{"id":"https://openalex.org/W2005659414","doi":"https://doi.org/10.1016/j.memsci.2013.04.022","title":"Validity of the Boltzmann equation to describe Donnan equilibrium at the membrane\u2013solution interface","display_name":"Validity of the Boltzmann equation to describe Donnan equilibrium at the membrane\u2013solution interface","publication_year":2013,"publication_date":"2013-04-17","ids":{"openalex":"https://openalex.org/W2005659414","doi":"https://doi.org/10.1016/j.memsci.2013.04.022","mag":"2005659414"},"language":"en","primary_location":{"id":"doi:10.1016/j.memsci.2013.04.022","doi":"https://doi.org/10.1016/j.memsci.2013.04.022","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.memsci.2013.04.022","pdf_url":null,"source":{"id":"https://openalex.org/S119469986","display_name":"Journal of Membrane Science","issn_l":"0376-7388","issn":["0376-7388","1873-3123"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Membrane Science","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.wur.nl/en/publications/validity-of-the-boltzmann-equation-to-describe-donnan-equilibrium","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033215736","display_name":"A.H. Galama","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405261053","display_name":"Wetsus, European Centre of Excellence for Sustainable Water Technology","ror":"https://ror.org/04pk9k962","country_code":"NL","type":"nonprofit","lineage":["https://openalex.org/I4405261053"]},{"id":"https://openalex.org/I913481162","display_name":"Wageningen University & Research","ror":"https://ror.org/04qw24q55","country_code":"NL","type":"education","lineage":["https://openalex.org/I913481162"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"A.H. Galama","raw_affiliation_strings":["Department of Environmental Technology, Wageningen University, Bornse Weilanden 9, 6708 WG Wageningen, the Netherlands","Wetsus, Centre of Excellence for Sustainable Water Technology, Agora 1, 8934 CJ Leeuwarden, the Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Environmental Technology, Wageningen University, Bornse Weilanden 9, 6708 WG Wageningen, the Netherlands","institution_ids":["https://openalex.org/I913481162"]},{"raw_affiliation_string":"Wetsus, Centre of Excellence for Sustainable Water Technology, Agora 1, 8934 CJ Leeuwarden, the Netherlands","institution_ids":["https://openalex.org/I4405261053"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110198770","display_name":"J.W. Post","orcid":"https://orcid.org/0000-0003-4793-4102","observed_orcids":["https://orcid.org/0000-0003-4793-4102"]},"institutions":[{"id":"https://openalex.org/I4210139073","display_name":"KWR Water Research Institute","ror":"https://ror.org/04f1mvy95","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210139073"]},{"id":"https://openalex.org/I913481162","display_name":"Wageningen University & Research","ror":"https://ror.org/04qw24q55","country_code":"NL","type":"education","lineage":["https://openalex.org/I913481162"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"J.W. Post","raw_affiliation_strings":["Department of Environmental Technology, Wageningen University, Bornse Weilanden 9, 6708 WG Wageningen, the Netherlands","KWR Watercycle Research Institute, Groningenhaven 7, 3433 PE Nieuwegein, the Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Environmental Technology, Wageningen University, Bornse Weilanden 9, 6708 WG Wageningen, the Netherlands","institution_ids":["https://openalex.org/I913481162"]},{"raw_affiliation_string":"KWR Watercycle Research Institute, Groningenhaven 7, 3433 PE Nieuwegein, the Netherlands","institution_ids":["https://openalex.org/I4210139073"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091109441","display_name":"Martinus A. Cohen Stuart","orcid":"https://orcid.org/0000-0001-6880-7861","observed_orcids":["https://orcid.org/0000-0001-6880-7861"]},"institutions":[{"id":"https://openalex.org/I913481162","display_name":"Wageningen University & Research","ror":"https://ror.org/04qw24q55","country_code":"NL","type":"education","lineage":["https://openalex.org/I913481162"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"M.A. Cohen Stuart","raw_affiliation_strings":["Department of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB Wageningen, the Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB Wageningen, the Netherlands","institution_ids":["https://openalex.org/I913481162"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063655870","display_name":"Pieter Maarten Biesheuvel","orcid":"https://orcid.org/0000-0002-5468-559X","observed_orcids":["https://orcid.org/0000-0002-5468-559X"]},"institutions":[{"id":"https://openalex.org/I4405261053","display_name":"Wetsus, European Centre of Excellence for Sustainable Water Technology","ror":"https://ror.org/04pk9k962","country_code":"NL","type":"nonprofit","lineage":["https://openalex.org/I4405261053"]},{"id":"https://openalex.org/I913481162","display_name":"Wageningen University & Research","ror":"https://ror.org/04qw24q55","country_code":"NL","type":"education","lineage":["https://openalex.org/I913481162"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"P.M. Biesheuvel","raw_affiliation_strings":["Department