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Air sheet contraction

Published online by Cambridge University Press:  20 July 2020

Zhen Jian Open the ORCID record for Zhen Jian [Opens in a new window] ,
Peng Deng Open the ORCID record for Peng Deng [Opens in a new window]  and
Marie-Jean Thoraval Open the ORCID record for Marie-Jean Thoraval [Opens in a new window]
Zhen Jian
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, International Center for Applied Mechanics, School of Aerospace, Xi’an Jiaotong University, Xi’an710049, PR China
Peng Deng
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, International Center for Applied Mechanics, School of Aerospace, Xi’an Jiaotong University, Xi’an710049, PR China
Marie-Jean Thoraval*
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, International Center for Applied Mechanics, School of Aerospace, Xi’an Jiaotong University, Xi’an710049, PR China
*
†Email address for correspondence: [email protected]
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Abstract

A two-dimensional air sheet in a surrounding liquid contracts under surface tension. We investigate numerically and analytically this contraction dynamics for a range of Ohnesorge numbers $Oh$. In a similar way as for liquid films, three contraction regimes can be identified based on the $Oh$: vortex shedding, smooth contraction and viscous regime. For $Oh\leqslant 0.02$, the rim can even pinch-off due to the rim deformations caused by the vortex shedding. In contrast with a liquid film that continuously accelerates towards the Taylor–Culick velocity when the surrounding fluid can be neglected, the air film contraction velocity first rises to a maximum value $U_{max}$ before decreasing due to the drag of the external fluid on the moving rim. This $U_{max}$ follows a capillary-inertial scaling at low $Oh$ and continuously shifts to a capillary-viscous scaling with increasing $Oh$. We demonstrate that the decreasing contraction velocity scales as $t^{-0.15}$, which is faster than the scaling $t^{-0.2}$ derived under the assumption of a constant drag coefficient. The transition between the capillary-inertial and capillary-viscous regimes can be characterised by the local time evolving Ohnesorge number $Oh_{\unicode[STIX]{x1D6FF}}$ based on the thickness of the rim. The oscillations of the rim appear at a critical local Weber number $We_{\unicode[STIX]{x1D6FF}}$. Then they follow a well-defined oscillation frequency with a characteristic Strouhal number. Beyond a local Reynolds number larger than 200, the oscillations become more irregular with more complex vortex sheddings, eventually leading to the pinch-off of the rim.

JFM classification

Drops and Bubbles: Drops and Bubbles
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A7
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

‡

These authors contributed equally to this work.

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Jian et al. supplementary movie 1

Figure 4(a,d,g): Oh = 0.05, t* from 0 to 500

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Jian et al. supplementary movie 2

Figure 4(b,e,h): Oh = 0.3, t* from 0 to 500

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Jian et al. supplementary movie 3

Figure 4(c,f,i): Oh = 7, t* from 0 to 500

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Jian et al. supplementary movie 4

Figure 5(a,c-e): Oh = 0.01, t* from 0 to 500

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Supplementary material: PDF

Jian et al. supplementary material

Supplementary data

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