Український математичний конгрес - 2009
Jonathan J Wylie (City University of Hong Kong, Kowloon, Hong Kong)
Extensional flows with viscous heating
In this talk we will investigate the role played by viscous heating in extensional flows of viscous threads with temperature-dependent viscosity. We will show that there exists an interesting interplay between the effects of viscous heating, which accelerates thinning, and inertia, which prevents pinch-off. We will first consider the steady drawing of a thread that is fed through a fixed aperture at given speed and pulled with a constant force at a fixed downstream location. For pulling forces above a critical value, we will show that inertialess solutions cannot exist and inertia is crucial in controlling the dynamics. We will also consider the unsteady stretching of a thread that is fixed at one end and pulled with a constant force at the other end. In contrast to the case in which inertia is neglected, the thread will always pinch at the end where the force is applied. Our results show that viscous heating can have a profound effect on the final shape and total extension at pinching.