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Non-Galilean Taylor–Culick law governs sheet dynamics in unsteady fragmentation

Published online by Cambridge University Press:  15 August 2023

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, MA 02139, USA
L. Bourouiba*
Affiliation:
The Fluid Dynamics of Disease Transmission Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: lbouro@mit.edu
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Abstract

We present the results of a combined experimental and theoretical investigation of sheet evolution, expansion and retraction, under unsteady fragmentation upon drop impact on a surface of comparable size to that of the drop. We quantify and model the effect of the continuous time-varying – unsteady – shedding of droplets from the sheet via its bounding rim. We present and validate especially developed advanced image processing algorithms that quantify, with high accuracy, the key quantities involved in such unsteady fragmentation, from sheet, to rim, to ligaments, to droplet properties. With these high precision measurements, we show the important effect of continuous unsteady droplet shedding on the sheet dynamics. We combine experiments and theory to derive and validate governing equations of the sheet that incorporate such continuous shedding – associated with continuous loss of momentum and mass – from unsteady fragmentation. Combining this theory with the universal unsteady rim dynamics discovered in Wang et al. (Phys. Rev. Lett., vol. 120, 2018, 204503), we show that the governing equation of the sheet can be reduced to a continuous-shedding, non-Galilean Taylor–Culick law, from which we deduce new analytical expressions for the time evolution of the sheet radius. We show the robustness of the predictions to changes of fluid properties, including surface tension and moderate fluid viscosity and elasticity, including use of physiological mucosalivary fluid. We also reconcile prior literature's inconsistent experimental results on the sheet dynamics upon drop impact.

JFM classification

Drops and Bubbles: Aerosols/atomization Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 969 , 25 August 2023 , A19
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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