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    Inertial rise of a meniscus on a vertical cylinder

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    Type
    Article
    Authors
    O’Kiely, Doireann
    Whiteley, Jonathan P.
    Oliver, James M.
    Vella, Dominic
    KAUST Grant Number
    KUKC1-013-04
    Date
    2015-03-03
    Online Publication Date
    2015-03-03
    Print Publication Date
    2015-04
    Permanent link to this record
    http://hdl.handle.net/10754/598615
    
    Metadata
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    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.
    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.
    Publisher
    Cambridge University Press (CUP)
    Journal
    Journal of Fluid Mechanics
    DOI
    10.1017/jfm.2015.89
    ae974a485f413a2113503eed53cd6c53
    10.1017/jfm.2015.89
    Scopus Count
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    Publications Acknowledging KAUST Support

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