A spline-based method to obtain spatially dependent viscosity in confined flows

A spline-based method to obtain spatially dependent viscosity in confined flows | 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 A spline-based method to obtain spatially dependent viscosity in confined flows Bruce Palmer, Pauline Simmonin, Jaehun Chun This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9034253/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 Coupling chemical physics to continuum theories is a critical step to understanding multi-scale phenomena. This paper will connect non-equilibrium molecular dynamics simulations to a continuum-based Navier-Stokes equation that has relaxed the assumption of spatial uniformity in viscosity. Using a form for the viscosity based on spline interpolation, the viscosity as a function of position is obtained from a least squares fit of the velocity profile measured from non-equilibrium molecular simulations of flow in a nanochannel. Results are compared with viscosity profiles obtained by integrating the conservation of momentum across the channel width and close agreement is found. Viscosity can vary widely, particularly near the channel boundaries, indicating that a uniform viscosity is no longer appropriate. The variation of the viscosity and velocity near the channel surfaces with different mineral surfaces and solution compositions implies that solution and surface chemistry may need to be considered to rigorously understand molecular-scale flows in nanochannels. 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-9034253","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":606025729,"identity":"9fe7446b-f6d0-4585-8c84-871ff55e4f4d","order_by":0,"name":"Bruce Palmer","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIiWNgGAWjYBACAxiDD0R8gDGI0sIGxIwzoAzitTDzEKPFXPqM4YcPDHfk2cQOH/tsu+NOHhsD+8XHPHi0WPblGEvOYHhm2Cadljw798yzYjYGnmJjfFoMzvCYAd1zmLFNOseYObftcGIbA0+a5AxCWv4wHLZvk87/zGxJtBYGBqBK6RxmZkawFvZjEh/w+aWHrViyx+BZMtAvxoy9Z4BamHmYDfBpMedh3vjhR8Ud237p5McMP3ccTuxnb3/4IAGPFqjzDkBoxgYGUOwY4FEKB8haGNgfEKNlFIyCUTAKRg4AAJw7Ri7ZEtPEAAAAAElFTkSuQmCC","orcid":"","institution":"Pacific Northwest National Laboratory","correspondingAuthor":true,"prefix":"","firstName":"Bruce","middleName":"","lastName":"Palmer","suffix":""},{"id":606025730,"identity":"e26b577c-9213-451b-8f61-273750afca78","order_by":1,"name":"Pauline Simmonin","email":"","orcid":"","institution":"Pacific Northwest National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Pauline","middleName":"","lastName":"Simmonin","suffix":""},{"id":606025731,"identity":"7ed8e656-b911-438f-8dce-4101e90e6f1c","order_by":2,"name":"Jaehun Chun","email":"","orcid":"","institution":"Pacific Northwest National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Jaehun","middleName":"","lastName":"Chun","suffix":""}],"badges":[],"createdAt":"2026-03-04 23:23:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9034253/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9034253/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107031232,"identity":"8e777994-642f-426b-9926-61c8dfefa15f","added_by":"auto","created_at":"2026-04-16 02:56:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3205035,"visible":true,"origin":"","legend":"","description":"","filename":"paper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9034253/v1_covered_97fe217e-45a2-4b79-b2e1-42bfc6196520.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A spline-based method to obtain spatially dependent viscosity in confined flows","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-9034253/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9034253/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCoupling chemical physics to continuum theories is a critical step to understanding multi-scale phenomena. 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