{"id":"https://openalex.org/W7225737672","doi":"https://doi.org/10.9734/arjom/2026/v22i111185","title":"A Dimensionless Two-Dimensional Model of Chlorine Transport and Pathogen Inactivation in Baffled Contact Tanks: Analysis, a Stable Dufort\u2013Frankel Scheme and Numerical Experiments","display_name":"A Dimensionless Two-Dimensional Model of Chlorine Transport and Pathogen Inactivation in Baffled Contact Tanks: Analysis, a Stable Dufort\u2013Frankel Scheme and Numerical Experiments","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225737672","doi":"https://doi.org/10.9734/arjom/2026/v22i111185"},"language":"en","primary_location":{"id":"doi:10.9734/arjom/2026/v22i111185","doi":"https://doi.org/10.9734/arjom/2026/v22i111185","is_oa":true,"landing_page_url":"https://doi.org/10.9734/arjom/2026/v22i111185","pdf_url":null,"source":{"id":"https://openalex.org/S4210207970","display_name":"Asian Research Journal of Mathematics","issn_l":"2456-477X","issn":["2456-477X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asian Research Journal of Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.9734/arjom/2026/v22i111185","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139410522","display_name":"Owuor Lucas Otieno","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210106600","display_name":"Kibabii University","ror":"https://ror.org/0111z3553","country_code":"KE","type":"education","lineage":["https://openalex.org/I4210106600"]}],"countries":["KE"],"is_corresponding":false,"raw_author_name":"Owuor Lucas Otieno","raw_affiliation_strings":["Department of Mathematics, Kibabii University, Bungoma, Kenya"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kibabii University, Bungoma, Kenya","institution_ids":["https://openalex.org/I4210106600"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5161393580","display_name":"Martha Konje","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210106600","display_name":"Kibabii University","ror":"https://ror.org/0111z3553","country_code":"KE","type":"education","lineage":["https://openalex.org/I4210106600"]}],"countries":["KE"],"is_corresponding":false,"raw_author_name":"Martha Konje","raw_affiliation_strings":["Department of Mathematics, Kibabii University, Bungoma, Kenya"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kibabii University, Bungoma, Kenya","institution_ids":["https://openalex.org/I4210106600"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210106600"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"11","first_page":"125","last_page":"136"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11493","display_name":"Water Treatment and Disinfection","score":0.6718999743461609,"subfield":{"id":"https://openalex.org/subfields/2307","display_name":"Health, Toxicology and Mutagenesis"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11493","display_name":"Water Treatment and Disinfection","score":0.6718999743461609,"subfield":{"id":"https://openalex.org/subfields/2307","display_name":"Health, Toxicology and Mutagenesis"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11331","display_name":"Fecal contamination and water quality","score":0.10090000182390213,"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"}},{"id":"https://openalex.org/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.0478999987244606,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C131396349","wikidata":"https://www.wikidata.org/wiki/Q913675","display_name":"Baffle","level":2,"score":0.9176999926567078},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.7731000185012817},{"id":"https://openalex.org/C505241676","wikidata":"https://www.wikidata.org/wiki/Q688","display_name":"Chlorine","level":2,"score":0.703000009059906},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5616999864578247},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.47279998660087585},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.45719999074935913},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4059000015258789},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.3937000036239624},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3806999921798706},{"id":"https://openalex.org/C191545125","wikidata":"https://www.wikidata.org/wiki/Q383758","display_name":"Plug flow","level":2,"score":0.35839998722076416},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3276999890804291},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.32679998874664307},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C164205550","wikidata":"https://www.wikidata.org/wiki/Q193340","display_name":"Spark plug","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C33373654","wikidata":"https://www.wikidata.org/wiki/Q5164821","display_name":"Contact