Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T18:39:21.641Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of the interface between miscible liquids subjected to horizontal vibration

Published online by Cambridge University Press:  04 November 2015

Y. A. Gaponenko ,
M. Torregrosa ,
V. Yasnou ,
A. Mialdun  and
V. Shevtsova
Y. A. Gaponenko*
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
M. Torregrosa
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
V. Shevtsova
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
*
†Email address for correspondence: ygaponen@ulb.ac.be
Get access Rights & Permissions [Opens in a new window]

Abstract

We present experimental evidence of the existence of an interfacial instability between two miscible liquids of similar (but non-identical) viscosities and densities under horizontal vibration. A stably stratified two-layer system is composed of the same binary mixture with different concentrations placed in a confined cell (with length twice as large as the height). Unlike the case of immiscible fluids, here, the interface is a transient layer of small but non-zero thickness. In the experiments, the frequency and amplitude were varied within the ranges 2–24 Hz and 1.5–16 mm, respectively. When the value of the oscillatory forcing increases, the amplitudes of the interface perturbations grow continuously, forming a saw-tooth frozen structure. This evolution is also examined numerically. In addition to the solutions of full 3-D Navier–Stokes equations, an averaging approach with separation of time scales is used for situations in which the forcing period is very small compared to the natural time scales of the problem. The simulation of averaged equations provides the explanation of the instability development, the calculations of the full nonlinear equations shed light on the decay of a wavy pattern. The results of numerical modelling perfectly support the experimental observations.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Nonlinear Dynamical Systems: Pattern formation Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 784 , 10 December 2015 , pp. 342 - 372
Check for updates
Copyright
© 2015 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

