Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T04:40:18.572Z Has data issue: false hasContentIssue false
  • English
  • Français

The Faraday threshold in small cylinders and the sidewall non-ideality

Published online by Cambridge University Press:  24 July 2013

W. Batson ,
F. Zoueshtiagh  and
R. Narayanan
W. Batson*
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32601, USA Université Lille 1, Institut d’Electronique, de Microélectronique et de Nanotechnologie (IEMN), UMR, CNRS 8520, Avenue Poincaré, 59652 Villeneuve d’Ascq, France
F. Zoueshtiagh
Affiliation:
Université Lille 1, Institut d’Electronique, de Microélectronique et de Nanotechnologie (IEMN), UMR, CNRS 8520, Avenue Poincaré, 59652 Villeneuve d’Ascq, France
R. Narayanan
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32601, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this work we investigate, by way of experiments and theory, the Faraday instability threshold in cylinders at low frequencies. This implies large wavelengths where effects from mode discretization cannot be ignored. Careful selection of the working fluids has resulted in an immiscible interface whose apparent contact line with the sidewall can glide over a tiny film of the more wetting fluid, without detachment of its actual contact line. This unique behaviour has allowed for a system whose primary dissipation is defined by the bulk viscous effects, and in doing so, for the first time, close connection is seen with the viscous linear stability theory for which a stress-free condition is assumed at the sidewalls. As predicted, mode selection and co-dimension 2 points are observed in the experiment for a frequency range including subharmonic, harmonic, and superharmonic modes. While agreement with the predictions are generally excellent, there are deviations from the theory for certain modes and these are explained in the context of harmonic meniscus waves. A review of previous work on single-mode excitation in cylinders is given, along with comparison to the viscous model and analysis based upon the conclusions of the current experiments.

JFM classification

Waves/Free-surface Flows: Faraday waves Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 729 , 25 August 2013 , pp. 496 - 523
Copyright
©2013 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

