An Electromechanical Model for Electrowetting With Finite Droplet Size

Abstract

We present an electromechanical model for the 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 Maxwell stresses at the ambiance–substrate (A–S) interface, the droplet–substrate (D–S) interface, and the droplet–ambiance (D–A) interface induce an electric force on the three-phase contact line which is responsible for the modification of the apparent contact angle in electrowetting. For a classical electrowetting configuration with a flat substrate, we show that the electric force on the contact line (or the electrowetting number) is mainly due to the Maxwell stresses at the D–A interface. The model is validated by its excellent agreement with the classical Young-Lippmann (Y-L) model for sufficiently large droplets and comparable electric permittivities between A and S phases. Interestingly, our new model reveals that the finite size of droplet produces profound effects on the electrowetting that the electrowetting number becomes dependent on the permittivity of A phase and the equilibrium contact angle, which is in stark contrast to the Y-L model. The reasons for these remarkable effects are elaborated and clarified. The findings in the current study are complementary to the classical Y-L model and provide new insights into the electrowetting phenomenon.