{"id":"https://openalex.org/W1582422220","doi":"https://doi.org/10.1137/140968082","title":"Homogenization of the Poisson--Nernst--Planck equations for Ion Transport in Charged Porous Media","display_name":"Homogenization of the Poisson--Nernst--Planck equations for Ion Transport in Charged Porous Media","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1582422220","doi":"https://doi.org/10.1137/140968082","mag":"1582422220"},"language":"en","primary_location":{"id":"doi:10.1137/140968082","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140968082","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1202.1916","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010145500","display_name":"Markus Schmuck","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Markus Schmuck","raw_affiliation_strings":["School of Mathematical & Computer Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical & Computer Sciences","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070486479","display_name":"Martin Z. Bazant","orcid":"https://orcid.org/0000-0002-8200-4501"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Martin Z. Bazant","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3381,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.81578082,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"75","issue":"3","first_page":"1369","last_page":"1401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12274","display_name":"Electrostatics and Colloid Interactions","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T12274","display_name":"Electrostatics and Colloid Interactions","score":0.9987999796867371,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11362","display_name":"Membrane Separation and Gas Transport","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/debye-length","display_name":"Debye length","score":0.6478880643844604},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.47084924578666687},{"id":"https://openalex.org/keywords/permittivity","display_name":"Permittivity","score":0.4517582356929779},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.44897547364234924},{"id":"https://openalex.org/keywords/surface-charge","display_name":"Surface charge","score":0.4290081262588501},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.41136878728866577},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3406149744987488},{"id":"https://openalex.org/keywords/ion","display_name":"Ion","score":0.28763651847839355},{"id":"https://openalex.org/keywords/dielectric","display_name":"Dielectric","score":0.24139630794525146},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.2106737196445465},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15446066856384277},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.08320960402488708}],"concepts":[{"id":"https://openalex.org/C184654806","wikidata":"https://www.wikidata.org/wiki/Q898268","display_name":"Debye length","level":3,"score":0.6478880643844604},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.47084924578666687},{"id":"https://openalex.org/C168651791","wikidata":"https://www.wikidata.org/wiki/Q211569","display_name":"Permittivity","level":3,"score":0.4517582356929779},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.44897547364234924},{"id":"https://openalex.org/C2780358262","wikidata":"https://www.wikidata.org/wiki/Q1540423","display_name":"Surface charge","level":2,"score":0.4290081262588501},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.41136878728866577},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3406149744987488},{"id":"https://openalex.org/C145148216","wikidata":"https://www.wikidata.org/wiki/Q36496","display_name":"Ion","level":2,"score":0.28763651847839355},{"id":"https://openalex.org/C133386390","wikidata":"https://www.wikidata.org/wiki/Q184996","display_name":"Dielectric","level":2,"score":0.24139630794525146},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.2106737196445465},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15446066856384277},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.08320960402488708}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/140968082","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140968082","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1202.1916","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1202.1916","pdf_url":"https://arxiv.org/pdf/1202.1916","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:1582422220","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1202.1916","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:dspace.mit.edu:1721.1/98489","is_oa":true,"landing_page_url":"https://dspace.mit.edu/bitstream/1721.1/98489/1/Schmuck-2015-Homogenization.