Fluid flow in thin fractured porous media using a TPM-phase-field model and microfluidic experiments

Fluid flow in thin fractured porous media using a TPM-phase-field model and microfluidic experiments | 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 Fluid flow in thin fractured porous media using a TPM-phase-field model and microfluidic experiments Yann Rivas, Nikolaos Karadimitriou, Holger Steeb, Wolfgang Ehlers, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6077893/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Sep, 2025 Read the published version in Archive of Applied Mechanics → Version 1 posted You are reading this latest preprint version Abstract The Theory of Porous Media (TPM) with an embedded phase-field approach to fracture provides an elegant opportunity to study complex flow phenomena in fractured porous materials in a unified single-domain approach. On this basis, the interactive flow behaviour between free flow and porous-media flow is studied using the example of flow through a thin porous plate containing a rectangular channel. By considering different boundary conditions and investigating the flow behaviour for a range of hydraulic conductivities, our study is designed to reveal insights into phenomena which are relevant for various sub-surface geo-engineered applications. Furthermore, we show that the applied macroscopic single-domain approach is able to reveal local flow effects near the porous interface (channel walls), namely the so-called velocity profile inversion phenomenon. Moreover, we introduce a geometrically motivated estimation of the length-scale parameter ε used in phase-field approaches, which is directly related to the roughness of the fracture surface. Thus, values for ε are proposed for microfluidic devices and different rock types. Furthermore, we apply full three-dimensional simulations to evaluate the influence of the thickness of thin porous plates on the overall flow resistance, which is typically relevant in microfluidic devices. In a combined numerical-experimental study, we compare results from representative microfluidic experiments and simulations and confirmed the choice of ε to correctly predict the flow transition across the porous interface. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 26 Sep, 2025 Read the published version in Archive of Applied Mechanics → Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6077893","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":430706791,"identity":"d941f9a6-cdb1-4d7e-b3bb-6bdbf76abddc","order_by":0,"name":"Yann Rivas","email":"","orcid":"","institution":"University of Stuttgart","correspondingAuthor":false,"prefix":"","firstName":"Yann","middleName":"","lastName":"Rivas","suffix":""},{"id":430706793,"identity":"e134a3d8-8868-4298-8c78-33d2cd2c9979","order_by":1,"name":"Nikolaos Karadimitriou","email":"","orcid":"","institution":"University of Stuttgart","correspondingAuthor":false,"prefix":"","firstName":"Nikolaos","middleName":"","lastName":"Karadimitriou","suffix":""},{"id":430706794,"identity":"e2cc7148-e643-4852-b7db-088b34dd1a53","order_by":2,"name":"Holger Steeb","email":"","orcid":"","institution":"University of Stuttgart","correspondingAuthor":false,"prefix":"","firstName":"Holger","middleName":"","lastName":"Steeb","suffix":""},{"id":430706796,"identity":"6cee14f4-9a42-4055-abe7-8d08a56117ce","order_by":3,"name":"Wolfgang Ehlers","email":"","orcid":"","institution":"University of Stuttgart","correspondingAuthor":false,"prefix":"","firstName":"Wolfgang","middleName":"","lastName":"Ehlers","suffix":""},{"id":430706802,"identity":"3e4c6b9a-4d3b-4c52-829e-0813cb4d2fd2","order_by":4,"name":"Arndt Wagner","email":"data:image/png;base64,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","orcid":"","institution":"University of Stuttgart","correspondingAuthor":true,"prefix":"","firstName":"Arndt","middleName":"","lastName":"Wagner","suffix":""}],"badges":[],"createdAt":"2025-02-21 09:08:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6077893/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6077893/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00419-025-02892-7","type":"published","date":"2025-09-26T15:56:58+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":92430497,"identity":"1dcf2227-d806-423e-b1f0-980935101f3a","added_by":"auto","created_at":"2025-09-29 16:05:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4113042,"visible":true,"origin":"","legend":"","description":"","filename":"Riea2025AoAM.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6077893/v1_covered_e22bbdfa-a08d-4c34-8e0a-2e918de67fb2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Fluid flow in thin fractured porous media using a TPM-phase-field model and microfluidic experiments\n\n\n","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6077893/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6077893/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe Theory of Porous Media (TPM) with an embedded phase-field approach to fracture provides an elegant opportunity to study complex flow phenomena in fractured porous materials in a unified single-domain approach. On this basis, the interactive flow behaviour between free flow and porous-media flow is studied using the example of flow through a thin porous plate containing a rectangular channel. By considering different boundary conditions and investigating the flow behaviour for a range of hydraulic conductivities, our study is designed to reveal insights into phenomena which are relevant for various sub-surface geo-engineered applications. Furthermore, we show that the applied macroscopic single-domain approach is able to reveal local flow effects near the porous interface (channel walls), namely the so-called velocity profile inversion phenomenon. Moreover, we introduce a geometrically motivated estimation of the length-scale parameter \u003cstrong\u003eε\u003c/strong\u003e used in phase-field approaches, which is directly related to the roughness of the fracture surface. Thus, values for \u003cstrong\u003eε\u003c/strong\u003e are proposed for microfluidic devices and different rock types. Furthermore, we apply full three-dimensional simulations to evaluate the influence of the thickness of thin porous plates on the overall flow resistance, which is typically relevant in microfluidic devices. In a combined numerical-experimental study, we compare results from representative microfluidic experiments and simulations and confirmed the choice of \u003cstrong\u003eε\u003c/strong\u003e to correctly predict the flow transition across the porous interface.\u003c/p\u003e","manuscriptTitle":"Fluid flow in thin fractured porous media using a TPM-phase-field model and microfluidic experiments","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-20 12:01:11","doi":"10.21203/rs.3.rs-6077893/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b7ad0472-16f7-4063-84f3-b74196181b8f","owner":[],"postedDate":"March 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-09-29T16:01:14+00:00","versionOfRecord":{"articleIdentity":"rs-6077893","link":"https://doi.org/10.1007/s00419-025-02892-7","journal":{"identity":"archive-of-applied-mechanics","isVorOnly":false,"title":"Archive of Applied Mechanics"},"publishedOn":"2025-09-26 15:56:58","publishedOnDateReadable":"September 26th, 2025"},"versionCreatedAt":"2025-03-20 12:01:11","video":"","vorDoi":"10.1007/s00419-025-02892-7","vorDoiUrl":"https://doi.org/10.1007/s00419-025-02892-7","workflowStages":[]},"version":"v1","identity":"rs-6077893","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6077893","identity":"rs-6077893","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}