同心筒体中毛细不稳定性的数值模拟及其在复合微结构纤维中的应用
Capillary instability in concentric-cylindrical shell: numerical simulation and applications in composite microstructured fibers
摘要：
最近的实验观察表明，微结构玻璃/聚合物纤维在热拉伸过程中存在有趣的不稳定现象，这些观察促使我们研究粘性流体同心筒体中表面张力驱动的不稳定性。在本文中，我们专注于一个单一的不稳定性机制：经典的毛细不稳定性的形式，径向波动，解决了完整的纳维-斯托克斯方程数值。在等粘度的情况下，分析线性理论是可用的，我们比较完整的数值解，并描绘的制度，其中线性理论是有效的。我们还考虑不等粘度的情况下（类似于实验），其中没有公布的线性理论，并解释了一个简单的渐近分析的数值结果。然后将这些结果应用于实验热拉伸系统。我们发现，所观察到的不稳定性与径向波动分析是一致的，但不能单独预测径向波动-一个额外的机制是必需的。然而，我们展示了如何单独使用径向波动来分析热拉伸的各种候选材料系统，清楚地排除了一些可能性，同时提出了其他尚未在实验中考虑的可能性。
英文摘要：
Recent experimental observations have demonstrated interesting instability phenomenon during thermal drawing of microstructured glass/polymer fibers, and these observations motivate us to examine surface-tension-driven instabilities in concentric cylindrical shells of viscous fluids. In this paper, we focus on a single instability mechanism: classical capillary instabilities in the form of radial fluctuations, solving the full Navier--Stokes equations numerically. In equal-viscosity cases where an analytical linear theory is available, we compare to the full numerical solution and delineate the regime in which the linear theory is valid. We also consider unequal-viscosity situations (similar to experiments) in which there is no published linear theory, and explain the numerical results with a simple asymptotic analysis. These results are then applied to experimental thermal drawing systems. We show that the observed instabilities are consistent with radial-fluctuation analysis, but cannot be predicted by radial fluctuations alone---an additional mechanism is required. We show how radial fluctuations alone, however, can be used to analyze various candidate material systems for thermal drawing, clearly ruling out some possibilities while suggesting others that have not yet been considered in experiments.
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