-number":["685579"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>The hydrodynamics of electrodialysis and reverse electrodialysis is commonly studied by neglecting membrane deformation caused by transmembrane pressure (TMP). However, large frictional pressure drops and differences in fluid velocity or physical properties in adjacent channels may lead to significant TMP values. In previous works, we conducted one-way coupled structural-CFD simulations at the scale of one periodic unit of a profiled membrane\/channel assembly and computed its deformation and frictional characteristics as functions of TMP. In this work, a novel fluid\u2013structure interaction model is presented, which predicts, at the channel pair scale, the changes in flow distribution associated with membrane deformations. The continuity and Darcy equations are solved in two adjacent channels by treating them as porous media and using the previous CFD results to express their hydraulic permeability as a function of the local TMP. Results are presented for square stacks of 0.6-m sides in cross and counter flow at superficial velocities of 1 to 10 cm\/s. At low velocities, the corresponding low TMP does not significantly affect the flow distribution. As the velocity increases, the larger membrane deformation causes significant fluid redistribution. In the cross flow, the departure of the local superficial velocity from a mean value of 10 cm\/s ranges between \u221227% and +39%.<\/jats:p>","DOI":"10.3390\/en12224259","type":"journal-article","created":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T11:30:19Z","timestamp":1573212619000},"page":"4259","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fluid\u2013Structure Interaction and Flow Redistribution in Membrane-Bounded Channels"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8094-0710","authenticated-orcid":false,"given":"Giuseppe","family":"Battaglia","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 degli Studi di Palermo, viale delle Scienze Ed. 6, 90128 Palermo, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8443-6025","authenticated-orcid":false,"given":"Luigi","family":"Gurreri","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 degli Studi di Palermo, viale delle Scienze Ed. 6, 90128 Palermo, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0570-195X","authenticated-orcid":false,"given":"Andrea","family":"Cipollina","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 degli Studi di Palermo, viale delle Scienze Ed. 6, 90128 Palermo, Italy"}]},{"given":"Antonina","family":"Pirrotta","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 degli Studi di Palermo, viale delle Scienze Ed. 6, 90128 Palermo, Italy"},{"name":"Department of Mathematical Sciences, University of Liverpool, Liverpool L3 5TR, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9446-0897","authenticated-orcid":false,"given":"Svetlozar","family":"Velizarov","sequence":"additional","affiliation":[{"name":"Associated Laboratory for Green Chemistry\u2014Clean Technologies and Processes (LAQV), REQUIMTE, Chemistry Department, FCT, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5648-978X","authenticated-orcid":false,"given":"Michele","family":"Ciofalo","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 degli Studi di Palermo, viale delle Scienze Ed. 6, 90128 Palermo, Italy"}]},{"given":"Giorgio","family":"Micale","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 degli Studi di Palermo, viale delle Scienze Ed. 6, 90128 Palermo, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.desal.2017.12.044","article-title":"Electrodialysis for water desalination: A critical assessment of recent developments on process fundamentals, models and applications","volume":"434","author":"Campione","year":"2018","journal-title":"Desalination"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.apenergy.2018.04.111","article-title":"Progress and prospects in reverse electrodialysis for salinity gradient energy conversion and storage","volume":"225","author":"Tufa","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.memsci.2014.03.020","article-title":"Pressure drop in reverse electrodialysis: Experimental and modeling studies for stacks with variable number of cell pairs","volume":"462","author":"Pawlowski","year":"2014","journal-title":"J. Memb. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.memsci.2017.03.003","article-title":"Improved fluid mixing and power density in reverse electrodialysis stacks with chevron-profiled membranes","volume":"531","author":"Pawlowski","year":"2017","journal-title":"J. Memb. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.memsci.2014.05.058","article-title":"CFD prediction of concentration polarization phenomena in spacer-filled channels for reverse electrodialysis","volume":"468","author":"Gurreri","year":"2014","journal-title":"J. Memb. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1016\/j.memsci.2017.07.030","article-title":"Coupling CFD with a one-dimensional model to predict the performance of reverse electrodialysis stacks","volume":"541","author":"Liberto","year":"2017","journal-title":"J. Memb. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.memsci.2015.11.031","article-title":"Computational fluid dynamics (CFD) assisted analysis of profiled membranes performance in reverse electrodialysis","volume":"502","author":"Pawlowski","year":"2016","journal-title":"J. Memb. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.memsci.2008.10.007","article-title":"A numerical and experimental study of mass transfer in spacer-filled channels: Effects of spacer geometrical characteristics and Schmidt number","volume":"326","author":"Koutsou","year":"2009","journal-title":"J. Memb. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1016\/j.memsci.2008.08.022","article-title":"Extending potential flow modelling of flat-sheet geometries as applied in membrane-based systems","volume":"325","author":"Dirkse","year":"2008","journal-title":"J. Memb. