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The equilibrium states correspond to local minima of the total perimeter. (i) We nd an approximate value of the global minimum perimeter, and a marker to determine directly from an image how far a foam is from its ground state. (ii) For (small) area disorder, small bubbles tend to sort inwards and large bubbles sort outwards. (iii) Topological charges of the same signs `repel\u0026amp;amp;#39; while charges of the opposite signs `attract\u0026amp;amp;#39;. 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{"work":{"id":100112654,"created_at":"2023-04-12T11:16:38.988-07:00","from_world_paper_id":231590416,"updated_at":"2023-04-12T11:38:43.648-07:00","_data":{"abstract":"We study the equilibrium energies of 2D non-coarsening uid foams which consist of bubbles with xed areas. The equilibrium states correspond to local minima of the total perimeter. (i) We nd an approximate value of the global minimum perimeter, and a marker to determine directly from an image how far a foam is from its ground state. (ii) For (small) area disorder, small bubbles tend to sort inwards and large bubbles sort outwards. (iii) Topological charges of the same signs `repel\u0026#39; while charges of the opposite signs `attract\u0026#39;. (iv) We also discuss : boundary conditions; uniqueness of pattern when topology is prescribed; extensions to 3D."},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Energy landscape of 2D uid foams","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [1776753]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":101023125,"attachmentType":"pdf"}"><img alt="First page of “Energy landscape of 2D uid foams”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/101023125/mini_magick20230412-1-bp6gj0.png?1681323442" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Energy landscape of 2D uid foams</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="1776753" href="https://indiana.academia.edu/JamesGlazier"><img alt="Profile image of James Glazier" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/1776753/608490/755868/s65_james.glazier.jpg" />James Glazier</a></div><div class="ds-work-card--detail"><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">9 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 100112654; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=100112654"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">We study the equilibrium energies of 2D non-coarsening uid foams which consist of bubbles with xed areas. The equilibrium states correspond to local minima of the total perimeter. (i) We nd an approximate value of the global minimum perimeter, and a marker to determine directly from an image how far a foam is from its ground state. (ii) For (small) area disorder, small bubbles tend to sort inwards and large bubbles sort outwards. (iii) Topological charges of the same signs `repel&#39; while charges of the opposite signs `attract&#39;. (iv) We also discuss : boundary conditions; uniqueness of pattern when topology is prescribed; extensions to 3D.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":101023125,"attachmentType":"pdf","workUrl":"https://www.academia.edu/100112654/Energy_landscape_of_2D_uid_foams"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":101023125,"attachmentType":"pdf","workUrl":"https://www.academia.edu/100112654/Energy_landscape_of_2D_uid_foams"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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Present computer resources have enabled us to circumvent this problem. Using a dataset of 600 000 simulations, we are able to compute the polydisperse foam excess energy all the way from the dry to the wet limit. We also present data and a simple empirical function for the number distribution of n-sided bubbles for all values of the average contact number Z. Furthermore we show that, starting from a dry foam, incremental increases in liquid fraction bring with them a steadily increasing number n of bubbles involved in rearrangements. The size distribution of these rearrangements is found to be exponential, p(n) ∼ exp (−λn), where the mean, 1/λ, increases in the wet limit.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Statistics and topological changes in 2D foam from the dry to the wet limit","attachmentId":88242510,"attachmentType":"pdf","work_url":"https://www.academia.edu/82579494/Statistics_and_topological_changes_in_2D_foam_from_the_dry_to_the_wet_limit","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/82579494/Statistics_and_topological_changes_in_2D_foam_from_the_dry_to_the_wet_limit"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="16077617" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/16077617/The_equilibrium_state_of_2D_foams">The equilibrium state of 2D foams</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="35204094" href="https://independent.academia.edu/MirFaezMiri">MirFaez Miri</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Europhysics Letters (EPL), 2001</p><p class="ds-related-work--abstract ds2-5-body-sm">PACS. 82.70.Rr -Aerosols and foams. PACS. 64.60.Cn -Order-disorder transformations; statistical mechanics of model systems. PACS. 05.90.