title: What is the Shape of an Air Bubble on a Liquid Surface?
abstract: We have calculated the equilibrium shape of the axially symmetric meniscus along which a spherical bubble contacts a flat liquid surface by analytically integrating the Young-Laplace equation in the presence of gravity, in the limit of large Bond numbers. This method has the advantage that it provides semianalytical expressions for key geometrical properties of the bubble in terms of the Bond number. Results are in good overall agreement with experimental data and are consistent with fully numerical (Surface Evolver) calculations. In particular, we are able to describe how the bubble shape changes from hemispherical, with a flat, shallow bottom, to lenticular, with a deeper, curved bottom, as the Bond number is decreased.
authors.affiliation: Department of Meteorology, University of Reading Earley Gate , P.O. Box 243, Reading RG6 6BB, United Kingdom.|Institut d'Electronique, de Microélectronique et de Nanotechnologie (IEMN) CNRS UMR8520, The University of Lille Cité Scientifique , Avenue Poincaré, 59652 Villeneuve d'Ascq, France.|Department of Mathematics, Aberystwyth University Aberystwyth , Ceredigion SY23 3BZ, United Kingdom.|ISEL - Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa Rua Conselheiro Emídio Navarro 1 , 1959-007 Lisbon, Portugal.|Centro de Física Teórica e Computacional, Faculdade de Ciências da Universidade de Lisboa Campo Grande , Edifício C8, 1749-016 Lisbon, Portugal.
authors.forename: Miguel A C
authors.initials: MA
authors.lastname: Teixeira
authors.affiliation: Department of Meteorology, University of Reading Earley Gate , P.O. Box 243, Reading RG6 6BB, United Kingdom.|Institut d'Electronique, de Microélectronique et de Nanotechnologie (IEMN) CNRS UMR8520, The University of Lille Cité Scientifique , Avenue Poincaré, 59652 Villeneuve d'Ascq, France.|Department of Mathematics, Aberystwyth University Aberystwyth , Ceredigion SY23 3BZ, United Kingdom.|ISEL - Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa Rua Conselheiro Emídio Navarro 1 , 1959-007 Lisbon, Portugal.|Centro de Física Teórica e Computacional, Faculdade de Ciências da Universidade de Lisboa Campo Grande , Edifício C8, 1749-016 Lisbon, Portugal.
authors.forename: Steve
authors.initials: S
authors.lastname: Arscott
authors.affiliation: Department of Meteorology, University of Reading Earley Gate , P.O. Box 243, Reading RG6 6BB, United Kingdom.|Institut d'Electronique, de Microélectronique et de Nanotechnologie (IEMN) CNRS UMR8520, The University of Lille Cité Scientifique , Avenue Poincaré, 59652 Villeneuve d'Ascq, France.|Department of Mathematics, Aberystwyth University Aberystwyth , Ceredigion SY23 3BZ, United Kingdom.|ISEL - Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa Rua Conselheiro Emídio Navarro 1 , 1959-007 Lisbon, Portugal.|Centro de Física Teórica e Computacional, Faculdade de Ciências da Universidade de Lisboa Campo Grande , Edifício C8, 1749-016 Lisbon, Portugal.
authors.forename: Simon J
authors.initials: SJ
authors.lastname: Cox
authors.affiliation: Department of Meteorology, University of Reading Earley Gate , P.O. Box 243, Reading RG6 6BB, United Kingdom.|Institut d'Electronique, de Microélectronique et de Nanotechnologie (IEMN) CNRS UMR8520, The University of Lille Cité Scientifique , Avenue Poincaré, 59652 Villeneuve d'Ascq, France.|Department of Mathematics, Aberystwyth University Aberystwyth , Ceredigion SY23 3BZ, United Kingdom.|ISEL - Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa Rua Conselheiro Emídio Navarro 1 , 1959-007 Lisbon, Portugal.|Centro de Física Teórica e Computacional, Faculdade de Ciências da Universidade de Lisboa Campo Grande , Edifício C8, 1749-016 Lisbon, Portugal.
authors.forename: Paulo I C
authors.initials: PI
authors.lastname: Teixeira