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dc.typeArtigo de periódicopt_BR
dc.titleDoughnut-shaped Soap Bubblespt_BR
dc.contributor.authorDeison; Saapt_BR
unicamp.authorSaa, Alberto] IMECC UNICAMP, Dept Matemat Aplicada, BR-13083859 Campinas, SP, Brazilpt_BR[Preve, Deisonpt
dc.subjectPhysics, Fluids & Plasmaspt_BR
dc.subjectPhysics, Mathematicalpt_BR
dc.description.abstractSoap bubbles are thin liquid films enclosing a fixed volume of air. Since the surface tension is typically assumed to be the only factor responsible for conforming the soap bubble shape, the realized bubble surfaces are always minimal area ones. Here, we consider the problem of finding the axisymmetric minimal area surface enclosing a fixed volume V and with a fixed equatorial perimeter L. It is well known that the sphere is the solution for V = L-3/6 pi(2), and this is indeed the case of a free soap bubble, for instance. Surprisingly, we show that for V < alpha L-3/6 pi(2), with alpha approximate to 0.21, such a surface cannot be the usual lens-shaped surface formed by the juxtaposition of two spherical caps, but is rather a toroidal surface. Practically, a doughnut-shaped bubble is known to be ultimately unstable and, hence, it will eventually lose its axisymmetry by breaking apart in smaller bubbles. Indisputably, however, the topological transition from spherical to toroidal surfaces is mandatory here for obtaining the global solution for this axisymmetric isoperimetric problem. Our result suggests that deformed bubbles with V < alpha L-3/6 pi(2) cannot be stable and should not exist in foams, for instance.en
dc.relation.ispartofPHYSICAL REVIEW Ept_BR
dc.publisher.countryCOLLEGE PKpt_BR
dc.publisherAMER PHYSICAL SOCpt_BR
dc.identifier.citationDoughnut-shaped Soap Bubbles. Amer Physical Soc, v. 92, p. OCT-2015.pt_BR
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)pt_BR
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)pt_BR
dc.description.sponsorship1Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)pt_BR
dc.description.sponsorship1Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)pt_BR
dc.description.sponsordocumentnumberFAPESP [2013/09357-9]pt
dc.description.sponsordocumentnumberCNPq [304378/2014-3, 441349/2014-5]pt
dc.description.provenanceMade available in DSpace on 2016-06-07T13:20:25Z (GMT). No. of bitstreams: 1 wos_000362497800005.pdf: 1057377 bytes, checksum: dee415ee3e36b61ddeac5475b9cc75f0 (MD5) Previous issue date: 2015en
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