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The electrostatically forced Faraday instability: theory and experiments

Published online by Cambridge University Press:  14 January 2019

Kevin Ward Open the ORCID record for Kevin Ward [Opens in a new window] ,
Satoshi Matsumoto  and
Ranga Narayanan
Kevin Ward*
Affiliation:
University of Florida, Department of Chemical Engineering, Gainesville, FL 32611, USA University of Lille, IEMN CNRS 8520, 59655, Lille, France
Satoshi Matsumoto
Affiliation:
Human Spaceflight Technology Directorate, Japan Aerospace Exploration Agency, Tsukuba, Ibaraki 305-8505, Japan
Ranga Narayanan*
Affiliation:
University of Florida, Department of Chemical Engineering, Gainesville, FL 32611, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The onset of interfacial instability in two-fluid systems using a viscous, leaky dielectric model is studied. The instability arises as a result of resonance between the parametric frequency of an imposed electric field and the system’s natural frequency. In addition to a rigorous model that uses Floquet instability analysis, where both viscous and charge effects are considered, this study also provides convincing validating experiments. In other results, it is shown that (a) the imposition of a periodic electrostatic potential acts to counter gravity and this countering effect becomes more effective if a DC voltage is also added, (b) a critical DC voltage exists at which the interface becomes unstable such that no parametric frequency is required to completely destabilize the interface and (c) the leaky dielectric model approaches a model for a perfect dielectric/perfect conductor pair as the conductivity ratio becomes large. It is also shown via experiments that parametric resonant instability using electrostatic forcing may be reliably used to estimate interfacial tension to sufficient accuracy.

JFM classification

Waves/Free-surface Flows: Faraday waves Instability: Parametric instability Nonlinear Dynamical Systems: Pattern formation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 696 - 731
Copyright
© 2019 Cambridge University Press 

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Ward et al. supplementary movie

Example video of an electrostatically forced Faraday instability within an infinite geometry. The system is that described by Test A in Table 2, forced at a frequency of 4.75 Hz and an amplitude of 5 kV.

Download Ward et al. supplementary movie(Video)
Video 5.7 MB