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Fluids", "DOI": "10.1063/1.1830486", "citationKey": "", "url": "http://link.aip.org/link/?PHF/17/031504/1", "accessDate": "2009-12-11T18:05:19Z", "PMID": "", "PMCID": "", "ISSN": "", "archive": "", "archiveLocation": "", "shortTitle": "The method of regularized Stokeslets in three dimensions", "language": "", "libraryCatalog": "Scitation", "callNumber": "", "rights": "", "extra": "", "tags": [ { "tag": "biological fluid dynamics", "type": 1 }, { "tag": "cell motility", "type": 1 }, { "tag": "microorganisms", "type": 1 }, { "tag": "non-Newtonian fluids", "type": 1 }, { "tag": "pipe flow", "type": 1 }, { "tag": "rotational flow", "type": 1 } ], "collections": [ "GSU3CSK7" ], "relations": {}, "dateAdded": "2009-12-11T18:05:59Z", "dateModified": "2009-12-11T18:05:59Z" } }, { "key": "8GMN28D7", "version": 1, "library": { "type": "group", "id": 5893, "name": "UNC_Math-Bio_FRG", "links": { "alternate": { "href": "https://www.zotero.org/groups/unc_math-bio_frg", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/5893/items/8GMN28D7", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/unc_math-bio_frg/items/8GMN28D7", "type": "text/html" } }, "meta": { "createdByUser": { "id": 60096, "username": "minion", "name": "Michael Minion", "links": { "alternate": { "href": "https://www.zotero.org/minion", "type": "text/html" } } }, "creatorSummary": "Cortez", "parsedDate": "2001-01", "numChildren": 1 }, "data": { "key": "8GMN28D7", "version": 1, "itemType": "journalArticle", "title": "The Method of Regularized Stokeslets", "creators": [ { "creatorType": "author", "firstName": "Ricardo", "lastName": "Cortez" } ], "abstractNote": "", "publicationTitle": "SIAM Journal on Scientific Computing", "publisher": "", "place": "", "date": "January 00, 2001", "volume": "23", "issue": "4", "section": "", "partNumber": "", "partTitle": "", "pages": "1204-1225", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "SIAM J. Sci. Comput.", "DOI": "10.1137/S106482750038146X", "citationKey": "", "url": "http://link.aip.org/link/?SCE/23/1204/1", "accessDate": "2009-12-11T17:55:09Z", "PMID": "", "PMCID": "", "ISSN": "", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "Scitation", "callNumber": "", "rights": "", "extra": "", "tags": [ { "tag": "Stokes flow", "type": 1 }, { "tag": "immersed boundaries", "type": 1 } ], "collections": [ "GSU3CSK7" ], "relations": {}, "dateAdded": "2009-12-11T18:05:59Z", "dateModified": "2009-12-11T18:05:59Z" } }, { "key": "E9NKKQEF", "version": 1, "library": { "type": "group", "id": 5893, "name": "UNC_Math-Bio_FRG", "links": { "alternate": { "href": "https://www.zotero.org/groups/unc_math-bio_frg", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/5893/items/E9NKKQEF", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/unc_math-bio_frg/items/E9NKKQEF", "type": "text/html" } }, "meta": { "createdByUser": { "id": 60096, "username": "minion", "name": "Michael Minion", "links": { "alternate": { "href": "https://www.zotero.org/minion", "type": "text/html" } } }, "creatorSummary": "Cogan and Chellam", "parsedDate": "2008-06-20", "numChildren": 2 }, "data": { "key": "E9NKKQEF", "version": 1, "itemType": "journalArticle", "title": "Regularized Stokeslets solution for 2-D flow in dead-end microfiltration: Application to bacterial deposition and fouling", "creators": [ { "creatorType": "author", "firstName": "N.G.", "lastName": "Cogan" }, { "creatorType": "author", "firstName": "Shankar", "lastName": "Chellam" } ], "abstractNote": "Dead-end microfiltration is an effective method for removing particulate matter including protozoa and bacteria in a variety of settings. As the filtered components accumulate on the filter, the flux declines during constant pressure operation necessitating periodic back-washing. It has been recently reported empirically that the filtered components are not homogeneously distributed on the filter. This must be accounted for in any mathematical theory describing the filtering process. We present a method for determining the coupled fluid