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| Content Provider | Springer Nature Link |
|---|---|
| Author | McCuan, John |
| Copyright Year | 2009 |
| Abstract | Archimedes’ beautiful principle may be used to determine how an object floats in a vessel of liquid. This, in turn may be used to determine the global configuration associated with a floating object under the assumption that the surface of the liquid is planar. There are instances, however, in which capillary effects conspire to produce significantly nonplanar liquid interfaces and phenomena which is strikingly at odds with the predictions of the Archimedean principle. A most notable instance involves floatation of convex objects with density greater than that of the liquid.The effects of capillarity on liquid interface configurations invariably manifest themselves globally over the entire system, though the magnitude of such effects is often so small as to be overlooked. This phenomenon presents a major difficulty in obtaining an appropriate generalization of Archimedes’ principle which incorporates capillarity.For a floating sphere we determine the local level of floating which is found to depend on a combination of buoyancy, capillary influence, and the curvature of the interface where it meets the floating sphere. Our formula is presented as a direct generalization of Archimedes’ principle applied to this special case through the addition of extra terms. The extra terms allow for floating of objects with density greater than that of the liquid as well as giving a precise quantitative description of all floating spheres which may be tested both experimentally and numerically. |
| Ending Page | 396 |
| Page Count | 12 |
| Starting Page | 385 |
| File Format | |
| ISSN | 14249286 |
| e-ISSN | 14249294 |
| Journal | Milan Journal of Mathematics |
| Issue Number | 1 |
| Volume Number | 77 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Basel |
| Publisher Date | 2009-09-11 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | floating Analysis Capillarity (surface tension) Optimization of shapes other than minimal surfaces Mathematics Archimedes’ principle capillarity |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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