+ Site Statistics
+ Search Articles
+ Subscribe to Site Feeds
Most Shared
PDF Full Text
+ PDF Full Text
Request PDF Full Text
+ Follow Us
Follow on Facebook
Follow on Twitter
Follow on LinkedIn
+ Translate
+ Recently Requested

Doughnut-shaped soap bubbles

Doughnut-shaped soap bubbles

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 92(4): 042402

Soap 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)/6π(2), and this is indeed the case of a free soap bubble, for instance. Surprisingly, we show that for V<αL(3)/6π(2), with α≈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<αL(3)/6π(2) cannot be stable and should not exist in foams, for instance.

(PDF emailed within 0-6 h: $19.90)

Accession: 057659344

Download citation: RISBibTeXText

PMID: 26565252

DOI: 10.1103/PhysRevE.92.042402

Related references

Soap bubbles in analytical chemistry. Conductometric determination of sub-parts per million levels of sulfur dioxide with a soap bubble. Analytical Chemistry 78(8): 2786-2793, 2006

Generating Soap Bubbles by Blowing on Soap Films. Physical Review Letters 116(7): 077801, 2016

Soap bubbles. Journal of Analytical Chemistry 62(1): 1-1, 2007

Doughnut Shaped Parathyroid Adenoma. Molecular Imaging and Radionuclide Therapy 28(1): 41-43, 2019

Doughnut-shaped zinc oxide particles. Journal of Materials Science 42(24): 9990-9994, 2007

Doughnut-shaped manifestation of pulmonary adenocarcinoma. Qjm 106(3): 277-278, 2013

Interference colours of soap bubbles. Visual Computer 19(4): 252-270, 2003

On the shape of giant soap bubbles. Proceedings of the National Academy of Sciences of the United States of America 114(10): 2515-2519, 2017

Growth laws for 3D soap bubbles. Physical Review Letters 72(3): 420-423, 1994

Soap opera bubbles out of a health centre. Nursing Times 81(3): 16-17, 1985

Statics and dynamics of adhesion between two soap bubbles. European Physical Journal. E, Soft Matter 24(2): 109-117, 2007

Acoustic Pressures in Case of Soap Bubbles. Proceedings of the National Academy of Sciences of the United States of America 12(8): 480-482, 1926

Bacterial contamination of children's soap bubbles. American Journal of Diseases of Children 125(2): 224-226, 1973

The elasticity of soap bubbles containing wormlike micelles. Langmuir 30(3): 727-732, 2014

Hydrothermal growth and optical properties of doughnut-shaped ZnO microparticles. Journal of Physical Chemistry. B 109(19): 9463-9467, 2006