Bubble breakup and coalescence in vertical magma conduits: implications for Hawaiian and Strombolian volcanisms

Bubble breakup and coalescence in vertical magma conduits: implications for Hawaiian and Strombolian volcanisms | 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 Bubble breakup and coalescence in vertical magma conduits: implications for Hawaiian and Strombolian volcanisms Pallab Jyoti Hazarika, Amiya Baruah, Santanu Misra, Snehamoy Majumder, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7471870/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 Magmas ascending through volcanic conduits generate bubbles in large volume fractions due to the decompression-induced degassing of volatile matters. It is recognized that the bubble-forming process can significantly influence dynamics of magma eruptions. However, interactions between densely-packed ascending bubbles require further investigation, particularly to elucidate transient eruption behaviors. Using scaled analogue experiments and computational fluid dynamics (CFD) simulations, employing a framework of the level-set method for multiphase flows, we address this critical issue and demonstrate the hydrodynamic interactions of vertically ascending bubbles and their effects on deformation, coalescence, and post-coalescence breakup processes. These phenomena are analyzed as a function of density (ρ*) and viscosity (µ*) ratios of bubbles relative to ambient magma. Our results show that two consecutive bubbles in a vertical arrangement undergo contrasting deformations before coalescing; the trailing bubble elongates along the ascent direction, while the leading bubble flattens horizontally. A series of simulations systematically examine the conditions for bubble ascent with and without post-coalescence breakup. The findings suggest that repeated breakup and coalescence events can induce an unsteady state of magma flow in the conduit. We provide an estimate of the threshold spatial separation (d* = 1.5) required for coalescence. Based on this estimate, we propose that a bubble occupancy of 50% by volume can trigger a transition from Hawaiian (bubbly flows) to Strombolian (slug flows) eruptions. This study enhances our understanding of the interplay between bubble dynamics and magma flow behavior inside a conduit, offering insights into the mechanisms driving transient volcanic eruptions. two-phase flow CFD bubble-coalescence rheology magma ascent Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Full Text Additional Declarations Table 1 is available in the Supplementary Files section. Supplementary Files Table1.docx Graphicalabstract.jpg 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-7471870","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":518441384,"identity":"996d49bd-9d8a-43c9-b9a1-02118837dbf9","order_by":0,"name":"Pallab Jyoti Hazarika","email":"","orcid":"","institution":"Cotton University","correspondingAuthor":false,"prefix":"","firstName":"Pallab","middleName":"Jyoti","lastName":"Hazarika","suffix":""},{"id":518441385,"identity":"19ccbedc-5768-4cdd-852f-a57ad29deb80","order_by":1,"name":"Amiya 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04:26:22","extension":"html","order_by":39,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":232056,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/12de3717461eeae0b8ac0b16.html"},{"id":92689490,"identity":"00ffc43c-062b-4c28-92b6-89d372265c5b","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":341749,"visible":true,"origin":"","legend":"\u003cp\u003eThe four primary types of flow regimes in a two-phase system of magma and volatile phases. a) \u003cem\u003e\u003cstrong\u003eBubbly flow\u003c/strong\u003e\u003c/em\u003e: tiny bubble droplets are dispersed within the liquid phase. b) \u003cem\u003e\u003cstrong\u003eSlug flow\u003c/strong\u003e\u003c/em\u003e: bubbles coalesce to form large drops, often reaching the size of the diameter of conduit. c) \u003cem\u003e\u003cstrong\u003eAnnular flow\u003c/strong\u003e\u003c/em\u003e: liquid phase is contained within a column of volatile phase, and the liquid phase outlines the conduit wall all along. d) \u003cem\u003e\u003cstrong\u003eDispersed flow:\u003c/strong\u003e\u003c/em\u003etiny droplets of magma are dispersed within a large volatile phase (After, Wallis, 1969; Vergniolle and Gaudemer, 2015).\u003c/p\u003e","description":"","filename":"image1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/2a1a0c64b6ae1703c61ae20d.jpeg"},{"id":92689480,"identity":"e30daa27-baae-4e82-a032-292b2354e6cf","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":151293,"visible":true,"origin":"","legend":"\u003cp\u003eLaboratory experiments for bubble simulations in two-fluid physical models. Low-viscosity buoyant fluid (dyed in red color) was injected into another immiscible fluid, forming a train of bubbles showing mutual interactions. a)-h) various stages of the experiment throughout the time: \u003cem\u003epinching, break-up, coalescence\u003c/em\u003e and \u003cem\u003edeformation\u003c/em\u003eof the bubbles.\u003c/p\u003e","description":"","filename":"image2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/1cc448a772f8f4aa57364611.jpeg"},{"id":92689484,"identity":"1d77757d-2a6a-4d0e-80c3-d39e2db35596","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":143275,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic illustration of the four key stages of bubble evolution. \u003cem\u003eStage I\u003c/em\u003e: bubble formation as a spherical volume, \u003cem\u003eStage II\u003c/em\u003e: bubble multiplication and mutual interactions, \u003cem\u003eStage III\u003c/em\u003e: large contrasting deformations due to the interactions of the leading and the trailing bubbles, and \u003cem\u003eStage IV\u003c/em\u003e: bubble coalescence.