Weakly Nonlinear Acoustics of Gas–Liquid–Shell Three-Layer Microbubbles

Weakly Nonlinear Acoustics of Gas–Liquid–Shell Three-Layer Microbubbles | 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 Weakly Nonlinear Acoustics of Gas–Liquid–Shell Three-Layer Microbubbles Ryoki Kawahata, Tetsuya Kanagawa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7984086/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 Microbubbles encapsulated by shells have been utilized in ultrasound diagnosis to enhance imaging resolution. Additionally, liquid droplets covered with shells are attracting considerable attention for their potential applications in targeted drug delivery systems. While theoretical studies have been conducted on the mechanical properties of single-bubble dynamics, research on pressure ultrasound propagation in liquids containing multiple bubbles remains limited. In this study, we derive an evolution equation for the first-order perturbation of liquid pressure by combining a volume-averaged, two-fluid model, which accounts for the effects of multiple bubbles in a liquid, using the equation of motion for a single liquid droplet obtained from previous studies [Gubaidullin and Fedorov, 2020] and the perturbation method. We impose volume conservation on both the shell and the inner liquid, allowing the shell thickness to vary with radius rather than assuming it constant. The nonlinearity and attenuation of pressure in the liquid medium are qualitatively evaluated using the evolution equation. The derived evolution equation provides explicit coefficients for ultrasound nonlinearity, viscous and thermal attenuation, and dispersion. It shows that shell-coated liquid droplets reduce the effective nonlinearity relative to free bubbles, whereas viscous attenuation increases owing to the shell and the inner liquid layer. For representative material properties, the attenuation budget is dominated by shell viscosity, with smaller contributions from the internal and surrounding liquids. 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. 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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-7984086","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":558078528,"identity":"39a80395-b87a-4b4b-8b3a-dcba100fb06b","order_by":0,"name":"Ryoki Kawahata","email":"","orcid":"","institution":"University of Tsukuba","correspondingAuthor":false,"prefix":"","firstName":"Ryoki","middleName":"","lastName":"Kawahata","suffix":""},{"id":558078529,"identity":"4d8b6416-ed0e-4936-a3ec-07afc0a6f5b7","order_by":1,"name":"Tetsuya Kanagawa","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABWklEQVRIie2RMUvDQBiGvyNw02nWCynNX7gQOIdS81caAnUpLgUtVDQSiEuwq6I/QhfnSqBd0naWLOmewYBIxKJeatU27eImmGd6+fge7k0+gJKSPwhdH0l9FM8DAbwY9TcrGJDzGRoSA2C/UzAtKCsoZ6P79Oko0EBzh9MXTwRMeJfAzGRhyOMMdjVAo+VnVLJvq5VBoDsYW+6WlwfCIwLMuhn5O7oPtu7AuLGkVKHFVIojJDZ1F3kBcjR/rjTYhHBKQBLrIVtW5MR4pW+R6WA5PRXFzPyVtlDMXFFmcFJUVNriSupFlthEjiiWBy4JBYliXCUQFBXlIuE1dP5ue7ipX5Hxngi4rVwzw7oMB4dGhQ11b/Vb6KRlPGTPzXpPCuI0O6jVe1i6fUw6VXM7tO+mSaeryXTlj+WIGvB1AncRvpuIgGlYvA3KfvLx2uUEsr9pWlJSUvJv+ABj33JwWS1EugAAAABJRU5ErkJggg==","orcid":"","institution":"University of Tsukuba","correspondingAuthor":true,"prefix":"","firstName":"Tetsuya","middleName":"","lastName":"Kanagawa","suffix":""}],"badges":[],"createdAt":"2025-10-30 02:08:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7984086/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7984086/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98019390,"identity":"f366223d-96ad-4b9d-aee7-cde9b9d7518e","added_by":"auto","created_at":"2025-12-11 22:59:44","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1299817,"visible":true,"origin":"","legend":"","description":"","filename":"2mainv17251030.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7984086/v1/f78aef934b50d353f2e24733.pdf"},{"id":98019389,"identity":"652c7e27-6be9-48be-92a0-97229d45cee4","added_by":"auto","created_at":"2025-12-11 22:59:44","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4379,"visible":true,"origin":"","legend":"","description":"","filename":"de963d154d5b4271b358b536a70eeeb7.json","url":"https://assets-eu.researchsquare.com/files/rs-7984086/v1/64bec8c941094c9c142c2b93.json"},{"id":101730671,"identity":"5bab6c03-03ac-4cfa-9024-d175c4e72613","added_by":"auto","created_at":"2026-02-03 05:56:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1554112,"visible":true,"origin":"","legend":"","description":"","filename":"2mainv17251030.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7984086/v1_covered_38e030f9-3ac8-4c49-8e20-22cda189532d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Weakly Nonlinear Acoustics of Gas–Liquid–Shell Three-Layer Microbubbles","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-7984086/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7984086/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Microbubbles encapsulated by shells have been utilized in ultrasound diagnosis to enhance imaging resolution. 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