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Eccentricity effect on horizontal capillary emptying

Published online by Cambridge University Press:  29 July 2022

Dongwen Tan Open the ORCID record for Dongwen Tan [Opens in a new window] ,
Xinping Zhou Open the ORCID record for Xinping Zhou [Opens in a new window] ,
Gang Zhang Open the ORCID record for Gang Zhang [Opens in a new window] ,
Chengwei Zhu  and
Chenyu Fu Open the ORCID record for Chenyu Fu [Opens in a new window]
Dongwen Tan
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China
Xinping Zhou*
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, PR China
Gang Zhang
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, PR China
Chengwei Zhu
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, PR China
Chenyu Fu
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China
*
†Email address for correspondence: xpzhou08@hust.edu.cn
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Abstract

This paper theoretically studies the effect of eccentricity on the conditions of capillary emptying (determined by critical Bond number) in a horizontal annular tube in a downward gravity field. Experiments are conducted to compare with theoretical results. We find that non-horizontal eccentricity can lead to the occurrence of a re-entrant liquid-state transition (from liquid non-occlusion to liquid plug to liquid non-occlusion) with increasing Bond number, when the eccentricity (e) or inner-to-outer radius ratio (χ) is large enough, and the two liquid non-occlusion states correspond to different emptying mechanisms dominated by the gravity effect and the ‘wedge’ effect, respectively. Existence of the re-entrant transition is accompanied by occurrence of unconditional liquid non-occlusion at large enough or small enough contact angles regardless of Bond numbers. The critical Bond numbers at a contact angle γ for vertical upward eccentricity are equal to those at a contact angle 180° − γ for vertical downward eccentricity. In a parameter space (γ, e/(1 − χ)), the region with the re-entrant transition becomes larger with the eccentric angle varying from 0° (horizontal) to 90° (vertical). Optimization of geometrical parameters and inner and outer contact angles can lead to better effect of capillary emptying. This paper provides a very effective scheme for removing a liquid blockage from a capillary in optofluidics/microfluidics.

JFM classification

Interfacial Flows (free surface): Capillary flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 946 , 10 September 2022 , A7
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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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
Carrasco-Teja, M., Frigaard, I.A., Seymour, B.R. & Storey, S. 2008 Viscoplastic fluid displacements in horizontal narrow eccentric annuli: stratification and travelling wave solutions. J. Fluid Mech. 605, 293–327.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
Choueiri, G.H. & Tavoularis, S. 2015 Experimental investigation of flow development and gap vortex street in an eccentric annular channel. Part 2. Effects of inlet conditions, diameter ratio, eccentricity and Reynolds number. J. Fluid Mech. 768, 294–315.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
Finn, R. 1986 Equilibrium Capillary Surfaces. Springer-Verlag.CrossRefGoogle Scholar
Lamarche-Gagnon, M-É & Tavoularis, S. 2021 Further experiments and analysis on flow instability in eccentric annular channels. J. Fluid Mech. 915, A34.CrossRefGoogle Scholar
Lee, C.C., Wu, A. & Li, M. 2020 Venous air embolism during neurosurgery. In Essentials of Neurosurgical Anesthesia & Critical Care: Strategies for Prevention, Early Detection, and Successful Management of Perioperative Complications, pp. 287–291. Springer International Publishing.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
Manning, R.E. & Collicott, S.H. 2015 Existence of static capillary plugs in horizontal rectangular cylinders. Microfluid Nanofluid 19, 1159–1168.CrossRefGoogle Scholar
Nikitin, N., Wang, H. & Chernyshenko, S. 2009 Turbulent flow and heat transfer in eccentric annulus. J. Fluid Mech. 638, 95–116.CrossRefGoogle Scholar
Parry, A.O., Rascón, C., Jamie, E.A.G. & Aarts, D.G.A.L. 2012 Capillary emptying and shortrange wetting. Phys. Rev. Lett. 108 (24), 246101.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
Protiere, S., Duprat, C. & Stone, H.A. 2013 Wetting on two parallel fibers: drop to column transitions. Soft Matt. 9 (1), 271–276.CrossRefGoogle Scholar
Rascón, C., Parry, A.O. & Aarts, D.G.A.L. 2016 Geometry-induced capillary emptying. Proc. Natl Acad. Sci. USA 113, 12633–12636.CrossRefGoogle ScholarPubMed
Renteria, A. & Frigaard, I.A. 2020 Primary cementing of horizontal wells. Displacement flows in eccentric horizontal annuli. Part 1. Experiments. J. Fluid Mech. 905, A7.CrossRefGoogle Scholar
Reyssat, E. 2015 Capillary bridges between a plane and a cylindrical wall. J. Fluid Mech. 773, R1.CrossRefGoogle Scholar
Smedley, G. 1990 Containments for liquids at zero gravity. Microgravity Sci. Technol. 3, 13–23.Google Scholar
Verma, G., Saraj, C.S., Yadav, G., Singh, S.C. & Guo, C. 2020 Generalized emptying criteria for finite-lengthed capillary. Phys. Rev. Fluids 5, 112201(R).CrossRefGoogle 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
Zhou, X., Zhang, G., Zhu, C., Tan, D. & Fu, C. 2021 Inside rod induced horizontal capillary emptying. J. Fluid Mech. 924, A23.CrossRefGoogle Scholar
Zhu, C., Zhou, X. & Zhang, G. 2020 Capillary plugs in horizontal rectangular tubes with non-uniform contact angles. J. Fluid Mech. 901, R1.CrossRefGoogle Scholar