Handle URI:
http://hdl.handle.net/10754/598615
Title:
Inertial rise of a meniscus on a vertical cylinder
Authors:
O’Kiely, Doireann; Whiteley, Jonathan P.; Oliver, James M.; Vella, Dominic
Abstract:
© © 2015 Cambridge University PressA. We consider the inertia-dominated rise of a meniscus around a vertical circular cylinder. Previous experiments and scaling analysis suggest that the height of the meniscus, h-{m}, grows with the time following the initiation of rise, t, like h-{m}\propto t^{1/2}. This is in contrast to the rise on a vertical plate, which obeys the classic capillary-inertia scaling h-{m}\propto t^{2/3}. We highlight a subtlety in the scaling analysis that yielded h-{m}\propto t^{1/2} and investigate the consequences of this subtlety. We develop a potential flow model of the dynamic problem, which we solve using the finite element method. Our numerical results agree well with previous experiments but suggest that the correct early time behaviour is, in fact, h-{m}\propto t^{2/3}. Furthermore, we show that at intermediate times the dynamic rise of the meniscus is governed by two parameters: the contact angle and the cylinder radius measured relative to the capillary length scale, t^{2/3}. This result allows us to collapse previous experimental results with different cylinder radii (but similar static contact angles) onto a single master curve.
Citation:
O’Kiely D, Whiteley JP, Oliver JM, Vella D (2015) Inertial rise of a meniscus on a vertical cylinder. Journal of Fluid Mechanics 768. Available: http://dx.doi.org/10.1017/jfm.2015.89.
Publisher:
Cambridge University Press (CUP)
Journal:
Journal of Fluid Mechanics
KAUST Grant Number:
KUKC1-013-04
Issue Date:
3-Mar-2015
DOI:
10.1017/jfm.2015.89
Type:
Article
ISSN:
0022-1120; 1469-7645
Sponsors:
This publication is based on work supported in part by Award No KUKC1-013-04, made by King Abdullah University of Science and Technology (KAUST). We are grateful to the participants of the Oxford-Princeton Collaborative Workshop Initiative 2014 for their comments on this work and to C. Clanet for sharing the original experimental images in figure 1.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorO’Kiely, Doireannen
dc.contributor.authorWhiteley, Jonathan P.en
dc.contributor.authorOliver, James M.en
dc.contributor.authorVella, Dominicen
dc.date.accessioned2016-02-25T13:33:10Zen
dc.date.available2016-02-25T13:33:10Zen
dc.date.issued2015-03-03en
dc.identifier.citationO’Kiely D, Whiteley JP, Oliver JM, Vella D (2015) Inertial rise of a meniscus on a vertical cylinder. Journal of Fluid Mechanics 768. Available: http://dx.doi.org/10.1017/jfm.2015.89.en
dc.identifier.issn0022-1120en
dc.identifier.issn1469-7645en
dc.identifier.doi10.1017/jfm.2015.89en
dc.identifier.urihttp://hdl.handle.net/10754/598615en
dc.description.abstract© © 2015 Cambridge University PressA. We consider the inertia-dominated rise of a meniscus around a vertical circular cylinder. Previous experiments and scaling analysis suggest that the height of the meniscus, h-{m}, grows with the time following the initiation of rise, t, like h-{m}\propto t^{1/2}. This is in contrast to the rise on a vertical plate, which obeys the classic capillary-inertia scaling h-{m}\propto t^{2/3}. We highlight a subtlety in the scaling analysis that yielded h-{m}\propto t^{1/2} and investigate the consequences of this subtlety. We develop a potential flow model of the dynamic problem, which we solve using the finite element method. Our numerical results agree well with previous experiments but suggest that the correct early time behaviour is, in fact, h-{m}\propto t^{2/3}. Furthermore, we show that at intermediate times the dynamic rise of the meniscus is governed by two parameters: the contact angle and the cylinder radius measured relative to the capillary length scale, t^{2/3}. This result allows us to collapse previous experimental results with different cylinder radii (but similar static contact angles) onto a single master curve.en
dc.description.sponsorshipThis publication is based on work supported in part by Award No KUKC1-013-04, made by King Abdullah University of Science and Technology (KAUST). We are grateful to the participants of the Oxford-Princeton Collaborative Workshop Initiative 2014 for their comments on this work and to C. Clanet for sharing the original experimental images in figure 1.en
dc.publisherCambridge University Press (CUP)en
dc.subjectcapillary flowsen
dc.subjectinterfacial flows (free surface)en
dc.titleInertial rise of a meniscus on a vertical cylinderen
dc.typeArticleen
dc.identifier.journalJournal of Fluid Mechanicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUKC1-013-04en
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