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A theory for the slip and drag of superhydrophobic surfaces with surfactant.

cam.issuedOnline2019-11-25
cam.orpheus.successThu Jan 30 10:38:31 GMT 2020 - Embargo updated
dc.contributor.authorLandel, Julien R
dc.contributor.authorPeaudecerf, François J
dc.contributor.authorTemprano-Coleto, Fernando
dc.contributor.authorGibou, Frédéric
dc.contributor.authorGoldstein, Raymond E
dc.contributor.authorLuzzatto-Fegiz, Paolo
dc.contributor.orcidGoldstein, Raymond [0000-0003-2645-0598]
dc.date.accessioned2019-10-18T23:30:14Z
dc.date.available2019-10-18T23:30:14Z
dc.date.issued2020-01-25
dc.description.abstractSuperhydrophobic surfaces (SHSs) have the potential to reduce drag at solid boundaries. However, multiple independent studies have recently shown that small amounts of surfactant, naturally present in the environment, can induce Marangoni forces that increase drag, at least in the laminar regime. To obtain accurate drag predictions, one must solve the mass, momentum, bulk surfactant and interfacial surfactant conservation equations. This requires expensive simulations, thus preventing surfactant from being widely considered in SHS studies. To address this issue, we propose a theory for steady, pressure-driven, laminar, two-dimensional flow in a periodic SHS channel with soluble surfactant. We linearise the coupling between flow and surfactant, under the assumption of small concentration, finding a scaling prediction for the local slip length. To obtain the drag reduction and interfacial shear, we find a series solution for the velocity field by assuming Stokes flow in the bulk and uniform interfacial shear. We find how the slip and drag depend on the nine dimensionless groups that together characterize the surfactant transport near SHSs, the gas fraction and the normalized interface length. Our model agrees with numerical simulations spanning orders of magnitude in each dimensionless group. The simulations also provide the constants in the scaling theory. Our model significantly improves predictions relative to a surfactant-free one, which can otherwise overestimate slip and underestimate drag by several orders of magnitude. Our slip length model can provide the boundary condition in other simulations, thereby accounting for surfactant effects without having to solve the full problem.
dc.description.sponsorshipRaymond and Beverly Sackler Foundation, the European Research Council Grant 247333, Mines ParisTech, the Schlumberger Chair Fund, the California NanoSystems Institute through a Challenge Grant, ARO MURI W911NF-17- 1-0306 and ONR MURI N00014-17-1-2676
dc.format.mediumPrint-Electronic
dc.identifier.doi10.17863/CAM.44976
dc.identifier.eissn1469-7645
dc.identifier.issn0022-1120
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/297922
dc.languageeng
dc.language.isoeng
dc.publisherCambridge University Press (CUP)
dc.publisher.urlhttp://dx.doi.org/10.1017/jfm.2019.857
dc.rightsAll rights reserved
dc.subjectdrag reduction
dc.subjectmicrofluidics
dc.titleA theory for the slip and drag of superhydrophobic surfaces with surfactant.
dc.typeArticle
dcterms.dateAccepted2019-10-02
prism.publicationDate2020
prism.publicationNameJ Fluid Mech
prism.volume883
pubs.funder-project-idEuropean Research Council (247333)
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/M017982/1)
rioxxterms.licenseref.startdate2020-01
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.typeJournal Article/Review
rioxxterms.versionAM
rioxxterms.versionofrecord10.1017/jfm.2019.857

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