Retraction of levitating drops

Retraction of levitating drops | 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Article Retraction of levitating drops Kindness Isukwem, Elie Hachem, Anselmo Pereira This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7508062/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 This theoretical and numerical study focuses on the physical mechanisms driving the retraction of levitating Newtonian micrometric/millimetric/centimetric drops surrounded by air and under zero-gravity conditions. The drops present a pancake-like initial shape, gradually converging towards a spherical one under surface tension effects. Three drop retraction regimes are observed: capillary-inertial; mixed capillary-inertio-viscous; and capillary-viscous. In the first regime, the retraction is essentially driven by a competition between capillary pressure and inertial stresses, which induces a complex flow with equivalent shear, uniaxial and biaxial components. As the viscous stress becomes comparable to the capillary and the inertial stresses, the second regime emerges while shear-based deformations tend to vanish. Lastly, the third regime is dominated by a balance between capillary and viscous stresses, essentially exhibiting axial deformation. These physical features are underlined through multiphase three-dimensional numerical simulations and analysed in light of retraction dynamics, energy transfer and scaling laws. Our results are rationalised in a two-dimensional diagram linking the drop retraction time with the observed retraction regimes through a single dimensionless parameter combining capillary, inertial, viscous and geometrical effects, i.e., the \textit{retraction number}. 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-7508062","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":541015753,"identity":"5b016399-ca34-48d8-8df7-9f1d9ea07908","order_by":0,"name":"Kindness Isukwem","email":"","orcid":"","institution":"PSL University, UMR CNRS 7635","correspondingAuthor":false,"prefix":"","firstName":"Kindness","middleName":"","lastName":"Isukwem","suffix":""},{"id":541015756,"identity":"aedea418-32a6-4298-ad49-32c739da682e","order_by":1,"name":"Elie Hachem","email":"","orcid":"","institution":"PSL University, UMR CNRS 7635","correspondingAuthor":false,"prefix":"","firstName":"Elie","middleName":"","lastName":"Hachem","suffix":""},{"id":541015757,"identity":"219536e9-69a1-43d3-94c3-dfcec6c806c3","order_by":2,"name":"Anselmo Pereira","email":"data:image/png;base64,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","orcid":"","institution":"PSL University, UMR CNRS 7635","correspondingAuthor":true,"prefix":"","firstName":"Anselmo","middleName":"","lastName":"Pereira","suffix":""}],"badges":[],"createdAt":"2025-09-01 11:53:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7508062/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7508062/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":95344022,"identity":"702a8de6-b0f4-4fc0-8429-c4d367f86e4e","added_by":"auto","created_at":"2025-11-07 02:50:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4868393,"visible":true,"origin":"","legend":"","description":"","filename":"RetractionDFMrd1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7508062/v1/955b8e3b2450a400f265f62d.pdf"},{"id":95344021,"identity":"07f92b98-a2eb-48b1-8a24-651746bba9b5","added_by":"auto","created_at":"2025-11-07 02:50:38","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5778,"visible":true,"origin":"","legend":"","description":"","filename":"f699ca25a4dc439bb396ad7d4a5464aa.json","url":"https://assets-eu.researchsquare.com/files/rs-7508062/v1/4a02d0fa0d1d9ad477525fb5.json"},{"id":102419764,"identity":"f2edb581-ac79-4514-800b-ff2a94cfb262","added_by":"auto","created_at":"2026-02-11 13:28:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3129728,"visible":true,"origin":"","legend":"","description":"","filename":"RetractionDFMr.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7508062/v1_covered_f177645c-9ee0-427a-a76f-0a7a2ef24ff3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Retraction of levitating drops","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":"","lastPublishedDoi":"10.21203/rs.3.rs-7508062/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7508062/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This theoretical and numerical study focuses on the physical mechanisms driving the retraction of levitating Newtonian micrometric/millimetric/centimetric drops surrounded by air and under zero-gravity conditions. The drops present a pancake-like initial shape, gradually converging towards a spherical one under surface tension effects. Three drop retraction regimes are observed: capillary-inertial; mixed capillary-inertio-viscous; and capillary-viscous. In the first regime, the retraction is essentially driven by a competition between capillary pressure and inertial stresses, which induces a complex flow with equivalent shear, uniaxial and biaxial components. As the viscous stress becomes comparable to the capillary and the inertial stresses, the second regime emerges while shear-based deformations tend to vanish. Lastly, the third regime is dominated by a balance between capillary and viscous stresses, essentially exhibiting axial deformation. These physical features are underlined through multiphase three-dimensional numerical simulations and analysed in light of retraction dynamics, energy transfer and scaling laws. Our results are rationalised in a two-dimensional diagram linking the drop retraction time with the observed retraction regimes through a single dimensionless parameter combining capillary, inertial, viscous and geometrical effects, i.e., the \\textit{retraction number}. 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