论文标题
电介质电视的有限元方法
A Finite Element Method for Electrowetting on Dielectric
论文作者
论文摘要
我们考虑介电（EWOD）上电工的问题。该系统涉及在施加电压下的介电底物上浸入另一种介电液中的导电液滴的动力学。流体动力学是由具有标准界面条件的两相不可压缩的Navier-Stokes方程建模的，底物上的Navier滑动条件以及与动态接触角和接触线速度相关的接触角条件，以及界面演化的运动条件。作用在流体界面上的电力由介电液和介电底物占据的域中的麦克斯韦方程建模。我们根据模型的弱形式为模型开发一种数值方法。此方法结合了用于固定散装网格上Navier-Stokes方程的有限元方法，以及用于流体界面动力学的参数有限元方法，以及沿流体界面的电力的边界积分方法。提出了数值示例，以证明数值方法的准确性和收敛性，各种物理参数对界面曲线的影响以及其他有趣的现象，例如由施加的非均匀电势差驱动的液滴的运输。
We consider the problem of electrowetting on dielectric (EWoD). 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 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 the applied non-uniform electric potential difference.