+m -Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The equilibrium state of 2D foams","attachmentId":42759434,"attachmentType":"pdf","work_url":"https://www.academia.edu/16077617/The_equilibrium_state_of_2D_foams","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/16077617/The_equilibrium_state_of_2D_foams"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="47901160" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/47901160/Topological_changes_in_a_two_dimensional_foam_cluster">Topological changes in a two-dimensional foam cluster</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="19256534" href="https://independent.academia.edu/denisweaire">denis weaire</a></div><p class="ds-related-work--metadata ds2-5-body-xs">The European Physical Journal E - Soft Matter, 2003</p><p class="ds-related-work--abstract ds2-5-body-sm">Experiments on a small cluster of bubbles in a nominally two-dimensional foam show an instability in which a topological change forces one of the bubbles to be ejected to the outside of the cluster at a point where this is not predicted by a two-dimensional model of a foam. This is interpreted in terms of the energy of the initial and ejected states and of the finite liquid content of the experimental system. A description of the distribution of liquid in various experimental set-ups suggests that the exact response may depend critically upon the type of system used. This is demonstrated experimentally with reference to small clusters of bubbles undergoing a single topological change.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Topological changes in a two-dimensional foam cluster","attachmentId":66790475,"attachmentType":"pdf","work_url":"https://www.academia.edu/47901160/Topological_changes_in_a_two_dimensional_foam_cluster","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/47901160/Topological_changes_in_a_two_dimensional_foam_cluster"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="81464876" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/81464876/Geometry_and_foams_2D_dynamics_and_3D_statics">Geometry and foams: 2D dynamics and 3D statics</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32328183" href="https://csregistry.academia.edu/JAvron">Joseph (Yosi) Avron</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review Letters, 1992</p><p class="ds-related-work--abstract ds2-5-body-sm">We discuss the implications of the classical Gauss-Bonnet formula to foam in two and three dimensions. For a two-dimensional foam it gives a generalization of the von Neumann law for the coarsening of foams to curved surfaces. As a consequence of this we find that the stability properties of stationary bubbles of such a froth depend on the Gaussian curvature of the surface. For three-dimensional foam we find a relation between the average Gaussian curvature of a soap film and the average number of vertices for each face.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Geometry and foams: 2D dynamics and 3D statics","attachmentId":87499037,"attachmentType":"pdf","work_url":"https://www.academia.edu/81464876/Geometry_and_foams_2D_dynamics_and_3D_statics","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/81464876/Geometry_and_foams_2D_dynamics_and_3D_statics"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="18997913" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/18997913/Long_range_geometrical_correlations_in_two_dimensional_foams">Long-range geometrical correlations in two-dimensional foams</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="39147086" href="https://independent.academia.edu/NicolasRivier">Nicolas Rivier</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Physics A: Mathematical and General, 1998</p><p class="ds-related-work--abstract ds2-5-body-sm">The statistical properties of two-dimensional, space-filling random cellular structures (foams, or their dual, random triangulations) in statistical equilibrium are obtained by maximum entropy inference and topological simulations. We show by maximum entropy inference that for a broad class of foams (shell-structured, including three-sided cell inclusions), all two-cell topological correlators A j (k, n) (average number of pairs of k-cell and n-cell at a topological distance j ) are linear in n and k, the numbers of neighbours of the cells. This generalizes a correlation known for neighbouring cells (j = 1) which implies the linearity of Aboav's relation (between the total number of neighbours of the cells adjacent to a n-neighboured cell and n). Our results, verified by simulations, also build up Gauss's theorem for cellular structures. Any additional restriction in exploring local cell configurations, besides the constraints of filling space at random, will manifest itself through a deviation from linearity of the correlators A j (k, n) and the Aboav relation. Notably, foams made of Feynman diagrams have additional, contextdependent restrictions and their Aboav relation is slightly curved. It is essential that the local random variable n denotes the number of neighbours of the cell and not that of its sides, whenever the two are different.