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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
Affiliation:
Department of Mechanical Engineering, Seoul National University, Seoul08826, Korea
Hyungmin Park*
Affiliation:
Department of Mechanical Engineering, Seoul National University, Seoul08826, Korea Institute of Advanced Machines and Design, Seoul National University, Seoul08826, Korea
*
Email address for correspondence: hminpark@snu.ac.kr

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.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Anthony, C.R., Kamat, P.M., Harris, M.T. & Basaran, O.A. 2019 Dynamics of contracting filaments. Phys. Rev. Fluids 4, 093601.CrossRefGoogle Scholar
Berman, A.S., Bradford, J. & Lundgren, T.S. 1978 Two-fluid spin-up in a centrifuge. J. Fluid Mech. 84, 411431.CrossRefGoogle Scholar
Beysens, D., Wunenburger, R., Chabot, C. & Garrabos, Y. 1998 Effect of oscillatory accelerations on two-phase fluids. Microgravity Sci. Technol. 11, 113118.Google Scholar
Boomkamp, P.A.M. & Miesen, R.H.M. 1996 Classification of instabilities in parallel two-phase flow. Intl J. Multiphase Flow 22, 6788.CrossRefGoogle Scholar
Charru, F. & Hinch, E.J. 2000 ‘Phase diagram’ of interfacial instabilities in a two-layer Couette flow and mechanism of the long-wave instability. J. Fluid Mech. 414, 195223.CrossRefGoogle Scholar
Couder, Y., Fort, E., Gautier, C.H. & Boudaoud, A. 2005 From bouncing to floating: noncoalescence of drops on a fluid bath. Phys. Rev. Lett. 94, 177801.CrossRefGoogle ScholarPubMed
Donnelly, T.D., Hogan, J., Mugler, A., Schommer, N., Schubmehl, M., Bernoff, A.J. & Forrest, B. 2004 An experimental study of micron-scale droplet aerosols produced via ultrasonic atomization. Phys. Fluids 16, 28432851.CrossRefGoogle Scholar
Douady, S. 1990 Experimental study of the Faraday instability. J. Fluid Mech. 221, 383409.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.CrossRefGoogle Scholar
Gaponenko, Y.A., Torregrosa, M., Yasnou, V., Mialdun, A. & Shevtsova, V. 2015 Dynamics of the interface between miscible liquids subjected to horizontal vibration. J. Fluid Mech. 784, 342372.CrossRefGoogle Scholar
Goller, H. & Ranov, T. 1968 Unsteady rotating flow in a cylinder with a free surface. Trans. ASME J. Basic Engng 90, 445454.CrossRefGoogle Scholar
Goodridge, C.L., Shi, W.T., Hentschel, H.G.E. & Lathrop, D.P. 1997 Viscous effects in droplet-ejecting capillary waves. Phys. Rev. E 56, 472.CrossRefGoogle Scholar
Goodridge, C.L., Shi, W.T. & Lathrop, D.P. 1996 Threshold dynamics of singular gravity-capillary waves. Phys. Rev. Lett. 76, 1824.CrossRefGoogle ScholarPubMed
Govindarajan, R. & Sahu, K.C. 2014 Instabilities in viscosity-stratified flow. Annu. Rev. Fluid Mech. 46, 331353.CrossRefGoogle Scholar
Hooper, A.P. & Boyd, W.G.C. 1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507528.CrossRefGoogle Scholar
Hu, H.H. & Joseph, D.D. 1989 Lubricated pipelining: stability of core annular flow. Part 2. J. Fluid Mech. 205, 359396.CrossRefGoogle Scholar
Ivanova, A.A., Kozlov, V.G. & Evesque, P. 2001 Interface dynamics of immiscible fluids under horizontal vibration. Fluid Dyn. 36, 362368.CrossRefGoogle Scholar
Jalikop, S.V. & Juel, A. 2009 Steep capillary-gravity waves in oscillatory shear-driven flows. J. Fluid Mech. 640, 131150.CrossRefGoogle Scholar
James, A.J., Smith, M.K. & Glezer, A. 2003 Vibration-induced drop atomization and the numerical simulation of low-frequency single-droplet ejection. J. Fluid Mech. 476, 2962.CrossRefGoogle Scholar