of Environmental Technology, Wageningen University, Bornse Weilanden 9, 6708 WG Wageningen, the Netherlands","Wetsus, Centre of Excellence for Sustainable Water Technology, Agora 1, 8934 CJ Leeuwarden, the Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Environmental Technology, Wageningen University, Bornse Weilanden 9, 6708 WG Wageningen, the Netherlands","institution_ids":["https://openalex.org/I913481162"]},{"raw_affiliation_string":"Wetsus, Centre of Excellence for Sustainable Water Technology, Agora 1, 8934 CJ Leeuwarden, the Netherlands","institution_ids":["https://openalex.org/I4405261053"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063655870"],"corresponding_institution_ids":["https://openalex.org/I4405261053","https://openalex.org/I913481162"],"apc_list":{"value":4890,"currency":"USD","value_usd":4890},"apc_paid":null,"fwci":7.4006,"has_fulltext":false,"cited_by_count":173,"citation_normalized_percentile":{"value":0.98494333,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"442","issue":null,"first_page":"131","last_page":"139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12074","display_name":"Membrane-based Ion Separation Techniques","score":0.6723999977111816,"subfield":{"id":"https://openalex.org/subfields/1506","display_name":"Filtration and Separation"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12074","display_name":"Membrane-based Ion Separation Techniques","score":0.6723999977111816,"subfield":{"id":"https://openalex.org/subfields/1506","display_name":"Filtration and Separation"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12274","display_name":"Electrostatics and Colloid Interactions","score":0.3093000054359436,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10197","display_name":"Membrane Separation Technologies","score":0.015799999237060547,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/donnan-equilibrium","display_name":"Donnan equilibrium","score":0.9860000014305115},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.9850000143051147},{"id":"https://openalex.org/keywords/membrane-solution-interface","display_name":"membrane-solution interface","score":0.9139999747276306},{"id":"https://openalex.org/keywords/electric-double-layer","display_name":"electric double layer","score":0.8569999933242798},{"id":"https://openalex.org/keywords/excluded-volume","display_name":"excluded volume","score":0.5559999942779541},{"id":"https://openalex.org/keywords/nacl-solution","display_name":"NaCl solution","score":0.7630000114440918},{"id":"https://openalex.org/keywords/ion-desorption","display_name":"ion desorption","score":0.7009999752044678},{"id":"https://openalex.org/keywords/charge-balance","display_name":"charge balance","score":0.6320000290870667}],"concepts":[{"id":"https://openalex.org/C94421946","wikidata":"https://www.wikidata.org/wiki/Q17043863","display_name":"Donnan potential","level":4,"score":0.8446550369262695},{"id":"https://openalex.org/C41625074","wikidata":"https://www.wikidata.org/wiki/Q176088","display_name":"Membrane","level":2,"score":0.7529502511024475},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.7122912406921387},{"id":"https://openalex.org/C34814092","wikidata":"https://www.wikidata.org/wiki/Q2268418","display_name":"Counterion","level":3,"score":0.594200849533081},{"id":"https://openalex.org/C145148216","wikidata":"https://www.wikidata.org/wiki/Q36496","display_name":"Ion","level":2,"score":0.5844740867614746},{"id":"https://openalex.org/C184651966","wikidata":"https://www.wikidata.org/wiki/Q906356","display_name":"Aqueous solution","level":2,"score":0.5379801988601685},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.4998135566711426},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.4228239357471466},{"id":"https://openalex.org/C113196181","wikidata":"https://www.wikidata.org/wiki/Q485223","display_name":"Analytical Chemistry (journal)","level":2,"score":0.37673306465148926},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.3016820251941681},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.14670097827911377},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12319570779800415},{"id":"https://openalex.org/C17525397","wikidata":"https://www.wikidata.org/wiki/Q176140","display_name":"Electrode","level":2,"score":0.08877941966056824},{"id":"https://openalex.org/C68801617","wikidata":"https://www.wikidata.org/wiki/Q162908","display_name":"Electrolyte","level":3,"score":0.0813460648059845},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.07580327987670898},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/j.memsci.2013.04.022","doi":"https://doi.org/10.1016/j.memsci.2013.04.022","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.memsci.2013.04.022","pdf_url":null,"source":{"id":"https://openalex.org/S119469986","display_name":"Journal of Membrane Science","issn_l":"0376-7388","issn":["0376-7388","1873-3123"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Membrane