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"10025","DOI":"10.1021\/ie901129j","article-title":"On the fluid mechanics of spiral-wound membrane modules","volume":"48","author":"Kostoglou","year":"2009","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4653","DOI":"10.1021\/ie102083j","article-title":"Mathematical analysis of the meso-scale flow field in spiral-wound membrane modules","volume":"50","author":"Kostoglou","year":"2011","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.memsci.2010.11.042","article-title":"Spatially two-dimensional mathematical model of the flow hydrodynamics in a channel filled with a net-like spacer","volume":"368","author":"Bouzek","year":"2011","journal-title":"J. Memb. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1016\/j.memsci.2015.03.099","article-title":"Spatially two-dimensional mathematical model of the flow hydrodynamics in a spacer-filled channel\u2014The effect of inertial forces","volume":"492","author":"Bouzek","year":"2015","journal-title":"J. Memb. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.memsci.2013.05.061","article-title":"Effect of feed spacer induced membrane deformation on the performance of pressure retarded osmosis (PRO): Implications for PRO process operation","volume":"445","author":"She","year":"2013","journal-title":"J. Memb. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1016\/j.memsci.2017.12.037","article-title":"Comprehensive performance assessment of spacers in spiral-wound membrane modules accounting for compressibility effects","volume":"549","author":"Karabelas","year":"2018","journal-title":"J. Memb. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.memsci.2016.01.015","article-title":"Membrane deflection in a flat membrane microcontactor: Experimental study of spacer features","volume":"504","author":"Hereijgers","year":"2016","journal-title":"J. Memb. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"11386","DOI":"10.1021\/acs.est.6b02668","article-title":"The Breathing Cell: Cyclic Intermembrane Distance Variation in Reverse Electrodialysis","volume":"50","author":"Moreno","year":"2016","journal-title":"Environ. Sci. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Park, S.-M., and Lee, S. (2019). Influence of Hydraulic Pressure on Performance Deterioration of Direct Contact Membrane Distillation (DCMD) Process. Membranes, 9.","DOI":"10.3390\/membranes9030037"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.desal.2017.10.047","article-title":"Impact of module design in forward osmosis and pressure assisted osmosis: An experimental and numerical study","volume":"426","author":"Lian","year":"2018","journal-title":"Desalination"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.memsci.2019.02.045","article-title":"Pressure-retarded membrane distillation for low-grade heat recovery: The critical roles of pressure-induced membrane deformation","volume":"579","author":"Yuan","year":"2019","journal-title":"J. Memb. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5287","DOI":"10.1007\/s12206-016-1047-z","article-title":"Experimental and numerical studies on pressure drop in reverse electrodialysis: Effect of unit cell configuration","volume":"30","author":"Hong","year":"2016","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Battaglia, G., Gurreri, L., Air\u00f2 Farulla, G., Cipollina, A., Pirrotta, A., Micale, G., and Ciofalo, M. (2019). Membrane Deformation and Its Effects on Flow and Mass Transfer in the Electromembrane Processes. Int. J. Mol. Sci., 20.","DOI":"10.3390\/ijms20081840"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Battaglia, G., Gurreri, L., Air\u00f2 Farulla, G., Cipollina, A., Pirrotta, A., Micale, G., and Ciofalo, M. (2019). Pressure-Induced Deformation of Pillar-Type Profiled Membranes and Its Effects on Flow and Mass Transfer. Computation, 7.","DOI":"10.3390\/computation7020032"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"012003","DOI":"10.1088\/1742-6596\/796\/1\/012003","article-title":"Unsteadiness and transition to turbulence in woven spacer filled channels for Membrane Distillation","volume":"796","author":"Ciofalo","year":"2017","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/0011-9164(87)90107-X","article-title":"Mass transfer and pressure loss in spiral wound modules","volume":"64","author":"Schock","year":"1987","journal-title":"Desalination"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1029\/TR039i004p00702","article-title":"On the theoretical derivation of Darcy and Forchheimer formulas","volume":"39","author":"Irmay","year":"1958","journal-title":"Eos Trans. Am. Geophys. Union"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.desal.2010.04.069","article-title":"Electrodialysis, a mature technology with a multitude of new applications","volume":"264","author":"Strathmann","year":"2010","journal-title":"Desalination"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3391","DOI":"10.1080\/19443994.2014.947781","article-title":"Analysis and simulation of scale-up potentials in reverse electrodialysis","volume":"55","author":"Tedesco","year":"2014","journal-title":"Desalin. Water Treat."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"10856","DOI":"10.1021\/acs.est.8b01886","article-title":"Upscaling Reverse Electrodialysis","volume":"52","author":"Moreno","year":"2018","journal-title":"Environ. Sci. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.desal.2018.04.018","article-title":"A robust model of brackish water electrodialysis desalination with experimental comparison at different size scales","volume":"443","author":"Wright","year":"2018","journal-title":"Desalination"}],"container-title":["Energies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1073\/12\/22\/4259\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:32:57Z","timestamp":1760189577000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1073\/12\/22\/4259"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,8]]},"references-count":30,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["en12224259"],"URL":"https:\/\/doi.org\/10.3390\/en12224259","relation":{},"ISSN":["1996-1073"],"issn-type":[{"type":"electronic","value":"1996-1073"}],"subject":[],"published":{"date-parts":[[2019,11,8]]}}}