Effects of cake formation on flow and transport in a pleated membrane filter

Effects of cake formation on flow and transport in a pleated membrane filter | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Effects of cake formation on flow and transport in a pleated membrane filter Sima Moshafi, Daniel Fong, Yi Jiang, Pejman Sanaei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7266889/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Jan, 2026 Read the published version in Journal of Engineering Mathematics → Version 1 posted 9 You are reading this latest preprint version Abstract Pleated membrane filters are essential in various filtration applications due to their greater surface area-to-volume ratio compared to flat filters. This research introduces a mathematical model to understand several fouling mechanisms, especially focusing on cake formation as well as the feed flow dynamics in pleated filters. Our three-dimensional model assumes the pleated filter consisting of six distinct sub-regions: the empty, support layer plus, cake layer, membrane, support layer minus, and hollow regions. We use Darcy’s law and the Stokes equations to model the feed flow, and the advection-diffusion-reaction equation to simulate the particle transport within the corresponding aforementioned regions. To reduce the complexity of the model, we apply asymptotic analysis, based on the small aspect ratios of the filter and pleated membrane. The implications of our findings provide critical insights to improve the filter efficiency in terms of maximizing the filtrate fluid while keeping the particle concentration within designated limits and discovering the effects of the filter geometry. We find the total accumulated particle concentration steadily decreases as the number of pleats increases, while an optimal pleat packing density maximizes the total throughput. Additionally, the presence of a cake layer enhances the total throughput of the filter, albeit at the cost of a slower filtration process. Fluid dynamics mathematical modeling filtration Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 11 Jan, 2026 Read the published version in Journal of Engineering Mathematics → Version 1 posted Editorial decision: Revision requested 23 Sep, 2025 Reviews received at journal 23 Sep, 2025 Reviewers agreed at journal 30 Aug, 2025 Reviews received at journal 11 Aug, 2025 Reviewers agreed at journal 11 Aug, 2025 Reviewers invited by journal 07 Aug, 2025 Editor assigned by journal 06 Aug, 2025 Submission checks completed at journal 06 Aug, 2025 First submitted to journal 31 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7266889","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":498807345,"identity":"d20e80ce-d625-4e47-833c-db70c4f66488","order_by":0,"name":"Sima Moshafi","email":"","orcid":"","institution":"Georgia State University","correspondingAuthor":false,"prefix":"","firstName":"Sima","middleName":"","lastName":"Moshafi","suffix":""},{"id":498807346,"identity":"8d6fe94f-72ad-414f-b058-07fb9b5c240c","order_by":1,"name":"Daniel Fong","email":"","orcid":"","institution":"United States Merchant Marine Academy","correspondingAuthor":false,"prefix":"","firstName":"Daniel","middleName":"","lastName":"Fong","suffix":""},{"id":498807347,"identity":"9dd208ee-b952-47c0-8422-0c6e307d8b0d","order_by":2,"name":"Yi Jiang","email":"","orcid":"","institution":"Georgia State University","correspondingAuthor":false,"prefix":"","firstName":"Yi","middleName":"","lastName":"Jiang","suffix":""},{"id":498807348,"identity":"5448f3b3-7dca-4e24-909a-12700c79fa9a","order_by":3,"name":"Pejman Sanaei","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuUlEQVRIiWNgGAWjYPACCTkIzUaCFmOStTAkNhCtxZz/8LMHPyos0uf7nzFg+FB2mLAWyxlp5oY9ZyRyN97IMWCccY4ILQY3GMwkeNuAWmbwGDDzthGj5fzxb5J//0mkG/afMWD+S5SWAzlm0rwNEgnyDDkGzIzEaLGckVMmLXNMwnCDRFrBwZ5z6YS1mPMf3yb5pqZOXr7/8MYHP8qsiXAYwoUMDAcIq0fWIt9AlPpRMApGwSgYiQAAgF033zSvEu0AAAAASUVORK5CYII=","orcid":"","institution":"Georgia State University","correspondingAuthor":true,"prefix":"","firstName":"Pejman","middleName":"","lastName":"Sanaei","suffix":""}],"badges":[],"createdAt":"2025-08-01 03:23:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7266889/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7266889/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10665-025-10500-4","type":"published","date":"2026-01-11T15:58:32+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":100070028,"identity":"30184ff4-8706-4b9e-8216-cb6d720f5931","added_by":"auto","created_at":"2026-01-12 16:16:00","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1645524,"visible":true,"origin":"","legend":"","description":"","filename":"submissionzip.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7266889/v1_covered_fc9ec7e4-c5f1-4993-8b64-f6e8773a3fce.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Effects of cake formation on flow and transport in a pleated membrane filter","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-engineering-mathematics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"engi","sideBox":"Learn more about [Journal of Engineering Mathematics](http://link.springer.com/journal/10665)","snPcode":"10665","submissionUrl":"https://submission.nature.com/new-submission/10665/3","title":"Journal of Engineering Mathematics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Fluid dynamics, mathematical modeling, filtration","lastPublishedDoi":"10.21203/rs.3.rs-7266889/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7266889/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Pleated membrane filters are essential in various filtration applications due to their greater surface area-to-volume ratio compared to flat filters. 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