area","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2547000050544739},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.2531999945640564}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.9734/arjom/2026/v22i111185","doi":"https://doi.org/10.9734/arjom/2026/v22i111185","is_oa":true,"landing_page_url":"https://doi.org/10.9734/arjom/2026/v22i111185","pdf_url":null,"source":{"id":"https://openalex.org/S4210207970","display_name":"Asian Research Journal of Mathematics","issn_l":"2456-477X","issn":["2456-477X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asian Research Journal of Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.9734/arjom/2026/v22i111185","doi":"https://doi.org/10.9734/arjom/2026/v22i111185","is_oa":true,"landing_page_url":"https://doi.org/10.9734/arjom/2026/v22i111185","pdf_url":null,"source":{"id":"https://openalex.org/S4210207970","display_name":"Asian Research Journal of Mathematics","issn_l":"2456-477X","issn":["2456-477X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asian Research Journal of Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Chlorine":[0,242],"contact":[1,243],"tanks":[2,244],"are":[3,232,245,470],"usually":[4,246],"modelled":[5,247],"in":[6,39,99,112,222,248,281,332,345,460],"one":[7,249],"dimension,":[8,250],"which":[9,79,135,251,317,368],"cannot":[10,252],"represent":[11,253],"baffles":[12,165,254,398],"or":[13,255],"short-circuiting.":[14,256],"We":[15,70,217,257,308,455],"extend":[16,258],"a":[17,26,43,47,52,59,128,146,259,268,285,289,294,301,361,379],"one-dimensional":[18,228,260,466],"modified":[19,261],"convection\u2013diffusion":[20,262],"model":[21,57,263,299],"of":[22,102,212,225,264,335,450,463],"chlorine":[23,265],"transport":[24,35,266,277],"to":[25,85,142,166,176,185,195,201,267,323,375,399,409,415,427,436],"depth-averaged":[27,269],"planar":[28,270],"advection\u2013dispersion\u2013decay":[29,271],"model,":[30,272],"derived":[31,273],"from":[32,134,174,183,193,199,274,367,407,413,425,434],"the":[33,56,100,108,150,171,206,213,223,226,275,298,333,341,383,404,443,451,461,464],"three-dimensional":[34,276],"law":[36,278],"and":[37,46,87,91,145,182,198,205,279,288,325,329,378,412,433,442],"written":[38,280],"dimensionless":[40,282],"form":[41,283],"with":[42,73,159,284,311,392],"P\u00e9clet":[44,286],"number":[45,49,287,291],"Damk\u00f6hler":[48,290],".":[50,188,292,307],"With":[51,293],"Danckwerts":[53,295],"inlet":[54,296],"condition":[55,297],"has":[58,300],"unique":[60,302],"weak":[61,303],"solution":[62,304],"that":[63,305],"satisfies":[64,306],"0":[65],"\u2264":[66,68,97],"c":[67],"1..":[69],"solve":[71,309],"it":[72,310],"an":[74,121,138,167,220,312,354,371,400,458],"explicit":[75,313],"two-dimensional":[76,314],"Dufort\u2013Frankel":[77,315],"scheme,":[78,316],"is":[80,88,110,117,127,318,326,343,350,360],"consistent":[81,319],"only":[82,92,209,320,330,447],"when":[83,321],"tends":[84,322],"zero":[86,324],"stable":[89,327],"if":[90,93,328,331],"Cx2":[94],"+":[95],"Cy2":[96],"1/2":[98],"absence":[101,334],"decay,":[103,336],"for":[104,149,337,382],"every":[105,338],"diffusion":[106,339],"number;":[107,340],"bound":[109,342],"proved":[111,344],"closed":[113,346],"form.":[114,347],"The":[115,189,230,348,421,468],"scheme":[116,349],"second-order":[118,351],"accurate":[119,352],"on":[120,155,353,388],"exact":[122,355],"solution.":[123,356],"A":[124,357],"new":[125,358],"contribution":[126,359],"one-way":[129,362],"coupled":[130,363],"Chick\u2013Watson":[131,364],"pathogen":[132,365],"equation,":[133,366],"we":[136,369],"define":[137,370],"efficiency":[139,190,372,422],"index":[140,191,373,423],"relative":[141,374],"plug":[143,376],"flow":[144,377],"conservatism":[147,380],"ratio":[148,381],"residual-times-":[151],"rule.":[152,385],"In":[153,386],"experiments":[154,387],"three":[156,389],"baffle":[157,390],"layouts":[158,391],"ideal":[160,393],"(potential)":[161,394],"flow,":[162,395],"adding":[163,396],"four":[164,397],"open":[168,401],"basin":[169,402],"raised":[170,403],"baffling":[172,405],"factor":[173,406],"0.28":[175,408],"0.75":[177,410],"at":[178,187,197,203,411,417,429,438],"Pe":[179,418,430,439],"=":[180,419,431,440],"1":[181,432],"0.70":[184,414],"0.88":[186,416],"rose":[192,424],"0.41":[194,426],"0.86":[196,428],"0.85":[200,435],"0.97":[202,437],",":[204],"rule":[207,445],"gave":[208,446],"about":[210,448],"half":[211,449],"computed":[214,452],"log":[215,453],"inactivation.":[216,454],"also":[218,456],"correct":[219,457],"error":[221,459],"algorithm":[224,462],"earlier":[227,465],"study.":[229,467],"results":[231,469],"verified":[233,471],"numerically":[234,472],"but":[235,473],"not":[236,474],"yet":[237,475],"calibrated":[238,476],"against":[239,477],"tracer":[240,478],"data.":[241,479],"residual-times-t10":[384],"50.":[420],"50,":[441],"t10":[444]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}