Skip to main content Accessibility help
×
Home

Experimental and numerical study of miscible Faraday instability

  • F. ZOUESHTIAGH (a1), S. AMIROUDINE (a2) and R. NARAYANAN (a3)

Abstract

A study of the Faraday instability of diffuse interfaces between pairs of miscible liquids of different densities, by means of experiments and by a nonlinear numerical model, is presented. The experimental set-up consisted of a rectangular cell in which the lighter liquid was placed above the denser one. The cell in this initially stable configuration was then subjected to vertical vibrations. The subsequent behaviour of the ‘interface’ between the two liquids was observed with a high-speed camera. This study shows that above a certain acceleration threshold an instability developed at the interface. The amplitude of the instability grew during the experiments which then led to the mixing of the liquids. The instability finally disappeared once the two liquids were fully mixed over a volume, considerably larger than the initial diffuse region. The results of a companion two-dimensional nonlinear numerical model that employs a finite volume method show very good agreement with the experiments. A physical explanation of the instability and the observations are advanced.

Copyright

Corresponding author

Email address for correspondence: Farzam.Zoueshtiagh@univ-lille1.fr

References

Hide All
Amiroudine, S., Bontoux, P., Larroude, P., Gilly, B. & Zappoli, B. 2001 Direct numerical simulation of instabilities in a two-dimensional near-critical fluid layer heated from below. J. Fluid Mech. 442, 119140.
Amiroudine, S., Ouazzani, J., Carles, P. & Zappoli, B. 1997 Numerical solutions of 1-D unsteady near-critical fluid flows using finite volume methods. Eur. J. Mech. B-Fluids 16 (5), 665680.
Amiroudine, S. & Zappoli, B. 2003 Piston-effect-induced thermal oscillations at the Rayleigh–Benard threshold in supercritical He-3. Phys. Rev. Lett. 90 (10).
Ballesta, P. & Manneville, S. 2006 Shear-thickening induced by Faraday waves in dilute wormlike micelles. Europhys. Lett. 76 (3), 429435.
Benjamin, T. B. & Ursell, F. 1954 The stability of the plane free surface of a liquid in vertical periodic motion. In Proc. R. Soc. Lond. A 225 (1163), 505515.
Faraday, M. 1831 On the forms and states of fluids on vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 121, 319340.
Fauve, S., Kumar, K., Laroche, C., Beyssens, D. & Garrabos, Y. 1992 Parametric instability of a liquid–vapor interface close to the critical point. Phys. Rev. Lett. 68, 3160.
James, A. J., Vukasinovic, B., Smith, M. K. & Glezer, A. 2003 Vibration-induced drop atomization and bursting. J. Fluid Mech. 476, 128.
Kumar, S. & Matar, O. K. 2004 On the Faraday instability in a surfactant-covered liquid. Phys. Fluids 16 (1), 3946.
Kumar, K. & Tuckerman, L. S. 1994 Parametric instability of the interface between two fluids. J. Fluid Mech. 329, 4968.
Lide, D. R. 2004 CRC Handbook of Chemistry and Physics, edn 85. Taylor and Francis.
McLachlan, N. W. 1947 Theory and Application of Mathieu Functions. Oxford University Press.
Nayfeh, A. H. 1981 Introduction to Perturbation Techniques. Wiley Interscience.
Patankar, S. 1980 Numerical Heat Transfer and Fluid Flows. McGraw Hill.
Shukla, P. K. & Narayanan, R. 2002 The effect of time-dependent gravity with multiple frequencies on the thermal convective stability of a fluid layer. Intl J. Heat Mass Transfer 45 (19), 40114020.
Tipton, C. R. & Mullin, T. 2004 An experimental study of Faraday waves formed on the interface between two immiscible liquids. Phys. Fluids 16 (7), 23362341.
Ubal, S., Giavedoni, M. D. & Saita, F. A. 2005 a Elastic effects of an insoluble surfactant on the onset of two-dimensional Faraday waves: a numerical experiment. J. Fluid Mech. 524, 305329.
Ubal, S., Giavedoni, M. D. & Saita, F. A. 2005 b The formation of Faraday waves on a liquid covered with an insoluble surfactant: Influence of the surface equation of state. Latin Am. Appl. Res. 35 (1), 5966.
Zoueshtiagh, F., Legendre, M., Caps, H., Vandewalle, N., Petitjeans, Ph. & Kurowski, P. 2006 Air bubbles under vertical vibrations. Eur. Phys. J. E 20, 317325.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO
Type Description Title
VIDEO
Movies

Zoueshtiagh et al. supplementary movie
Movie 1. Faraday instability between miscible fluids. Experimental parameters are: A=3 cm, f=4 Hz, t0= 5 min.

 Video (8.1 MB)
8.1 MB
VIDEO
Movies

Zoueshtiagh et al. supplementary movie
Movie 2. Faraday instability between miscible fluids. Experimental parameters are: A=1 cm, f=8 Hz, t0= 5 min.

 Video (10.1 MB)
10.1 MB

Experimental and numerical study of miscible Faraday instability

  • F. ZOUESHTIAGH (a1), S. AMIROUDINE (a2) and R. NARAYANAN (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.