Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T21:47:29.110Z Has data issue: false hasContentIssue false
  • English
  • Français

Capillary plugs in horizontal rectangular tubes with non-uniform contact angles

Published online by Cambridge University Press:  19 August 2020

Chengwei Zhu ,
Xinping Zhou Open the ORCID record for Xinping Zhou [Opens in a new window]  and
Gang Zhang
Chengwei Zhu
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan430074, PR China Department of Mechanics, Huazhong University of Science and Technology, Wuhan430074, PR China
Xinping Zhou*
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan430074, PR China
Gang Zhang
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan430074, PR China Department of Mechanics, Huazhong University of Science and Technology, Wuhan430074, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The aim of this paper is to make the formation of liquid plugs as difficult as possible in liquid partially filling a horizontal rectangular tube in a downward gravity field by setting the walls to have differing contact angles. Manning et al.'s method (J. Fluid Mech., vol. 682, 2011, pp. 397–414), extended from Concus–Finn theory, is applied to the existence of capillary plugs in rectangular tubes. The critical Bond numbers ($B_c$) determining the existence of capillary plugs in a rectangular tube are studied for different settings of the non-uniform contact angles, and the influence of the aspect ratio (defined as the width-to-height ratio) of the rectangular cross-section on $B_c$ is examined. Compared to the maximum and minimum of $B_c$ reached for uniform contact angles, the maximum of $B_c$ is higher, which is attained for the bottom contact angle $\gamma _2=135^{\circ }$, the top contact angle $\gamma _4=45^{\circ }$, and the side contact angles $\gamma _1=\gamma _3=90^{\circ }$; while the minimum is considerably lowered to zero, which is reached for $\gamma _1=\gamma _2=45^{\circ }$ and $\gamma _3=\gamma _4=135^{\circ }$. The aspect ratio of the rectangle has no influence on the maximum and minimum $B_c$ for a tube with walls of differing contact angles. There is only one non-occluded liquid topology in a square, while two topologies may occur in a rectangle with aspect ratio 2, and the transition between the two topologies is accompanied by a kink of the curve of $B_c$. Optimization of the non-uniform contact angles can facilitate or effectively block the capillary plugs in rectangular tubes regardless of the aspect ratios.

JFM classification

Interfacial Flows (free surface): Capillary flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , R1
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bhatnagar, R. & Finn, R. 2016 On the capillarity equation in two dimensions. J. Math. Fluid Mech. 18, 731–738.CrossRefGoogle Scholar
Brakke, K. A. 1992 The surface evolver. Exp. Maths 1, 141–165.CrossRefGoogle Scholar
Chen, Y. & Collicott, S. H. 2006 Study of wetting in an asymmetrical vane–wall gap in propellant tanks. AIAA J. 44, 859–867.CrossRefGoogle Scholar
Concus, P. & Finn, R. 1969 On the behavior of a capillary surface in a wedge. Proc. Natl Acad. Sci. 63, 292–299.10.1073/pnas.63.2.292CrossRefGoogle Scholar
De Lazzer, A., Langbein, D., Dreyer, M. & Rath, H. J. 1996 Mean curvature of liquid surfaces in cylindrical containers of arbitrary cross-section. Microgravity Sci. Technol. 9, 208–219.Google Scholar
De Lazzer, A., Stange, M., Dreyer, M. & Rath, H. 2003 Influence of lateral acceleration on capillary interfaces between parallel plates. Microgravity Sci. Technol. 14, 3–20.10.1007/BF02870942CrossRefGoogle Scholar
Finn, R. 1986 Equilibrium Capillary Surfaces. Springer.CrossRefGoogle Scholar
Gravesen, P., Branebjerg, J. & Jensen, O. S. 1993 Microfluidics – a review. J. Micromech. Microengng 3, 168–182.CrossRefGoogle Scholar
Herescu, A. & Allen, J. S. 2012 The influence of channel wettability and geometry on water plug formation and drop location in a proton exchange membrane fuel cell flow field. J. Power Sources 216, 337–344.CrossRefGoogle Scholar
Manning, R. E. & Collicott, S. H. 2015 Existence of static capillary plugs in horizontal rectangular cylinders. Microfluid Nanofluid 19, 1159–1168.CrossRefGoogle Scholar
Manning, R., Collicott, S. & Finn, R. 2011 Occlusion criteria in tubes under transverse body forces. J. Fluid Mech. 682, 397–414.CrossRefGoogle Scholar
Pour, N. B. & Thiessen, D. B. 2019 Equilibrium configurations of drops or bubbles in an eccentric annulus. J. Fluid Mech. 863, 364–385.CrossRefGoogle Scholar
Rascón, C., Parry, A. O. & Aarts, D. G. A. L. 2016 Geometry-induced capillary emptying. Proc. Natl. Acad. Sci. 113, 12633–12636.CrossRefGoogle ScholarPubMed
Smedley, G. 1990 Containments for liquids at zero gravity. Microgravity Sci. Technol. 3, 13–23.Google Scholar
Zhang, F. Y., Yang, X. G. & Wang, C. Y. 2006 Liquid water removal from a polymer electrolyte fuel cell. J. Electrochem. Soc. 153, A225–A232.CrossRefGoogle Scholar
Zhou, X. & Zhang, F. 2017 Bifurcation of a partially immersed plate between two parallel plates. J. Fluid Mech. 817, 122–137.CrossRefGoogle Scholar