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Computational fluid dynamics model of rhythmic motion of charged droplets between parallel electrodes

Published online by Cambridge University Press:  06 June 2017

Rudolf Flittner Open the ORCID record for Rudolf Flittner [Opens in a new window]  and
Michal Přibyl Open the ORCID record for Michal Přibyl [Opens in a new window]
Rudolf Flittner
Affiliation:
Department of Chemical Engineering, University of Chemistry and Technology, Prague, 166 28 Prague 6, Czech Republic
Michal Přibyl*
Affiliation:
Department of Chemical Engineering, University of Chemistry and Technology, Prague, 166 28 Prague 6, Czech Republic
*
†Email address for correspondence: pribylm@vscht.cz
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Abstract

A mathematical model of rhythmic motion of a charged droplet between two parallel electrodes is developed in this study. The work is motivated by recent experimental findings that report oscillatory behaviour of water in oil droplets under a direct current electric field. The model considers the presence of a charged droplet placed in a dielectric medium. The droplet is immediately attracted to the electrode with the opposite polarity. When approaching the electrode, the electric charge is electrochemically reversed within the droplet, which is then repelled to the other electrode. The entire process can periodically repeat. The model is able to track a deformable liquid–liquid interface, the dynamics of the wetting process at the electrodes and the dynamics of electrochemical charge transfer between the droplet and the electrodes. The dependences of the oscillation frequency, charge acquired by the droplet and charging time on several model parameters (surface charge density on electrodes, kinetic parameter of charging, droplet–electrode contact angle, droplet size, liquid permittivity) are examined. Qualitative agreement of the model predictions with available experimental data is obtained, e.g. the oscillation frequency increases with growing electric field strength or droplet size. Our model represents the first successful attempt to predict oscillatory motion of aqueous droplets by a pseudo-three-dimensional two-phase approach. Our model also strongly supports the theory that the oscillatory motion relies on the combination of electrochemical charge injection at the electrodes and electrostatic attraction/repulsion processes.

JFM classification

Drops and Bubbles: Drops MHD and Electrohydrodynamics: MHD and Electrohydrodynamics Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 822 , 10 July 2017 , pp. 31 - 53
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Copyright
© 2017 Cambridge University Press 

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Flittner and Přibyl supplementary movie

Aqueous droplet dispersed in a dielectric fluid oscillates between electrodes under DC electric field.

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