Numerical Modelling of Electrowetting by a Shape Inverse Approach

Abstract. We model an electrified droplet spreading a solid surface. The model aims to seek a drop shape minimizing its total energy (capillary, electrostatic 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.