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Long-range geometrical correlations in two-dimensional foams","attachmentId":40373644,"attachmentType":"pdf","work_url":"https://www.academia.edu/18997913/Long_range_geometrical_correlations_in_two_dimensional_foams","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/18997913/Long_range_geometrical_correlations_in_two_dimensional_foams"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="50345313" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/50345313/Dynamics_and_stationary_configurations_of_heterogeneous_foams">Dynamics and stationary configurations of heterogeneous foams</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="103158157" href="https://independent.academia.edu/AndrejCherkaev">Andrej Cherkaev</a></div><p class="ds-related-work--metadata ds2-5-body-xs">PLOS ONE</p><p class="ds-related-work--abstract ds2-5-body-sm">We consider the variational foam model, where the goal is to minimize the total surface area of a collection of bubbles subject to the constraint that the volume of each bubble is prescribed. We apply sharp interface methods to develop an efficient computational method for this problem. In addition to simulating time dynamics, we also report on stationary states of this flow for ≤ 21 bubbles in two dimensions and ≤ 17 bubbles in three dimensions. For small numbers of bubbles, we recover known analytical results, which we briefly discuss. In two dimensions, we also recover the previous numerical results of Cox et. al. (2003), computed using other methods. Particular attention is given to locally optimal foam configurations and heterogeneous foams, where the volumes of the bubbles are not equal. Configurational transitions are reported for the quasi-stationary flow where the volume of one of the bubbles is varied and, for each volume, the stationary state is computed. The results from these numerical experiments are described and accompanied by many figures and videos.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Dynamics and stationary configurations of heterogeneous foams","attachmentId":68367474,"attachmentType":"pdf","work_url":"https://www.academia.edu/50345313/Dynamics_and_stationary_configurations_of_heterogeneous_foams","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/50345313/Dynamics_and_stationary_configurations_of_heterogeneous_foams"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="27249838" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/27249838/The_evolution_of_defects_in_a_two_dimensional_wet_foam">The evolution of defects in a two-dimensional wet foam</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="51291853" href="https://independent.academia.edu/BogdanDlugogorski">Bogdan Dlugogorski</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Physics: Condensed Matter, 1999</p><p class="ds-related-work--abstract ds2-5-body-sm">This paper investigates the evolution of defects in two-dimensional (2D) wet foams by using the dynamic bubble simulation approach. Two defect types are considered: a single large bubble, and a cluster of small bubbles inserted in an otherwise monodisperse hexagonal lattice. In the case of a single large defect bubble, the disorder of the cluster associated with the defect is seen to increase and peak before returning to a state having a degree of order different from that of the disordered foam scaling state. This long-timescale behaviour agrees with recent 2D wet-foam experiments yet disagrees with the majority of existing simulations on dry foam. The inclusion of a finite liquid content in the present simulations is identified as a possible reason for the improved predictions. In the case of a defect of small bubbles, coarsening trends observed in experiments are reproduced. Unlike the case for a single large bubble defect, no peak was observed in the disorder of the bubble cluster.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The evolution of defects in a two-dimensional wet foam","attachmentId":47508898,"attachmentType":"pdf","work_url":"https://www.academia.edu/27249838/The_evolution_of_defects_in_a_two_dimensional_wet_foam","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/27249838/The_evolution_of_defects_in_a_two_dimensional_wet_foam"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="47901166" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/47901166/Pre_empting_Plateau_The_nature_of_topological_transitions_in_foam">Pre-empting Plateau: The nature of topological transitions in foam</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="19256534" href="https://independent.academia.edu/denisweaire">denis weaire</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Europhysics Letters (EPL), 2007</p><p class="ds-related-work--abstract ds2-5-body-sm">When the area of a face in a dry foam approaches zero in some quasistatic processes, Plateau's rules dictate that there must be an instability. This is more subtle than generally supposed. We argue that it is generally pre-empted, that is, the instability arises before an unstable multiple vertex is formed. Experiments and calculations which simulate Plateau's wire frame experiments support this view.