A Mixed Finite Element Method for EWOD That Directly Computes the Position of the Moving Interface

A new mixed finite element method is proposed and analyzed for simulating two-phase droplet motion in a micro-scale device driven by Electrowetting-On-Dielectric (EWOD). The new feature of the method is that the finite element scheme is based on a weak formulation of the problem which includes the position of the moving interface and the curvature of its boundary as basic unknowns to be determined along with the velocity field and pressure. Well-posedness of the semi-discrete and fully discrete formulations and error estimates with minimal regularity assumptions are proved. Numerical examples are given to illustrate the robustness of the method.