Boundary integral method for the evolution of slender viscous fibres containing holes in the cross-section
Boundary integral method for the evolution of slender viscous fibres containing holes in the cross-section
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截面含孔细长粘性纤维演化的边界积分法
DOI：
10.1017/s0022112008004783
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发表时间：
2009
影响因子：
3.7
通讯作者：
W. Chiu
中科院分区：
文献类型：
--
作者：
S. Chakravarthy;W. Chiu
我们考虑细长粘性纤维的演变与横截面包含孔的微结构光纤的制造应用。纤维的演变是由指定的速度或纤维端部的力驱动的，并且自由表面在表面张力、内部加压、惯性和重力的影响下演变。我们使用的事实，即典型的纤维半径的典型的纤维长度的比率是小的进行渐近分析的全三维Navier-Stokes方程类似于早期的工作非轴对称（但简单连接）的纤维。基于对Sherman-Lauricella方程的求解，给出了多连通稳态拉深问题的数值解法。不同的绘图和材料参数，如表面张力，重力，惯性和内部加压上的绘图的影响进行了检查，并提出了该方法的扩展到非等温演变。
We consider the evolution of slender viscous fibres with cross-section containing holes with application to fabrication of microstructured optical fibres. The fibre evolution is driven by either prescribing velocity or a force at the ends of the fibre, and the free surfaces evolve under the influence of surface tension, internal pressurization, inertia and gravity. We use the fact that ratio of the typical fibre radius to the typical fibre length is small to perform an asymptotic analysis of the full three-dimensional Navier–Stokes equations similar to earlier work on non-axisymmetric (but simply connected) fibres. A numerical solution to the multiply connected steady-state drawing problem is formulated based on the solution the Sherman–Lauricella equation. The effects of different drawing and material parameters like surface tension, gravity, inertia and internal pressurization on the drawing are examined, and extension of the method to non-isothermal evolution is presented.