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Pre-empting Plateau: The nature of topological transitions in foam","attachmentId":66790479,"attachmentType":"pdf","work_url":"https://www.academia.edu/47901166/Pre_empting_Plateau_The_nature_of_topological_transitions_in_foam","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/47901166/Pre_empting_Plateau_The_nature_of_topological_transitions_in_foam"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="71945707" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/71945707/Dynamical_transition_in_a_jammed_state_of_a_quasi_two_dimensional_foam">Dynamical transition in a jammed state of a quasi-two-dimensional foam</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="133486588" href="https://independent.academia.edu/ReiKurita">Rei Kurita</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E</p><p class="ds-related-work--abstract ds2-5-body-sm">The states of foam are empirically classified into dry foam and wet foam by the volume fraction of the liquid. Recently, a transition between the dry foam state and the wet foam state has been found by characterizing the bubble shapes [Furuta et al., Sci. Rep. 6, 37506 (2016)]. In the literature, it is indirectly ascertained that the transition from the dry to the wet form is related to the onset of the rearrangement of the bubbles, namely, the liquid fraction at which the bubbles become able to move to replace their positions. The bubble shape is a static property, and the rearrangement of the bubbles is a dynamic property. Thus, we investigate the relation between the bubble shape transition and the rearrangement event occurring in a collapsing process of the bubbles in a quasi-two-dimensional foam system. The current setup brings a good advantage to observe the above transitions, since the liquid fraction of the foam continuously changes in the system. It is revealed that the rearrangement of the bubbles takes place at the dry-wet transition point where the characteristics of the bubble shape change.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Dynamical transition in a jammed state of a quasi-two-dimensional foam","attachmentId":81080353,"attachmentType":"pdf","work_url":"https://www.academia.edu/71945707/Dynamical_transition_in_a_jammed_state_of_a_quasi_two_dimensional_foam","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/71945707/Dynamical_transition_in_a_jammed_state_of_a_quasi_two_dimensional_foam"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="113666219" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/113666219/The_effect_of_cell_boundary_on_2D_foam">The effect of cell boundary on 2D foam</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="238637791" href="https://independent.academia.edu/AtefAbdelkader3">Atef Abdelkader</a></div><p class="ds-related-work--metadata ds2-5-body-xs">MATEC Web of Conferences, 2018</p><p class="ds-related-work--abstract ds2-5-body-sm">We have studied the effect of cell boundary on 2D foam, with particular attention to perfect arrays of identical bubbles, and those containing only a single defect with time. We have also examined the effect of the wetness of the foam, observing the stability of two-dimensional foam comprising bubble rafts constrained to a fixed area of liquid surface. Perfectly six-fold coordinated foam appear to be unstable against loss of cohesion, but the lifetime to breakage of the perfect foam increases systematically with changing the cell boundaries. Foams containing a single defect are stable against such breakage due to the elastic stress fields around it.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The effect of cell boundary on 2D foam","attachmentId":110568057,"attachmentType":"pdf","work_url":"https://www.academia.edu/113666219/The_effect_of_cell_boundary_on_2D_foam","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/113666219/The_effect_of_cell_boundary_on_2D_foam"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":101023125,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":101023125,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_101023125" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="59225100" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/59225100/The_foam_geometry_paradox">The foam geometry "paradox</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="3983050" href="https://imperial.academia.edu/StephenNeethling">Stephen Neethling</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Canadian Journal of Physics, 2001</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" 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href="https://www.academia.edu/47901485/Uniqueness_stability_and_Hessian_eigenvalues_for_two_dimensional_bubble_clusters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="4" data-entity-id="100112650" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/100112650/Foams_out_of_stable_equilibrium_Cell_elongation_and_side_swapping">Foams out of stable equilibrium: Cell elongation and side swapping</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="1776753" href="https://indiana.academia.edu/JamesGlazier">James Glazier</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Philosophical Magazine 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class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="5" data-entity-id="25877165" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/25877165/Topological_Analysis_of_Foams_and_Tetrahedral_Structures">Topological Analysis of Foams and Tetrahedral Structures</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38325109" href="https://independent.academia.edu/RaphaelBlumenfeld">Raphael Blumenfeld</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Advanced Engineering Materials, 2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Topological Analysis of Foams and Tetrahedral 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