A model of electrowetting, reversed electrowetting, and contact angle saturation.

While electrowetting has many applications, it is limited at large voltages by contact angle saturation, a phenomenon that is still not well understood. We propose a generalized approach for electrowetting that, among other results, can shed new light on contact angle saturation. The model assumes the existence of a minimum (with respect to the contact angle) in the electric energy and accounts for a quadratic voltage dependence ∼U(2) in the low-voltage limit, compatible with the Young-Lippmann formula, and an ∼U(-2) saturation at the high-voltage limit. Another prediction is the surprising possibility of a reversed electrowetting regime, in which the contact angle increases with applied voltage. By explicitly taking into account the effect of the counter-electrode, our model is shown to be applicable to several AC and DC experimental electrowetting-on-dielectric (EWOD) setups. Several features seen in experiments compare favorably with our results. Furthermore, the AC frequency dependence of EWOD agrees quantitatively with our predictions. Our numerical results are complemented with simple analytical expressions for the saturation angle in two practical limits.