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Universality of capillary rising in corners

Published online by Cambridge University Press:  11 August 2020

Jiajia Zhou Open the ORCID record for Jiajia Zhou [Opens in a new window]  and
Masao Doi
Jiajia Zhou*
Affiliation:
Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education, School of Chemistry, Beihang University, Beijing100191, China Center of Soft Matter Physics and its Applications, Beihang University, Beijing100191, China
Masao Doi*
Affiliation:
Center of Soft Matter Physics and its Applications, Beihang University, Beijing100191, China
*
†Email addresses for correspondence: jjzhou@buaa.edu.cn, masao.doi@buaa.edu.cn
†Email addresses for correspondence: jjzhou@buaa.edu.cn, masao.doi@buaa.edu.cn
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Abstract

We study the dynamics of viscous capillary rising in small corners between two curved walls described by a function $y=cx^n$ with $n \ge 1$. Using the Onsager principle, we derive a partial differential equation that describes the time evolution of the meniscus profile. By solving the equation both numerically and analytically, we show that the capillary rising dynamics is quite universal. Our theory explains the surprising finding by Ponomarenko et al. (J. Fluid Mech., vol. 666, 2011, pp. 146–154) that the time dependence of the height not only obeys the universal power-law of $t^{1/3}$, but also that the prefactor is almost independent of $n$.

JFM classification

Interfacial Flows (free surface): Capillary flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A29
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Clanet, C. & Quéré, D. 2002 Onset of menisci. J. Fluid Mech. 460, 131–149.CrossRefGoogle Scholar
Concus, P. & Finn, R. 1969 On the behavior of a capillary surface in a wedge. Proc. Natl Acad. Sci. USA 63, 292–299.CrossRefGoogle Scholar
Doi, M. 2013 Soft Matter Physics. Oxford University Press.CrossRefGoogle Scholar
Dong, M. & Chatzis, I. 1995 The imbibition and flow of a wetting liquid along the corners of a square capillary tube. J. Colloid Interface Sci. 172, 278–288.CrossRefGoogle Scholar
Finn, R. 1999 Capillary surface interfaces. Not. AMS 46, 770–781.Google Scholar
Finn, R. 2002 Some properties of capillary surfaces. Milan J. Maths 70, 1–23.CrossRefGoogle Scholar
de Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena. Springer.CrossRefGoogle Scholar
Hauksbee, F. 1710 X. An account of an experiment touching the ascent of water between two glass planes, in an hyperbolick figure. Phil. Trans. R. Soc. Lond. 27, 539–540.Google Scholar
Higuera, F. J., Medina, A. & Liñán, A. 2008 Capillary rise of a liquid between two vertical plates making a small angle. Phys. Fluids 20, 102102.CrossRefGoogle Scholar
Langbein, D. 1990 The shape and stability of liquid menisci at solid edges. J. Fluid Mech. 213, 251–265.CrossRefGoogle Scholar
Lucas, R. 1918 Ueber das zeitgesetz des kapillaren aufstiegs von flüssigkeiten. Kolloid Z. 23, 15–22.CrossRefGoogle Scholar
Onsager, L. 1931 a Reciprocal relations in irreversible processes. I. Phys. Rev. 37, 405–426.CrossRefGoogle Scholar
Onsager, L. 1931 b Reciprocal relations in irreversible processes. II. Phys. Rev. 38, 2265–2279.CrossRefGoogle Scholar
Ponomarenko, A., Quéré, D. & Clanet, C. 2011 A universal law for capillary rise in corners. J. Fluid Mech. 666, 146–154.CrossRefGoogle Scholar
Quéré, D. 1997 Inertial capillarity. Europhys. Lett. 39, 533–538.CrossRefGoogle Scholar
Tang, L.-H. & Tang, Y. 1994 Capillary rise in tubes with sharp grooves. J. Phys. II 4, 881–890.Google Scholar
Taylor, B. 1710 IX. Part of a letter from Mr. Brook Taylor, F. R. S. to Dr. Hans Sloane R. S. Secr. concerning the ascent of water between two glass planes. Phil. Trans. R. Soc. Lond. 27, 538–538.Google Scholar
Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273–283.CrossRefGoogle Scholar
Weislogel, M. M. 2001 Capillary flow in interior corners: the infinite column. Phys. Fluids 13, 3101.CrossRefGoogle Scholar
Weislogel, M. M., Baker, J. A. & Jenson, R. M. 2011 Quasi-steady capillarity-driven flows in slender containers with interior edges. J. Fluid Mech. 685, 271–305.CrossRefGoogle Scholar
Weislogel, M. M. & Lichter, S. 1998 Capillary flow in an interior corner. J. Fluid Mech. 373, 349–378.CrossRefGoogle Scholar
Yu, T., Jiang, Y., Zhou, J. & Doi, M. 2019 Dynamics of Taylor rising. Langmuir 35, 5183–5190.Google Scholar