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Statics and dynamics of a viscous ligament drawn out of a pure-liquid bath

Published online by Cambridge University Press:  07 July 2021

Xiaofeng Wei ,
Javier Rivero-Rodríguez Open the ORCID record for Javier Rivero-Rodríguez [Opens in a new window] ,
Jun Zou Open the ORCID record for Jun Zou [Opens in a new window]  and
Benoit Scheid Open the ORCID record for Benoit Scheid [Opens in a new window]
Xiaofeng Wei
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, PR China
Javier Rivero-Rodríguez
Affiliation:
TIPs – Fluid Physics Unit, Université Libre de Bruxelles, C.P. 165/67, 1050Brussels, Belgium Escuela Técnica Superior de Ingenieros Industriales, Universidad de Málaga, Plaza El Ejido s/n, 29013Málaga, Spain
Jun Zou*
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, PR China
Benoit Scheid*
Affiliation:
TIPs – Fluid Physics Unit, Université Libre de Bruxelles, C.P. 165/67, 1050Brussels, Belgium
*
†Email addresses for correspondence: junzou@zju.edu.cn, bscheid@ulb.ac.be
†Email addresses for correspondence: junzou@zju.edu.cn, bscheid@ulb.ac.be
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Abstract

In this paper we investigate the statics and the dynamics of large-viscosity ligaments attached to a rod and drawn out of a pure-liquid bath. Following the similar work of films pulling out of a bath (Champougny et al., J. Fluid Mech., vol. 811, 2017, pp. 499–524), a one-dimensional model is applied to describe the ligaments drawn at constant velocities. We focus on the whole drawing dynamics of the ligament up to breakup, for which the breakup height is determined. The breakup height coincides with the maximum static meniscus height for very slow drawing, whose process can be described by quasi-static solutions. We present the numerical results of the static menisci and analytically unravel the mechanism in the low gravity case. Starting from a stable static meniscus, the breakup height of faster drawing depends separately on the rod radius and the drawing velocity, the latter dependency being fully determined by considering the agravic limit. Next, it is shown that the entire lifetime of the ligament drawing can be sequenced into a ductility stage, a capillarity stage and a pinch-off stage, the latter being shown to be almost instantaneous. The ductility and capillarity stages are decorrelated with the help of an approximate solution of the ductility stage, and the transition between the two stages corresponds to the time at which the capillarity-induced contraction velocity exceeds the ductility-induced one. The one-dimensional predictions of the breakup height and the entrained liquid volume attached to the rod quantitatively agree with experimental results of silicone oil ligaments, and the deviations are rationalized in comparison with a two-dimensional model.

JFM classification

Interfacial Flows (free surface): Liquid bridges Low-Reynolds-number flows: Slender-body theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , A14
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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