气流中带电粘毛细射流的 whipping 振荡
Whipping of electrified visco-capillary jets in airflows
AI总结：
针对带电粘毛细射流的whipping不稳定性问题，提出基于渐近Cosserat杆描述的模型框架，结合旋转参考系方法与延拓-配置法，实现高维参数空间下的高效稳健仿真，定性刻画whipping效应。
摘要：
带电粘毛细射流会根据所处的参数区间呈现出不同的动力学行为，例如锥面形成、破碎为液滴、whipping 振荡与卷绕等。对静电纺丝至关重要的 whipping 不稳定性在以往研究中多通过稳定性分析方法开展研究。本研究另辟蹊径，提出了一套模型框架，可将该不稳定性直接作为渐近 Cosserat 杆描述的稳定定常解进行计算。为此，我们采用了 Ribe（《伦敦皇家学会会刊A辑》，2004）提出的方法，在一个以预先未知的 whipping 频率旋转的参考系中描述射流动力学，该频率本身也成为解的一部分。该杆模型支持拉伸、弯曲与扭转作用，同时考虑了惯性、粘度、表面张力、电场与空气阻力的影响。针对由此得到的常微分方程参数化边值问题，我们提出了一种延拓-配置法。在五阶隐式 Runge-Kutta 格式的基础上，我们开发的延拓流程能够实现高效稳健的仿真，且支持在高维参数空间中进行参数遍历。尽管所采用的电场力模型较为简单，但数值结果具有说服力，能够在定性层面很好地刻画 whipping 效应的特征。
英文摘要：
An electrified visco-capillary jet shows different dynamic behavior, such as cone forming, breakage into droplets, whipping and coiling, depending on the considered parameter regime. The whipping instability that is of fundamental importance for electrospinning has been approached by means of stability analysis in previous papers. In this work we alternatively propose a model framework in which the instability can be computed straightforwardly as the stable stationary solution of an asymptotic Cosserat rod description. For this purpose, we adopt a procedure by Ribe (Proc. Roy. Soc. Lond. A, 2004) describing the jet dynamics with respect to a frame rotating with the a priori unknown whipping frequency that itself becomes part of the solution. The rod model allows for stretching, bending and torsion, taking into account inertia, viscosity, surface tension, electric field and air drag. For the resulting parametric boundary value problem of ordinary differential equations we present a continuation-collocation method. On top of an implicit Runge-Kutta scheme of fifth order, our developed continuation procedure makes the efficient and robust simulation and navigation through a high-dimensional parameter space possible. Despite the simplicity of the employed electric force model the numerical results are convincing, the whipping effect is qualitatively well characterized.
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