\u003c/p\u003e","description":"","filename":"image3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/c56ac6edce9fd17caafdc139.jpeg"},{"id":92689482,"identity":"52fcdd03-9c2b-4d85-bb1a-84096a44f231","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":215048,"visible":true,"origin":"","legend":"\u003cp\u003ea) Bubble nucleation, growth and fragmentation within a volcanic conduit. b) Numerical model set-up and boundary conditions used for the simulation of bubble hydrodynamics.\u003c/p\u003e","description":"","filename":"image4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/ac43570199abb82d4eb869e4.jpeg"},{"id":92689495,"identity":"f386a2ad-3e05-415d-a57d-25837c553eb1","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":136322,"visible":true,"origin":"","legend":"\u003cp\u003eDefinition of the control volume formulation scheme in the numerical models. Locations of scalar (\u003cem\u003eu\u003c/em\u003e\u003csub\u003e\u003cem\u003ei,j\u003c/em\u003e\u003c/sub\u003e) and vector variables (\u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003ei,j\u003c/em\u003e\u003c/sub\u003e) are shown in the control volume (\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ei,j\u003c/em\u003e\u003c/sub\u003e).\u003c/p\u003e","description":"","filename":"image5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/42016b3950315718f821d1af.jpeg"},{"id":92689841,"identity":"5c0f7020-da06-45fb-89ed-04abb3a4ef48","added_by":"auto","created_at":"2025-10-03 04:26:22","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":252510,"visible":true,"origin":"","legend":"\u003cp\u003eTime series analysis (non-dimensionalized with shear rate and time) of bubble deformations in control-volume models: a) \u003cem\u003et = 0\u003c/em\u003e, and b) \u003cem\u003et = 0.25\u003c/em\u003e. Note that the in-axis bubbles undergo a strong mechanical interaction, resulting in flattening deformation of the leading bubble (marked 1), and distortion of the trailing bubble (marked 2) leading to a conical shape.\u003c/p\u003e","description":"","filename":"image6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/3a8ceda2a59a51a35d66acec.jpeg"},{"id":92689834,"identity":"f3470767-ab83-4df6-83bc-a306b3d1b476","added_by":"auto","created_at":"2025-10-03 04:26:21","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":469114,"visible":true,"origin":"","legend":"\u003cp\u003eProgressive stages of coalescence of two in-axis bubbles forming a mushroom-like structure. Individual bubbles develop isolated flow circulations in the pre-coalescence stage, which evolves into a single, large vortex in the post-coalescence stage.\u003c/p\u003e","description":"","filename":"image7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/6fef4b058eef000aace17af7.jpeg"},{"id":92689487,"identity":"a9435cc0-87a4-4773-b61c-cedc29ddae57","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":222970,"visible":true,"origin":"","legend":"\u003cp\u003eVariations in the ascent velocity of bubbles with their progressive upward movement for different (a) viscosity and (b) density ratios.\u003c/p\u003e","description":"","filename":"image8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/67ffabd22d5a4f547adfd4e2.jpeg"},{"id":92689497,"identity":"3cc6a985-68dd-4e90-b45c-0270112e0326","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":241919,"visible":true,"origin":"","legend":"\u003cp\u003eBubble coalescence and post-coalescence break-up in numerical simulations run for different density ratios: (a) 𝜌1:𝜌2 = 2:1, (b) 𝜌1:𝜌2= 10:1, and (c) 𝜌1:𝜌2= 100:1. The viscosity contrast is held constant at 10:1.\u003c/p\u003e","description":"","filename":"image9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/a4a5f865cb8ad9ea855b4784.jpeg"},{"id":92689485,"identity":"a3dcd985-12d4-4205-860c-8b14e18dba37","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"jpeg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":254402,"visible":true,"origin":"","legend":"\u003cp\u003eNumerical simulations of coalescence and break-up patterns of bubbles for different viscosity ratios, (a) 𝜇1:𝜇2 = 2:1, (b) 𝜇1:𝜇2= 10:1, and (c) 𝜇1:𝜇2= 100:1. Density ratio is held constant throughout the simulation at 10:1.\u003c/p\u003e","description":"","filename":"image10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/a2cde9fdbcbb90863c9ea6a2.jpeg"},{"id":92689501,"identity":"12826521-7b32-40f2-af0f-d5f7e715aefe","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"jpeg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":227264,"visible":true,"origin":"","legend":"\u003cp\u003eCoalescence of two identical bubbles as a function of their initial vertical separation, \u003cem\u003ed* \u003c/em\u003e(normalized with the bubble diameter). According to the present study, \u003cem\u003ed*\u0026gt; 1.5 \u003c/em\u003ewill not lead to coalescence of two in-axis bubbles. Such bubbles will continue to ascend independently, albeit with a mutual interaction leading to their deformation.