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Propagation of the rim under a liquid-curtain breakup

Published online by Cambridge University Press:  14 July 2022

Harumichi Kyotoh Open the ORCID record for Harumichi Kyotoh [Opens in a new window] ,
Genki Sekine  and
Md Roknujjaman
Harumichi Kyotoh*
Affiliation:
Department of Engineering Mechanics and Energy, University of Tsukuba, Tsukuba, Ibaraki 305-0006, Japan
Genki Sekine
Affiliation:
Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan
Md Roknujjaman
Affiliation:
Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan
*
†Email address for correspondence: kyotoh@kz.tsukuba.ac.jp
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Abstract

The propagation speed, shape and stability of the rim generated by a liquid-curtain breakup are studied. In the experiment, a liquid curtain surrounded by a slot die, edge guides and the surface of a roller breaks at the contact point between the edge guide and roller in a low-Weber-number range, and the rim propagates in the horizontal direction. Except for the initial time, the rim is almost straight and has a nearly constant propagation speed. For an Ohnesorge number much smaller than 1, unevenness occurs on the rim and the droplets separate from it. When the Ohnesorge number is of the order of unity, the rim becomes convex vertically downward, and the liquid lump flows down. The shape, propagation speed and surface stability of the rim are discussed by analysing the equation proposed by Entov & Yarin (J. Fluid Mech., vol. 140, 1984, pp. 91–111). It is shown that the volume flow rate condition at the slot die exit is important to explain the propagation of the rim. Additionally, in the initial stage of the curtain breakup, the Plateau–Rayleigh instability causes unevenness on the rim surface, and after the rim reaches the slot die exit, the Rayleigh–Taylor instability generates a liquid lump on the rim, which grows into droplets when the Ohnesorge number is much less than 1.

JFM classification

Instability: Absolute/convective instability Interfacial Flows (free surface): Liquid bridges Waves/Free-surface Flows: Capillary waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 945 , 25 August 2022 , A12
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Kyotoh Supplementary Movie 1

Front view of the curtain breakup in experiment CA, i.e., CA-L1-Q1, CA-L1-Q2, CA-L2-Q1, CA-L2-Q2, CA-L3-Q1 and CA-L3-Q2 in table 2.
Download Kyotoh Supplementary Movie 1(Video)
Video 6.5 MB

Kyotoh Supplementary Movie 2

Front view of the curtain breakup in experiment CB, i.e., CB-L4-Q0, CB-L5-Q0 and CB-L6-Q0 in table 2.

Download Kyotoh Supplementary Movie 2(Video)
Video 2.4 MB