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Growth and breakup of ligaments in unsteady fragmentation

Published online by Cambridge University Press:  18 January 2021

Y. Wang Open the ORCID record for Y. Wang [Opens in a new window]  and
L. Bourouiba Open the ORCID record for L. Bourouiba [Opens in a new window]
Y. Wang
Affiliation:
The Fluid Dynamics of Disease Transmission Laboratory, Massachusetts Institute of Technology, Cambridge, MA02139, USA
L. Bourouiba*
Affiliation:
The Fluid Dynamics of Disease Transmission Laboratory, Massachusetts Institute of Technology, Cambridge, MA02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

We elucidate the physics underlying the birth, evolution and breakup of ligaments on a rim bounding an unsteady liquid sheet. This rim destabilizes into corrugations that can grow into ligaments, which in turn, break into secondary droplets via end-pinching. Combining experiments and theory, we show that not all corrugations can grow into ligaments. The number of corrugations is captured by linear instability coupled with nonlinear rim thickness self-adjustment ($\text {Bond number} = 1 \text { criterion}$, Wang et al. (Phys. Rev. Lett., vol. 120, 2018, 204503)) and scales as $N_c \sim We^{3/4}$ with Weber number, $We$. The number of ligaments scales as $N_{\ell } \sim We^{3/8}$. The growth of a ligament is governed by the competition between the constraint imposed by the geometry of the local rim–ligament junction; the local force balance including the fictitious force from the continuously decelerating rim; and the global rim mass conservation constraint. The temporal evolution of the average width of ligaments is predicted. Key to understanding the ligament population, a minimum distance between two corrugations is required to enable their actual transition into ligaments. By predicting this minimal distance, we derive the evolution of the number of ligaments. We show that droplets are shed, one at a time, following a chaotic dripping end-pinching regime independent of $We$. Finally, the number of droplets shed per unit of time decreases over time and scales as $S_d \sim We^{3/4}$; while the volume shed per unit of time increases over time and is independent of $We$. Theoretical predictions are validated without fitting parameters.

