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Interfacial phenomena in immiscible liquids subjected to vibrations in microgravity

Published online by Cambridge University Press:  28 February 2019

P. Salgado Sánchez
Affiliation:
Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
V. Yasnou
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles, av. F. D. Roosevelt 50, B-1050 Brussels, Belgium
Y. Gaponenko
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles, av. F. D. Roosevelt 50, B-1050 Brussels, Belgium
A. Mialdun
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles, av. F. D. Roosevelt 50, B-1050 Brussels, Belgium
J. Porter
Affiliation:
Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
V. Shevtsova*
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles, av. F. D. Roosevelt 50, B-1050 Brussels, Belgium
*
Email address for correspondence: vshev@ulb.ac.be

Abstract

We consider the response to periodic forcing between 5 Hz and 50 Hz of an interface separating immiscible fluids under the microgravity conditions of a parabolic flight. Two pairs of liquids with viscosity ratios differing by one order of magnitude are investigated. By combining experimental data with numerical simulations, we describe a variety of dynamics including harmonic and subharmonic (Faraday) waves, frozen waves and drop ejection, determining their thresholds and scaling properties when possible. Interaction between these various modes is facilitated in microgravity by the relative ease with which the interface can move, altering its orientation with respect to the forcing axis. The effects of key factors controlling pattern selection are analysed, including vibrational forcing, viscosity ratio, finite-size effects and residual gravity. Complex behaviour often arises with features on several spatial scales, such as Faraday waves excited on the interface of a larger columnar structure that develops due to the frozen wave instability – this type of state was previously seen in miscible fluid experiments but is described for the first time here in the immiscible case.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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References

Amiroudine, S. & Beysens, D. 2008 Thermovibrational instability in supercritical fluids under weightlessness. Phys. Rev. E 78 (3), 036325.Google Scholar
Ancherbak, S., Yasnou, V., Mialdun, A. & Shevtsova, V. 2018 Coexistence curve, density, and viscosity for the binary system of perfluorohexane + silicone oil. J. Chem. Engng Data 63 (8), 30083017.10.1021/acs.jced.8b00278Google Scholar
Arbell, H. & Fineberg, J. 2002 Pattern formation in two-frequency forced parametric waves. Phys. Rev. E 65 (3), 036224.10.1103/PhysRevE.65.036224Google Scholar
Batson, W., Zoueshtiagh, F. & Narayanan, R. 2013 Dual role of gravity on the Faraday threshold for immiscible viscous layers. Phys. Rev. E 88 (6), 063002.10.1103/PhysRevE.88.063002Google Scholar
Benjamin, T. B. & Ursell, F. 1954 The stability of the plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. Lond. A 225 (1163), 505515.Google Scholar
Beyer, K., Gawriljuk, I., Günther, M., Lukovsky, I. & Timokha, A. 2001 Compressible potential flows with free boundaries. Part I. Vibrocapillary equilibria. Z. Angew. Math. Mech. 81 (4), 261271.10.1002/1521-4001(200104)81:4<261::AID-ZAMM261>3.0.CO;2-T3.0.CO;2-T>Google Scholar
Beysens, D. 2014 Critical point in space: a quest for universality. Microgravity Sci. Technol. 26 (4), 201218.10.1007/s12217-014-9373-1Google Scholar
Beysens, D., Garrabos, Y., Chatain, D. & Evesque, P. 2009 Phase transition under forced vibrations in critical CO2 . Eur. Phys. Lett. 86 (1), 16003.10.1209/0295-5075/86/16003Google Scholar
