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Nonlinear dynamics of electrostatic Faraday instability in thin films

Published online by Cambridge University Press:  21 September 2018

Dipin S. Pillai Open the ORCID record for Dipin S. Pillai [Opens in a new window]  and
R. Narayanan
Dipin S. Pillai*
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
R. Narayanan
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
*
†Email address for correspondence: [email protected]
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Abstract

The nonlinear evolution of an interface between a perfect conducting liquid and a perfect dielectric gas subject to periodic electrostatic forcing is studied under the long-wave approximation. It is shown that inertial thin films become unstable to finite-wavelength Faraday modes at the onset, prior to the long-wave pillaring instability reported in the lubrication limit. It is further shown that the pillaring-mode instability is subcritical in nature, with the interface approaching either the top or the bottom wall, depending on the liquid–gas holdup. On the other hand, the Faraday modes exhibit subharmonic or harmonic oscillations that nonlinearly saturate to standing waves at low forcing amplitudes. Unlike the pillaring mode, wherein the interface approaches the wall, Faraday modes may exhibit saturated standing waves when the instability is subcritical. At higher forcing amplitudes, the interface may approach either wall, again depending on the liquid–gas holdup. It is also shown that a gravitationally unstable configuration of such thin films, under the long-wave approximation, cannot be stabilized by periodic electrostatic forcing, unlike mechanical Faraday forcing. In this case, it is observed that the interface exhibits oscillatory sliding behaviour, approaching the wall in an ‘earthworm-like’ motion.

JFM classification

Drops and Bubbles: Electrohydrodynamic effects Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , R4
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Copyright
© 2018 Cambridge University Press 

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Pillai Supplementary Movie 1

Spatiotemporal evolution of the interface in the pillaring mode for low liquid-gas holdup (k=0.1, A=28.5kV, β=10)

Download Pillai Supplementary Movie 1(Video)
Video 6 MB

Pillai Supplementary Movie 2

Spatiotemporal evolution of the interface, depicting the subharmonic (k=0.19, A=5.6kV) and harmonic (k=0.33, A=8.1kV) Faraday responses.

Download Pillai Supplementary Movie 2(Video)
Video 4.2 MB

Pillai Supplementary Movie 3

Gravitationally stable interface exhibiting sliding dynamics akin to RT instability when subject to electrostatic forcing. ( β=10, Ω=0, A=26kV, k=0.2).

Download Pillai Supplementary Movie 3(Video)
Video 1 MB

Pillai Supplementary Movie 4

Spatiotemporal evolution of a RT unstable interface subject to periodic forcing. The interface exhibits oscillatory sliding dynamics similar to an earthworm motion.

Download Pillai Supplementary Movie 4(Video)
Video 2.3 MB