Can flexibility help you float?
We consider the role of flexibility in the weight-bearing characteristics of bodies floating at an interface. Specifically, we develop a theoretical model for a two-dimensional thin floating plate that yields the maximum stable plate load and optimal stiffness for weight support. Plates small relati...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Institute of Physics
2013
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| Online Access: | http://hdl.handle.net/1721.1/80721 https://orcid.org/0000-0002-7936-7256 |
| _version_ | 1811080420322705408 |
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| author | Burton, Lisa Janelle Bush, John W. M. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Burton, Lisa Janelle Bush, John W. M. |
| author_sort | Burton, Lisa Janelle |
| collection | MIT |
| description | We consider the role of flexibility in the weight-bearing characteristics of bodies floating at an interface. Specifically, we develop a theoretical model for a two-dimensional thin floating plate that yields the maximum stable plate load and optimal stiffness for weight support. Plates small relative to the capillary length are primarily supported by surface tension, and their weight-bearing potential does not benefit from flexibility. Above a critical size comparable to the capillary length, flexibility assists interfacial flotation. For plates on the order of and larger than the capillary length, deflection from an initially flat shape increases the force resulting from hydrostatic pressure, allowing the plate to support a greater load. In this large plate limit, the shape that bears the most weight is a semicircle, which displaces the most fluid above the plate for a fixed plate length. Exact results for maximum weight-bearing plate shapes are compared to analytic approximations made in the limits of large and small plate sizes. The value of flexibility for floating to a number of biological organisms is discussed in light of our study. |
| first_indexed | 2024-09-23T11:31:22Z |
| format | Article |
| id | mit-1721.1/80721 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:31:22Z |
| publishDate | 2013 |
| publisher | American Institute of Physics |
| record_format | dspace |
| spelling | mit-1721.1/807212022-10-01T04:08:44Z Can flexibility help you float? Burton, Lisa Janelle Bush, John W. M. Massachusetts Institute of Technology. Department of Mathematics Massachusetts Institute of Technology. Department of Mechanical Engineering Bush, John W. M. Burton, Lisa Janelle We consider the role of flexibility in the weight-bearing characteristics of bodies floating at an interface. Specifically, we develop a theoretical model for a two-dimensional thin floating plate that yields the maximum stable plate load and optimal stiffness for weight support. Plates small relative to the capillary length are primarily supported by surface tension, and their weight-bearing potential does not benefit from flexibility. Above a critical size comparable to the capillary length, flexibility assists interfacial flotation. For plates on the order of and larger than the capillary length, deflection from an initially flat shape increases the force resulting from hydrostatic pressure, allowing the plate to support a greater load. In this large plate limit, the shape that bears the most weight is a semicircle, which displaces the most fluid above the plate for a fixed plate length. Exact results for maximum weight-bearing plate shapes are compared to analytic approximations made in the limits of large and small plate sizes. The value of flexibility for floating to a number of biological organisms is discussed in light of our study. National Science Foundation (U.S.). Graduate Research Fellowship Program 2013-09-13T15:28:42Z 2013-09-13T15:28:42Z 2012-10 2012-06 Article http://purl.org/eprint/type/JournalArticle 10706631 1089-7666 http://hdl.handle.net/1721.1/80721 Burton, L. J., and J. W. M. Bush. “Can flexibility help you float?” Physics of Fluids 24, no. 10 (2012): 101701. © 2012 American Institute of Physics. https://orcid.org/0000-0002-7936-7256 en_US http://dx.doi.org/10.1063/1.4757121 Physics of Fluids Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Institute of Physics MIT web domain |
| spellingShingle | Burton, Lisa Janelle Bush, John W. M. Can flexibility help you float? |
| title | Can flexibility help you float? |
| title_full | Can flexibility help you float? |
| title_fullStr | Can flexibility help you float? |
| title_full_unstemmed | Can flexibility help you float? |
| title_short | Can flexibility help you float? |
| title_sort | can flexibility help you float |
| url | http://hdl.handle.net/1721.1/80721 https://orcid.org/0000-0002-7936-7256 |
| work_keys_str_mv | AT burtonlisajanelle canflexibilityhelpyoufloat AT bushjohnwm canflexibilityhelpyoufloat |