The deformation, stationarity and stability of a drop rotating axisymmetrically in an immiscible viscous fluid, under the influence of an externally imposed flow are studied. The ambient fluid, slightly heavier or lighter than the drop is under simultaneous rotating and compressional or extensional forcing flow at infinity. The problem is formulated and solved via an integral equation having unknown surface velocity considering low Reynolds number with equal viscosity inside the drop and of the ambient fluid. Numerical simulations are carried out by using the boundary integral method. The drop stationarity is discussed for a variety of Bond numbers, $Bo$, and capillary numbers, $Ca$, for the simultaneous action of both flow fields. The critical bounds of $Ca$ for the stability of stationary flat and extended shapes of the drop were established for the considered range of $Bo$.

中文翻译：

---

压缩/延伸流中粘性旋转液滴的形状和稳定性

研究了在不相溶的粘性流体中，在外部流动的影响下，轴对称旋转的液滴的变形，平稳性和稳定性。在无限旋转的同时旋转和压缩或拉伸强制流动下，比液滴稍微重或更轻的环境流体。考虑到低雷诺数且液滴内部和周围流体的粘度相同，通过具有未知表面速度的积分方程来解决该问题。使用边界积分法进行了数值模拟。讨论了各种债券编号的跌落平稳性，$乙Ø$和毛细管数， $C\mathrm{一种}$，用于两个流场的同时作用。的临界范围$C\mathrm{一种}$ 为固定平面的稳定性和液滴的扩展形状建立了考虑的范围 $乙Ø$。