AI 中文总结
研究不溶性表面活性剂和径向电场对垂直纤维上粘性液体薄膜稳定性的耦合影响，通过推导简化模型和线性稳定性分析确定不稳定模式，揭示电场位置β对模式的不同影响及相关变化规律。
AI 中文摘要
本研究调查了不溶性表面活性剂和径向电场对沿垂直纤维流动的粘性液体薄膜稳定性的耦合影响。从二维控制方程出发，利用长波近似推导出一维简化模型来描述界面和表面活性剂传输的耦合演化。线性稳定性分析确定了两种不同的不稳定模式。径向电场的影响由外电极位置β决定，β<e时电场增强两种不稳定性并缩小稳定区间，β>e时电场抑制两种模式甚至可消除与Marangoni模式相关的不稳定区域。行波解的延续表明β<e时相对界面运动幅度随Eb增大，而Marangoni对流强度在较小Eb时变化微弱，电场足够强时才明显增加。对流函数和相对界面速度的分析表明电应力主要增强波峰下方的再循环并重塑相对界面速度的空间分布。
英文摘要
This study investigates the coupled effects of an insoluble surfactant and a radial electric field on the stability of a viscous liquid film flowing down a vertical fiber. Starting from the governing equations in two dimensions, a reduced model in one dimension is derived using the long wave approximation to describe the coupled evolution of the interface and surfactant transport. Linear stability analysis identifies two distinct unstable modes: the Rayleigh-Plateau mode, which dominates at lower values of the Marangoni number $Ma$, and the Marangoni mode, which becomes dominant at higher values of $Ma$. The influence of the radial electric field is determined by the position of the outer electrode $β$. When $β<\mathrm{e}$, the electric field enhances both instabilities and narrows the stable interval in $Ma$ between the two modes. When $β>\mathrm{e}$, the electric field suppresses both modes and can completely eliminate the unstable region associated with the Marangoni mode even at a relatively small electric Weber number $E_b$. Continuation of the traveling wave solutions further shows that, when $β<\mathrm{e}$, the magnitude of the relative interfacial motion $I_{RP}$, generally increases with $E_b$. By contrast, the intensity of Marangoni convection $I_{M}$ varies only weakly at smaller values of $E_b$ and increases appreciably only when the electric field becomes sufficiently strong. Analysis of the stream function and the relative interfacial velocity reveals that the electric stress primarily intensifies the recirculation beneath the wave crest and reshapes the spatial distribution of the relative interfacial velocity.
