Mathematical modelling of non-axisymmetric capillary tube drawing
Mathematical modelling of non-axisymmetric capillary tube drawing
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DOI：
10.1017/s002211200800147x
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发表时间：
2008-06-25
影响因子：
3.7
通讯作者：
Howell, P. D.
中科院分区：
文献类型：
--
作者：
Griffiths, I. M.;Howell, P. D.
本文介绍了用Vello工艺制造非轴对称毛细管的方法，即熔融的玻璃通过模具输送并垂直拉出。当横截面向下游流动时，横截面的形状在表面张力的作用下演变。我们的目标是获得给定的期望最终形状，通常是正方形或矩形，我们的目标是确定所需的模具形状。我们使用的结果是，假设管子在轴向缓慢变化，当用适当比例的拉格朗日坐标表示时，每个横截面都像二维斯托克斯流一样发展。这使得我们可以使用先前导出的模型来描述细长的二维粘性管的表面张力驱动的演化。因此，我们得到并解析地求解控制管子的轴向速度、厚度和周长以及管子形状的方程。对模型进行了扩展，考虑了非等温效应。
This paper concerns the manufacture of non-axisymmetric capillary tubing via the Vello process, in which molten glass is fed through a die and drawn off vertically. The shape of the cross-section evolves under surface tension as it flows downstream. The aim is to achieve a given desired final shape, typically square or rectangular, and our goal is to determine the required die shape.We use the result that, provided the tube is slowly varying in the axial direction, each cross-section evolves like a two-dimensional Stokes flow when expressed in suitably scaled Lagrangian coordinates. This allows us to use a previously derived model for the surface-tension-driven evolution of a thin two-dimensional viscous tube. We thus obtain, and solve analytically, equations governing the axial velocity, thickness and circumference of the tube, as well as its shape. The model is extended to include non-isothermal effects.