Capillary instability on a hydrophilic stripe
A recent experiment showed that cylindrical segments of water filling a hydrophilic stripe on an otherwise hydrophobic surface display a capillary instability when their volume is increased beyond the critical volume at which their apparent contact angle on the surface reaches 90° (Gau et al 1999 Sc...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
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Institute of Physics Publishing
2012
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| Online Access: | http://hdl.handle.net/1721.1/70536 |
| _version_ | 1811090436581752832 |
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| author | Speth, Raymond L. Lauga, Eric |
| author2 | Massachusetts Institute of Technology. Department of Chemical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Chemical Engineering Speth, Raymond L. Lauga, Eric |
| author_sort | Speth, Raymond L. |
| collection | MIT |
| description | A recent experiment showed that cylindrical segments of water filling a hydrophilic stripe on an otherwise hydrophobic surface display a capillary instability when their volume is increased beyond the critical volume at which their apparent contact angle on the surface reaches 90° (Gau et al 1999 Science 283 46–9). Surprisingly, the fluid segments did not break up into droplets—as would be expected for a classical Rayleigh–Plateau instability—but instead displayed a long-wavelength instability where all excess fluid gathered in a single bulge along each stripe. We consider here the dynamics of the flow instability associated with this setup. We perform a linear stability analysis of the capillary flow problem in the inviscid limit. We first confirm previous work showing that all cylindrical segments are linearly unstable if (and only if) their apparent contact angle is larger than 90°. We then demonstrate that the most unstable wavenumber for the surface perturbation decreases to zero as the apparent contact angle of the fluid on the surface approaches 90°, allowing us to re-interpret the creation of bulges in the experiment as a zero-wavenumber capillary instability. A variation of the stability calculation is also considered for the case of a hydrophilic stripe located on a wedge-like geometry. |
| first_indexed | 2024-09-23T14:46:08Z |
| format | Article |
| id | mit-1721.1/70536 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:46:08Z |
| publishDate | 2012 |
| publisher | Institute of Physics Publishing |
| record_format | dspace |
| spelling | mit-1721.1/705362022-10-01T22:19:03Z Capillary instability on a hydrophilic stripe Speth, Raymond L. Lauga, Eric Massachusetts Institute of Technology. Department of Chemical Engineering Speth, Raymond L. Speth, Raymond L. A recent experiment showed that cylindrical segments of water filling a hydrophilic stripe on an otherwise hydrophobic surface display a capillary instability when their volume is increased beyond the critical volume at which their apparent contact angle on the surface reaches 90° (Gau et al 1999 Science 283 46–9). Surprisingly, the fluid segments did not break up into droplets—as would be expected for a classical Rayleigh–Plateau instability—but instead displayed a long-wavelength instability where all excess fluid gathered in a single bulge along each stripe. We consider here the dynamics of the flow instability associated with this setup. We perform a linear stability analysis of the capillary flow problem in the inviscid limit. We first confirm previous work showing that all cylindrical segments are linearly unstable if (and only if) their apparent contact angle is larger than 90°. We then demonstrate that the most unstable wavenumber for the surface perturbation decreases to zero as the apparent contact angle of the fluid on the surface approaches 90°, allowing us to re-interpret the creation of bulges in the experiment as a zero-wavenumber capillary instability. A variation of the stability calculation is also considered for the case of a hydrophilic stripe located on a wedge-like geometry. National Science Foundation (U.S.) (grant CTS-0624830) National Science Foundation (U.S.) (grant CBET-0746285) 2012-05-07T20:44:50Z 2012-05-07T20:44:50Z 2009-07 2009-01 Article http://purl.org/eprint/type/JournalArticle 1367-2630 http://hdl.handle.net/1721.1/70536 Speth, Raymond L, and Eric Lauga. “Capillary Instability on a Hydrophilic Stripe.” New Journal of Physics 11.7 (2009): 075024. Web. en_US http://dx.doi.org/10.1088/1367-2630/11/7/075024 New Journal of Physics Creative Commons Attribution 3.0 http://creativecommons.org/licenses/by/3.0/ application/pdf Institute of Physics Publishing New Journal of Physics |
| spellingShingle | Speth, Raymond L. Lauga, Eric Capillary instability on a hydrophilic stripe |
| title | Capillary instability on a hydrophilic stripe |
| title_full | Capillary instability on a hydrophilic stripe |
| title_fullStr | Capillary instability on a hydrophilic stripe |
| title_full_unstemmed | Capillary instability on a hydrophilic stripe |
| title_short | Capillary instability on a hydrophilic stripe |
| title_sort | capillary instability on a hydrophilic stripe |
| url | http://hdl.handle.net/1721.1/70536 |
| work_keys_str_mv | AT spethraymondl capillaryinstabilityonahydrophilicstripe AT laugaeric capillaryinstabilityonahydrophilicstripe |