Hydrodynamic Metamaterials Enable Radial Fingering Instabilities of Liquid Metals via Cartesian Topography

Hydrodynamic Metamaterials Enable Radial Fingering Instabilities of Liquid Metals via Cartesian Topography | 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 Hydrodynamic Metamaterials Enable Radial Fingering Instabilities of Liquid Metals via Cartesian Topography Xiaolin Wang, Yahua He, Jing You, Jianbo Tang, Zhao Wang, Anthony Somers, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8411847/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 Fluid instabilities produce complex patterns across natural and industrial systems, yet their precise control remains a fundamental challenge. Here, we demonstrate that hydrodynamic metamaterials, consisting of substrates patterned with Cartesian topographies, enable programmable fingering instabilities in liquid metals. Electrochemical oxidation dramatically lowers the metal’s effective interfacial tension, yet a basic NaOH(aq) electrolyte dissolves the oxidized species, creating a dynamic balance that drives spreading and fractal-like growth. Remarkably, substrates with rectangular arrays of posts or wells dictate the type of highly radial fluidic metal patterns, even though the topographical features are significantly smaller than the instability scale. These results suggest that engineered topographies can steer the coupled electrochemical and hydrodynamic processes, offering a general strategy for controlling the fluid instabilities by harnessing interfacial tension distribution. Physical sciences/Chemistry/Chemical engineering Physical sciences/Engineering/Chemical engineering Physical sciences/Physics/Fluid dynamics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files VideoS6.mp4 SUPPLEMENTARY VIDEO S6 VideoS4.mp4 SUPPLEMENTARY VIDEO S4 VideoS14.mp4 SUPPLEMENTARY VIDEO S14 VideoS10.mp4 SUPPLEMENTARY VIDEO S10 VideoS11.mp4 SUPPLEMENTARY VIDEO S11 VideoS3.mp4 SUPPLEMENTARY VIDEO S3 VideoS2.mp4 SUPPLEMENTARY VIDEO S2 VideoS12.mp4 SUPPLEMENTARY VIDEO S12 VideoS9.mp4 SUPPLEMENTARY VIDEO S9 VideoS1.mp4 SUPPLEMENTARY VIDEO S1 VideoS8.mp4 SUPPLEMENTARY VIDEO S8 VideoS5.mp4 SUPPLEMENTARY VIDEO S5 VideoS13.mp4 SUPPLEMENTARY VIDEO S13 VideoS15.mp4 SUPPLEMENTARY VIDEO S15 SupplementaryInformation.docx SUPPLEMENTARY INFORMATION VideoS7.mp4 SUPPLEMENTARY VIDEO S7 VideoS16.mp4 SUPPLEMENTARY VIDEO S16 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-8411847","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":592463362,"identity":"3ca82bec-241c-484d-b54e-074629220061","order_by":0,"name":"Xiaolin Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYDACZiB+YMAgB+GxEaslwYDBmAQtIJDAwJDYQLQWg+PMDx8kFNxJ33C8x4DhQ9lhBv4ZCfi1SDazGRskGDzL3XDmjAHjjHOHGSRuENDCz8xgJpFgcDh3w43cDcy8bYcZGAhpYWNm/wbSkm4A0vIXqEWesC08YFsSwFoYgVoMCGmRbOYpBvrlsOHMM+c/HOw5l85jeOYBfi0G549vfPDhz2F5vuNtiQ9+lFnLyR0nYAsKOADEPCSoHwWjYBSMglGACwAAQKVEOZccq30AAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-4150-0848","institution":"University of Wollongong","correspondingAuthor":true,"prefix":"","firstName":"Xiaolin","middleName":"","lastName":"Wang","suffix":""},{"id":592463363,"identity":"9f5c2444-d6cf-48c8-a3a1-f70234683039","order_by":1,"name":"Yahua He","email":"","orcid":"https://orcid.org/0000-0003-0674-808X","institution":"Deakin University","correspondingAuthor":false,"prefix":"","firstName":"Yahua","middleName":"","lastName":"He","suffix":""},{"id":592463364,"identity":"51dd57df-127b-4c43-a993-414cad4d2ab4","order_by":2,"name":"Jing You","email":"","orcid":"","institution":"University of New South Wales","correspondingAuthor":false,"prefix":"","firstName":"Jing","middleName":"","lastName":"You","suffix":""},{"id":592463365,"identity":"0bcbc2f5-feac-4a53-bf7b-f829096718cd","order_by":3,"name":"Jianbo Tang","email":"","orcid":"https://orcid.org/0000-0002-0155-6807","institution":"Westlake University","correspondingAuthor":false,"prefix":"","firstName":"Jianbo","middleName":"","lastName":"Tang","suffix":""},{"id":592463366,"identity":"b49b3f2e-a9ff-4cd5-94da-d58fd17ac3df","order_by":4,"name":"Zhao Wang","email":"","orcid":"","institution":"Hubei University","correspondingAuthor":false,"prefix":"","firstName":"Zhao","middleName":"","lastName":"Wang","suffix":""},{"id":592463367,"identity":"0d0c1396-94ef-4fb9-8694-268dd585c13d","order_by":5,"name":"Anthony Somers","email":"","orcid":"","institution":"Deakin University","correspondingAuthor":false,"prefix":"","firstName":"Anthony","middleName":"","lastName":"Somers","suffix":""},{"id":592463368,"identity":"7b65ae08-438d-4473-af07-c93e965d7d31","order_by":6,"name":"Wenrong Yang","email":"","orcid":"","institution":"Deakin University","correspondingAuthor":false,"prefix":"","firstName":"Wenrong","middleName":"","lastName":"Yang","suffix":""},{"id":592463369,"identity":"92d13d2a-4a23-4f5e-834c-a297527a1f0e","order_by":7,"name":"Michael