Under consideration for publication in J. Fluid Mech. 1 Extensional flows with viscous heating

We consider the role played by viscous heating in extensional flows of viscous threads with temperature-dependent viscosity. The results show that there exists an interesting interplay between the effects of viscous heating, which accelerates thinning, and inertia, which prevents pinch-off. We consider 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 show that inertialess solutions cannot exist and investigate the role played by inertia in controlling the dynamics. We also consider the unsteady stretching of a thread that is fixed at one end 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. Viscous heating can have a pround effect on the total extension at pinching. 1