TY - JOUR

T1 - Inertial rise of a meniscus on a vertical cylinder

AU - O’Kiely, Doireann

AU - Whiteley, Jonathan P.

AU - Oliver, James M.

AU - Vella, Dominic

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUKC1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2015/3/3

Y1 - 2015/3/3

N2 - © © 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.

AB - © © 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.

UR - http://hdl.handle.net/10754/598615

UR - https://www.cambridge.org/core/product/identifier/S0022112015000890/type/journal_article

UR - http://www.scopus.com/inward/record.url?scp=84924048138&partnerID=8YFLogxK

U2 - 10.1017/jfm.2015.89

DO - 10.1017/jfm.2015.89

M3 - Article

VL - 768

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -