Thermal Effects on the Dynamics of Singularity Formation in Viscous Threads

本计画研究由非线性偏微分方程式所控制的自由边界问题，其中局部加热控制表面张力驱动流动中奇异点形成的动态。 热效应可以导致有趣的动态，这是非常不同的等温情况下的动态。 该项目将研究温度对粘性和表面张力在粘性线成形中的作用。 所研究的问题涉及不均匀的流体圆柱体和圆柱形管的粘度和/或表面张力随温度迅速变化。 为了更好地理解流体圆柱或管道的坍塌机理，该项目研究描述以下内容的模型问题：1）圆柱螺纹的夹断; 2）无限介质中圆柱孔的坍塌; 3）管道的坍塌; 4）管的退火，和5）这些问题的扩展与流动。本项目分析了温度对粘性材料的线程的影响，其用于许多制造工艺中。 由于表面张力的作用，薄的粘性线（如印刷中的喷墨）夹断成液滴，这往往会使液体的表面积最小化。 夹断现象也发生在其它应用中，例如，在涂布流中产生的薄膜中。 加热可以显著改变表面张力，这导致热毛细效应，其中温度梯度引起驱动流动的表面张力梯度。 制造过程需要玻璃和聚合物材料处于高温下以使它们变形，这导致由于粘度的大变化而导致的热粘性效应。 例子包括拉光纤电缆和形成用于电生理学的玻璃微电极。 近年来，半导体纳米团簇和高纯度纳米线已经使用各种技术生产，并且在退火阶段通常需要加热。 在所有这些过程中，加热在控制最终产品的形状方面起着至关重要的作用。 该项目将有助于详细了解加热对粘度和表面张力的影响，从而可能改进这些材料的制造工艺。

This project investigates free boundary problems governed by nonlinear partial differential equations where localized heating controls the dynamics of the formation of singularities in surface-tension-driven flows. Thermal effects can lead to interesting dynamics that are very different from the dynamics in isothermal cases. The project will investigate the role temperature effects on viscosity and surface tension play in shaping viscous threads. The problems under study involve nonuniform fluid cylinders and cylindrical tubes with viscosity and/or surface tension that change rapidly with temperature. To better understand the collapse mechanism of fluid cylinders or tubes, the project studies model problems that describe: 1) pinch off of cylindrical threads; 2) collapse of a cylindrical hole in an infinite medium; 3) collapse of tubes; 4) annealing of tubes, and 5) extensions of these problems with flow.This project analyzes the effects of temperature on threads of viscous material, which are used in many manufacturing processes. Thin viscous threads (such ink jets in printing) pinch off into droplets due to the effect of surface tension, which tends to minimize the surface area of the liquid. Pinch-off phenomena also occur in other applications, e.g., in thin films that arise in coating flows. Heating can significantly modify surface tension, which leads to thermocapillary effects, in which temperature gradients cause surface tension gradients that drive flows. Manufacturing processes require glass and polymeric materials to be at high temperatures to deform them, which leads to thermoviscous effects due to due to the resultant large changes in viscosity. Examples include the pulling of fiber optic cables and formation of glass microelectrodes used in electrophysiology. In recent years, semiconductor nanoclusters and high-purity nanowires have been produced using various techniques, and heating is normally required in the annealing stage. In all these processes, heating plays a crucial role in controlling the shape of final products. This project will contribute to detailed knowledge of the effects of heating on viscosity and surface tension, potentially leading to improved manufacturing processes for these materials.