This article presents a sharp immersed method for simulating electrohydrodynamic (EHD) flows that involve charge evaporation. This well-known multi-scale, multi-physics problem is widely used in various fields, including industry and medicine. The method adopts a fully sharp model, where surface tension and Maxwell stress are treated as surface forces and free charges are concentrated on the zero thickness liquid-vacuum interface. Incorporating charge evaporation imposes strict restrictions on the time-step, as the rate of evaporation sharply increases with surface evolution. To overcome this challenge, an iterative algorithm that couples the electric field and surface charge density is proposed to obtain accurate results, even with significantly large time-steps. To mitigate the numerical residuals near the interface, which may introduce parasitic flows and cause numerical instability, an immersed interface method-based iterative projection method for the Navier–Stokes equations is proposed, in which a traction boundary condition involving multiple surface forces is imposed on the sharp interface. Numerical experiments were carried out, and the results show that the method is splitting-error-free and stable. The sharp immersed method is applied to simulate the electric-induced deformation of an ionic liquid drop with charge evaporation. The results indicate that charge evaporation can suppress the sharp development of Taylor cones at the ends of the drops. These findings have significant implications for the design and optimization of EHD systems in various applications.

中文翻译：

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一种伴随电荷蒸发的电流体动力学流动的锐浸入法

本文提出了一种用于模拟涉及电荷蒸发的电流体动力学 (EHD) 流的锐浸入式方法。这个著名的多尺度、多物理问题广泛应用于各个领域，包括工业和医学。该方法采用全锐模型，将表面张力和麦克斯韦应力视为表面力，自由电荷集中在零厚度液-真空界面上。结合电荷蒸发对时间步长施加了严格的限制，因为蒸发速率随着表面演化而急剧增加。为了克服这一挑战，提出了一种耦合电场和表面电荷密度的迭代算法，即使时间步长很大，也能获得准确的结果。为了减轻界面附近可能引入寄生流并导致数值不稳定的数值残差，提出了一种基于浸入界面法的纳维-斯托克斯方程迭代投影方法，其中对涉及多个表面力的牵引边界条件施加了影响锐利的界面。进行了数值实验，结果表明该方法无分裂误差且稳定。采用锐浸入法模拟离子液体滴因电荷蒸发而产生的电致变形。结果表明，电荷蒸发可以抑制液滴末端泰勒锥的急剧发展。这些发现对于各种应用中 EHD 系统的设计和优化具有重要意义。