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Confinements regulate capillary instabilities of fluid threads

Published online by Cambridge University Press:  28 June 2019

Xiaodong Chen ,
Chundong Xue  and
Guoqing Hu Open the ORCID record for Guoqing Hu [Opens in a new window]
Xiaodong Chen
Affiliation:
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
Chundong Xue
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
Guoqing Hu*
Affiliation:
Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
*
†Email addresses for correspondence: ghu@zju.edu.cn, guoqing.hu@imech.ac.cn
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Abstract

We study the breakup of confined fluid threads at low flow rates to understand instability mechanisms. To determine the critical conditions between the earlier quasi-stable necking stage and the later unstable collapse stage, simulations and experiments are designed to operate at an extremely low flow rate. The critical mean radii at the neck centres are identified by the stop-flow method for elementary microfluidic configurations. Two distinct origins of capillary instabilities are revealed for different confinement situations. One is the gradient of capillary pressure induced by the confinements of geometry and external flow, whereas the other is the competition between the capillary pressure and internal pressure determined by the confinements.

JFM classification

Drops and Bubbles: Breakup/coalescence Micro-/Nano-fluid dynamics: Microfluidics Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 816 - 834
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Copyright
© 2019 Cambridge University Press 

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Footnotes

‡

The original version of this article was published with an incorrect author name. A notice detailing this has been published and the error rectified in the online and print PDF and HTML copies.