Beysens, D. 2006 Vibrations in space as an artificial gravity? Europhys. News 37 (3), 22–25.CrossRefGoogle Scholar
Chandrasekhar, S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover.Google Scholar
Gandikota, G., Chatain, D., Amiroudine, S., Lyubimova, T. & Beysens, D. 2014a Frozen-wave instability in near-critical hydrogen subjected to horizontal vibration under various gravity fields. Phys. Rev. E 89, 012309.CrossRefGoogle ScholarPubMed
Gandikota, G., Chatain, D., Amiroudine, S., Lyubimova, T. & Beysens, D. 2014b Dynamic equilibrium under vibrations of H2 liquid–vapor interface at various gravity levels. Phys. Rev. E 89, 063003.Google Scholar
Gaponenko, Y. & Shevtsova, V. 2008 Mixing under vibrations in reduced gravity. Microgravity Sci. Technol. 20 (3–4), 307–311.Google Scholar
Gaponenko, Y. & Shevtsova, V. 2010 Effects of vibrations on dynamics of miscible liquids. Acta Astronaut. 66, 174–182.Google Scholar
Gaponenko, Y., Torregrosa, M. M., Yasnou, V., Mialdun, A. & Shevtsova, V. 2015 Interfacial pattern selection in miscible liquids under vibration. Soft Matt. doi:10.1039/c5sm02110c.Google Scholar
Gershuni, G. Z. & Lyubimov, D. V. 1998 Thermal Vibrational Convection. Wiley & Sons.Google Scholar
Gonzalez-Vinas, W. & Salan, J. 1994 Surface waves periodically excited in a $\text{CO}_{2}$ tube. Europhys. Lett. 26, 665–670.CrossRefGoogle Scholar
Higuera, M., Vega, J. M. & Knobloch, E. 2002 Coupled amplitude-mean flow equations for nearly-inviscid Faraday waves in moderate aspect ratio containers. J. Nonlinear Sci. 12, 505–551.Google Scholar
Ivanova, A. A., Kozlov, V. G. & Evesque, P. 2001 Interface dynamics of immiscible fluids under horizontal vibrations. Fluid Dyn. 36 (3), 362–368.Google Scholar
Jalikop, S. V. & Juel, A. 2009 Steep capillary-gravity waves in oscillatory shear-driven flows. J. Fluid Mech. 640, 131–150.Google Scholar
Kheniene, A. & Vorobev, A. 2013 Linear stability analysis of a horizontal phase boundary separating two miscible liquids. Phys. Rev. E 88, 022404.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.CrossRefGoogle Scholar
Lacaze, L., Guenoun, P., Beysens, D., Delsanti, M., Petitjeans, P. & Kurowski, P. 2010 Transient surface tension in miscible liquids. Phys. Rev. E 82, 041606.Google Scholar
Legendre, M., Petitjeans, P. & Kurowski, P. 2003 Instabilités à l’interface entre fluides miscibles par forcage oscillant horizontal. C. R. Méc. 331, 617–622.Google Scholar
Lyubimov, D. V. & Cherepanov, A. 1987 Development of a steady relief at the interface of fluids in a vibrational field. Fluid Dyn. 86, 849–854.Google Scholar
Mazzoni, S., Shevtsova, V., Mialdun, A., Melnikov, D., Gaponenko, Yu., Lyubimova, T. & Saghir, M. Z. 2010 Vibrating liquids in space. Europhys. News 41 (6), 14–16.Google Scholar
Mialdun, A., Ryzhkov, I. I., Melnikov, D. E. & Shevtsova, V. 2008 Experimental evidence of thermal vibrational convection in a non-uniformly heated fluid in a reduced gravity environment. Phys. Rev. Lett. 101, 084501.Google Scholar
Mialdun, A., Yasnou, V., Shevtsova, V., Königer, A., Köhler, W., Alonso de Mezquia, D. & Bou-Ali, M. M. 2012 A comprehensive study of diffusion, thermodiffusion, and Soret coefficients of water-isopropanol mixtures. J. Chem. Phys. 136, 244512.Google Scholar
Pojman, J. A., Whitmore, C., Liveri, M. L. T., Lombardo, R., Marszalek, J., Parker, R. & Zoltowski, B. 2006 Evidence for the existence of an effective interfacial tension between miscible fluids: isobutyric acid–water and 1-butanol–water in a spinning-drop tensiometer. Langmuir 22, 2569–2577.Google Scholar
Shevtsova, V., Gaponenko, Y. A., Sechenyh, V., Melnikov, D. E., Lyubimova, T. & Mialdun, A. 2015a Dynamics of a binary mixture subjected to a temperature gradient and oscillatory forcing. J. Fluid Mech. 767, 290–322.Google 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, 5550–5553.Google Scholar
Shevtsova, V., Lyubimova, T., Saghir, Z., Melnikov, D., Gaponenko, Y., Sechenyh, V., Legros, J. C. & Mialdun, A. 2011 IVIDIL: on-board g-jitters and diffusion controlled phenomena. J. Phys.: Conf. Ser. 327, 012031.Google Scholar
Shevtsova, V., Ryzhkov, I. I., Melnikov, D. E., Gaponenko, Y. A. & Mialdun, A. 2010 Experimental and theoretical study of vibration-induced thermal convection in low gravity. J. Fluid Mech. 648, 53–82.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, 45–68.Google Scholar
Talib, E. & Juel, A. 2007 Instability of a viscous interface under horizontal oscillation. Phys. Fluids 19, 092102.CrossRefGoogle Scholar
Varas, F. & Vega, J. M. 2007 Modulated surface waves in large-aspect-ratio horizontally vibrated containers. J. Fluid Mech. 579, 271–304.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. 1969 The dynamic stabilization of the Rayleigh–Taylor Instability and the corresponding dynamic equilibrium. Z. Phys. 227, 291–300.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
Wunenburger, R., Evesque, P., Chabot, C., Garrabos, Y., Fauve, S. & Beysens, D. 1999 Frozen wave induced by high frequency horizontal vibrations on a $\text{CO}_{2}$ liquid–gas interface near the critical point. Phys. Rev. E 59, 5440–5445.Google Scholar
Yoshikawa, H. N. & Wesfreid, J. E. 2011a Oscillatory Kelvin–Helmholtz instability. Part 1. A viscous theory. J. Fluid Mech. 675, 223–248.Google Scholar
Yoshikawa, H. N. & Wesfreid, J. E. 2011b Oscillatory Kelvin–Helmholtz instability. Part 2. An experiment in fluids with a large viscosity contrast. J. Fluid Mech. 675, 249–267.Google Scholar
Zeldovich, Y. B. 1949 Interfacial tension between miscible liquids (in Russian). Zhur. Fiz. Khim XXIII, 931–935.Google Scholar