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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]
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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 

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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