Type
ArticleKAUST Grant Number
KUKC1-013-04Date
2015-03-03Online Publication Date
2015-03-03Print Publication Date
2015-04Permanent link to this record
http://hdl.handle.net/10754/598615
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© © 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 Mechanicsae974a485f413a2113503eed53cd6c53
10.1017/jfm.2015.89