Burnysheva, A. V., Lyubimov, D. V. & Lyubimova, T. P. 2011 Disturbance spectrum of a plane fluid–fluid interface in the field of tangential high-frequency vibrations under weightlessness. Fluid Dyn. 46 (6), 10001009.10.1134/S0015462811060184Google Scholar
Castrejón-Pita, J. R., Castrejón-Pita, A. A., Thete, S. S., Sambath, K., Hutchings, I. M., Hinch, J., Lister, J. R. & Basaran, O. A. 2015 Plethora of transitions during breakup of liquid filaments. Proc. Natl Acad. Sci. USA 112 (15), 45824587.10.1073/pnas.1418541112Google Scholar
Codina, R. 1993 A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection–diffusion equation. Comput. Meth. Appl. Mech. Engng 110 (3–4), 325342.10.1016/0045-7825(93)90213-HGoogle Scholar
Diwakar, S. V., Jajoo, V., Amiroudine, S., Matsumoto, S., Narayanan, R. & Zoueshtiagh, F. 2018 Influence of capillarity and gravity on confined Faraday waves. Phys. Rev. Fluids 3 (7), 73902.10.1103/PhysRevFluids.3.073902Google Scholar
Douady, S. 1990 Experimental study of the Faraday instability. J. Fluid Mech. 221, 383409.10.1017/S0022112090003603Google Scholar
Erlicher, S., Bonaventura, L. & Bursi, O. 2002 The analysis of the generalized 𝛼 methods for non-linear dynamic problems. Method for non-linear dynamic problems. Comput. Mech. 28, 83104.10.1007/s00466-001-0273-zGoogle Scholar
Faraday, M. 1831 On peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 121, 299340.Google Scholar
Fernández, J., Salgado Sánchez, P., Tinao, I., Porter, J. & Ezquerro, J. M. 2017a The CFVib experiment: control of fluids in microgravity with vibrations. Microgravity Sci. Technol. 29 (5), 351364.10.1007/s12217-017-9556-7Google Scholar
Fernández, J., Tinao, I., Porter, J. & Laverón-Simavilla, A. 2017b Instabilities of vibroequilibria in rectangular containers. Phys. Fluids 29 (2), 024108.10.1063/1.4976719Google Scholar
Gandikota, G., Chatain, D., Amiroudine, S., Lyubimova, T. & Beysens, D. 2014a Faraday instability in a near-critical fluid under weightlessness. Phys. Rev. E 89 (1), 013022.10.1103/PhysRevE.89.013022Google Scholar
Gandikota, G., Chatain, D., Amiroudine, S., Lyubimova, T. & Beysens, D. 2014b Frozen-wave instability in near-critical hydrogen subjected to horizontal vibration under various gravity fields. Phys. Rev. E 89 (1), 012309.10.1103/PhysRevE.89.012309Google Scholar
Ganiev, R. F., Lakiza, V. D. & Tsapenko, A. S. 1977 Dynamic behavior of the free liquid surface subject to vibrations under conditions of near-zero gravity. Mekhanika 13 (5), 499503.Google Scholar
Gaponenko, Y. A., Mialdun, A. & Shevtsova, V. 2018 Pattern selection in miscible liquids under periodic excitation in microgravity: effect of interface width. Phys. Fluids 30 (6), 062103.10.1063/1.5032107Google Scholar
Gaponenko, Y. A., Torregrosa, M. M., Yasnou, V., Mialdun, A. & Shevtsova, V. 2015a Dynamics of the interface between miscible liquids subjected to horizontal vibration. J. Fluid Mech. 784, 342372.10.1017/jfm.2015.586Google Scholar
Gaponenko, Y. A., Torregrosa, M. M., Yasnou, V., Mialdun, A. & Shevtsova, V. 2015b Interfacial pattern selection in miscible liquids under vibration. Soft Matt. 11 (42), 82218224.10.1039/C5SM02110CGoogle Scholar
Garrett, J. R. 1970 A theory of the Krakatoa tide gauge disturbances. J. Fluid Mech. 22 (1), 4352.Google Scholar
Gavrilyuk, I., Lukovsky, I. & Timokha, A. 2004 Two-dimensional variational vibroequilibria and Faraday’s drops. Z. Angew. Math. Phys. 55 (6), 10151033.10.1007/s00033-004-2092-5Google Scholar
