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A Contact Line Dynamic Model for a Conducting Water Drop on an Electrowetting Device

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Two-phase and multiphase flows Magnetohydrodynamics and electrohydrodynamics

Published online by Cambridge University Press:  31 August 2016

Dongdong He  and
Huaxiong Huang
Dongdong He*
Affiliation:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China
Huaxiong Huang*
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada Fields Institute, Toronto, Ontario, M5T 3J1, Canada
*
*Corresponding author. Email addresses:dongdonghe@tongji.edu.cn (D. He), hhuang@yorku.ca (H. Huang)
*Corresponding author. Email addresses:dongdonghe@tongji.edu.cn (D. He), hhuang@yorku.ca (H. Huang)
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Abstract

The static shape of drop under electrowetting actuation is well studied and recent electrowetting theory and experiments confirm that the local contact angle (microscopic angle) is unaffected while the apparent contact angle (macroscopic angle) is characterized by the Lippmann-Young equation. On the other hand, the evolution of the drop motion under electrowetting actuation has received less attention. In this paper, we investigate the motion of a conducting water drop on an electrowetting device (EWD) using the level set method. We derive a contact line two-phase flow model under electrowetting actuation using energy dissipation by generalizing an existing contact line model without the electric field. Our model is consistent with the static electrowetting theory as the dynamic contact angle satisfies the static Young's equation under equilibrium conditions. Our steady state results show that the apparent contact angle predicted by our model satisfies the Lippmann-Young's relation. Our numerical results based on the drop maximum deformation agree with experimental observations and static electrowetting theory. Finally, we show that for drop motion our results are not as good due to the difficulty of computing singular electric field accurately. Nonetheless, they provide useful insights and ameaningful first step towards the understanding of the drop dynamics under electrowetting actuation.

Keywords

Moving contact linecontact anglelevel set methodelectrowettingslip conditions

MSC classification

Secondary: 76T99: None of the above, but in this section 76W05: Magnetohydrodynamics and electrohydrodynamics 65M06: Finite difference methods
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 3 , September 2016 , pp. 811 - 834
Copyright
Copyright © Global-Science Press 2016 

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