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Dynamics of droplet breakup in a T-junction

Published online by Cambridge University Press:  07 February 2013

D. A. Hoang ,
L. M. Portela ,
C. R. Kleijn ,
M. T. Kreutzer  and
V. van Steijn
D. A. Hoang
Affiliation:
Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628BL, Delft, The Netherlands
L. M. Portela
Affiliation:
Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628BL, Delft, The Netherlands
C. R. Kleijn
Affiliation:
Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628BL, Delft, The Netherlands
M. T. Kreutzer*
Affiliation:
Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628BL, Delft, The Netherlands
V. van Steijn
Affiliation:
Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628BL, Delft, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

The breakup of droplets due to creeping motion in a confined microchannel geometry is studied using three-dimensional numerical simulations. Analogously to unconfined droplets, there exist two distinct breakup phases: (i) a quasi-steady droplet deformation driven by the externally applied flow; and (ii) a surface-tension-driven three-dimensional rapid pinching that is independent of the externally applied flow. In the first phase, the droplet relaxes back to its original shape if the externally applied flow stops; if the second phase is reached, the droplet will always break. Also analogously to unconfined droplets, there exist two distinct critical conditions: (i) one that determines whether the droplet reaches the second phase and breaks, or it reaches a steady shape and does not break; and (ii) one that determines when the rapid autonomous pinching starts. We analyse the second phase using stop–flow simulations, which reveal that the mechanism responsible for the autonomous breakup is similar to the end-pinching mechanism for unconfined droplets reported in the literature: the rapid pinching starts when, in the channel mid-plane, the curvature at the neck becomes larger than the curvature everywhere else. The same critical condition is observed in simulations in which we do not stop the flow: the breakup dynamics and the neck thickness corresponding to the crossover of curvatures are similar in both cases. This critical neck thickness depends strongly on the aspect ratio, and, unlike unconfined flows, depends only weakly on the capillary number and the viscosity contrast between the fluids inside and outside the droplet.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops and Bubbles Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Micro-/Nano-fluid dynamics: Microfluidics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 717 , 25 February 2013 , R4
Copyright
©2013 Cambridge University Press

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References

Afkhami, S., Leshansky, A. M. & Renardy, Y. 2011 Numerical investigation of elongated drops in a microfluidic t-junction. Phys. Fluids 23 (2), 022002.Google Scholar
Bedram, A. & Moosavi, A. 2011 Droplet breakup in an asymmetric microfluidic T junction. Eur. Phys. J. E 34 (8), 78.Google Scholar
Berberovic, E., van Hinsberg, N. P., Jakirlić, S., Roisman, I. V. & Tropea, C. 2009 Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution. Phys. Rev. E 79 (3), 036306.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10 (2), 166–188.Google Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71 (3), 036601.Google Scholar
Fu, T., Ma, Y., Funfschilling, D. & Li, H. Z. 2011 Dynamics of bubble breakup in a microfluidic T-junction divergence. Chem. Engng Sci. 66 (18), 4184–4195.Google Scholar
Hoang, D. A., van Steijn, V., Portela, L. M., Kreutzer, M. T. & Kleijn, C. R. 2012 Modelling of low-capillary number segmented flows in microchannels using openfoam. AIP Conference Proceedings 1479 (1), 86–89.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
Leshansky, A. M., Afkhami, S., Jullien, M.-C. & Tabeling, P. 2012 Obstructed breakup of slender drops in a microfluidic T junction. Phys. Rev. Lett. 108, 264502.Google Scholar
Leshansky, A. M. & Pismen, L. M. 2009 Breakup of drops in a microfluidic T junction. Phys. Fluids 21 (2), 023303.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
Papageorgiou, D. T. 1995 On the breakup of viscous liquid threads. Phys. Fluids 7 (7), 1529–1544.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, 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
Stone, H. A. & Leal, L. G. 1989 Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399–427.Google Scholar
Tanner, L. H. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 12 (9), 1473.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146 (858), 0501–0523.Google Scholar
Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys. 12 (6), 620–631.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