Goldobin, D. S., Pimenova, A. V., Kovalevskaya, K. V., Lyubimov, D. V. & Lyubimova, T. P. 2015 Running interfacial waves in a two-layer fluid system subject to longitudinal vibrations. Phys. Rev. E 91 (5), 053010.10.1103/PhysRevE.91.053010Google Scholar
Goodridge, C. L., Shi, W., Hentschel, H. & Lathrop, D. P. 1997 Viscous effects in droplet-ejecting capillary waves. Phys. Rev. E 56 (1), 472475.Google Scholar
Goodridge, C. L., Shi, W. T. & Lathrop, D. P. 1996 Threshold dynamics of singular gravity-capillary waves. Phys. Rev. Lett. 76 (11), 18241827.10.1103/PhysRevLett.76.1824Google Scholar
Harari, I. & Hughes, T. J. R. 1992 What are C and h? Inequalities for the analysis and design of finite element methods. Comput. Meth. Appl. Mech. Engng 97 (2), 157192.10.1016/0045-7825(92)90162-DGoogle Scholar
Jalikop, S. V. & Juel, A. 2009 Steep capillary-gravity waves in oscillatory shear-driven flows. J. Fluid Mech. 640, 131150.10.1017/S0022112009991509Google Scholar
James, A. J., Smith, M. K. & Glezer, A. 2003a Vibration-induced drop atomization and the numerical simulation of low-frequency single-droplet ejection. J. Fluid Mech. 476, 2962.10.1017/S0022112002002860Google Scholar
James, A. J., Vukasinovic, B., Smith, M. K. & Glezer, A. 2003b Vibration-induced drop atomization and bursting. J. Fluid Mech. 476, 128.10.1017/S0022112002002835Google Scholar
Jones, A. F. 1984 The generation of cross-waves in a long deep channel by parametric resonance. J. Fluid Mech. 138, 5374.10.1017/S0022112084000033Google Scholar
Jounet, A., Mojtabi, A., Ouazzani, J. & Zappoli, B. 2000 Low-frequency vibrations in a near-critical fluid. Phys. Fluids 12 (1), 197204.10.1063/1.870295Google 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 (6), 10851101.10.1016/S0997-7546(99)00143-0Google Scholar
Kothe, D. B., Mjolsness, R. C. & Torrey, M. D. 1991 RIPPLE: a computer program for incompressible flows with free surfaces. Rep. LA-12007-MS. Los Alamos National Laboratory.Google Scholar
Krieger, M. S. 2017 Interfacial fluid instabilities and Kapitsa pendula. Eur. Phys. J. E 40 (7).Google Scholar
Kumar, K. & Tuckerman, L. S. 1994 Parametric instability of the interface between two fluids. J. Fluid Mech. 279, 4968.10.1017/S0022112094003812Google Scholar
Li, Y. & Umemura, A. 2014 Threshold condition for spray formation by Faraday instability. J. Fluid Mech. 759, 73103.10.1017/jfm.2014.569Google Scholar
Lyubimov, D. V. & Cherepanov, A. A. 1986 Development of a steady relief at the interface of fluids in a vibrational field. Fluid Dyn. 21 (6), 849854.10.1007/BF02628017Google Scholar
Lyubimov, D. V., Cherepanov, A. A., Lyubimova, T. P. & Roux, B. 1997 Interface orienting by vibration. C. R. Acad. Sci. Paris II 325 (1), 391396.Google Scholar
Lyubimov, D. V., Ivantsov, A. O., Lyubimova, T. P. & Khilko, G. L. 2016 Numerical modeling of frozen wave instability in fluids with high viscosity contrast. Fluid Dyn. Res. 48 (6), 061415.10.1088/0169-5983/48/6/061415Google Scholar
Lyubimov, D. V., Khenner, M. & Shotz, M. M. 1998 Stability of a fluid interface under tangential vibrations. Fluid Dyn. 33, 318323.10.1007/BF02698179Google Scholar
Lyubimova, T. P., Ivantsov, A. O., Garrabos, Y., Lecoutre, C., Gandikota, G. & Beysens, D. 2017 Band instability in near-critical fluids subjected to vibration under weightlessness. Phys. Rev. E 95 (1), 013105.Google Scholar
Miles, J. & Henderson, D. M. 1990 Parametrically forced surface-waves. Annu. Rev. Fluid Mech. 22, 143165.10.1146/annurev.fl.22.010190.001043Google Scholar
Olsson, E. & Kreiss, G. 2005 A conservative level set method for two phase flow. J. Comput. Phys. 210 (1), 225246.10.1016/j.jcp.2005.04.007Google Scholar
