{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:26:07Z","timestamp":1787225167700,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1615719"],"award-info":[{"award-number":["DMS-1615719"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:p>We analyze the performance of membrane filters represented by pore networks using two criteria: (1) total volumetric throughput of filtrate over the filter lifetime and (2) accumulated foulant concentration in the filtrate. We first formulate the governing equations of fluid flow on a general network, and we model transport and adsorption of particles (foulants) within the network by imposing an advection equation with a sink term on each pore (edge) as well as conservation of fluid and foulant volumetric flow rates at each pore junction (network vertex). Such a setup yields a system of partial differential equations on the network. We study the influence of three geometric network parameters on filter performance: (1) average number of neighbors of each vertex, (2) initial total void volume of the pore network, and (3) tortuosity of the network. We find that total volumetric throughput depends more strongly on the initial void volume than on average number of neighbors. Tortuosity, however, turns out to be a universal parameter, leading to almost perfect collapse of all results for a variety of different network architectures. In particular, the accumulated foulant concentration in the filtrate shows an exponential decay as tortuosity increases.<\/jats:p>","DOI":"10.1137\/21m1424743","type":"journal-article","created":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T12:00:42Z","timestamp":1653998442000},"page":"950-975","source":"Crossref","is-referenced-by-count":9,"title":["A Graphical Representation of Membrane Filtration"],"prefix":"10.1137","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3509-242X","authenticated-orcid":true,"given":"Binan","family":"Gu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lou","family":"Kondic","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Linda J.","family":"Cummings","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,5,31]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/S1350-4487(01)00228-1"},{"key":"atypb2","first-page":"150","author":"Bonato A.","year":"2015","journal-title":"New York"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2018.10.049"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"A. Chapman and M. Mesbahi,\n                      Advection on graphs\n                      , in Proceedings of the 50th IEEE Conference on Decision and Control, 2011, pp. 1461-1466,https:\/\/doi.org\/10.1109\/CDC.2011.6161471.","DOI":"10.1109\/CDC.2011.6161471"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.2115"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/080716372"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.66.016121"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1177\/1550147717748898"},{"key":"atypb9","unstructured":"L. J. Grady,\n                      Discrete Calculus: Applied Analysis on Graphs for Computational Science\n                      , Springer, New York, 2010."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.memsci.2019.117664"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2020.520"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"Y. Hatano, A. K. Das, and M. Mesbahi,\n                      Agreement in presence of noise: pseudogradients on random geometric networks\n                      , in Proceedings of the 44th IEEE Conference on Decision Control, 2005, pp. 6382-6387,https:\/\/doi.org\/10.1109\/CDC.2005.1583185.","DOI":"10.1109\/CDC.2005.1583185"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1080\/07373937.2012.683123"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.96.013310"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2013.0016"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"M. Penrose,\n                      Random Geometric Graphs\n                      , Oxford University Press, New York, 2003.","DOI":"10.1093\/acprof:oso\/9780198506263.001.0001"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"R. F. Probstein,\n                      Physicochemical Hydrodynamics\n                      , Wiley-Interscience, New York, 1994.","DOI":"10.1002\/0471725137"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevFluids.3.094305"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.3390\/membranes6030040"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.memsci.2007.07.040"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1021\/acs.iecr.6b00387"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s10853-011-5754-7"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/11085431X"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.joi.2016.02.001"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1038\/srep05568"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1424743","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T10:52:08Z","timestamp":1787223128000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1424743"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,31]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["10.1137\/21M1424743"],"URL":"https:\/\/doi.org\/10.1137\/21m1424743","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,31]]}}}