Micromechanics-based model for the effective thermal conductivity of three-phase composites with bimodal particle size distribution

Micromechanics-based model for the effective thermal conductivity of three-phase composites with bimodal particle size distribution | 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 Micromechanics-based model for the effective thermal conductivity of three-phase composites with bimodal particle size distribution Yunpeng Jiang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8525348/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 Particles with high thermal conductivity exhibiting a bimodal size distribution can significantly improve the effective thermal conductivity (ETC) of particulate reinforced three-phase composites (TPCs). Traditionally, the primary mechanisms governing ETC have been elucidated through the concept of packing density, as established in granular powder mechanics for hybrid particle mixtures with bimodal size distributions. However, this conventional packing density is inapplicable to TPCs prepared by mechanical mixing and mold casting, where porosity reduction is absent. To date, a micromechanics-based model specifically addressing this phenomenon remains undeveloped. Given that the matrix phase possesses low thermal conductivity, the matrix regions distant from high TC fillers are analogous to air voids in granular materials, and are thus termed ineffective matrix. According to packing theory, the utilization of a binary size distribution effectively reduces the volume fraction of the ineffective matrix. Based on this concept, the interpolated double inclusion method was employed to construct a fictitious inclusion comprising the particle and its surrounding matrix. The Chang-Deng model was applied to quantify the concentration of the ineffective matrix, and the Zehner, Bauer and Schlunder model was used to predict the ETC of TPCs. The predictions were validated against relevant experiments to assess the validity of the developed model. Additionally, parametric analyses were performed to elucidate the effect of various factors on model performance. The proposed micromechanics model demonstrates potential as an effective tool for the design and optimization of multiphase composites with enhanced ETCs. Mechanical Engineering Three-phase composites (TPCs) Effective thermal conductivity (ETC) Micromechanics-based model Bimodal particle size distribution Packing density Full Text Additional Declarations The authors declare no competing interests. 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-8525348","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":569864485,"identity":"fc5da2ee-e6d5-436a-b0f3-22e17905a35b","order_by":0,"name":"Yunpeng 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distribution\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Nanjing University of Aeronautics and Astronautics","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":"Three-phase composites (TPCs), Effective thermal conductivity (ETC), Micromechanics-based model, Bimodal particle size distribution, Packing density","lastPublishedDoi":"10.21203/rs.3.rs-8525348/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8525348/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eParticles with high thermal conductivity exhibiting a bimodal size distribution can significantly improve the effective thermal conductivity (ETC) of particulate reinforced three-phase composites (TPCs). Traditionally, the primary mechanisms governing ETC have been elucidated through the concept of packing density, as established in granular powder mechanics for hybrid particle mixtures with bimodal size distributions. However, this conventional packing density is inapplicable to TPCs prepared by mechanical mixing and mold casting, where porosity reduction is absent. To date, a micromechanics-based model specifically addressing this phenomenon remains undeveloped. Given that the matrix phase possesses low thermal conductivity, the matrix regions distant from high TC fillers are analogous to air voids in granular materials, and are thus termed ineffective matrix. According to packing theory, the utilization of a binary size distribution effectively reduces the volume fraction of the ineffective matrix. Based on this concept, the interpolated double inclusion method was employed to construct a fictitious inclusion comprising the particle and its surrounding matrix. The Chang-Deng model was applied to quantify the concentration of the ineffective matrix, and the Zehner, Bauer and Schlunder model was used to predict the ETC of TPCs. The predictions were validated against relevant experiments to assess the validity of the developed model. Additionally, parametric analyses were performed to elucidate the effect of various factors on model performance. The proposed micromechanics model demonstrates potential as an effective tool for the design and optimization of multiphase composites with enhanced ETCs.\u003c/p\u003e","manuscriptTitle":"Micromechanics-based model for the effective thermal conductivity of three-phase composites with bimodal particle size distribution","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-07 03:48:09","doi":"10.21203/rs.3.rs-8525348/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":"3bbdcdad-83af-4752-a78a-510708abd705","owner":[],"postedDate":"January 7th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":60635834,"name":"Mechanical Engineering"}],"tags":[],"updatedAt":"2026-02-09T15:23:32+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-07 03:48:09","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8525348","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8525348","identity":"rs-8525348","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}