Perez-Gracia, J. M., Porter, J., Varas, F. & Vega, J. M. 2014 Subharmonic capillary–gravity waves in large containers subject to horizontal vibrations. J. Fluid Mech. 739, 196228.10.1017/jfm.2013.606Google Scholar
Pletser, V., Rouquette, S., Friedrich, U., Clervoy, J. F., Gharib, T., Gai, F. & Mora, C. 2016 The First European Parabolic Flight Campaign with the Airbus A310 ZERO-G. Microgravity Sci. Technol. 28 (6), 587601.10.1007/s12217-016-9515-8Google Scholar
Porter, J., Tinao, I., Laverón-Simavilla, A. & López, C. A. 2012 Pattern selection in a horizontally vibrated container. Fluid Dyn. Res. 44 (6), 065501.10.1088/0169-5983/44/6/065501Google Scholar
Prinet, N., Juric, D. & Tuckerman, L. S. 2009 Numerical simulation of Faraday waves. J. Fluid Mech. 635, 024111.Google Scholar
Salgado Sánchez, P., Porter, J., Tinao, I. & Laverón-Simavilla, A. 2016 Dynamics of weakly coupled parametrically forced oscillators. Phys. Rev. E 94 (2), 022216.Google Scholar
Sharma, D., Erriguible, A. & Amiroudine, S. 2017 Cooling beyond the boundary value in supercritical fluids under vibration. Phys. Rev. E 96 (6), 63102.Google Scholar
Shevtsova, V., Gaponenko, Y. A., Sechenyh, V., Melnikov, D. E., Lyubimova, T. P. & Mialdun, A. 2015a Dynamics of a binary mixture subjected to a temperature gradient and oscillatory forcing. J. Fluid Mech. 767, 290322.10.1017/jfm.2015.50Google Scholar
Shevtsova, V., Gaponenko, Y. A., Yasnou, V., Mialdun, A. & Nepomnyashchy, A. 2015b Wall-generated pattern on a periodically excited miscible liquid/liquid interface. Langmuir 31 (20), 55505553.10.1021/acs.langmuir.5b01229Google Scholar
Shevtsova, V., Gaponenko, Y. A., Yasnou, V., Mialdun, A. & Nepomnyashchy, A. 2016 Two-scale wave patterns on a periodically excited miscible liquid–liquid interface. J. Fluid Mech. 795, 409422.10.1017/jfm.2016.222Google Scholar
Skeldon, A. C. & Rucklidge, A. M. 2015 Can weakly nonlinear theory explain Faraday wave patterns near onset? J. Fluid Mech. 777, 604632.10.1017/jfm.2015.388Google Scholar
Someya, S. & Munakata, T. 2005 Measurement of the interface tension of immiscible liquids interface. J. Cryst. Growth 275 (1–2), 343348.10.1016/j.jcrysgro.2004.10.123Google Scholar
Talib, E., Jalikop, S. V. & Juel, A. 2007 The influence of viscosity on the frozen wave stability: theory and experiment. J. Fluid Mech. 584, 4568.10.1017/S0022112007006283Google Scholar
Tinao, I., Porter, J., Laverón-Simavilla, A. & Fernández, J. 2014 Cross-waves excited by distributed forcing in the gravity-capillary regime. Phys. Fluids 26 (2), 024111.10.1063/1.4865949Google Scholar
Varas, F. & Vega, J. M. 2007 Modulated surface waves in large-aspect-ratio horizontally vibrated containers. J. Fluid Mech. 579, 271304.10.1017/S0022112007005071Google Scholar
Wolf, G. H. 1969 The dynamic stabilization of the Rayleigh–Taylor instability and the corresponding dynamic equilibrium. Z. Phys. 227 (3), 291300.10.1007/BF01397662Google Scholar
Wolf, G. H. 1970 Dynamic stabilization of the interchange instability of a liquid–gas interface. Phys. Rev. Lett. 24 (9), 444446.10.1103/PhysRevLett.24.444Google Scholar
Wolf, G. H. 2018 Dynamic stabilization of the Rayleigh–Taylor instability of miscible liquids and the related ‘frozen waves’. Phys. Fluids 30 (2), 021701.10.1063/1.5017846Google Scholar
Wollman, A., Weislogel, M., Wiles, B., Pettit, D. & Snyder, T. 2016 More investigations in capillary fluidics using a drop tower. Exp. Fluids 57 (4), 57.10.1007/s00348-016-2138-4Google Scholar
Yoshikawa, H. N. & Wesfreid, J. E. 2011 Oscillatory Kelvin–Helmholtz instability. Part 2. An experiment in fluids with a large viscosity contrast. J. Fluid Mech. 675, 249267.10.1017/S0022112011000152Google Scholar