Science","raw_type":"journal-article"},{"id":"pmh:oai:library.wur.nl:wurpubs/440297","doi":null,"is_oa":true,"landing_page_url":"https://research.wur.nl/en/publications/validity-of-the-boltzmann-equation-to-describe-donnan-equilibrium","pdf_url":null,"source":{"id":"https://openalex.org/S4210201231","display_name":"Socio-Environmental Systems Modeling","issn_l":"2663-3027","issn":["2663-3027"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ISSN: 0376-7388","raw_type":"Article/Letter to editor"},{"id":"pmh:wur:oai:library.wur.nl:wurpubs/440297","doi":null,"is_oa":false,"landing_page_url":"https://research.wur.nl/en/publications/validity-of-the-boltzmann-equation-to-describe-donnan-equilibrium","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Membrane Science, 442, 131 - 139","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:library.wur.nl:wurpubs/440297","doi":null,"is_oa":true,"landing_page_url":"https://research.wur.nl/en/publications/validity-of-the-boltzmann-equation-to-describe-donnan-equilibrium","pdf_url":null,"source":{"id":"https://openalex.org/S4210201231","display_name":"Socio-Environmental Systems Modeling","issn_l":"2663-3027","issn":["2663-3027"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ISSN: 0376-7388","raw_type":"Article/Letter to editor"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320323721","display_name":"Technion-Israel Institute of Technology","ror":"https://ror.org/03qryx823"},{"id":"https://openalex.org/F4320334893","display_name":"Stichting voor de Technische Wetenschappen","ror":"https://ror.org/057tq3593"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":88,"referenced_works":["https://openalex.org/W570973647","https://openalex.org/W610905774","https://openalex.org/W1965060315","https://openalex.org/W1965071973","https://openalex.org/W1966700454","https://openalex.org/W1973089985","https://openalex.org/W1975129910","https://openalex.org/W1975267024","https://openalex.org/W1975371784","https://openalex.org/W1977554778","https://openalex.org/W1979937753","https://openalex.org/W1982350332","https://openalex.org/W1985874233","https://openalex.org/W1988160811","https://openalex.org/W1991161668","https://openalex.org/W1991429698","https://openalex.org/W1992970800","https://openalex.org/W1993036733","https://openalex.org/W1994209760","https://openalex.org/W1994472684","https://openalex.org/W1995313456","https://openalex.org/W2002498314","https://openalex.org/W2006386608","https://openalex.org/W2008113907","https://openalex.org/W2009634876","https://openalex.org/W2011049761","https://openalex.org/W2011468157","https://openalex.org/W2012332789","https://openalex.org/W2014482742","https://openalex.org/W2014559353","https://openalex.org/W2017666228","https://openalex.org/W2018108592","https://openalex.org/W2021747225","https://openalex.org/W2021858012","https://openalex.org/W2022543738","https://openalex.org/W2024459347","https://openalex.org/W2025125179","https://openalex.org/W2025346738","https://openalex.org/W2029783391","https://openalex.org/W2036040429","https://openalex.org/W2037815035","https://openalex.org/W2038948513","https://openalex.org/W2039666416","https://openalex.org/W2043217685","https://openalex.org/W2045908713","https://openalex.org/W2046565260","https://openalex.org/W2049892872","https://openalex.org/W2050914752","https://openalex.org/W2053831933","https://openalex.org/W2053995031","https://openalex.org/W2057101376","https://openalex.org/W2057343892","https://openalex.org/W2058873361","https://openalex.org/W2059700179","https://openalex.org/W2060157768","https://openalex.org/W2065892945","https://openalex.org/W2067396545","https://openalex.org/W2072955934","https://openalex.org/W2073137213","https://openalex.org/W2074868396","https://openalex.org/W2075243823","https://openalex.org/W2080134841","https://openalex.org/W2082356198","https://openalex.org/W2083838227","https://openalex.org/W2084583747","https://openalex.org/W2086542099","https://openalex.org/W2094617388","https://openalex.org/W2096623033","https://openalex.org/W2111797199","https://openalex.org/W2126585909","https://openalex.org/W2131156059","https://openalex.org/W2131550127","https://openalex.org/W2135971056","https://openalex.org/W2141411626","https://openalex.org/W2144069121","https://openalex.org/W2148209374","https://openalex.org/W2149102577","https://openalex.org/W2156323373","https://openalex.org/W2163170096","https://openalex.org/W2165155256","https://openalex.org/W2169834631","https://openalex.org/W2170804474","https://openalex.org/W2252296554","https://openalex.org/W2325191757","https://openalex.org/W2344847715","https://openalex.org/W2952278646","https://openalex.org/W3195263827","https://openalex.org/W4255287189"],"related_works":["https://openalex.org/W2038382358","https://openalex.org/W1996051970","https://openalex.org/W2944999755","https://openalex.org/W3217029149","https://openalex.org/W2073137213","https://openalex.org/W1985413266","https://openalex.org/W7171206106","https://openalex.org/W7208573541","https://openalex.org/W4398231054","https://openalex.org/W2348600455"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":6}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}