From polycrystalline materials to beer head : Discovering kinetic relation describing capillarity-driven transformation rate

From polycrystalline materials to beer head : Discovering kinetic relation describing capillarity-driven transformation rate | 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 From polycrystalline materials to beer head : Discovering kinetic relation describing capillarity-driven transformation rate Divyansh Joshi, Modassir Islam, Tauqueer Aftab, P G Kubendran Amos This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7760048/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 Capillarity-driven transformation is observed in a wide range of materials, from polycrystalline alloys to foams, and it noticeably influences their behaviour. During this transformation, the temporal change in the size of individual entities (grains or foams) is often claimed to be dictated by several factors, including topological and geometrical features of the evolving unit, its neighbours, and the entire system. Despite extensive theoretical and experimental investigations, a convincing understanding is yet to be gained on the significance of these factors in the evolution of the entities. In this work, going beyond conventional data analysis, the role of the different geometrical and topological features of the entities, neighbours, and entire system in dictating the capillarity-driven evolution is definitively realised. More importantly, a kinetic relation, applicable to a wide range of curvature-driven evolution, that describes and predicts the quantitative temporal evolution of individual units is discovered. The resulting kinetic relation unravels that the temporal change in the size of individual entities, during capillarity-driven transformation, can be convincingly described by the interplay of the size and number of sides of the evolving unit alone. In other words, this study decisively affirms the marginal significance of neighbouring entities in the capillarity-driven transformation of individual units. Additionally, the coherence of the present data-driven kinetic law with the existing understanding of curvature-driven evolution is briefly discussed. Grain growth capillarity-driven transformation polycrystalline system cellular materials grains foams symbolic regression law discovery Full Text Additional Declarations The authors declare no competing interests. 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-7760048","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":523406237,"identity":"e7e9cef1-f5c8-4bf0-96b5-ba19859ca3c9","order_by":0,"name":"Divyansh Joshi","email":"","orcid":"","institution":"National Institute of Technology Tiruchirappalli","correspondingAuthor":false,"prefix":"","firstName":"Divyansh","middleName":"","lastName":"Joshi","suffix":""},{"id":523406570,"identity":"70b5c615-ce3c-4bc1-8312-247d6a397a9a","order_by":1,"name":"Modassir Islam","email":"","orcid":"","institution":"National Institute of Technology Tiruchirappalli","correspondingAuthor":false,"prefix":"","firstName":"Modassir","middleName":"","lastName":"Islam","suffix":""},{"id":523406769,"identity":"5e4192bd-42eb-438e-a9e7-ad00e815ab75","order_by":2,"name":"Tauqueer Aftab","email":"","orcid":"","institution":"National Institute of Technology Tiruchirappalli","correspondingAuthor":false,"prefix":"","firstName":"Tauqueer","middleName":"","lastName":"Aftab","suffix":""},{"id":523406804,"identity":"06bf21cb-886f-49d4-a9e4-61c3257feee2","order_by":3,"name":"P G Kubendran Amos","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAqElEQVRIiWNgGAWjYFACxgYgYcPABuawEa8ljYGNjZloLWBwGKiaWC3m0ofbHvyoOJ/HJ99/gOFD2WHCWiz7EtsNe87cLgY5jHHGOSK0GJxhbJNmbLud2AbUwszbRrSWf+cgWv4Sr6XhAEQLIzFaLHsY2yR7jiUDtSQbHOw5l05YizkP+zOJHzV2ifObDz588KPMmgiHIXMOEFaPrmUUjIJRMApGAVYAACkkNBFKVWbGAAAAAElFTkSuQmCC","orcid":"","institution":"National Institute of Technology Tiruchirappalli","correspondingAuthor":true,"prefix":"","firstName":"P","middleName":"G Kubendran","lastName":"Amos","suffix":""}],"badges":[],"createdAt":"2025-10-01 13:43:40","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7760048/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7760048/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92694602,"identity":"13bd6efa-e44d-4ad5-9593-830711ffa7e2","added_by":"auto","created_at":"2025-10-03 06:38:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1517769,"visible":true,"origin":"","legend":"","description":"","filename":"SymGG.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7760048/v1_covered_9cacddd9-7f82-4e70-80c3-9fe8c3704fc2.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eFrom polycrystalline materials to beer head : Discovering kinetic relation describing capillarity-driven transformation rate\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"National Institute of Technology Tiruchirappalli","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":"Grain growth, capillarity-driven transformation, polycrystalline system, cellular materials, grains, foams, symbolic regression, law discovery","lastPublishedDoi":"10.21203/rs.3.rs-7760048/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7760048/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCapillarity-driven transformation is observed in a wide range of materials, from polycrystalline alloys to foams, and it noticeably influences their behaviour. 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