Thermal Effects on the Dynamics of Singularity Formation in Viscous Threads

该项目研究由非线性偏微分方程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点形成的动力学。热效应可以导致有趣的动力学，与等温情况下的动力学非常不同。该项目将研究温度对粘度和表面张力的影响在形成粘性螺纹中的作用。所研究的问题涉及粘度和/或表面张力随温度迅速变化的非均匀流体圆柱体和圆柱管。为了更好地理解流体缸或管的崩溃机制，该项目研究了以下模型问题：1)圆柱形螺纹的夹断；2)无限介质中圆柱形孔的坍缩；3)管道坍塌；4)管的退火，5)这些问题的流动扩展。本项目分析了温度对粘性材料螺纹的影响，这在许多制造过程中都有使用。由于表面张力的影响，细的粘性线（如印刷中的喷墨）会挤压成液滴，这往往会使液体的表面积最小化。掐断现象也发生在其他应用中，例如，在涂层流动中产生的薄膜中。加热可以显著改变表面张力，从而导致热毛细效应，其中温度梯度引起表面张力梯度，从而驱动流动。制造过程要求玻璃和聚合物材料在高温下变形，这导致热粘性效应，因为由此产生的粘度变化很大。例子包括在电生理学中使用的光纤电缆的牵引和玻璃微电极的形成。近年来，采用各种技术制备半导体纳米团簇和高纯度纳米线，通常在退火阶段需要加热。在所有这些过程中，加热对控制最终产品的形状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，从而有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.