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Partial coalescence from bubbles to drops

Published online by Cambridge University Press:  07 October 2015

F. H. Zhang ,
M.-J. Thoraval Open the ORCID record for M.-J. Thoraval [Opens in a new window] ,
S. T. Thoroddsen Open the ORCID record for S. T. Thoroddsen [Opens in a new window]  and
P. Taborek
F. H. Zhang
Affiliation:
Division of Physical Sciences and Engineering, and Clean Combustion Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
M.-J. Thoraval
Affiliation:
Division of Physical Sciences and Engineering, and Clean Combustion Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia Physics of Fluids Group, Faculty of Science and Technology, MESA+ Institute, University of Twente, 7500 AE Enschede, The Netherlands
S. T. Thoroddsen*
Affiliation:
Division of Physical Sciences and Engineering, and Clean Combustion Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
P. Taborek
Affiliation:
Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA
*
†Email address for correspondence: [email protected]
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Abstract

The coalescence of drops is a fundamental process in the coarsening of emulsions. However, counter-intuitively, this coalescence process can produce a satellite, approximately half the size of the original drop, which is detrimental to the overall coarsening. This also occurs during the coalescence of bubbles, while the resulting satellite is much smaller, approximately 10 %. To understand this difference, we have conducted a set of coalescence experiments using xenon bubbles inside a pressure chamber, where we can continuously raise the pressure from 1 up to 85 atm and thereby vary the density ratio between the inner and outer fluid, from 0.005 up to unity. Using high-speed video imaging, we observe a continuous increase in satellite size as the inner density is varied from the bubble to emulsion-droplet conditions, with the most rapid changes occurring as the bubble density grows up to 15 % of that of the surrounding liquid. We propose a model that successfully relates the satellite size to the capillary wave mode responsible for its pinch-off and the overall deformations from the drainage. The wavelength of the primary wave changes during its travel to the apex, with the instantaneous speed adjusting to the local wavelength. By estimating the travel time of this wave mode on the bubble surface, we also show that the model is consistent with the experiments. This wavenumber is determined by both the global drainage as well as the interface shapes during the rapid coalescence in the neck connecting the two drops or bubbles. The rate of drainage is shown to scale with the density of the inner fluid. Empirically, we find that the pinch-off occurs when 60 % of the bubble fluid has drained from it. Numerical simulations using the volume-of-fluid method with dynamic adaptive grid refinement can reproduce these dynamics, as well as show the associated vortical structure and stirring of the coalescing fluid masses. Enhanced stirring is observed for cases with second-stage pinch-offs. Numerous sub-satellites are observed when the length of the top protrusion of the drop exceeds the Rayleigh instability wavelength. We also find a parameter regime where the focusing of more than one capillary wave can pinch-off satellites. One realization shows a sequence of three pinch-offs, where the middle one pinches off a toroidal bubble.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops and Bubbles Complex Fluids: Emulsions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 782 , 10 November 2015 , pp. 209 - 239
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© 2015 Cambridge University Press 

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Zhang et al. supplementary movie

High-speed video of partial coalescence inside the pressure chamber for density ratio of 0.03. Corresponding to Figure 3(a). Video frame rate is about 125 kfps.

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Video 42.2 KB

Zhang et al. supplementary movie

High-speed video of partial coalescence inside the pressure chamber for density ratio of 0.13. Corresponding to Figure 3(b). Video frame rate is about 125 kfps.

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Video 19.6 KB

Zhang et al. supplementary movie

High-speed video of partial coalescence inside the pressure chamber for density ratio of 0.35. Corresponding to Figure 3(c). Video frame rate is about 64 kfps.

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Video 23.9 KB

Zhang et al. supplementary movie

High-speed video of partial coalescence inside the pressure chamber for density ratio of 0.71. Corresponding to Figure 3(d). Video frame rate is about 81 kfps.

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Video 60.7 KB

Zhang et al. supplementary movie

Numerical simulation of partial coalescence, comparing the dynamics for different density ratios, of 0.03, 0.13, 0.35 and 0.71. Corresponds to Figure 3.

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Video 6 MB

Zhang et al. supplementary movie

Numerical simulation of partial coalescence and resulting vorticity structures inside the father bubble, comparing the dynamics for different density ratios, of 0.03, 0.13, 0.35 and 0.71. Same conditions as in Figure 3.

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Video 15.8 MB

Zhang et al. supplementary movie

Numerical simulation of partial coalescence for a range of density ratios, $D=\rho_i/\rho_o =$~0.001 (black), 0.015 (green), 0.050 (red), 0.100 (blue), 0.300 (magenta), and 1.000 (cyan). , Corresponds to Figure 5(a).

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Video 16.9 MB

Zhang et al. supplementary movie

Formation of multiple satellites. Corresponding to Figure 15(a). Frame rate is about 66 kfps.

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Video 826.5 KB

Zhang et al. supplementary movie

Formation of multiple satellites, from focusing of subsequent capillary waves. Corresponding to Figure 17(a). Frame rate is about 129 kfps.

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Video 328.3 KB