{"id":"https://openalex.org/W2509413600","doi":"https://doi.org/10.1137/15m1039389","title":"The Steady-State Convection-Diffusion Equation at High P\u00e9clet Numbers for a Cluster of Spheres: An Extension of Levich's Theory","display_name":"The Steady-State Convection-Diffusion Equation at High P\u00e9clet Numbers for a Cluster of Spheres: An Extension of Levich's Theory","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2509413600","doi":"https://doi.org/10.1137/15m1039389","mag":"2509413600"},"language":"en","primary_location":{"id":"doi:10.1137/15m1039389","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1039389","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://escholarship.org/content/qt1d42775x/qt1d42775x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007530896","display_name":"Joseph A. Biello","orcid":"https://orcid.org/0000-0001-9717-7643"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Joseph A. Biello","raw_affiliation_strings":["Department of Mathematics, University of California, Davis, CA 95616"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Davis, CA 95616","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065304884","display_name":"Ren\u00e9 Samson","orcid":"https://orcid.org/0000-0002-2503-0738"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ren\u00e9 Samson","raw_affiliation_strings":["\u2021 Jacob van Lennepkade 29-hs, Amsterdam, 1054 ZE, The Netherlands"],"affiliations":[{"raw_affiliation_string":"\u2021 Jacob van Lennepkade 29-hs, Amsterdam, 1054 ZE, The Netherlands","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072285082","display_name":"Eugene Sigal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eugene Sigal","raw_affiliation_strings":["Nabla Works, Europaweg 151, Zoetermeer, 2711 ER, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Nabla Works, Europaweg 151, Zoetermeer, 2711 ER, The Netherlands","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007530896"],"corresponding_institution_ids":["https://openalex.org/I84218800"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09066883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"76","issue":"4","first_page":"1515","last_page":"1534"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12350","display_name":"Particle Dynamics in Fluid Flows","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12350","display_name":"Particle Dynamics in Fluid Flows","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13951","display_name":"Fluid dynamics and aerodynamics studies","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12383","display_name":"Aeolian processes and effects","score":0.9842000007629395,"subfield":{"id":"https://openalex.org/subfields/1904","display_name":"Earth-Surface Processes"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/p\u00e9clet-number","display_name":"P\u00e9clet number","score":0.7766750454902649},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.7117168307304382},{"id":"https://openalex.org/keywords/wake","display_name":"Wake","score":0.6496350765228271},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.6196209788322449},{"id":"https://openalex.org/keywords/damk\u00f6hler-numbers","display_name":"Damk\u00f6hler numbers","score":0.5348336696624756},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.5343778133392334},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.489729642868042},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4881923794746399},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4874115288257599},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.48654451966285706},{"id":"https://openalex.org/keywords/boundary-layer","display_name":"Boundary layer","score":0.46195554733276367},{"id":"https://openalex.org/keywords/hard-spheres","display_name":"Hard spheres","score":0.4511777460575104},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4279429614543915},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.42691415548324585},{"id":"https://openalex.org/keywords/absorption","display_name":"Absorption (acoustics)","score":0.41146326065063477},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3364081382751465},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28038695454597473},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26806819438934326},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.22127294540405273},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.13682830333709717},{"id":"https://openalex.org/keywords/turbulence","display_name":"Turbulence","score":0.10071301460266113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08241879940032959}],"concepts":[{"id":"https://openalex.org/C205684552","wikidata":"https://www.wikidata.org/wiki/Q899769","display_name":"P\u00e9clet number","level":2,"score":0.7766750454902649},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.7117168307304382},{"id":"https://openalex.org/C48939323","wikidata":"https://www.wikidata.org/wiki/Q294879","display_name":"Wake","level":2,"score":0.6496350765228271},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.6196209788322449},{"id":"https://openalex.org/C39343618","wikidata":"https://www.wikidata.org/wiki/Q115767","display_name":"Damk\u00f6hler numbers","level":3,"score":0.5348336696624756},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5343778133392334},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.489729642868042},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4881923794746399},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4874115288257599},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.48654451966285706},{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.46195554733276367},{"id":"https://openalex.org/C99987037","wikidata":"https://www.wikidata.org/wiki/Q2435125","display_name":"Hard spheres","level":2,"score":0.4511777460575104},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4279429614543915},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.42691415548324585},{"id":"https://openalex.org/C125287762","wikidata":"https://www.wikidata.org/wiki/Q1758948","display_name":"Absorption (acoustics)","level":2,"score":0.41146326065063477},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3364081382751465},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28038695454597473},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26806819438934326},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.22127294540405273},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.13682830333709717},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.10071301460266113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08241879940032959},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/15m1039389","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1039389","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:qt1d42775x","is_oa":true,"landing_page_url":"http://www.escholarship.org/uc/item/1d42775x","pdf_url":"https://escholarship.org/content/qt1d42775x/qt1d42775x.