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Interfacial instability for droplet formation in two-layer immiscible liquids under rotational oscillation

Published online by Cambridge University Press:  12 August 2021

Linfeng Piao  and
Hyungmin Park
Linfeng Piao
Affiliation:
Department of Mechanical Engineering, Seoul National University, Seoul 08826, Korea
Hyungmin Park*
Affiliation:
Department of Mechanical Engineering, Seoul National University, Seoul 08826, Korea Institute of Advanced Machines and Design, Seoul National University, Seoul 08826, Korea
*
†Email address for correspondence: [email protected]
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Abstract

We experimentally investigate the interfacial instabilities governing the dynamics of an interface between two superposed immiscible liquids (oil and water) in a cylindrical container oscillating about its axis. The viscosity and density contrasts are $100$ and $0.968$, respectively. Depending on the vibrational Froude number, the evolution of interfacial wave is categorized into single-droplet (SD) formation (at the core region) and multiple/emulsion-droplet formation (at the near-wall region), and the breakage of the deformed interface into a SD is analysed for the first time. The thresholds for the onset of different instabilities responsible for each regime are presented by the amplitude and frequency of rotation, of which the boundaries predicted through the inviscid theory and scaling arguments are in good agreement with measurement. For SD formation, in particular, it is related to the critical rise velocity of the interface, represented by the vibrational Froude number. We emphasize the opposing contributions between (i) the viscous effect, i.e. the dimensionless thickness of the Stokes boundary layer, and (ii) the inviscid effect, i.e. the dimensionless maximum interface rise at the centre region (inviscid core), promoting and preventing the formation of a falling jet, respectively, which is necessary for SD formation. Our results indicate that viscosity plays an important role in shaping the boundary of SD and multiple-droplet regimes, especially at a relatively small (high) oscillating amplitude (frequency). When the amplitude is small, the enhanced viscous effect forces the deformed interface to migrate to multiple-droplet formation, skipping SD formation, with increasing frequency.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 924 , 10 October 2021 , A32
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Piao and Park Supplementary Movie 1

Oscillating wave patterns developing on an interface between two superposed immiscible liquids (silicone oil of 100 mm2/s in upper layer and DI water in lower layer) along the periphery (near-wall region) of the azimuthally oscillating cylindrical container. The typical angular amplitude and frequency are Фo = 180° and fω =1.2 Hz, respectively. The movie plays 4 times slower than the real time.

Download Piao and Park Supplementary Movie 1(Video)
Video 4.4 MB

Piao and Park Supplementary Movie 2

Single water droplet forming on the interface between two superposed immiscibleliquids (silicone oil of 100 mm2/s in upper layer and DI water in lower layer) at the core (center) region of the cylindrical container during rotational oscillation. This droplet bounces off according to the periodic up-downs of the interface while staying above the center area. The typical angular amplitude and frequency are Фo = 175° and fω = 1.44 Hz, respectively. The movie plays 4 times slower than the real time.

Download Piao and Park Supplementary Movie 2(Video)
Video 7.1 MB

Piao and Park Supplementary Movie 3

Multiple water droplets breaking off from the wavy interface between two superposed immiscible liquids (silicone oil of 100 mm2/s in upper layer and DI water in lower layer) at the near-wall region of the cylindrical container during rotational oscillation. It will take some time for the appearance of multiple-droplet. The typical angular amplitude and frequency are Фo = 160° and fω = 2.30 Hz, respectively. The movie plays in the real time.

Download Piao and Park Supplementary Movie 3(Video)
Video 3.8 MB

Piao and Park Supplementary Movie 4

Emulsion droplets (oil-in-water) forming in two superposed immiscible liquids (silicone oil of 100 mm2/s in upper layer and DI water in lower layer) in the azimuthally oscillating cylindrical container. The population of the oil droplets in water formed at the near-wall region increase explosively at t* > 5.0 (t* = tω/2π). The typical angular amplitude and frequency are Фo = 175° and fω = 2.26 Hz, respectively. The movie plays in the real time.

Download Piao and Park Supplementary Movie 4(Video)
Video 6.4 MB
Supplementary material: PDF

Piao and Park Supplementary Material

Piao and Park Supplementary Material

Download Piao and Park Supplementary Material(PDF)
PDF 3.4 MB