Dickey","email":"","orcid":"https://orcid.org/0000-0003-1251-1871","institution":"North Carolina State University","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"","lastName":"Dickey","suffix":""}],"badges":[],"createdAt":"2025-12-20 11:30:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8411847/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8411847/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108491350,"identity":"a19bb7ec-b0b7-4f50-9657-979502beacc3","added_by":"auto","created_at":"2026-05-05 09:53:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1791479,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1_covered_d4786c68-77c8-414a-b2c9-8dbbac0feaf2.pdf"},{"id":102888333,"identity":"84771d7c-f3f6-42dc-a93d-f2785e1ab38e","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"mp4","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1942337,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S6","description":"","filename":"VideoS6.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/d223cac0da37dd747dfd27ba.mp4"},{"id":102888331,"identity":"09aa1d9f-b63d-4d71-a18f-7e63f3fbf8fc","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"mp4","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":2243328,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S4","description":"","filename":"VideoS4.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/404396135a8776c3624ee043.mp4"},{"id":102963380,"identity":"b10beac0-7efa-44da-ac1d-6794c16cd59f","added_by":"auto","created_at":"2026-02-19 04:16:25","extension":"mp4","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":1721391,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S14","description":"","filename":"VideoS14.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/1a798382286658ced3bfcfef.mp4"},{"id":102888332,"identity":"13c01071-e509-410d-b590-08298ce32757","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"mp4","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":2305530,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S10","description":"","filename":"VideoS10.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/564f03bfc262085d9d5ddc4a.mp4"},{"id":102888336,"identity":"967fa060-83f0-4272-bbe1-0c200d8b89e0","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"mp4","order_by":5,"title":"","display":"","copyAsset":false,"role":"supplement","size":2967296,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S11","description":"","filename":"VideoS11.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/7c593c2cbc6a2c065c625eb3.mp4"},{"id":102963764,"identity":"16d915e4-6607-4865-a6e8-c109826be1eb","added_by":"auto","created_at":"2026-02-19 04:20:28","extension":"mp4","order_by":6,"title":"","display":"","copyAsset":false,"role":"supplement","size":2456037,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S3","description":"","filename":"VideoS3.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/8c9c9a865cd14d5617d1ac2e.mp4"},{"id":102963778,"identity":"727f97ae-69d7-4c23-893a-dd9012709360","added_by":"auto","created_at":"2026-02-19 04:20:32","extension":"mp4","order_by":7,"title":"","display":"","copyAsset":false,"role":"supplement","size":1894032,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S2","description":"","filename":"VideoS2.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/d137646c9477321a5e5bd0dc.mp4"},{"id":102963793,"identity":"92f09537-c1d8-4f45-a0c6-caf30ee892a8","added_by":"auto","created_at":"2026-02-19 04:20:34","extension":"mp4","order_by":8,"title":"","display":"","copyAsset":false,"role":"supplement","size":3031647,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S12","description":"","filename":"VideoS12.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/6c21e4e0a24120693cc8421b.mp4"},{"id":102888347,"identity":"f945f6bd-bb35-4dbf-a3d1-3cf2972934b2","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"mp4","order_by":9,"title":"","display":"","copyAsset":false,"role":"supplement","size":2141379,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S9","description":"","filename":"VideoS9.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/6c46d640723aeec08fcc8d1b.mp4"},{"id":102888345,"identity":"cf2563d2-edce-485a-a5af-0d4ccacfefa9","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"mp4","order_by":10,"title":"","display":"","copyAsset":false,"role":"supplement","size":2792993,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S1","description":"","filename":"VideoS1.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/daa93deaed91907a932b5ff7.mp4"},{"id":102888343,"identity":"9cd0a2ea-cb54-43d5-8f43-10ebf1e6718a","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"mp4","order_by":11,"title":"","display":"","copyAsset":false,"role":"supplement","size":2651637,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S8","description":"","filename":"VideoS8.