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Biello, Joseph A; Samson, Rene; &amp; Sigal, Eugene. (2016). The Steady-State Convection-Diffusion Equation at High Peclet Numbers for a Cluster of Spheres: An Extension of Levich's Theory. SIAM Journal on Applied Mathematics, 76(4), 1515 - 1534. doi: 10.1137/15M1039389. UC Davis: Retrieved from: http://www.escholarship.org/uc/item/1d42775x","raw_type":"article"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt1d42775x","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/1d42775x","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Mathematics, vol 76, iss 4","raw_type":"article"}],"best_oa_location":{"id":"pmh:qt1d42775x","is_oa":true,"landing_page_url":"http://www.escholarship.org/uc/item/1d42775x","pdf_url":"https://escholarship.org/content/qt1d42775x/qt1d42775x.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Biello, Joseph A; Samson, Rene; &amp; Sigal, Eugene. (2016). The Steady-State Convection-Diffusion Equation at High Peclet Numbers for a Cluster of Spheres: An Extension of Levich's Theory. SIAM Journal on Applied Mathematics, 76(4), 1515 - 1534. doi: 10.1137/15M1039389. UC Davis: Retrieved from: http://www.escholarship.org/uc/item/1d42775x","raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.5899999737739563,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G2264138651","display_name":"Multiscale Asymptotic Analysis of  Tropical Atmosphere Dynamics","funder_award_id":"1313477","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2286505987","display_name":null,"funder_award_id":"NSF-DMS 1313477","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2509413600.pdf","grobid_xml":"https://content.openalex.org/works/W2509413600.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1967283291","https://openalex.org/W1985746657","https://openalex.org/W1998801933","https://openalex.org/W2007745549","https://openalex.org/W2026276300","https://openalex.org/W2026956602","https://openalex.org/W2028561404","https://openalex.org/W2032657155","https://openalex.org/W2034485600","https://openalex.org/W2062536867","https://openalex.org/W2064835927","https://openalex.org/W2127183837","https://openalex.org/W2132260633","https://openalex.org/W2134066908","https://openalex.org/W2141155874","https://openalex.org/W3016843226"],"related_works":["https://openalex.org/W2024719553","https://openalex.org/W2116159225","https://openalex.org/W2075135979","https://openalex.org/W1986398751","https://openalex.org/W2027173173","https://openalex.org/W2161187883","https://openalex.org/W2004256241","https://openalex.org/W2125897515","https://openalex.org/W72270576","https://openalex.org/W2022584528"],"abstract_inverted_index":{"This":[0,78,228],"paper":[1],"describes":[2],"an":[3],"approximate":[4],"analytical":[5,146,197],"model":[6,71,82,87,113,147,177,198,221],"of":[7,12,16,37,46,53,68,101,169,184],"competitive":[8,84],"effects":[9],"between":[10,144,195,240],"members":[11],"a":[13],"dense":[14],"cluster":[15],"absorbing":[17,25],"objects,":[18],"which":[19],"are":[20,136],"modeled":[21],"as":[22],"spheres.":[23],"Neighboring":[24],"spheres":[26,93,244],"compete":[27],"for":[28,74,90],"diffusing":[29],"species":[30],"and":[31,129,148,159,199],"thereby":[32],"reduce":[33],"each":[34],"other's":[35],"rate":[36],"absorption.":[38],"Levich's":[39],"well-known":[40],"asymptotic":[41],"(high":[42],"P\u00e9clet":[43,164],"number)":[44],"theory":[45],"convection-diffusion":[47],"considers":[48],"only":[49],"the":[50,54,62,69,75,96,99,102,109,139,142,145,149,170,174,186,190,193,196,200,220,225,232,238,251],"inner":[51],"region":[52],"concentration":[55],"boundary":[56],"layer;":[57],"it":[58],"does":[59],"not":[60,246],"describe":[61],"wake":[63,76],"zone":[64],"accurately.":[65],"An":[66,166],"extension":[67],"Levich":[70,176,187],"is":[72,79,105,114,152,203,229,245],"constructed":[73],"zone.":[77],"used":[80],"to":[81,118,223,231],"intersphere":[83,211],"effects.":[85,227],"The":[86,112],"demonstrates":[88],"that":[89,234],"two":[91,241],"neighboring":[92],"aligned":[94],"along":[95],"flow":[97,235],"direction,":[98],"absorption":[100],"downstream":[103],"sphere":[104,218],"substantially":[106],"reduced":[107],"vis-\u00e0-vis":[108],"upstream":[110],"sphere.":[111],"verified":[115],"by":[116],"comparison":[117],"numerical":[119,150,201],"simulation":[120],"studies.":[121],"Both":[122],"single-sphere":[123,140],"simulations":[124,131],"(reported":[125],"in":[126,237,250],"this":[127],"paper)":[128],"multisphere":[130,191],"(taken":[132],"from":[133,173,181],"existing":[134],"literature)":[135],"considered.":[137],"In":[138,189],"case,":[141,192],"discrepancy":[143],"results":[151],"maximally":[153],"10%":[154],"at":[155,162],"Pe":[156],"=":[157],"10":[158],"much":[160],"lower":[161],"higher":[163],"numbers.":[165],"appreciable":[167],"part":[168],"error":[171],"stems":[172],"original":[175],"itself,":[178],"rather":[179],"than":[180,206],"our":[182],"method":[183],"extending":[185],"model.":[188,252],"difference":[194],"studies":[202],"generally":[204],"less":[205],"30%":[207],".":[208],"At":[209],"small":[210],"separations":[212],"(say,":[213],"center-to-center":[214],"distances":[215],"$<$":[216],"5":[217],"radii),":[219],"tends":[222],"overestimate":[224],"interference":[226],"related":[230],"fact":[233],"stagnancy":[236],"space":[239],"closely":[242],"packed":[243],"taken":[247],"into":[248],"account":[249]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}