Gravitational Interactions of Two Small Evaporating Drops

Gravitational Interactions of Two Small Evaporating 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Research Article Gravitational Interactions of Two Small Evaporating Drops Michael Rother This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3922296/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Jul, 2024 Read the published version in Aerosol Science and Engineering → Version 1 posted 6 You are reading this latest preprint version Abstract Relative trajectories are determined for a pair of water drops falling in air with radii between 2 μm and 30 μm. The droplets are small enough that diffusion dominates convection in evaporation, but significant drop inertia at low Reynolds number is considered. In addition to hydrodynamic and lubrication forces, attractive van der Waals forces and Maxwell slip are taken into account. Because the loss of mass is not uniform due to the presence of a second drop, and mass transfer and momentum transfer are effectively decoupled, the droplet position needs to be assessed. Three outcomes are compared. The isolated drop result for both droplets is employed as a base case, since the mass loss is constant over each drop surface. Alternatively, the bispherical coordinate solution for two evaporating drops is applied, with the drop positions 1) fixed by the hydrodynamics or 2) allowed to move based on the nonspherical mass loss. In all three cases, evaporation leads to weaker inertial effects and stronger hydrodynamic effects. The single sphere model has the largest drop gap, followed by the bispherical coordinate solutions with a fixed and movable center, respectively. Critical horizontal offsets for coalescence are also calculated with a finite vertical offset. With both attractive molecular forces and slip, all three approaches to evaporation lead to similar results, making the choice of method nearly inconsequential. Moderate agreement between previous experiments and an approximate, generalized form of the current theory is obtained for the evaporation rate of falling drops. evaporation drops slip van der Waals forces Full Text Cite Share Download PDF Status: Published Journal Publication published 16 Jul, 2024 Read the published version in Aerosol Science and Engineering → Version 1 posted Editorial decision: Major revisions 14 Apr, 2024 Reviewers agreed at journal 28 Feb, 2024 Reviewers invited by journal 19 Feb, 2024 Editor invited by journal 14 Feb, 2024 Editor assigned by journal 09 Feb, 2024 First submitted to journal 01 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-3922296","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":273994816,"identity":"83be1151-27c9-4d0c-9423-4906aea7fa87","order_by":0,"name":"Michael Rother","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsUlEQVRIiWNgGAWjYJACZiCWYzgA4TA2EKGDsRlIGJOuJbGBaC26sw8ff1xQcS+97wCP6eYCBhvZDQcIaDE7l5bYPONMce7MAzxmt2cwpBkT1nKGx7CZty0hdwNICw/D4UQitfxLSDeAaPlPrJaGhASolgPEaGFLnM1zLMFw5mG2sts8BsnGMwlrYT7wmacmQZ7vePO22zwVdrJ9hLQgACgNMBgQrXwUjIJRMApGAT4AAMKcQ1m/O87jAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-9016-9640","institution":"University of Minnesota Duluth","correspondingAuthor":true,"prefix":"","firstName":"Michael","middleName":"","lastName":"Rother","suffix":""}],"badges":[],"createdAt":"2024-02-02 23:06:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3922296/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3922296/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s41810-024-00243-7","type":"published","date":"2024-07-16T16:05:03+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":61594730,"identity":"a81b6e6b-81a0-4697-8471-80b42bcbe115","added_by":"auto","created_at":"2024-08-01 17:16:41","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9142140,"visible":true,"origin":"","legend":"","description":"","filename":"conc2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3922296/v1_covered_9a82b329-8035-47d6-8760-411d2cfd8b49.pdf"}],"financialInterests":"","formattedTitle":"Gravitational Interactions of Two Small Evaporating Drops","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":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"aerosol-science-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"asen","sideBox":"Learn more about [Aerosol Science and Engineering](https://link.springer.com/journal/41810)","snPcode":"41810","submissionUrl":"https://www.editorialmanager.com/asen/default2.aspx","title":"Aerosol Science and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"evaporation, drops, slip, van der Waals forces","lastPublishedDoi":"10.21203/rs.3.rs-3922296/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3922296/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Relative trajectories are determined for a pair of water drops falling in air with radii between 2 μm and 30 μm. The droplets are small enough that diffusion dominates convection in evaporation, but significant drop inertia at low Reynolds number is considered. In addition to hydrodynamic and lubrication forces, attractive van der Waals forces and Maxwell slip are taken into account. Because the loss of mass is not uniform due to the presence of a second drop, and mass transfer and momentum transfer are effectively decoupled, the droplet position needs to be assessed. Three outcomes are compared. The isolated drop result for both droplets is employed as a base case, since the mass loss is constant over each drop surface. Alternatively, the bispherical coordinate solution for two evaporating drops is applied, with the drop positions 1) fixed by the hydrodynamics or 2) allowed to move based on the nonspherical mass loss. In all three cases, evaporation leads to weaker inertial effects and stronger hydrodynamic effects. The single sphere model has the largest drop gap, followed by the bispherical coordinate solutions with a fixed and movable center, respectively. Critical horizontal offsets for coalescence are also calculated with a finite vertical offset. With both attractive molecular forces and slip, all three approaches to evaporation lead to similar results, making the choice of method nearly inconsequential. Moderate agreement between previous experiments and an approximate, generalized form of the current theory is obtained for the evaporation rate of falling drops.","manuscriptTitle":"Gravitational Interactions of Two Small Evaporating Drops","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-22 06:20:48","doi":"10.21203/rs.3.rs-3922296/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revisions","date":"2024-04-14T19:52:00+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2024-02-29T01:38:48+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-02-20T02:30:52+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Aerosol Science and Engineering","date":"2024-02-14T21:08:29+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-09T13:13:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Aerosol Science and Engineering","date":"2024-02-01T15:29:45+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"aerosol-science-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"asen","sideBox":"Learn more about [Aerosol Science and Engineering](https://link.springer.com/journal/41810)","snPcode":"41810","submissionUrl":"https://www.editorialmanager.com/asen/default2.aspx","title":"Aerosol Science and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"380fa51d-0b07-4e42-8cd3-2d0c217c7e59","owner":[],"postedDate":"February 22nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-08-01T16:15:48+00:00","versionOfRecord":{"articleIdentity":"rs-3922296","link":"https://doi.org/10.1007/s41810-024-00243-7","journal":{"identity":"aerosol-science-and-engineering","isVorOnly":false,"title":"Aerosol Science and Engineering"},"publishedOn":"2024-07-16 16:05:03","publishedOnDateReadable":"July 16th, 2024"},"versionCreatedAt":"2024-02-22 06:20:48","video":"","vorDoi":"10.1007/s41810-024-00243-7","vorDoiUrl":"https://doi.org/10.1007/s41810-024-00243-7","workflowStages":[]},"version":"v1","identity":"rs-3922296","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3922296","identity":"rs-3922296","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}