Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-20T00:12:29.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental and numerical study of miscible Faraday instability

Published online by Cambridge University Press:  01 June 2009

F. ZOUESHTIAGH ,
S. AMIROUDINE  and
R. NARAYANAN
F. ZOUESHTIAGH*
Affiliation:
Institut d'Electronique, de Microélectronique et de Nanotechnologie UMR CNRS 8520, Avenue Poincaré, 59652 Villeneuve d'Ascq, France
S. AMIROUDINE
Affiliation:
LPMI-Arts et Métiers ParisTech., 2 Bd du Ronceray, BP 93525, 49035 Angers, France
R. NARAYANAN
Affiliation:
University of Florida, Department of Chemical Engineering, Gainesville, FL 32611-6005, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Instability: Instability Waves/Free-surface Flows: Faraday waves Mixing: Mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 43 - 55
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

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, 119–140.CrossRefGoogle Scholar
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), 665–680.Google Scholar
Amiroudine, S. & Zappoli, B. 2003 Piston-effect-induced thermal oscillations at the Rayleigh–Benard threshold in supercritical He-3. Phys. Rev. Lett. 90 (10).CrossRefGoogle Scholar
Ballesta, P. & Manneville, S. 2006 Shear-thickening induced by Faraday waves in dilute wormlike micelles. Europhys. Lett. 76 (3), 429–435.CrossRefGoogle Scholar
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), 505–515.Google Scholar
Faraday, M. 1831 On the forms and states of fluids on vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 121, 319–340.Google Scholar
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.CrossRefGoogle Scholar
James, A. J., Vukasinovic, B., Smith, M. K. & Glezer, A. 2003 Vibration-induced drop atomization and bursting. J. Fluid Mech. 476, 1–28.CrossRefGoogle Scholar
Kumar, S. & Matar, O. K. 2004 On the Faraday instability in a surfactant-covered liquid. Phys. Fluids 16 (1), 39–46.CrossRefGoogle Scholar
Kumar, K. & Tuckerman, L. S. 1994 Parametric instability of the interface between two fluids. J. Fluid Mech. 329, 49–68.CrossRefGoogle Scholar
Lide, D. R. 2004 CRC Handbook of Chemistry and Physics, edn 85. Taylor and Francis.Google Scholar
McLachlan, N. W. 1947 Theory and Application of Mathieu Functions. Oxford University Press.Google Scholar
Nayfeh, A. H. 1981 Introduction to Perturbation Techniques. Wiley Interscience.Google Scholar
Patankar, S. 1980 Numerical Heat Transfer and Fluid Flows. McGraw Hill.Google Scholar
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), 4011–4020.CrossRefGoogle Scholar
Tipton, C. R. & Mullin, T. 2004 An experimental study of Faraday waves formed on the interface between two immiscible liquids. Phys. Fluids 16 (7), 2336–2341.CrossRefGoogle Scholar
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, 305–329.CrossRefGoogle Scholar
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), 59–66.Google Scholar
Zoueshtiagh, F., Legendre, M., Caps, H., Vandewalle, N., Petitjeans, Ph. & Kurowski, P. 2006 Air bubbles under vertical vibrations. Eur. Phys. J. E 20, 317–325.CrossRefGoogle ScholarPubMed

Zoueshtiagh et al. supplementary movie

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

Download Zoueshtiagh et al. supplementary movie(Video)
Video 8.1 MB

Zoueshtiagh et al. supplementary movie

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

Download Zoueshtiagh et al. supplementary movie(Video)
Video 10.1 MB