Heterarchical modelling of comminution for rotary mills: Part II --- Particle crushing with segregation and mixing

Heterarchical modelling of comminution for rotary mills: Part II --- Particle crushing with segregation and mixing | 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 Heterarchical modelling of comminution for rotary mills: Part II --- Particle crushing with segregation and mixing Mukesh Singh Bisht, François Guillard, Paul Shelley, Benjy Marks, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3938203/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Aug, 2024 Read the published version in Granular Matter → Version 1 posted You are reading this latest preprint version Abstract In granular media, the crushing of individual particles is influenced by the number of contacts with neighbouring particles. This well-known phenomenon of ''cushioning'' shields the individual particles from crushing when the number of contacts is high. However, in open systems that involve extensive granular flow and bulk motion, like those found in industrial mills, the neighbouring particles continually exchange positions due to segregation and mixing, thereby altering the number of neighbouring contacts and their sizes, affecting the crushing of individual particles. Therefore, a critical challenge for properly modelling comminution in such systems lies in tracking the fluxes of the various particle size classes. Here, we explore the physics that governs the mechanisms of segregation and mixing within the multiscale heterarchical modelling paradigm. Building upon the framework developed in Part I, which integrated the heterarchical aspects of the physics of crushing along streamlines, we further account for segregation and mixing, and demonstrate their impact on the comminution efficiency of autogenous grinding mills. In particular, segregation is shown to greatly enhance the extent of particle crushing within the mill. Accordingly, we posit that this mechanism cannot be ignored. In summary, the new model sheds light on previously obscured dynamics within industrial mills, as well as enables the field to predict the time evolution of the particle size distribution at any point in the mill domain. This modelling capability opens the doors to new developments for estimating and improving milling efficiencies. Comminution Segregation Mixing Particle size distribution Heterarchy Rotary mills Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 16 Aug, 2024 Read the published version in Granular Matter → 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-3938203","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":272093862,"identity":"17fe8376-0014-4132-842f-248e97a7f7f8","order_by":0,"name":"Mukesh Singh Bisht","email":"","orcid":"","institution":"The University of Sydney","correspondingAuthor":false,"prefix":"","firstName":"Mukesh","middleName":"Singh","lastName":"Bisht","suffix":""},{"id":272093863,"identity":"7b0033f0-6cf9-41c5-9fdd-49ee52ce434d","order_by":1,"name":"François Guillard","email":"","orcid":"","institution":"The University of Sydney","correspondingAuthor":false,"prefix":"","firstName":"François","middleName":"","lastName":"Guillard","suffix":""},{"id":272093864,"identity":"2d86b0e3-9a9e-4fd4-8071-a0e89ac384d7","order_by":2,"name":"Paul Shelley","email":"","orcid":"","institution":"Molycop Innovation","correspondingAuthor":false,"prefix":"","firstName":"Paul","middleName":"","lastName":"Shelley","suffix":""},{"id":272093865,"identity":"3806d601-9970-454a-9a07-4ab8d719e0f3","order_by":3,"name":"Benjy Marks","email":"","orcid":"","institution":"The University of Sydney","correspondingAuthor":false,"prefix":"","firstName":"Benjy","middleName":"","lastName":"Marks","suffix":""},{"id":272093866,"identity":"8b9c0703-885a-4c33-b52c-d490a8d9a0a6","order_by":4,"name":"Itai Einav","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEklEQVRIiWNgGAWjYBACNiA+wMAgAaSYD0C4DBAubi1scC1sCcRpgSkCAh4D4rTwyTc/PMBQYZHHPyPn82eesjtyBgeYD97mYbBLbMDpMDaDAwxnJIolbuRuk+Y598zY4ABbsjUPQzIeLQwGBxjbJBIbzpzdxszbdjhxwwEeM2keBmY8Wtg/HGD8J5E4/8yZx5+BWuo3HOD/BtRSj0cLD9CWBonEDcd7GKSBWhIMDvCwAbUcxqMlp+BAwjGJxI3H28wk55w7bDjzMJux5RyD48a4tMg3H9/84UNNXeK8w8yPP7wpOyzPd7z54Y03FdWyuLSAQQKUZuIBEgqHQUwDfOqRAOMPkL14TR8Fo2AUjIKRCABe4VcA/kBNNAAAAABJRU5ErkJggg==","orcid":"","institution":"The University of Sydney","correspondingAuthor":true,"prefix":"","firstName":"Itai","middleName":"","lastName":"Einav","suffix":""}],"badges":[],"createdAt":"2024-02-07 22:29:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3938203/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3938203/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10035-024-01450-2","type":"published","date":"2024-08-16T15:58:12+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":63071243,"identity":"863b2527-3509-4f36-aa4f-be257497bc99","added_by":"auto","created_at":"2024-08-22 20:05:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7853687,"visible":true,"origin":"","legend":"","description":"","filename":"HeterarchicalrotarymillsPart2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3938203/v1_covered_4efc06a9-4d48-4aed-a069-7f9462fac320.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Heterarchical modelling of comminution for rotary mills: Part II --- Particle crushing with segregation and mixing","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"Comminution, Segregation, Mixing, Particle size distribution, Heterarchy, Rotary mills","lastPublishedDoi":"10.21203/rs.3.rs-3938203/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3938203/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In granular media, the crushing of individual particles is influenced by the number of contacts with neighbouring particles. 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