中文摘要：

外加电场作用下的液滴变形及力学行为是电流体动力学研究的重要内容．基于volumeof-ofluid（VOF）方法，将电场力作为源项添加到流体运动的Navier—Stokes方程中，提出了电流体流场与电场双向耦合的数值方法，分别研究了外加均匀电场与非均匀电场作用下，中性漏电液滴和带电液滴的变形／运动及其力学行为．小变形条件下，数值模拟得到的外加均匀电场中性漏电液滴的变形系数接近于理论值，验证了本文方法的正确性．研究结果表明，电场作用下，液滴与周围介质物理属性的差异导致液滴表面不同的自由电荷再分配形式及其变形状态；相对于电场方向，中性漏电液滴可能会发生“扁长型”或“扁平型”变形．均匀电场下，中性漏电液滴内部形成稳定的回转运动，液滴不会发生宏观运动；对于存在净电荷的液滴，由于库仑力的作用，液滴不仅会发生变形，同时也会沿电场线方向运动．非均匀电场下，中性漏电液滴与带电液滴都会沿电场线运动，并发生不同的变形．本文所提出电流体流场与电场双向耦合的数值方法为静电喷雾、电泳等复杂的工程电流体动力学研究提供了理论基础．

英文摘要：

Droplet deformation and mechanical behavior under external electric field are fundamental in electrohydrodynamic research. Based on the volume-of-fluid （VOF） method and adding electric force to Navier-Stokes equations as an additional source term, a simulation method considering fluid flow and electric field in two-way coupling is proposed. Using this method, the deformation/motion of leaky dielectric droplet and charged droplet under external uniform and non-uniform electric field is investigated respectively. The shape deformation coefficient calculated by the proposed method is close to the theory value of leaky dielectric droplet under uniform electric field in small deformation condition; thus the validity of the numerical method proposed in this study is verified. The results show that the charge redistribution modes of leaky dielectric droplet depend on the property difference between droplet and the around fluid, and the droplet may deform into either prolate or oblate shapes. The electric field strength only affects the droplet shape deformation coefficient. The external uniform electric field induces strong circulation motion inside the leaky dielectric droplet without moving the droplet. Because of the effect of Coulomb force, the charged droplet may deform into prolate and move along the electric field direction. However both leaky dielectric droplet and charged droplet may move along the electric field direction, resulting in different shapes simultaneously under the non-uniform electric field. The numerical method coupling fluid flow with electric field proposed in this paper could provide an effective approach to electrostatic spray, electrophoresis and other complex engineering electrohydrodynamic researches.