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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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