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Universality of capillary rising in corners

Published online by Cambridge University Press:  11 August 2020

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

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 $n$.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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