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/243efede5420ecba29abdd77.mp4"},{"id":102888337,"identity":"5c2a3e9f-0011-4357-8c10-596b8931929a","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"mp4","order_by":12,"title":"","display":"","copyAsset":false,"role":"supplement","size":2076707,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S5","description":"","filename":"VideoS5.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/4873c8e9634ce5fe159f77c2.mp4"},{"id":102888338,"identity":"620c55b6-bcac-4bdc-b70d-7994d66fc5b7","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"mp4","order_by":13,"title":"","display":"","copyAsset":false,"role":"supplement","size":2156752,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S13","description":"","filename":"VideoS13.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/f72fe7a5c61a2e7f625bf411.mp4"},{"id":102963379,"identity":"fb247886-5084-4923-9603-35af64c70c39","added_by":"auto","created_at":"2026-02-19 04:16:24","extension":"mp4","order_by":14,"title":"","display":"","copyAsset":false,"role":"supplement","size":2559370,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S15","description":"","filename":"VideoS15.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/1f59d9f975620db78a16e293.mp4"},{"id":102888346,"identity":"186b4c45-a6fb-44d8-93f8-8489b269db7b","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"docx","order_by":15,"title":"","display":"","copyAsset":false,"role":"supplement","size":17825913,"visible":true,"origin":"","legend":"SUPPLEMENTARY INFORMATION","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/4011c6966ff9111935662b40.docx"},{"id":102888341,"identity":"cecdad6e-ecc0-4f38-b7fc-4e7bb3c493f2","added_by":"auto","created_at":"2026-02-18 03:31:03","extension":"mp4","order_by":16,"title":"","display":"","copyAsset":false,"role":"supplement","size":1892610,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S7","description":"","filename":"VideoS7.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/169ad432a6eb431fbbd911ca.mp4"},{"id":102963612,"identity":"753e2af1-7a8f-4f2e-932c-09cc7528acb5","added_by":"auto","created_at":"2026-02-19 04:19:22","extension":"mp4","order_by":17,"title":"","display":"","copyAsset":false,"role":"supplement","size":2069724,"visible":true,"origin":"","legend":"SUPPLEMENTARY VIDEO S16","description":"","filename":"VideoS16.mp4","url":"https://assets-eu.researchsquare.com/files/rs-8411847/v1/014a43a1ebfe992f6b6e9bec.mp4"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Hydrodynamic Metamaterials Enable Radial Fingering Instabilities of Liquid Metals via Cartesian Topography","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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-8411847/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8411847/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Fluid instabilities produce complex patterns across natural and industrial systems, yet their precise control remains a fundamental challenge. Here, we demonstrate that hydrodynamic metamaterials, consisting of substrates patterned with Cartesian topographies, enable programmable fingering instabilities in liquid metals. Electrochemical oxidation dramatically lowers the metal’s effective interfacial tension, yet a basic NaOH(aq) electrolyte dissolves the oxidized species, creating a dynamic balance that drives spreading and fractal-like growth. Remarkably, substrates with rectangular arrays of posts or wells dictate the type of highly radial fluidic metal patterns, even though the topographical features are significantly smaller than the instability scale. These results suggest that engineered topographies can steer the coupled electrochemical and hydrodynamic processes, offering a general strategy for controlling the fluid instabilities by harnessing interfacial tension distribution.","manuscriptTitle":"Hydrodynamic Metamaterials Enable Radial Fingering Instabilities of Liquid Metals via Cartesian Topography","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-18 03:30:58","doi":"10.21203/rs.3.rs-8411847/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"b746cb40-1b37-45d7-a80e-ce9d35610a12","owner":[],"postedDate":"February 18th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Reject after peer review","date":"2026-04-30T19:10:39+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63039630,"name":"Physical sciences/Chemistry/Chemical engineering"},{"id":63039631,"name":"Physical sciences/Engineering/Chemical engineering"},{"id":63039632,"name":"Physical sciences/Physics/Fluid dynamics"}],"tags":[],"updatedAt":"2026-04-30T19:15:33+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-18 03:30:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8411847","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8411847","identity":"rs-8411847","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}