We theoretically investigate the deformation of a perfect dielectric drop suspended in a second dielectric liquid subject to a uniform electric field. Axisymmetric equilibrium shapes are found by solving simultaneously the Young–Laplace equation at the interface and Laplace equation for the electric field. Analytical solutions are constructed for the governing nonlinear boundary-value problem using domain perturbation method together with a special type of Hermite–Padé approximation. The results show the existence of a critical electric capillary number beyond which no axisymmetric figure is possible.

中文翻译：

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均匀电场作用下液滴的变形

从理论上讲，我们研究了悬浮在第二电介质液体中的均匀电介质液滴在均匀电场作用下的变形。通过同时求解界面处的Young-Laplace方程和电场的Laplace方程，可以找到轴对称的平衡形状。使用域摄动方法和特殊类型的Hermite-Padé近似，构造了控制非线性边值问题的解析解。结果表明存在一个临界电毛细管数，超过该值则不可能出现轴对称图形。