We consider the problem of electrowetting on dielectric. The system involves the dynamics of a conducting droplet, which is immersed in another dielectric fluid, on a dielectric substrate under an applied voltage. The fluid dynamics is modeled by the two-phase incompressible Navier-Stokes equations with the standard interface conditions, the Navier slip condition on the substrate and a contact angle condition which relates the dynamic contact angle and the contact line velocity, as well as the kinematic condition for the evolution of the interface. The electric force acting on the fluid interface is modeled by the Maxwell's equations in the domain occupied by the dielectric fluid and the dielectric substrate. We develop a numerical method for the model based on its weak form. This method combines the finite element method for the Navier-Stokes equations on a fixed bulk mesh with a parametric finite element method for the dynamics of the fluid interface, and the boundary integral method for the electric force along the fluid interface. Numerical examples are presented to demonstrate the accuracy and convergence of the numerical method, the effect of various physical parameters on the interface profile and other interesting phenomena such as the transportation of droplet driven by applied non-uniform voltage.

我们考虑电介质上电润湿的问题。该系统涉及在施加电压的情况下浸入电介质基板上的导电液滴的动力学，该液滴浸入另一电介质流体中。流体动力学是通过两相不可压缩的Navier-Stokes方程建模的，该方程具有标准的界面条件，基板上的Navier滑动条件以及与动态接触角和接触线速度以及运动学相关的接触角条件。接口演化的条件。作用在流体界面上的电势由介电流体和介电基板占据的区域中的麦克斯韦方程组建模。我们基于模型的弱形式开发了一种数值方法。该方法将用于固定块体网格上的Navier-Stokes方程的有限元方法与用于流体界面动力学的参数化有限元方法和用于沿流体界面的电力的边界积分方法相结合。数值例子表明了数值方法的准确性和收敛性，各种物理参数对界面轮廓的影响以及其他有趣的现象，例如由施加的不均匀电压驱动的液滴的传输。