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Dynamics of an Ellipse-Shaped Meniscus on a Substrate-Supported Drop under an Electric Field

Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
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Author to whom correspondence should be addressed.
Fluids 2019, 4(4), 200; https://doi.org/10.3390/fluids4040200
Received: 1 October 2019 / Revised: 12 November 2019 / Accepted: 26 November 2019 / Published: 29 November 2019
(This article belongs to the Special Issue Drop, Bubble and Particle Dynamics in Complex Fluids )
The behavior of a conducting droplet and a dielectric droplet placed under an electric potential is analyzed. Expressions for drop height based on electrode separation and the applied voltage are found, and problem parameters associated with breakup and droplet ejection are classified. Similar to previous theoretical work, the droplet interface is restricted to an ellipse shape. However, contrary to previous work, the added complexity of the boundary condition at the electrode is taken into account. To gain insight into this problem, a two-dimensional droplet is addressed. This allows for conformal maps to be used to solve for the potential surrounding the drop, which gives the total upward electrical force on the drop that is then balanced by surface tension and gravitational forces. For the conducting case, the maximum droplet height is attained when the distance between the electrode and the drop becomes sufficiently large, in which case, the droplet can stably grow to about 2.31 times its initial height before instabilities occur. In the dielectric case, hysteresis can occur for certain values of electrode separation and relative permittivity. View Full-Text
Keywords: electrified fluids; conformal map; Taylor cone electrified fluids; conformal map; Taylor cone
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Zaleski, P.; Afkhami, S. Dynamics of an Ellipse-Shaped Meniscus on a Substrate-Supported Drop under an Electric Field. Fluids 2019, 4, 200.

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