Numerical modeling of electrowetting by a shape inverse approach

Jerome Monnier (1) , Patrick Witomski (2) , Patrick Chow-Wing-Bom (1) , Claire Scheid (2)

1 MOISE - Modelling, Observations, Identification for Environmental Sciences
2 EDP - Equations aux Dérivées Partielles

We model an electrified droplet spreading on a solid surface. The model aims to seek a drop shape that minimizes its total energy (capillary, electrostatic, and gravitational). We derive the equations and the shape gradient; then we 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 except in the vicinity of the contact point, where it increases sharply.

Mots clés: shape optimal; design; electrowetting; contact point; energy minimization; curvature

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Micro et nanotechnologies/Microélectronique; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Jerome Monnier, Patrick Witomski, Patrick Chow-Wing-Bom, Claire Scheid. Numerical modeling of electrowetting by a shape inverse approach. SIAM Journal on Applied Mathematics, 2009, 69 (5), pp.1477-1500. ⟨10.1137/050624340⟩. ⟨hal-00380673⟩