The universal law behind long-lived interfaces in fully miscible fluids

The universal law behind long-lived interfaces in fully miscible fluids | 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 Article The universal law behind long-lived interfaces in fully miscible fluids Heon Sang Lee, Gyeong Min Choi, Ashhar Hussain This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8588310/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Miscible fluids come into contact ubiquitously across biological, industrial, and geophysical systems, yet sharp interfaces are widely assumed to be incompatible with fully miscible mixtures. Contrary to this expectation, sharply defined boundaries are repeatedly observed to form and persist far beyond molecular timescales, while the physical principles governing their emergence and stability have remained elusive. Here, we establish a closed variational theory that resolves this paradox by introducing a co-evolving enthalpic interaction, which couples self-consistently to the interfacial concentration field and evolves through a stepwise minimum-entropy-generation pathway. The theory predicts the emergence of an ultrathin interface governed by an exact Fermi–Dirac concentration profile, followed by deterministic thickening and eventual rupture. It identifies universal, parameter-free quantities, including the minimum nonequilibrium interfacial tension and the lifetime of the interface, in quantitative agreement with experiments on molecular liquids, polymer mixtures, and whole blood. The rupture point is fixed by a universal constant, Λ c , determined solely by the correlation length of the miscible fluid, rendering interfacial stability and lifetime predictable from first principles. Together, these results unify the birth, endurance, and dissolution of sharp interfaces within a single variational framework, providing a general nonequilibrium phase theory grounded in measurable physical quantities. Physical sciences/Physics/Condensed-matter physics/Surfaces, interfaces and thin films Physical sciences/Physics/Fluid dynamics Miscible interface Nonequilibrium thermodynamics Variational principle Phase-field theory Free-energy landscape Interfacial lifetime Full Text Additional Declarations There is NO Competing Interest. Supplementary Files ActingInterfaces.mp4 The universal law behind long-lived interfaces in fully miscible fluids Cite Share Download PDF Status: Under Review 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-8588310","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":588339323,"identity":"265495a6-8963-49ea-987d-b5b3c30970cc","order_by":0,"name":"Heon Sang Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYBACAxDxgIFBjuEAkgBhLQkMDMaka0lsIFqLOXvzsQcJFTbpfcfPGDD8qGEwNm8goMWy51i6QcKZtNyZZ3IMGHuOMZjJHCDksBs5ZhKJbYdzNxzIMWDgbWCwkSDkMIP7b4Ba/v1PNzj/xoDxL1FabvAAtTQcSABaZ8AMtMWMsJYzaWkSCceSDWfeeFZwWOaYhDFhLccPH5P4UGMnz3c+eePDNzU2hjMIaUEBBxgYCNoxCkbBKBgFo4AYAACrEz/SWd9bjAAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-6806-5666","institution":"Dong-A University","correspondingAuthor":true,"prefix":"","firstName":"Heon","middleName":"Sang","lastName":"Lee","suffix":""},{"id":588339324,"identity":"d13f91cf-1470-4dda-8cb7-f46f82ee2063","order_by":1,"name":"Gyeong Min Choi","email":"","orcid":"","institution":"Dong-A University","correspondingAuthor":false,"prefix":"","firstName":"Gyeong","middleName":"Min","lastName":"Choi","suffix":""},{"id":588339325,"identity":"b4c447ad-1d35-4d65-aa77-40b405d52d7a","order_by":2,"name":"Ashhar Hussain","email":"","orcid":"https://orcid.org/0009-0008-0081-9370","institution":"Dong-A University","correspondingAuthor":false,"prefix":"","firstName":"Ashhar","middleName":"","lastName":"Hussain","suffix":""}],"badges":[],"createdAt":"2026-01-13 07:06:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8588310/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8588310/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102397620,"identity":"60d88e11-4786-46c9-88fc-b08dadf00599","added_by":"auto","created_at":"2026-02-11 10:18:29","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1316872,"visible":true,"origin":"","legend":"Article File","description":"","filename":"NatureFVrev.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8588310/v1_covered_dbe3efaf-1dde-4612-9a9a-85637f90d23b.pdf"},{"id":102362604,"identity":"0bcfa974-b9d7-4856-a766-afebe3cf2fce","added_by":"auto","created_at":"2026-02-11 00:50:29","extension":"mp4","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3976780,"visible":true,"origin":"","legend":"The universal law behind long-lived interfaces in fully miscible fluids","description":"","filename":"ActingInterfaces.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8588310/v1/cfd9a1b4cba98a231d3568f0.mp4"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"The universal law behind long-lived interfaces in fully miscible fluids","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Miscible interface, Nonequilibrium thermodynamics, Variational principle, Phase-field theory, Free-energy landscape, Interfacial lifetime","lastPublishedDoi":"10.21203/rs.3.rs-8588310/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8588310/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Miscible fluids come into contact ubiquitously across biological, industrial, and geophysical systems, yet sharp interfaces are widely assumed to be incompatible with fully miscible mixtures. Contrary to this expectation, sharply defined boundaries are repeatedly observed to form and persist far beyond molecular timescales, while the physical principles governing their emergence and stability have remained elusive. Here, we establish a closed variational theory that resolves this paradox by introducing a co-evolving enthalpic interaction, which couples self-consistently to the interfacial concentration field and evolves through a stepwise minimum-entropy-generation pathway. The theory predicts the emergence of an ultrathin interface governed by an exact Fermi–Dirac concentration profile, followed by deterministic thickening and eventual rupture. It identifies universal, parameter-free quantities, including the minimum nonequilibrium interfacial tension and the lifetime of the interface, in quantitative agreement with experiments on molecular liquids, polymer mixtures, and whole blood. The rupture point is fixed by a universal constant, Λ\u003csub\u003ec\u003c/sub\u003e, determined solely by the correlation length of the miscible fluid, rendering interfacial stability and lifetime predictable from first principles. 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