References

Anna, S. L. 2016 Droplets and bubbles in microfluidic devices. Annu. Rev. Fluid Mech. 48, 285–309.Google Scholar
Beresnev, I. A., Li, W. Q. & Vigil, R. D. 2009 Condition for break-up of non-wetting fluids in sinusoidally constricted capillary channels. Trans. Porous Med. 80 (3), 581–604.Google Scholar
Bhat, P. P., Appathurai, S., Harris, M. T., Pasquali, M., McKinley, G. H. & Basaran, O. A. 2010 Formation of beads-on-a-string structures during break-up of viscoelastic filaments. Nat. Phys. 6 (8), 625–631.Google Scholar
Blanchette, F. & Bigioni, T. P. 2006 Partial coalescence of drops at liquid interfaces. Nat. Phys. 2 (4), 254–257.Google Scholar
Brakke, K. A. 1992 The surface evolver. Exp. Math. 1 (2), 141–165.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10 (2), 166–188.Google Scholar
Chen, X., Ma, D., Yang, V. & Popinet, S. 2013 High-fidelity simulations of impinging jet atomization. Atomiz. Sprays 23 (12), 1079–1101.Google Scholar
Chen, X., Xue, C., Zhang, L., Hu, G., Jiang, X. & Sun, J. 2014 Inertial migration of deformable droplets in a microchannel. Phys. Fluids 26 (11), 112003.Google Scholar
Chen, X. & Yang, V. 2014 Thickness-based adaptive mesh refinement methods for multi-phase flow simulations with thin regions. J. Comput. Phys. 269, 22–39.Google Scholar
Dangla, R., Fradet, E., Lopez, Y. & Baroud, C. N. 2013 The physical mechanisms of step emulsification. J. Phys. D: Appl. Phys. 46 (11), 114003.Google Scholar
De Menech, M., Garstecki, P., Jousse, F. & Stone, H. A. 2008 Transition from squeezing to dripping in a microfluidic T-shaped junction. J. Fluid Mech. 595, 141–161.Google Scholar
Delaunay, C. H. 1841 Sur la surface de révolution dont la courbure moyenne est constante. J. Math. Pures Appl. 16, 309–314.Google Scholar
Dollet, B., van Hoeve, W., Raven, J. P., Marmottant, P. & Versluis, M. 2008 Role of the channel geometry on the bubble pinch-off in flow-focusing devices. Phys. Rev. Lett. 100 (3), 034504.Google Scholar
Duclaux, V., Clanet, C. & Quere, D. 2006 The effects of gravity on the capillary instability in tubes. J. Fluid Mech. 556, 217–226.Google Scholar
Eggers, J., Fontelos, M. A., Leppinen, D. & Snoeijer, J. H. 2007 Theory of the collapsing axisymmetric cavity. Phys. Rev. Lett. 98 (9), 094502.Google Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71 (3), 036601.Google Scholar
Garstecki, P., Stone, H. A. & Whitesides, G. M. 2005 Mechanism for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions. Phys. Rev. Lett. 94 (16), 164501.Google Scholar
Ghorbanian, S., Qasaimeh, M. A. & Juncker, D.2010 Rapid prototyping of branched microfluidics in PDMS using capillaries. http://blogs.rsc.org/chipsandtips/2010/05/03/, [Accessed 22-May-2015].Google Scholar
Gordillo, J. M., Sevilla, A., Rodriguez-Rodriguez, J. & Martinez-Bazan, C. 2005 Axisymmetric bubble pinch-off at high Reynolds numbers. Phys. Rev. Lett. 95 (19), 194501.Google Scholar
Hoang, D. A., Portela, L. M., Kleijn, C. R., Kreutzer, M. T. & van Steijn, V. 2013 Dynamics of droplet breakup in a T-junction. J. Fluid Mech. 717, R4.Google Scholar
van Hoeve, W., Dollet, B., Versluis, M. & Lohse, D. 2011 Microbubble formation and pinch-off scaling exponent in flow-focusing devices. Phys. Fluids 23 (9), 092001.Google Scholar
van Hoeve, W., Gekle, S., Snoeijer, J. H., Versluis, M. L., Brenner, M. P. & Lohse, D. 2010 Breakup of diminutive Rayleigh jets. Phys. Fluids 22 (12), 122003.Google Scholar
Jullien, M. C., Ching, M. J. T. M., Cohen, C., Menetrier, L. & Tabeling, P. 2009 Droplet breakup in microfluidic T-junctions at small capillary numbers. Phys. Fluids 21 (7), 072001.Google Scholar
Link, D. R., Anna, S. L., Weitz, D. A. & Stone, H. A. 2004 Geometrically mediated breakup of drops in microfluidic devices. Phys. Rev. Lett. 92 (5), 054503.Google Scholar
Olbricht, W. L. 1996 Pore-scale prototypes of multiphase flow in porous media. Annu. Rev. Fluid Mech. 28 (1), 187–213.Google Scholar
Persistence of Vision Pty. Ltd, 2013 Persistence of vision raytracer (version 3.7.0),http://www.povray.org/.Google Scholar
Plateau, J. 1873 Experimental and Theoretical Steady State of Liquids Subjected to nothing but Molecular Forces. Gauthiers-Villars.Google Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228 (16), 5838–5866.Google Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. 1 (1), 4–13.Google Scholar
Roof, J. G. 1970 Snap-off of oil droplets in water-wet pores. Soc. Petrol. Engng J. 10 (1), 85–90.Google Scholar
Shui, L. L., Mugele, F., van den Berg, A. & Eijkel, J. C. T. 2008 Geometry-controlled droplet generation in head-on microfluidic devices. Appl. Phys. Lett. 93 (15), 153113.Google Scholar
Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77 (3), 977–1026.Google Scholar
van Steijn, V., Kleijn, C. R. & Kreutzer, M. T. 2009 Flows around confined bubbles and their importance in triggering pinch-off. Phys. Rev. Lett. 103 (21), 214501.Google Scholar
Stone, H. A., Bentley, B. J. & Leal, L. G. 1986 An experimental study of transient effects in the breakup of viscous drops. J. Fluid Mech. 173, 131–158.Google Scholar
Tagawa, Y., Oudalov, N., Visser, C. W., Peters, I. R., van der Meer, D., Sun, C., Prosperetti, A. & Lohse, D. 2012 Highly focused supersonic microjets. Phys. Rev. X 2 (3), 031002.Google Scholar
Taylor, G. I. 1961 Deposition of a viscous fluid on the wall of a tube. J. Fluid Mech. 10 (2), 161–165.Google Scholar
Wong, H., Radke, C. J. & Morris, S. 1995 The motion of long bubbles in polygonal capillaries. Part 1. Thin films. J. Fluid Mech. 292, 71–94.Google Scholar

Chen et al. supplementary movie 1

Interfacial evolution before the critical moment from experiments using the stop-flow method in figure 4(c).

Download Chen et al. supplementary movie 1(Video)
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Chen et al. supplementary movie 2

Interfacial evolution after the critical moment from experiments using the stop-flow method in figure 4(c).

Download Chen et al. supplementary movie 2(Video)
Video 470.3 KB

Chen et al. supplementary movie 3

Interfacial evolution before the critical moment from experiments using the stop-flow method in figure 10(c).

Download Chen et al. supplementary movie 3(Video)
Video 452.9 KB

Chen et al. supplementary movie 4

Interfacial evolution after the critical moment from experiments using the stop-flow method in figure 10(c).

Download Chen et al. supplementary movie 4(Video)
Video 454.3 KB
Supplementary material: File

Chen et al. supplementary material

Supplementary material

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