Joseph, D.D. & Renardy, Y. 1992 Fundamentals of Two-Fluid Dynamics. Part 1. Mathematical Theory and Applications, Springer.Google Scholar
Khenner, M.V., Lyubimov, D.V., Belozerova, T.S. & Roux, B. 1999 Stability of plane-parallel vibrational flow in a two-layer system. Eur. J. Mech. B/Fluids 18, 10851101.CrossRefGoogle Scholar
Kim, J., Moon, M.W. & Kim, H.-Y. 2020 Capillary rise in superhydrophilic rough channels. Phys. Fluids 32, 032105.CrossRefGoogle Scholar
Landau, L.D. & Lifshitz, E.M. 1987 Fluid mechanics, 2nd edn. Pergamon.Google Scholar
Lang, R.J. 1962 Ultrasonic atomization of liquids. J. Acoust. Soc. Am. 34, 68.CrossRefGoogle Scholar
Li, Y. & Umemura, A. 2014 Threshold condition for spray formation by Faraday instability. J. Fluid Mech. 759, 73103.CrossRefGoogle Scholar
Longuet-Higgins, M.S. 2001 Vertical jets from standing waves. Proc. R. Soc. Lond. A 457, 495510.CrossRefGoogle Scholar
Longuet-Higgins, M.S. & Dommermuth, D.G. 2001 On the breaking of standing waves by falling jets. Phys. Fluids 13, 16521659.CrossRefGoogle Scholar
Lyubimov, D.V. & Cherepanov, A.A. 1987 Development of a steady relief at the interface of fluids in a vibrational field. Fluid Dyn. 21, 849854.CrossRefGoogle Scholar
Marmottant, P. & Villermaux, E. 2004 a Fragmentation of stretched liquid ligaments. Phys. Fluids 16, 27322741.CrossRefGoogle Scholar
Marmottant, P. & Villermaux, E. 2004 b On spray formation. J. Fluid Mech. 498, 73111.CrossRefGoogle Scholar
Piao, L., Kim, N. & Park, H. 2017 Effects of geometrical parameters of an oil–water separator on the oil-recovery rate. J. Mech. Sci. Technol. 31, 28292837.CrossRefGoogle Scholar
Piao, L. & Park, H. 2019 Relation between oil–water interfacial flow structure and their separation in the oil–water mixture flow in a curved channel: an experimental study. Intl J. Multiphase Flow 120, 103089.CrossRefGoogle Scholar
Preziosi, L., Chen, K. & Joseph, D.D. 1989 Lubricated pipelining: stability of core-annular flow. J. Fluid Mech. 201, 323356.CrossRefGoogle Scholar
Puthenveettil, B.A. & Hopfinger, E.J. 2009 Evolution and breaking of parametrically forced capillary waves in a circular cylinder. J. Fluid Mech. 633, 355379.CrossRefGoogle Scholar
Ray, B., Biswas, G. & Sharma, A. 2010 Generation of secondary droplets in coalescence of a drop at a liquid–liquid interface. J. Fluid Mech. 655, 72104.CrossRefGoogle Scholar
Roberts, R.M., Ye, Y., Demekhin, E.A. & Chang, H.C. 2000 Wave dynamics in two-layer Couette flow. Chem. Engng Sci. 55, 345362.CrossRefGoogle Scholar
Sahu, K.C., Valluri, P., Spelt, P.D.M. & Matar, O.K. 2007 Linear instability of pressure-driven channel flow of a Newtonian and a Herschel–Bulkley fluid. Phys. Fluids 19, 122101.CrossRefGoogle Scholar
Sánchez, P.S., Gaponenko, Y., Yasnou, V., Mialdun, A., Porter, J. & Shevtsova, V. 2020 Effect of initial interface orientation on patterns produced by vibrational forcing in microgravity. J. Fluid Mech. 884, A38.CrossRefGoogle Scholar
Sánchez, P.S., Yasnou, V., Gaponenko, Y., Mialdun, A., Porter, J. & Shevtsova, V. 2019 Interfacial phenomena in immiscible liquids subjected to vibrations in microgravity. J. Fluid Mech. 865, 850883.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 2016 Boundary-layer Theory. Springer.Google Scholar
