Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-12-01T09:05:37.908Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-scale wave patterns on a periodically excited miscible liquid–liquid interface

Published online by Cambridge University Press:  15 April 2016

V. Shevtsova ,
Y. A. Gaponenko ,
V. Yasnou ,
A. Mialdun  and
A. Nepomnyashchy
V. Shevtsova*
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
Y. A. Gaponenko
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
V. Yasnou
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
A. Mialdun
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
A. Nepomnyashchy
Affiliation:
Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We have discovered a peculiar behaviour of the interface between two miscible liquids placed in a finite-size container under horizontal vibration. We provide evidence that periodic wave patterns created by the Kelvin–Helmholtz instability and Faraday waves simultaneously exist in the same system of miscible liquids. We show experimentally in reduced and normal gravity that large-scale frozen waves yield Faraday waves with a smaller wavelength on a diffusive interface. The emergence of the different scale patterns observed in the experiments is confirmed numerically and explained theoretically.

JFM classification

Instability: Instability Mixing: Mixing Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 409 - 422
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benilov, E. S. & Chugunova, M. 2010 Waves in liquid films on vibrating substrates. Phys. Rev. E 81, 036302.Google 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), 505–515.Google Scholar
Besson, Th., Edwards, W. S. & Tuckerman, L. S. 1996 Two-frequency parametric excitation of surface waves. Phys. Rev. E 54, 507–513.CrossRefGoogle ScholarPubMed
Borcia, R., Borcia, I. D. & Bestehorn, M. 2014 Can vibrations control drop motion? Langmuir 30, 14113–14117.CrossRefGoogle ScholarPubMed
Diwakar, S. V., Zoueshtiagh, F., Amiroudine, S. & Narayanan, R. 2015 The Faraday instability in miscible fluid systems. Phys. Fluids 27, 084111.Google Scholar
Gandikota, G., Chatain, D., Amiroudine, S., Lyubimova, T. & Beysens, D. 2014 Frozen-wave instability in near-critical hydrogen subjected to horizontal vibration under various gravity fields. Phys. Rev. E 89, 012309.CrossRefGoogle ScholarPubMed
Gaponenko, Y., Torregrosa, M., Yasnou, V., Mialdun, A. & Shevtsova, V. 2015a Dynamics of the interface between miscible liquids subjected to horizontal vibration. J. Fluid Mech. 784, 342–372.Google Scholar
Gaponenko, Y., Torregrosa, M. M., Yasnou, V., Mialdun, A. & Shevtsova, V. 2015b Interfacial pattern selection in miscible liquids under vibration. Soft Matt. 11, 8221–8224.CrossRefGoogle ScholarPubMed
Ivanova, A. A., Kozlov, V. G. & Evesque, P. 2001 Interface dynamics of immiscible fluids under horizontal vibrations. Fluid Dyn. 36, 362–368.CrossRefGoogle Scholar
Jalikop, S. V. & Juel, A. 2009 Steep capillary–gravity waves in oscillatory shear-driven flows. J. Fluid Mech. 640, 131–150.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, 1085–1101.Google Scholar
Kumar, K. & Tuckerman, L. 1994 Parametric instability of the interface between two fluids. J. Fluid Mech. 279, 49–68.Google Scholar
Kumar, S. 2000 Mechanism for the Faraday instability in viscous liquids. Phys. Rev. E 62, 1416–1419.Google Scholar
Kumar, S. 2001 Parametric instability of a liquid sheet. Proc. R. Soc. Lond. A 457, 1315–1326.Google Scholar
Lyubimov, D. V. & Cherepanov, A. 1986 Development of a steady relief at the interface of fluids in a vibrational field. Fluid Dyn. 21, 849–854.Google Scholar
Mialdun, A., Sechenyh, V., Legros, J. C., Ortiz de Zárate, J. M. & Shevtsova, V. 2013a Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane. J. Chem. Phys. 139, 104903.Google Scholar
Mialdun, A., Yasnou, V. & Shevtsova, V. 2013b Measurement of isothermal diffusion coefficients in ternary mixtures using counter flow diffusion cell. C. R. Méc. 341, 462–468.Google Scholar
Shevtsova, V., Gaponenko, Y., Yasnou, V., Mialdun, A. & Nepomnyashchy, A. 2015a Wall-generated pattern on a periodically excited miscible liquid/liquid interface. Langmuir 31, 5550–5553.Google Scholar
Shevtsova, V., Gaponenko, Y. A., Sechenyh, V., Melnikov, D. E., Lyubimova, T. & Mialdun, A. 2015b Dynamics of a binary mixture subjected to a temperature gradient and oscillatory forcing. J. Fluid Mech. 767, 290–322.CrossRefGoogle Scholar
Shevtsova, V., Ryzhkov, I., Melnikov, D., Gaponenko, Y. & Mialdun, A. 2010 Experimental and theoretical study of vibration-induced thermal convection in low gravity. J. Fluid Mech. 648, 53–82.Google 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, 45–68.CrossRefGoogle 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, 024111.Google Scholar
Vorobev, A. 2014 Dissolution dynamics of miscible liquid/liquid interfaces. Curr. Opin. Colloid Interface Sci. 19, 300–308.CrossRefGoogle Scholar
Wolf, G. H. 1970 Dynamic stabilization of the interchange instability of a liquid–gas interface. Phys. Rev. Lett. 24, 444–446.Google Scholar
Zoueshtiagh, F., Amiroudine, S. & Narayanan, R. 2009 Experimental and numerical study of miscible Faraday instability. J. Fluid Mech. 628, 43–55.Google Scholar

Shevtsova supplementary movie

VIPIL_Parabolic_Flight

Download Shevtsova supplementary movie(Video)
Video 7.5 MB