Electrohydrodynamic Modeling of Droplet Vibrations under the Influence of Electric Fields

This work focuses on numerical simulations of water droplet deformations under the influence of transient high-voltage electric fields. In the stationary case, the droplet elongates parallel to the electrostatic field. In the transient case, water droplets undergo a complicated oscillatory motion as the electric field and the droplet shape change simultaneously. This multiphysics phenomenon has been the subject of experimental studies but has never been simulated before in the case of a transient electric field. Practical applications of this work include the numerical study of the premature aging of polymer insulators used in power transmission lines and due to water droplets as well as the simulation of industrial processes such as electrowetting and dielectrophoresis. In this thesis, the motion of a single water droplet located on the hydrophobic surface of a silicone rubber insulator is simulated numerically. This is achieved by solving the transient, three-dimensional system composed of the full sets of electro-quasistatics and Navier-Stokes equations. The solution of the coupled system is obtained by using a computational approach based on the finite element method on a moving mesh for the electrical part of the problem and on the finite volume method on a fixed mesh for the fluid mechanical part. The electro-quasistatics finite element solver calculates on a moving curvilinear tetrahedral mesh the electric field, Maxwell stress tensor and electric force density with higher and mixed-element orders. The multiphase flow finite volume solver computes on a fixed Cartesian hexahedral grid the droplet deformation by tracking the evolution of the water-air interface with the volume of fluid method. Both solvers use an independent time integration scheme but are leapfrogged in a synchronized manner to provide a time accurate calculation of the droplet deformations. Several experimental investigations are performed to verify simulation results using a high speed camera. The comparison between simulation and experiment shows good agreement between the numerically computed droplet motion and the recorded video images for both horizontal and vertical applied AC electric fields. The simulation results are analyzed by applying a one-dimensional mechanical model of water droplet deformation based on the linear harmonic oscillator. The standard model which is limited to the steady-state regime is extended to include the transient regime. It is shown that the droplet vibrations occuring at frequencies below the driving frequency are not necessarily due to the accidental charging of the water droplet as it is sometimes suggested in the literature. Rather, they may be caused by underdamped droplet oscillations which originate in the transient regime. This finding is further supported by the fact that their frequencies correspond to the resonance frequencies of the sessile water droplets oscillating freely