Thermal Effects on the Dynamics of Singularity Formation in Viscous Threads

New Jersey Institute Of Technology, Newark NJ

Investigators

Abstract

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.