Spreading of rotating liquid annular ring with hysteresis effects

Spreading of rotating liquid annular ring with hysteresis effects | 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 Spreading of rotating liquid annular ring with hysteresis effects Konrad E.R. Boettcher, Peter Ehrhard This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3984842/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Sep, 2024 Read the published version in Journal of Engineering Mathematics → Version 1 posted 7 You are reading this latest preprint version Abstract The spreading of a liquid, subjected to centrifugal forces or an air jet, leads toa lowering of the liquid height at the center. If the system is partially wetting,experiments show a break up of the liquid and the appearance of a dry patch atthe center. In this article, the spreading of a droplet or a liquid film, featuring adry patch at the center, is investigated. Via a generalized Tanner’s law, we allowfor a contact–angle hysteresis in partially–wetting system. By means of the lubrication approximation, an analytical quasi–steady solution can be derived in thelimit of small capillary numbers. We find a power–law regime for the spreading,in which at least one of the contact lines follows a power law in time, almost independent of both static contact angles. The influence of the static contact anglesremains restricted to the beginning of the spreading and to transition periods.Four different types of spreading can be identified, namely spreading (i) with avery thin central liquid layer, (ii) as annular ring with central dry patch, (iii) intoa static equilibrium, and (iv) with closing of the central dry patch. In a flow map,these types of spreading are mapped as function of both static contact angles.Moreover, the dependency from gravitational and centrifugal forces is investigated and included in the flow map. For a perfectly–wetting system, a disjoiningpressure correction in combination with Tanner’s law prohibits negative liquidheights at the center. Hereby, the magnitudes of the Hamaker constants have anegligible influence and arbitrary–small values can be used, since the dynamicsof the contact line remains controlled by Tanner’s law. contact lines lubrication theory thin films annular liquid hysteresis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Sep, 2024 Read the published version in Journal of Engineering Mathematics → Version 1 posted Editorial decision: Revision requested 10 Apr, 2024 Reviews received at journal 24 Mar, 2024 Reviewers agreed at journal 27 Feb, 2024 Reviewers invited by journal 27 Feb, 2024 Editor assigned by journal 26 Feb, 2024 Submission checks completed at journal 26 Feb, 2024 First submitted to journal 24 Feb, 2024 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-3984842","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":275217110,"identity":"05c87f1d-0a01-4b5d-8bc7-ea455fab7853","order_by":0,"name":"Konrad E.R. Boettcher","email":"","orcid":"","institution":"TU Dortmund University","correspondingAuthor":false,"prefix":"","firstName":"Konrad","middleName":"E.R.","lastName":"Boettcher","suffix":""},{"id":275217111,"identity":"4ff7edb2-9c83-4ca3-8fd2-7bd939ce7a8f","order_by":1,"name":"Peter Ehrhard","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABE0lEQVRIiWNgGAWjYBCDBAYJIMlTAWFDwAEGA+yKmZG1nDGAaDlAtBbeNiK0mLP3H3xcwWCTZz67+dmHt/P+JDawJx/7/DHncB7fAeaND7Bosew5zGx4hiGtWObOMeOZc7cZJDbwPEuecXDb4WLJA2zF2KwxuJHMJtnAcDhxhkSCMTMvUMv+GznGDEAtiRsO8JhJYNNy/zH7zwaG/0At6Z+ZeecAbZFAaDH/gdUWZjbGBoYDQC05QFsaULWYYfO+ZU+ysWSDQTJISzHjnGPGxiC/MJzdlp448zBbMTaHmbMffPixocIO5LDNDG9q5GSBIXaYoXKbdWLf8eaNH7A5DIlEB8xYRXHF7ygYBaNgFIwCJAAA2iRqGKkptykAAAAASUVORK5CYII=","orcid":"","institution":"TU Dortmund University","correspondingAuthor":true,"prefix":"","firstName":"Peter","middleName":"","lastName":"Ehrhard","suffix":""}],"badges":[],"createdAt":"2024-02-24 11:46:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3984842/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3984842/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10665-024-10399-3","type":"published","date":"2024-09-21T15:57:34+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":65104471,"identity":"0ef7a96b-c1ea-4e71-b0d3-4fe688b2b267","added_by":"auto","created_at":"2024-09-23 16:13:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1702825,"visible":true,"origin":"","legend":"","description":"","filename":"BE2024submitted.