An electromechanical model for electrowetting

We present an electromechanical model for analysis of electrowetting by considering the balance between an electric force and a surface tension force acting on the contact line of three phases, namely the droplet (D) phase the substrate (S) phase and the ambiance (A) phase. We show that the electric force acting on the three-phase contact line generally is contributed by the Maxwell stresses at the ambiance-substrate (A-S) interface, the droplet-substrate (D-S) interface, and the droplet-ambiance (D-A) interface. It was identified that the change of contact angle in electrowetting is essentially a consequence of the modification of the electric force on the contact line. For a classical electrowetting configuration, we show that the electric force on the contact line is mainly due to the Maxwell stresses at the D-A interface. Then we examine comprehensively how the electric force on the contact line varies with the permittivity difference between A and S phases, the contact angle and size. It was found that our model agrees excellently with the classical Yong-Lippmann (Y-L) model when the permittivities of A and S phases are equal, while the difference between the two increases as the permittivity difference between A and S phases increases. The electric force increases with the increase of the contact angle for a given droplet size. Our model approaches the Y-L model with the increasing droplet size. The findings are complementary to the classical Y-L model and provide new insights into the electrowetting.