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Society for Industrial and Applied Mathematics","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1202.1916","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1202.1916","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"mag:2179260701","is_oa":false,"landing_page_url":"http://dspace.mit.edu/handle/1721.1/98489","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1202.1916","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1202.1916","pdf_url":"https://arxiv.org/pdf/1202.1916","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G1819990711","display_name":null,"funder_award_id":"PBSKP2-12459/1","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G3420727929","display_name":"FRG: Collaborative Research: Mathematical Modeling of Rechargeable Batteries","funder_award_id":"0948071","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":115,"referenced_works":["https://openalex.org/W100944330","https://openalex.org/W108023805","https://openalex.org/W165577513","https://openalex.org/W237209768","https://openalex.org/W613060151","https://openalex.org/W628977738","https://openalex.org/W1514053888","https://openalex.org/W1516439352","https://openalex.org/W1518531567","https://openalex.org/W1580090917","https://openalex.org/W1964865807","https://openalex.org/W1965125112","https://openalex.org/W1966495245","https://openalex.org/W1967203031","https://openalex.org/W1970865670","https://openalex.org/W1972576201","https://openalex.org/W1973142530","https://openalex.org/W1973751087","https://openalex.org/W1975249295","https://openalex.org/W1975458236","https://openalex.org/W1975840934","https://openalex.org/W1977546527","https://openalex.org/W1985404765","https://openalex.org/W1988421774","https://openalex.org/W1989002937","https://openalex.org/W1990265247","https://openalex.org/W1992465972","https://openalex.org/W1993775618","https://openalex.org/W1997596874","https://openalex.org/W2001910783","https://openalex.org/W2003984585","https://openalex.org/W2009021887","https://openalex.org/W2010085171","https://openalex.org/W2011372516","https://openalex.org/W2013351998","https://openalex.org/W2016271347","https://openalex.org/W2020888676","https://openalex.org/W2021762235","https://openalex.org/W2025148954","https://openalex.org/W2025883984","https://openalex.org/W2026337903","https://openalex.org/W2027239222","https://openalex.org/W2030247238","https://openalex.org/W2030261619","https://openalex.org/W2031182871","https://openalex.org/W2032488786","https://openalex.org/W2034649640","https://openalex.org/W2037635008","https://openalex.org/W2037776043","https://openalex.org/W2040613171","https://openalex.org/W2041620563","https://openalex.org/W2042770445","https://openalex.org/W2042932098","https://openalex.org/W2044812970","https://openalex.org/W2047696693","https://openalex.org/W2047841961","https://openalex.org/W2050964264","https://openalex.org/W2053340393","https://openalex.org/W2053748143","https://openalex.org/W2055656807","https://openalex.org/W2059073834","https://openalex.org/W2060224565","https://openalex.org/W2060368109","https://openalex.org/W2060668469","https://openalex.org/W2062716383","https://openalex.org/W2062726261","https://openalex.org/W2063776034","https://openalex.org/W2064765119","https://openalex.org/W2064858881","https://openalex.org/W2068148612","https://openalex.org/W2070257053","https://openalex.org/W2071216096","https://openalex.org/W2071449413","https://openalex.org/W2071717764","https://openalex.org/W2072242167","https://openalex.org/W2072892898","https://openalex.org/W2076803507","https://openalex.org/W2077489033","https://openalex.org/W2078238158","https://openalex.org/W2081704590","https://openalex.org/W2087800106","https://openalex.org/W2092950713","https://openalex.org/W2094921040","https://openalex.org/W2105926966","https://openalex.org/W2108708806","https://openalex.org/W2112769274","https://openalex.org/W2113270919","https://openalex.org/W2116801612","https://openalex.org/W2121927380","https://openalex.org/W2124097995","https://openalex.org/W2130869501","https://openalex.org/W2131346692","https://openalex.org/W2139836641","https://openalex.org/W2144419683","https://