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3984842/v1_covered_032f5a5f-96f1-45da-b86e-d0890ffe8774.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Spreading of rotating liquid annular ring with hysteresis effects","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-engineering-mathematics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"engi","sideBox":"Learn more about [Journal of Engineering Mathematics](http://link.springer.com/journal/10665)","snPcode":"10665","submissionUrl":"https://submission.nature.com/new-submission/10665/3","title":"Journal of Engineering Mathematics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"contact lines, lubrication theory, thin films, annular liquid, hysteresis","lastPublishedDoi":"10.21203/rs.3.rs-3984842/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3984842/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe spreading of a liquid, subjected to centrifugal forces or an air jet, leads toa lowering of the liquid height at the center. If the system is partially wetting,experiments show a break up of the liquid and the appearance of a dry patch atthe center. In this article, the spreading of a droplet or a liquid film, featuring adry patch at the center, is investigated. Via a generalized Tanner’s law, we allowfor a contact–angle hysteresis in partially–wetting system. By means of the lubrication approximation, an analytical quasi–steady solution can be derived in thelimit of small capillary numbers. We find a power–law regime for the spreading,in which at least one of the contact lines follows a power law in time, almost independent of both static contact angles. The influence of the static contact anglesremains restricted to the beginning of the spreading and to transition periods.Four different types of spreading can be identified, namely spreading (i) with avery thin central liquid layer, (ii) as annular ring with central dry patch, (iii) intoa static equilibrium, and (iv) with closing of the central dry patch. In a flow map,these types of spreading are mapped as function of both static contact angles.Moreover, the dependency from gravitational and centrifugal forces is investigated and included in the flow map. For a perfectly–wetting system, a disjoiningpressure correction in combination with Tanner’s law prohibits negative liquidheights at the center. Hereby, the magnitudes of the Hamaker constants have anegligible influence and arbitrary–small values can be used, since the dynamicsof the contact line remains controlled by Tanner’s law.\u003c/p\u003e","manuscriptTitle":"Spreading of rotating liquid annular ring with hysteresis effects","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-28 02:04:02","doi":"10.21203/rs.3.rs-3984842/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-04-11T03:38:55+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-03-24T19:30:46+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"48b0a107-b612-4873-b8f6-b840f55e0687","date":"2024-02-27T15:51:23+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-02-27T15:37:46+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-26T16:47:36+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-02-26T14:08:57+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Engineering Mathematics","date":"2024-02-24T11:21:39+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-engineering-mathematics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"engi","sideBox":"Learn more about [Journal of Engineering Mathematics](http://link.springer.com/journal/10665)","snPcode":"10665","submissionUrl":"https://submission.nature.com/new-submission/10665/3","title":"Journal of Engineering Mathematics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"eab4b31b-07da-4f85-afe7-4ea7b0e85ce7","owner":[],"postedDate":"February 28th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-09-23T16:10:43+00:00","versionOfRecord":{"articleIdentity":"rs-3984842","link":"https://doi.org/10.1007/s10665-024-10399-3","journal":{"identity":"journal-of-engineering-mathematics","isVorOnly":false,"title":"Journal of Engineering Mathematics"},"publishedOn":"2024-09-21 15:57:34","publishedOnDateReadable":"September 21st, 2024"},"versionCreatedAt":"2024-02-28 02:04:02","video":"","vorDoi":"10.1007/s10665-024-10399-3","vorDoiUrl":"https://doi.org/10.1007/s10665-024-10399-3","workflowStages":[]},"version":"v1","identity":"rs-3984842","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3984842","identity":"rs-3984842","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}