Thermal instability in drawing viscous threads

We consider the stretching of a thin viscous thread, whose viscosity depends on temperature, that is heated by a radiative heat source. The thread is fed into an apparatus at a fixed speed and stretched by imposing a higher pulling speed at a fixed downstream location. We show that thermal effects lead to the surprising result that steady states exist for which the force required to stretch the thread can decrease when the pulling speed is increased. By considering the nature of the solutions, we show that a simple physical mechanism underlies this counterintuitive behaviour. We study the stability of steady-state solutions and show that a complicated sequence of bifurcations can arise. In particular, both oscillatory and non-oscillatory instabilities can occur in small isolated windows of the imposed pulling speed.