openalex.org/W2145123561","https://openalex.org/W2146070336","https://openalex.org/W2146961931","https://openalex.org/W2160310928","https://openalex.org/W2162125983","https://openalex.org/W2163140042","https://openalex.org/W2164221793","https://openalex.org/W2167152334","https://openalex.org/W2169834631","https://openalex.org/W2322796893","https://openalex.org/W2323624172","https://openalex.org/W2332611593","https://openalex.org/W2469568014","https://openalex.org/W2504619654","https://openalex.org/W2610542513","https://openalex.org/W2887993292","https://openalex.org/W2943166583","https://openalex.org/W2963633987","https://openalex.org/W3099746599","https://openalex.org/W3100625614","https://openalex.org/W4248587126"],"related_works":["https://openalex.org/W2626601335","https://openalex.org/W610268560","https://openalex.org/W2002662641","https://openalex.org/W2072679657","https://openalex.org/W3019539529","https://openalex.org/W2041810554","https://openalex.org/W193533180","https://openalex.org/W2239262419","https://openalex.org/W2048994970","https://openalex.org/W1977877084","https://openalex.org/W2523641043","https://openalex.org/W2093127982","https://openalex.org/W2032350140","https://openalex.org/W1984472594","https://openalex.org/W2023099472","https://openalex.org/W2112378313","https://openalex.org/W3028093043","https://openalex.org/W2182483620","https://openalex.org/W2950957039","https://openalex.org/W2044329297"],"abstract_inverted_index":{"Effective":[0],"Poisson-Nernst-Planck":[1],"(PNP)":[2],"equations":[3,154,230],"are":[4,170,201],"derived":[5],"for":[6,191,234],"macroscopic":[7,106,183,216,228],"ion":[8,251],"transport":[9,252],"in":[10,65,123,143,150,253],"charged":[11],"porous":[12,110,254,261],"media":[13],"under":[14],"periodic":[15,31,159],"fluid":[16],"flow":[17],"by":[18,40,119,172,215],"an":[19,164],"asymptotic":[20],"multi-scale":[21],"expansion":[22],"with":[23],"drift.":[24],"The":[25,147,223],"microscopic":[26,114],"setting":[27],"is":[28,50,86,117,186,213],"a":[29,35,45,57,88,120,137,192],"two-component":[30],"composite":[32],"consisting":[33],"of":[34,99,108,207,226],"dilute":[36],"electrolyte":[37],"continuum":[38],"(described":[39],"standard":[41],"PNP":[42,153,229],"equations)":[43],"and":[44,55,74,96,128,176,198,220,242,263],"continuous":[46,138],"dielectric":[47],"matrix,":[48,167,194],"which":[49,185],"impermeable":[51],"to":[52,79,104,250],"the":[53,66,70,80,83,92,97,100,105,109,113,124,130,151,173,177,182,189,196,205,227,240],"ions":[54],"carries":[56],"given":[58],"surface":[59,131,221],"charge.":[60],"Four":[61],"new":[62],"features":[63],"arise":[64],"upscaled":[67,152],"equations:":[68],"(i)":[69],"effective":[71,84,125],"ionic":[72,219],"diffusivities":[73],"mobilities":[75],"become":[76],"tensors,":[77],"related":[78],"microstructure;":[81],"(ii)":[82],"permittivity":[85,94,197],"also":[87,232],"tensor,":[89,175],"depending":[90],"on":[91,239],"electrolyte/matrix":[93],"ratio":[95,98],"Debye":[101],"screening":[102],"length":[103,107],"medium;":[111],"(iii)":[112],"fluidic":[115],"convection":[116],"replaced":[118,214],"diffusion-dispersion":[121],"correction":[122],"diffusion":[126],"tensor;":[127],"(iv)":[129],"charge":[132,140],"per":[133],"volume":[134],"appears":[135],"as":[136,142],"\"background":[139],"density\",":[141],"classical":[144],"membrane":[145],"models.":[146],"coefficient":[148],"tensors":[149],"can":[155],"be":[156],"calculated":[157],"from":[158],"reference":[160],"cell":[161],"problems.":[162],"For":[163],"insulating":[165],"solid":[166],"all":[168],"gradients":[169],"corrected":[171],"same":[174],"Einstein":[178],"relation":[179],"holds":[180],"at":[181],"scale,":[184],"not":[187],"generally":[188],"case":[190],"polarizable":[193],"unless":[195],"electric":[199],"field":[200],"suitably":[202],"defined.":[203],"In":[204],"limit":[206],"thin":[208],"double":[209],"layers,":[210],"Poisson's":[211],"equation":[212],"electroneutrality":[217],"(balancing":[218],"charges).":[222],"general":[224],"form":[225],"may":[231],"hold":[233],"concentrated":[235],"solution":[236],"theories,":[237],"based":[238],"local-density":[241],"mean-field":[243],"approximations.":[244],"These":[245],"results":[246],"have":[247],"broad":[248],"applicability":[249],"electrodes,":[255],"separators,":[256],"membranes,":[257],"ion-exchange":[258],"resins,":[259],"soils,":[260],"rocks,":[262],"biological":[264],"tissues.":[265]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}