dynamics and bacterial transport for dead-end filtration. Results of numerical simulation indicate that the model is able to closely capture experimental data; moreover, the model predicts that the coupled system induces the experimentally observed patchy deposition patterns through spatial variability in the pore structure and porosity of the membrane.", "publicationTitle": "Journal of Membrane Science", "publisher": "", "place": "", "date": "June 20, 2008", "volume": "318", "issue": "1-2", "section": "", "partNumber": "", "partTitle": "", "pages": "379-386", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "", "DOI": "10.1016/j.memsci.2008.03.012", "citationKey": "", "url": "http://www.sciencedirect.com/science/article/B6TGK-4S2MHWG-1/2/c9c23129f676be5dc84c56a618c23fdc", "accessDate": "2009-12-11T18:00:12Z", "PMID": "", "PMCID": "", "ISSN": "0376-7388", "archive": "", "archiveLocation": "", "shortTitle": "Regularized Stokeslets solution for 2-D flow in dead-end microfiltration", "language": "", "libraryCatalog": "ScienceDirect", "callNumber": "", "rights": "", "extra": "", "tags": [ { "tag": "Biofilm", "type": 1 }, { "tag": "Biofouling", "type": 1 }, { "tag": "Dead-end filtration", "type": 1 }, { "tag": "Mathematical model", "type": 1 }, { "tag": "Microfiltration", "type": 1 }, { "tag": "Stokeslet", "type": 1 }, { "tag": "Waste water treatment", "type": 1 }, { "tag": "Water treatment", "type": 1 } ], "collections": [ "GSU3CSK7" ], "relations": {}, "dateAdded": "2009-12-11T18:05:59Z", "dateModified": "2009-12-11T18:05:59Z" } }, { "key": "PEM2RETC", "version": 1, "library": { "type": "group", "id": 5893, "name": "UNC_Math-Bio_FRG", "links": { "alternate": { "href": "https://www.zotero.org/groups/unc_math-bio_frg", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/5893/items/PEM2RETC", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/unc_math-bio_frg/items/PEM2RETC", "type": "text/html" } }, "meta": { "createdByUser": { "id": 60096, "username": "minion", "name": "Michael Minion", "links": { "alternate": { "href": "https://www.zotero.org/minion", "type": "text/html" } } }, "creatorSummary": "Ainley et al.", "parsedDate": "2008-04-20", "numChildren": 2 }, "data": { "key": "PEM2RETC", "version": 1, "itemType": "journalArticle", "title": "The method of images for regularized Stokeslets", "creators": [ { "creatorType": "author", "firstName": "Josephine", "lastName": "Ainley" }, { "creatorType": "author", "firstName": "Sandra", "lastName": "Durkin" }, { "creatorType": "author", "firstName": "Rafael", "lastName": "Embid" }, { "creatorType": "author", "firstName": "Priya", "lastName": "Boindala" }, { "creatorType": "author", "firstName": "Ricardo", "lastName": "Cortez" } ], "abstractNote": "The image system for the method of regularized Stokeslets is developed and implemented. The method uses smooth localized functions to approximate a delta distribution in the derivation of the fluid flow due to a concentrated force. In order to satisfy zero-flow boundary conditions at a plane wall, the method of images derived for a standard (singular) Stokeslet is extended to give exact cancellation of the regularized flow at the wall. As the regularization parameter vanishes, the expressions reduce to the known images for singular Stokeslets. The advantage of the regularized method is that it gives bounded velocity fields even for isolated forces or for distributions of forces along curves. These are useful in the simulation of ciliary beats, flagellar motion, and particle suspensions. The expression relating force and velocity can be inverted to find the forces that generate a given velocity boundary condition. The latter is exemplified by modeling a cilium as a filament moving in a three-dimensional flow. The cilium velocity at various times is constructed from known data and used to determine the force field along the filament. Those forces can then reproduce the flow everywhere. The validity of the method is evaluated by computing the drag on a sphere moving near a wall. 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