Sengupta, R., Khair, A.S. & Walker, L.M. 2020 Dynamic interfacial tension measurement under electric fields allows detection of charge carriers in nonpolar liquids. J. Colloid Interface Sci. 567, 1827.CrossRefGoogle ScholarPubMed
Shao, X., Gabbard, C.T., Bostwick, J.B. & Saylor, J.R. 2021 On the role of meniscus geometry in capillary wave generation. Exp. Fluids 62, 59.CrossRefGoogle Scholar
Shyh, C.K. & Munson, B.R. 1986 Interfacial instability of an oscillating shear layer. Trans. ASME J. Fluids Engng 108, 8992.CrossRefGoogle Scholar
Talib, E., Jalikop, S.V. & Juel, A. 2007 The influence of viscosity on the frozen wave instability: theory and experiment. J. Fluid Mech. 584, 4568.CrossRefGoogle Scholar
Talib, E. & Juel, A. 2007 Instability of a viscous interface under horizontal oscillation. Phys. Fluids 19, 092102.CrossRefGoogle Scholar
Thorpe, S.A. 1978 On the shape and breaking of finite amplitude internal gravity waves in a shear flow. J. Fluid Mech. 85, 731.CrossRefGoogle Scholar
Usha, R. & Sahu, K.C. 2019 Interfacial instability in pressure-driven core-annular pipe flow of a Newtonian and a Herschel–Bulkley fluid. J. Non-Newtonian Fluid Mech. 271, 104144.CrossRefGoogle Scholar
Valluri, P., Náraigh, L.Ó., Ding, H. & Spelt, P.D.M. 2010 Linear and nonlinear spatio-temporal instability in laminar two-layer flows. J. Fluid Mech. 656, 458480.CrossRefGoogle Scholar
Wang, F., Contò, F.P., Naz, N., Castrejón-Pita, J.R., Castrejón-Pita, A.A., Bailey, C.G., Wang, W., Feng, J.J. & Sui, Y. 2019 A fate-alternating transitional regime in contracting liquid filaments. J. Fluid Mech. 860, 640653.CrossRefGoogle Scholar
Wilkes, E.D. & Basaran, O.A. 1997 Forced oscillations of pendant (sessile) drops. Phys. Fluids 9, 15121528.CrossRefGoogle Scholar
Wilkes, E.D. & Basaran, O.A. 2001 Drop ejection from an oscillating rod. J. Colloid Interface Sci. 242, 180201.CrossRefGoogle Scholar
Wilkes, E.D., Phillips, S.D. & Basaran, O.A. 1999 Computational and experimental analysis of dynamics of drop formation. Phys. Fluids 11, 35773598.CrossRefGoogle Scholar
Wolf, G.H. 1969 The dynamic stabilization of the Rayleigh–Taylor instability and the corresponding dynamic equilibrium. Z. Phys. 227, 291300.CrossRefGoogle Scholar
Wolf, G.H. 2018 Dynamic stabilization of the Rayleigh–Taylor instability of miscible liquids and the related “frozen waves”. Phys. Fluids 30, 021701.CrossRefGoogle Scholar
Wunenburger, R., Evesque, P., Chabot, C., Garrabos, Y., Fauve, S. & Beysens, D. 1999 Frozen wave induced by high frequency horizontal vibrations on a CO2 liquid-gas interface near the critical point. Phys. Rev. E 59, 5440.CrossRefGoogle ScholarPubMed
Yih, C.S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337352.CrossRefGoogle Scholar
Yoshikawa, H.N. & Wesfreid, J.E. 2011 a Oscillatory Kelvin–Helmholtz instability. Part 1. A viscous theory. J. Fluid Mech. 675, 223248.CrossRefGoogle Scholar
Yoshikawa, H.N. & Wesfreid, J.E. 2011 b Oscillatory Kelvin–Helmholtz instability. Part 2. An experiment in fluids with a large viscosity contrast. J. Fluid Mech. 675, 249-267.CrossRefGoogle Scholar

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 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 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 4 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 MB
Supplementary material: PDF

Piao and Park Supplementary Material

Piao and Park Supplementary Material

Download Piao and Park Supplementary Material(PDF)
PDF 3 MB

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