A Transient Approach for Measuring Permeability and Pressure-Dependent Corrections for Porous Ablative Materials

A Transient Approach for Measuring Permeability and Pressure-Dependent Corrections for Porous Ablative Materials | 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 A Transient Approach for Measuring Permeability and Pressure-Dependent Corrections for Porous Ablative Materials Yejajul Hakim, Jack W. Wooten, Michael L. Mckinney, Michael W. Renfro This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9117715/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Accurate characterization of thermal protection system (TPS) materials requires reliable determination of permeability, which can vary by multiple ordersof- magnitude for charred samples with varying characteristic length of the microstructure. Traditional steady-state permeability measurements, while effective for moderately permeable materials, face challenges for low-permeability samples due to long equilibration times. To address this, a transient pressure decay experiment was conducted, enabling rapid and accurate determination of Klinkenberg permeability in the high-pressure regime. The technique is applied to Zuram® as a representative TPS material, which has been previously characterized. At low pressures the Klinkenberg model overestimates effective permeability due to elevated Knudsen numbers, a behavior consistently observed across all Zuram samples regardless of char level or pore radius. The transient method, previously used for low-permeability geological samples, was successfully applied to TPS materials, resulting in reduced experimental time. Comparisons of the Klinkenberg and Beskok–Karniadakis models revealed that both models agree at high pressures but overestimate permeability at low pressures. Leveraging the dependence of the Beskok–Karniadakis model on the effective pore radius, rp, the transient experiment allows estimation of rp through model comparison, providing insight into the characteristic length of the microstructure and its changes in charred materials. This methodology offers a novel approach for rapid high-pressure permeability measurement and microstructural characterization of TPS materials, overcoming limitations of steady-state methods while highlighting the constraints of both Klinkenberg and Beskok–Karniadakis models at low pressures. Thermal Protection System (TPS) Materials Transient Permeability Measurement Klinkenberg Model Beskok–Karniadakis Model Effective Pore Radius Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted 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-9117715","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":610805518,"identity":"febbec6b-1303-4f94-94ee-726a38862ae4","order_by":0,"name":"Yejajul Hakim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYHCCBAYJBgsGAwY2hgMMFUAaCCSI0CIB1XKGOC0QNSAtDIxtRGgxON7w8INlmwSDOfuxxEM35x02NjjAfPA2Dz4tZw4kS0gCtVj2pB04nLvtsJnBAbZka7xabiQkgLUYHEhvAGmxMTjAYyaNV8v9B8k/wFrOPwdqmQPSwv8Nv5YbDGkQW26AHNYAchgPG14tkmcS0iwkzknwGNx4lnA451i6seRhNmPLOXi08B0/k3xbosxGzuB8mvHnnBprw77jzQ9vvMGjReEATwIzMBoQLlE4jEc5CMg3sB9g/IAqQkDLKBgFo2AUjDgAAAL1Uh4+ovk0AAAAAElFTkSuQmCC","orcid":"","institution":"University of Kentucky","correspondingAuthor":true,"prefix":"","firstName":"Yejajul","middleName":"","lastName":"Hakim","suffix":""},{"id":610805520,"identity":"5719f894-14cd-426c-8a49-19030374cf0f","order_by":1,"name":"Jack W. Wooten","email":"","orcid":"","institution":"University of Kentucky","correspondingAuthor":false,"prefix":"","firstName":"Jack","middleName":"W.","lastName":"Wooten","suffix":""},{"id":610805523,"identity":"f1c8d807-4f32-458a-ba40-b10ffacb21eb","order_by":2,"name":"Michael L. Mckinney","email":"","orcid":"","institution":"University of Kentucky","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"L.","lastName":"Mckinney","suffix":""},{"id":610805524,"identity":"807d80fb-b4f5-4c84-890d-6b83416a31f9","order_by":3,"name":"Michael W. Renfro","email":"","orcid":"","institution":"University of Kentucky","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"W.","lastName":"Renfro","suffix":""}],"badges":[],"createdAt":"2026-03-13 19:38:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9117715/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9117715/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105565418,"identity":"77cae951-f667-48dc-9f9d-1cc8554ef664","added_by":"auto","created_at":"2026-03-27 12:53:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1906172,"visible":true,"origin":"","legend":"","description":"","filename":"TransientPermeability.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9117715/v1_covered_c2449c63-87ee-426a-81de-735070d4e033.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Transient Approach for Measuring Permeability and Pressure-Dependent Corrections for Porous Ablative Materials","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"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":"Thermal Protection System (TPS) Materials, Transient Permeability Measurement, Klinkenberg Model, Beskok–Karniadakis Model, Effective Pore Radius","lastPublishedDoi":"10.21203/rs.3.rs-9117715/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9117715/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAccurate characterization of thermal protection system (TPS) materials requires reliable determination of permeability, which can vary by multiple ordersof- magnitude for charred samples with varying characteristic length of the microstructure. Traditional steady-state permeability measurements, while effective for moderately permeable materials, face challenges for low-permeability samples due to long equilibration times. To address this, a transient pressure decay experiment was conducted, enabling rapid and accurate determination of Klinkenberg permeability in the high-pressure regime. The technique is applied to Zuram® as a representative TPS material, which has been previously characterized. At low pressures the Klinkenberg model overestimates effective permeability due to elevated Knudsen numbers, a behavior consistently observed across all Zuram samples regardless of char level or pore radius. The transient method, previously used for low-permeability geological samples, was successfully applied to TPS materials, resulting in reduced experimental time. Comparisons of the Klinkenberg and Beskok–Karniadakis models revealed that both models agree at high pressures but overestimate permeability at low pressures. Leveraging the dependence of the Beskok–Karniadakis model on the effective pore radius, rp, the transient experiment allows estimation of rp through model comparison, providing insight into the characteristic length of the microstructure and its changes in charred materials. This methodology offers a novel approach for rapid high-pressure permeability measurement and microstructural characterization of TPS materials, overcoming limitations of steady-state methods while highlighting the constraints of both Klinkenberg and Beskok–Karniadakis models at low pressures.\u003c/p\u003e","manuscriptTitle":"A Transient Approach for Measuring Permeability and Pressure-Dependent Corrections for Porous Ablative Materials","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-25 10:06:58","doi":"10.21203/rs.3.rs-9117715/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":"720ac705-963b-435e-965f-121e4c69582e","owner":[],"postedDate":"March 25th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-05T08:18:29+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-03T03:03:58+00:00","index":31,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-05T08:24:39+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-25 10:06:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9117715","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9117715","identity":"rs-9117715","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}