\u003c/p\u003e","description":"","filename":"image11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/36ae00d54315fbb01dbfa78e.jpeg"},{"id":92689504,"identity":"f73e3750-1ecd-411d-a2a2-f5ec62a2ef2a","added_by":"auto","created_at":"2025-10-03 04:18:22","extension":"jpeg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":252294,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic representation of different bubble flow regimes within a volcanic conduit and their corresponding volcanic eruption styles (top panel). Photographs of some archetypal volcanic eruptions (bottom panel); namely, (e) Lava flow from effusive vents, Etna, (f) Lava fountaining activity, (g) Slug bursts in a Strombolian activity, Etna, and (h) Plinian eruption, Mt. St. Helens. The photographs given in (e)-(g) are captured by Tom Pfeiffer, www.volcanodiscovery.com, used with permission; and the one in (h) is photographed by Robert Krimmel, US Geological Survey.\u003c/p\u003e","description":"","filename":"image12.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/d40d8e1590bf0721a33a1329.jpeg"},{"id":92689493,"identity":"086fc8f2-80d8-4a6c-a116-338a0b8604ec","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"jpeg","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":150423,"visible":true,"origin":"","legend":"\u003cp\u003eDensity(𝜌\u003csup\u003e∗\u003c/sup\u003e) and viscosity (𝜇\u003csup\u003e∗\u003c/sup\u003e)ratio vs. inter bubble distance (𝑑\u003csup\u003e∗\u003c/sup\u003e) plot showing the ideal conditions of different types of volcanic eruptions. Note that this plot does not consider other parameters that play important roles (see text for details) in eruption styles.\u003c/p\u003e","description":"","filename":"image13.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/d106be13f3859eab56ad2d5b.jpeg"},{"id":96246263,"identity":"934551e3-b6d8-49ac-995a-438359bc5913","added_by":"auto","created_at":"2025-11-19 07:25:13","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3684204,"visible":true,"origin":"","legend":"","description":"","filename":"EPSManuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1_covered_db583c0b-a627-4f94-8d76-6e187ce1b08c.pdf"},{"id":92689479,"identity":"235556b5-e2f0-4f60-b167-dc3fbc2181eb","added_by":"auto","created_at":"2025-10-03 04:18:21","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":15054,"visible":true,"origin":"","legend":"","description":"","filename":"Table1.docx","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/f58746ab73c31c17f9864e18.docx"},{"id":92689835,"identity":"f370f79c-073a-443f-aedf-7e9811826f1a","added_by":"auto","created_at":"2025-10-03 04:26:21","extension":"jpg","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":14531472,"visible":true,"origin":"","legend":"","description":"","filename":"Graphicalabstract.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7471870/v1/02d258d2bcf8153a726bd1f9.jpg"}],"financialInterests":"\u003cp\u003eTable 1 is available in the Supplementary Files section.\u003c/p\u003e","formattedTitle":"Bubble breakup and coalescence in vertical magma conduits: implications for Hawaiian and Strombolian volcanisms","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":"two-phase flow, CFD, bubble-coalescence, rheology, magma ascent","lastPublishedDoi":"10.21203/rs.3.rs-7471870/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7471870/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMagmas ascending through volcanic conduits generate bubbles in large volume fractions due to the decompression-induced degassing of volatile matters. It is recognized that the bubble-forming process can significantly influence dynamics of magma eruptions. However, interactions between densely-packed ascending bubbles require further investigation, particularly to elucidate transient eruption behaviors. Using scaled analogue experiments and computational fluid dynamics (CFD) simulations, employing a framework of the level-set method for multiphase flows, we address this critical issue and demonstrate the hydrodynamic interactions of vertically ascending bubbles and their effects on deformation, coalescence, and post-coalescence breakup processes. These phenomena are analyzed as a function of density (ρ*) and viscosity (\u0026micro;*) ratios of bubbles relative to ambient magma. Our results show that two consecutive bubbles in a vertical arrangement undergo contrasting deformations before coalescing; the trailing bubble elongates along the ascent direction, while the leading bubble flattens horizontally. A series of simulations systematically examine the conditions for bubble ascent with and without post-coalescence breakup. The findings suggest that repeated breakup and coalescence events can induce an unsteady state of magma flow in the conduit. We provide an estimate of the threshold spatial separation (d* = 1.5) required for coalescence. Based on this estimate, we propose that a bubble occupancy of 50% by volume can trigger a transition from Hawaiian (bubbly flows) to Strombolian (slug flows) eruptions. This study enhances our understanding of the interplay between bubble dynamics and magma flow behavior inside a conduit, offering insights into the mechanisms driving transient volcanic eruptions.\u003c/p\u003e","manuscriptTitle":"Bubble breakup and coalescence in vertical magma conduits: implications for Hawaiian and Strombolian volcanisms","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-03 04:18:16","doi":"10.21203/rs.3.rs-7471870/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":"ea5317f3-dd9f-494d-891a-ba13b0a585f0","owner":[],"postedDate":"October 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-11-15T11:37:31+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-03 04:18:16","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7471870","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7471870","identity":"rs-7471870","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}