JFM classification

Drops and Bubbles: Aerosols/atomization Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A39
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Agbaglah, G. & Deegan, R. D. 2014 Growth and instability of the liquid rim in the crown splash regime. J. Fluid Mech. 752, 485–496.CrossRefGoogle Scholar
Agbaglah, G., Josserand, C. & Zaleski, S. 2013 Longitudinal instability of a liquid rim. Phys. Fluids 25 (2), 022103.CrossRefGoogle Scholar
Ambravaneswaran, B., Subramani, H. J., Phillips, S. D. & Basaran, O. A. 2004 Dripping-jetting transitions in a dripping faucet. Phys. Rev. Lett. 93, 034501.CrossRefGoogle Scholar
Bourouiba, L. 2020 The fluid dynamics of disease transmission. Annu. Rev. Fluid Mech. 53, 473–508.CrossRefGoogle Scholar
Bourouiba, L., Dehandschoewercker, E. & Bush, J. W. M. 2014 Violent expiratory events: on coughing and sneezing. J. Fluid Mech. 745, 537–563.CrossRefGoogle Scholar
Clanet, C. & Lasheras, J. C. 1999 Transition from dripping to jetting. J. Fluid Mech. 383, 307–326.CrossRefGoogle Scholar
Coullet, P., Mahadevan, L. & Riera, C. S. 2005 Hydrodynamical models for the chaotic dripping faucet. J. Fluid Mech. 526, 1–17.CrossRefGoogle Scholar
Deegan, R. D., Brunet, P. & Eggers, J. 2008 Complexities of splashing. Nonlinearity 21 (1), C1–C11.CrossRefGoogle Scholar
Gilet, T. & Bourouiba, L. 2014 Rain-induced ejection of pathogens from leaves: revisiting the hypothesis of splash-on-film using high-speed visualization. Integr. Compar. Biol. 54, 974–84.CrossRefGoogle ScholarPubMed
Gilet, T. & Bourouiba, L. 2015 Fluid fragmentation shapes rain-induced foliar disease transmission. J. R. Soc. Interface 12, 20141092.CrossRefGoogle ScholarPubMed
Hoepffner, J. & Paré, G. 2013 Recoil of a liquid filament: escape from pinch-off through creation of a vortex ring. J. Fluid Mech. 734, 183–197.CrossRefGoogle Scholar
Josserand, C & Thoroddsen, S. T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48, 365–391.CrossRefGoogle Scholar
Keller, J. B. 1983 Breaking of liquid films and threads. Phys. Fluids 26, 3451–3453.CrossRefGoogle Scholar
Lejeune, S., Gilet, T. & Bourouiba, L. 2018 Edge-effect: Liquid sheet and droplets formed by drop impact close to an edge. Phys. Rev. Fluids. 3, 083601.CrossRefGoogle Scholar
Li, E. Q., Thoraval, M. J., Marston, J. O. & Thoroddsen, S. T. 2018 Early azimuthal instability during drop impact. J. Fluid Mech. 848, 821–835.CrossRefGoogle Scholar
Martien, P., Pope, S. E., Scott, P. L. & Shaw, R. S. 1985 The chaotic behavior of the leaky faucet. Phys. Lett. A 110 (7), 399–404.CrossRefGoogle Scholar
Peters, I. R., van der Meer, D. & Gordillo, J. M. 2013 Splash wave and crown breakup after disc impact on a liquid surface. J. Fluid Mech. 724, 553–580.CrossRefGoogle Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. R. Soc. Lond. A s1-10, 4–13.Google Scholar
Riboux, G. & Gordillo, J. M. 2014 Experiments of drops impacting a smooth solid surface: a model of the critical impact speed for drop splashing. Phys. Rev. Lett. 113, 1–13.Google Scholar
Roisman, I. V. 2010 On the instability of a free viscous rim. J. Fluid Mech. 661, 206–228.CrossRefGoogle Scholar
Roisman, I. V., Gambaryan-Roisman, T., Kyriopoulos, O., Stephan, P. & Tropea, C. 2007 Breakup and atomization of a stretching crown. Phys. Rev. E 76 (2), 1–9.CrossRefGoogle ScholarPubMed
Rozhkov, A., Prunet-Foch, B. & Vignes-Adler, M. 2002 Impact of water drops on small targets. Phys. Fluids 14, 3485.CrossRefGoogle Scholar
Scheller, B. L. & Bousfield, D. W. 1995 Newtonian drop impact with a solid surface. AIChE J. 41, 1357–1367.CrossRefGoogle Scholar
Taylor, G. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201, 192–196.Google Scholar
Traverso, G., Laken, S., Lu, C. C., Maa, R., Langer, R. & Bourouiba, L. 2013 Fluid fragmentation from hospital toilets. arXiv:1310.5511.Google Scholar
Vernay, C., Ramos, L. & Ligoure, C. 2015 Free radially expanding liquid sheet in air: time- and space-resolved measurement of the thickness field. J. Fluid Mech. 764, 428–444.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2011 Drop fragmentation on impact. J. Fluid Mech. 668, 412–435.CrossRefGoogle Scholar
Wang, Y. & Bourouiba, L. 2017 Drop impact on small surfaces: thickness and velocity profiles of the expanding sheet in the air. J. Fluid Mech. 814, 510–534.CrossRefGoogle Scholar
Wang, Y. & Bourouiba, L. 2018 Unsteady sheet fragmentation: droplet sizes and speeds. J. Fluid Mech. 848, 946–967.CrossRefGoogle Scholar
Wang, Y. & Bourouiba, L. 2020 a Mass, momentum, and energy partitioning in unsteady fragmentation. (under review).Google Scholar
Wang, Y. & Bourouiba, L. 2020 b Non-Galilean Taylor–Culick's law governs sheet dynamics in unsteady fragmentation. (in press).Google Scholar
Wang, Y., Dandekar, R., Bustos, N., Poulain, S. & Bourouiba, L. 2018 c Universal rim thickness in unsteady sheet fragmentation. Phys. Rev. Lett. 120, 204503.CrossRefGoogle ScholarPubMed
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing${\ldots }$. Annu. Rev. Fluid Mech. 38, 159–192.CrossRefGoogle Scholar
Zhang, L. V., Brunet, P., Eggers, J. & Deegan, R. D. 2010 Wavelength selection in the crown splash. Phys. Fluids 22, 1–9.CrossRefGoogle Scholar