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions, 10th edn. Dover.Google Scholar
Bechhoefer, J., Ego, V., Manneville, S. & Johnson, B. 1995 An experimental study of the onset of parametrically pumped surface waves in viscous fluids. J. Fluid Mech. 288, 325–350.Google Scholar
Benjamin, T. B. & Ursell, F. 1954 The stability of a plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. Lond. A 225, 505–515.Google Scholar
Case, K. M. & Parkinson, W. C. 1957 Damping of surface waves in an incompressible fluid. J. Fluid Mech. 2, 172–184.Google Scholar
Christiansen, B., Alstrøm, P. & Levinsen, M. T. 1994 Dissipation and ordering in capillary waves at high aspect ratios. J. Fluid Mech. 291, 323–341.Google Scholar
Ciliberto, S. & Gollub, J. P. 1985 Chaotic mode competition in parametrically forced surface waves. J. Fluid Mech. 158, 381–398.Google Scholar
Das, S. P. & Hopfinger, E. J. 2008 Parametrically forced gravity waves in a circular cylinder and finite-time singularity. J. Fluid Mech. 599, 205–228.Google Scholar
Dodge, F. T., Kana, D. D. & Abramson, H. N. 1965 Liquid surface oscillations in longitudinally excited rigid cylindrical containers. AIAA J. 3, 685–695.Google Scholar
Douady, S. 1990 Experimental study of the Faraday instability. J. Fluid Mech. 221, 383–409.Google Scholar
Fauve, S., Kumar, K., Laroche, C., Beysens, D. & Garrabos, Y. 1992 Parametric instability of a liquid–vapor interface close to the critical point. Phys. Rev. Lett. 68 (21), 3160–3163.Google Scholar
Friend, J. & Yeo, L. Y. 2011 Microscale acoustofluidics: microfluidics driven via acoustics and ultrasonics. Rev. Mod. Phys. 83, 647–704.Google Scholar
Henderson, D. & Miles, J. 1990 Single-mode Faraday waves in small cylinders. J. Fluid Mech. 213, 95–109.Google Scholar
Ito, T. & Kukita, Y. 2008 Interface behavior between two fluids vertically oscillated in a circular cylinder under nonlinear contact line condition. J. Fluid Sci. Technol. 3, 690–711.CrossRefGoogle Scholar
Ito, T., Tsuji, Y. & Kukita, Y. 1999 Interface waves excited by vertical vibration of stratified fluids in a circular cylinder. J. Nucl. Sci. Technol. 36, 508–521.Google Scholar
Keulegan, G. H. 1958 Energy dissipation in standing waves in rectangular basins. J. Fluid Mech. 6, 33–50.Google Scholar
Kityk, A. V., Embs, J., Mekhonoshin, V. V. & Wagner, C. 2005 Spatiotemporal characterization of interfacial Faraday waves by means of a light absorption technique. Phys. Rev. E 72, 036209.Google Scholar
Kumar, K. 1996 Linear theory of Faraday instability in viscous fluids. Proc. R. Soc. Lond. A 452, 1113–1126.Google Scholar
Kumar, K. & Tuckerman, L. 1994 Parametric instability of the interface between two fluids. J. Fluid Mech. 279, 49–67.Google Scholar
Landau, L. D. & Lifshitz, L. M. 1987 Fluid Mechanics, vol. 6. Course of Theoretical Physics, Butterworth-Heinemann.Google Scholar
Miles, J. W. 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297, 459–475.Google Scholar
Miles, J. W. 1984 Nonlinear Faraday resonance. J. Fluid Mech. 146, 285–302.Google Scholar
Milner, S. T. 1991 Square patterns and secondary instabilities in driven capillary waves. J. Fluid Mech. 225, 81–100.Google Scholar
Müller, H. W., Wittmer, H., Wagner, C., Albers, J. & Knorr, K. 1997 Analytic stability theory for Faraday waves and the observation of the harmonic surface response. Phys. Rev. Lett. 78 (12), 2357–2360.Google Scholar
Nayfeh, A. H. & Mook, D. T. 1979 Nonlinear Oscillations. Wiley.Google Scholar
Skeldon, A. C. & Guidoboni, G. 2007 Pattern selection for Faraday waves in an incompressible fluid. SIAM J. Appl. Maths. 67 (4), 1064–1100.Google Scholar
Someya, S. & Munakata, T. 2005 Measurement of the interface tension of immiscible liquids interface. J. Cryst. Growth 275, 343–348.Google Scholar
Tipton, C. 2003 Interfacial Faraday waves in a small cylindrical cell. PhD thesis, University of Manchester.Google Scholar
Tipton, C. R. & Mullin, T. 2004 An experimental study of Faraday waves formed on the interface between two immiscible liquids. Phys. Fluids 16, 2336–2341.Google Scholar
Virnig, J. C., Berman, A. S. & Sethna, P. R. 1988 On three-dimensional nonlinear subharmonic resonant surface waves in a fluid. Part 2. Experiment. Trans. ASME E: J. Appl. Mech. 55, 220–224.Google Scholar
Wagner, C., Müller, H.-W. & Knorr, K. 2003 Pattern formation at the bicritical point of the Faraday instability. Phys. Rev. E 68, 066204.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

Batson et al. supplementary movie

Experimental visualization of the FC70-1.5 cSt silicone oil interface. Parametric conditions are 6 Hz and 3.0 mm.

Download Batson et al. supplementary movie(Video)
Video 8.3 MB

Batson et al. supplementary movie

Experimental visualization of the excitation of a (0,1)sh mode in a FC70-1.5 cSt silicone oil system, excited at 7.5 Hz and 0.98 mm.

Download Batson et al. supplementary movie(Video)
Video 6 MB

Batson et al. supplementary movie

Film dynamics for a period of (0,1)sh motion in a FC70-50 cSt silicone oil system.

Download Batson et al. supplementary movie(Video)
Video 4.9 MB

Batson et al. supplementary movie

Film dynamics for a period of (0,1)sh in a FC70-1.5 cSt silicone oil system.

Download Batson et al. supplementary movie(Video)
Video 7.3 MB

Batson et al. supplementary movie

Experimental visualization of the growth and breakup of a co-dimension 2 point consisting of a (2,1)sh mode with a (0,1)sh mode.

Download Batson et al. supplementary movie(Video)
Video 9.6 MB