×

Dynamics of droplet breakup in a T-junction. (English) Zbl 1284.76371

Summary: 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.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] DOI: 10.1017/S0022112095001443 · Zbl 0843.76018 · doi:10.1017/S0022112095001443
[2] DOI: 10.1063/1.3549266 · Zbl 1308.76206 · doi:10.1063/1.3549266
[3] DOI: 10.1098/rspa.1934.0169 · doi:10.1098/rspa.1934.0169
[4] DOI: 10.1103/PhysRevLett.108.264502 · doi:10.1103/PhysRevLett.108.264502
[5] DOI: 10.1088/0022-3727/12/9/009 · doi:10.1088/0022-3727/12/9/009
[6] DOI: 10.1063/1.3170983 · Zbl 1183.76266 · doi:10.1063/1.3170983
[7] DOI: 10.1017/S0022112089000194 · doi:10.1017/S0022112089000194
[8] AIP Conference Proceedings 1479 pp 86– (2012)
[9] DOI: 10.1017/S0022112086001118 · doi:10.1017/S0022112086001118
[10] DOI: 10.1016/j.ces.2011.06.003 · doi:10.1016/j.ces.2011.06.003
[11] DOI: 10.1103/PhysRevLett.103.214501 · doi:10.1103/PhysRevLett.103.214501
[12] DOI: 10.1063/1.868540 · Zbl 1023.76526 · doi:10.1063/1.868540
[13] DOI: 10.1088/0034-4885/71/3/036601 · doi:10.1088/0034-4885/71/3/036601
[14] DOI: 10.1103/PhysRevLett.92.054503 · doi:10.1103/PhysRevLett.92.054503
[15] DOI: 10.1017/S0022112061000160 · Zbl 0096.20702 · doi:10.1017/S0022112061000160
[16] DOI: 10.1063/1.3078515 · Zbl 1183.76302 · doi:10.1063/1.3078515
[17] DOI: 10.1103/PhysRevE.79.036306 · doi:10.1103/PhysRevE.79.036306
[18] DOI: 10.1140/epje/i2011-11078-7 · doi:10.1140/epje/i2011-11078-7
[19] DOI: 10.1063/1.168744 · doi:10.1063/1.168744
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.