Some exact properties of the effective slip over surfaces with hydrophobic patternings
Shear flows of viscous fluid layers over nonuniformly hydrophobic surfaces are characterized in the far-field by an effective slip velocity, which relates to the applied stress through some mobility tensor characterizing the surface. Here, we identify two methods to determine the mobility tensor for...
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American Institute of Physics (AIP)
2013
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Online Access: | http://hdl.handle.net/1721.1/78878 https://orcid.org/0000-0002-5154-9787 |
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author | Six, Pierre Kamrin, Kenneth N. |
author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Six, Pierre Kamrin, Kenneth N. |
author_sort | Six, Pierre |
collection | MIT |
description | Shear flows of viscous fluid layers over nonuniformly hydrophobic surfaces are characterized in the far-field by an effective slip velocity, which relates to the applied stress through some mobility tensor characterizing the surface. Here, we identify two methods to determine the mobility tensor for flat surfaces with arbitrary slip-length variations. A family of “Cross Flow Identities” is then analyzed, which equate mobility components of different unidirectional patternings. We also calculate an analytical mobility solution for a family of continuously varying patterns. We validate the results numerically and discuss implications in various limits. |
first_indexed | 2024-09-23T10:30:14Z |
format | Article |
id | mit-1721.1/78878 |
institution | Massachusetts Institute of Technology |
language | en_US |
last_indexed | 2024-09-23T10:30:14Z |
publishDate | 2013 |
publisher | American Institute of Physics (AIP) |
record_format | dspace |
spelling | mit-1721.1/788782022-09-27T09:48:38Z Some exact properties of the effective slip over surfaces with hydrophobic patternings Six, Pierre Kamrin, Kenneth N. Massachusetts Institute of Technology. Department of Mechanical Engineering Kamrin, Kenneth N. Shear flows of viscous fluid layers over nonuniformly hydrophobic surfaces are characterized in the far-field by an effective slip velocity, which relates to the applied stress through some mobility tensor characterizing the surface. Here, we identify two methods to determine the mobility tensor for flat surfaces with arbitrary slip-length variations. A family of “Cross Flow Identities” is then analyzed, which equate mobility components of different unidirectional patternings. We also calculate an analytical mobility solution for a family of continuously varying patterns. We validate the results numerically and discuss implications in various limits. MIT-France Program 2013-05-14T14:58:32Z 2013-05-14T14:58:32Z 2013-02 2012-11 Article http://purl.org/eprint/type/JournalArticle 1070-6631 1089-7666 http://hdl.handle.net/1721.1/78878 Six, Pierre, and Ken Kamrin. Some Exact Properties of the Effective Slip over Surfaces with Hydrophobic Patternings. Physics of Fluids 25(2): 021703, 2013. © 2013 American Institute of Physics https://orcid.org/0000-0002-5154-9787 en_US http://dx.doi.org/10.1063/1.4790536 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 (AIP) MIT web domain |
spellingShingle | Six, Pierre Kamrin, Kenneth N. Some exact properties of the effective slip over surfaces with hydrophobic patternings |
title | Some exact properties of the effective slip over surfaces with hydrophobic patternings |
title_full | Some exact properties of the effective slip over surfaces with hydrophobic patternings |
title_fullStr | Some exact properties of the effective slip over surfaces with hydrophobic patternings |
title_full_unstemmed | Some exact properties of the effective slip over surfaces with hydrophobic patternings |
title_short | Some exact properties of the effective slip over surfaces with hydrophobic patternings |
title_sort | some exact properties of the effective slip over surfaces with hydrophobic patternings |
url | http://hdl.handle.net/1721.1/78878 https://orcid.org/0000-0002-5154-9787 |
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