{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T09:57:16Z","timestamp":1760522236155,"version":"build-2065373602"},"reference-count":24,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2004,4,16]],"date-time":"2004-04-16T00:00:00Z","timestamp":1082073600000},"content-version":"vor","delay-in-days":2207,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AIChE Journal"],"published-print":{"date-parts":[[1998,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Hollow\u2010fiber membrane separation or reaction processes, with a nonlinear boundary condition at the lumen interface, are analyzed numerically. Sixteen different nonlinear boundaly conditions in the literature were simplified to four dimensionless boundary conditions, in which only two parameters are needed to incorporate the effect on mass transport of membrane and shell resistances, lumen inlet Concentration, shell concentration, phase and\/or chemical equilibria, and interface reaction kinetics. The lumen mass\u2010transfer coefjicients were obtained by solving the continuity mass\u2010conservation equation with the corresponding boundary conditions. The calculated results demonstrate that the lumen mass\u2010transfer coefjicient is a function of lumen\u2010inlet concentration and shell concentration, as opposed to the case when a linear boundary condition occurs at the lumen interface. By using the empirical correlations of the lumen local mass\u2010transfer coefjicient, an ordina ry differential equation substituting a partial differential equation can be applied to obtain the lumen dimensionless mixed\u2010cup concentration with an absolute error of less than 0.005 in most cases, thus making it possible to design and evaluate the hollow\u2010fiber membrane separation or reaction processes.<\/jats:p>","DOI":"10.1002\/aic.690440409","type":"journal-article","created":{"date-parts":[[2004,4,16]],"date-time":"2004-04-16T14:28:24Z","timestamp":1082125704000},"page":"836-848","source":"Crossref","is-referenced-by-count":16,"title":["Lumen mass transfer in hollow\u2010fiber membrane processes with nonlinear boundary conditions"],"prefix":"10.1002","volume":"44","author":[{"given":"Yingjie","family":"Qin","sequence":"first","affiliation":[]},{"given":"Joaquim M. S.","family":"Cabral","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,4,16]]},"reference":[{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0376-7388(00)80922-9"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0009-2509(94)80026-X"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0376-7388(95)00228-6"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690370309"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0376-7388(95)00020-D"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1021\/ie9502392"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-3548-5_8"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/bit.260380706"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0376-7388(00)80520-7"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/0009-2509(88)85037-1"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0376-7388(00)80848-0"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/bit.260420417"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690420715"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-4660(199602)65:2<137::AID-JCTB406>3.0.CO;2-I"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690430807"},{"key":"e_1_2_1_17_1","doi-asserted-by":"crossref","unstructured":"Qin Y. 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S.Cabral \u201cInfluence of Nernst\u2010Planck Flux on Mass Transfer in Hollow Fiber Membrane Process \u201d in press (1998).","DOI":"10.1002\/aic.690440707"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/0376-7388(93)85129-K"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1080\/01496399408007375"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/0376-7388(92)85069-U"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1021\/ie00005a016"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1021\/ie00007a020"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/0376-7388(94)00237-S"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1021\/ie00007a017"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1021\/ie00018a026"}],"container-title":["AIChE Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Faic.690440409","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/aiche.onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/aic.690440409","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T16:57:57Z","timestamp":1759856277000},"score":1,"resource":{"primary":{"URL":"https:\/\/aiche.onlinelibrary.wiley.com\/doi\/10.1002\/aic.690440409"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,4]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,4]]}},"alternative-id":["10.1002\/aic.690440409"],"URL":"https:\/\/doi.org\/10.1002\/aic.690440409","archive":["Portico"],"relation":{},"ISSN":["0001-1541","1547-5905"],"issn-type":[{"type":"print","value":"0001-1541"},{"type":"electronic","value":"1547-5905"}],"subject":[],"published":{"date-parts":[[1998,4]]}}}