Numerical Modelling of Electrowetting by a Shape Inverse Approach

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Numerical Modelling of Electrowetting by a Shape Inverse Approach J. Monnier, P. Witomski, P. Chow-Wing-Bom, C. Scheid LJK, BP 53, F-38041 Grenoble Cedex 9, France. IDOPT project-team (CNRS-INPG-INRIA-UJF). Abstract. We model an electrified droplet spreading a solid surface. The model aims to seek a drop shape minimizing its total energy (capillary, electro- static and gravitational). We derive the equations and the shape gradient, then detail the shape optimization algorithm and present some numerical results. Up to a critical applied voltage value, the computed angles fit the predictions of Lippman's equation (plane capacitor approximation). Then, when increasing the voltage, we observe an overestimate of the Lippman prediction. Numerical computations of the curvature show that it remains constant everywhere but in a vicinity of the contact point, where it increases sharply. 1 Introduction Electrowetting can be defined as a tool for spreading liquid droplet (e.g. wa- ter) on hydrophobic solid surfaces (e.g. polymer film). This is quite a recent technique, [1], which holds very attractive properties for manipulation of tiny liquid volumes, as it is done in biotechnologies for example. The principle of electrowetting is to apply an electric field between the conductor liquid droplet and the solid surface in order to change the droplet spreading on the surface.