Phase Field Modeling and Numerical Algorithm for Dielectrowetting

We present a phase field-based method for numerical simulations of two-phase dielectric fluids and their interactions with solid wall surfaces and external electric fields. A physically consistent phase field model attained based on the conservation laws and thermodynamic principles is discussed first. Then we present an efficient numerical algorithm for solving the coupled system of governing equations. In particular, our algorithm requires only the solution of linear algebraic systems with constant and time-independent coefficient matrices upon discretization, even though the physical model involves two fluids with different dielectric constants. As a result, the presented algorithm is computationally highly efficient. Several examples of dielectrowetting simulations will be presented to demonstrate the performance of the presented method, with comparisons between the simulation and the experimental data or theoretical predictions.