Size dependent FSI model for tapping mode of atomic force microscopy cantilevers immersed in viscous fluid

Size dependent FSI model for tapping mode of atomic force microscopy cantilevers immersed in viscous fluid | 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 Size dependent FSI model for tapping mode of atomic force microscopy cantilevers immersed in viscous fluid Ehsan Taati This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8070537/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 In the tapping mode operation, atomic force microscopy (AFM) cantilevers are affected by a surrounding fluid medium and harmonic base excitation. This paper provides a size dependent fluid-structure interaction (FSI) model for presenting frequency response of AFM cantilevers excited around its resonance frequency. Based on the Navier–Stokes equation and the exponential decay assumption of velocity components, closed-form expression of pressure difference around an AFM cantilever moving in incompressible viscous flow is developed for the first time. The Galerkin method is used to solve the nonlocal couple stress Euler–Bernoulli beam equation including the effects of long-range cohesive interaction and microstructure local rotation. The closed-form solutions presented here for amplitude ratio of time-history response and quality factor can be used in the conceptual design of AFM cantilevers. For AFM cantilevers with low quality factor, there are significant errors for measuring driving forces, because the displacement of base is not negligible compared to the deflection of tip. The large differences are found to exist in the results of classical \(\:\:\) and modified couple stress theories and either different fluid mediums. Therefore, classical FSI model existing in the literature is inadequate for investigating performance of AFM cantilevers in force measuring and imaging modes. Physical sciences/Engineering Physical sciences/Materials science Physical sciences/Mathematics and computing Physical sciences/Physics AFM cantilevers Frequency response Size effect Fluid-structure interaction Viscous fluid 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-8070537","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":559016891,"identity":"a37f97e5-fdb9-4372-9b68-3fd22606c756","order_by":0,"name":"Ehsan 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fluid","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":"AFM cantilevers, Frequency response, Size effect, Fluid-structure interaction, Viscous fluid","lastPublishedDoi":"10.21203/rs.3.rs-8070537/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8070537/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn the tapping mode operation, atomic force microscopy (AFM) cantilevers are affected by a surrounding fluid medium and harmonic base excitation. This paper provides a size dependent fluid-structure interaction (FSI) model for presenting frequency response of AFM cantilevers excited around its resonance frequency. Based on the Navier\u0026ndash;Stokes equation and the exponential decay assumption of velocity components, closed-form expression of pressure difference around an AFM cantilever moving in incompressible viscous flow is developed for the first time. The Galerkin method is used to solve the nonlocal couple stress Euler\u0026ndash;Bernoulli beam equation including the effects of long-range cohesive interaction and microstructure local rotation. The closed-form solutions presented here for amplitude ratio of time-history response and quality factor can be used in the conceptual design of AFM cantilevers. For AFM cantilevers with low quality factor, there are significant errors for measuring driving forces, because the displacement of base is not negligible compared to the deflection of tip. The large differences are found to exist in the results of classical\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\)\u003c/span\u003e\u003c/span\u003eand modified couple stress theories and either different fluid mediums. Therefore, classical FSI model existing in the literature is inadequate for investigating performance of AFM cantilevers in force measuring and imaging modes.\u003c/p\u003e","manuscriptTitle":"Size dependent FSI model for tapping mode of atomic force microscopy cantilevers immersed in viscous fluid","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-12 09:04:32","doi":"10.21203/rs.3.rs-8070537/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":"7c06e2b0-2372-44e6-8657-91e97c60e58a","owner":[],"postedDate":"December 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":59512985,"name":"Physical sciences/Engineering"},{"id":59512986,"name":"Physical sciences/Materials science"},{"id":59512987,"name":"Physical sciences/Mathematics and computing"},{"id":59512988,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-02-09T15:27:23+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-12 09:04:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8070537","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8070537","identity":"rs-8070537","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}