The problem of stretching highly viscous threads arises from the glass and polymer industrial processing.  We consider the evolution of a long and thin vertically-aligned axisymmetric viscous thread, which is attached to a solid wall at its upper end, experiences gravity and is pulled at its lower end by a fixed force. The thread experiences either heating or cooling by its environment. Both the viscosity and surface tension are assumed to be functions of temperature. A set of one-dimensional model is derived through the formal slender body asymptotic analysis. When inertia is completely neglected and the temperature of the environment is spatially uniform, we obtain analytic solutions for an arbitrary initial shape and temperature profile. In addition, we determine the criteria for whether the cross-section of a given fluid element will ever become zero and hence determine the minimum stretching force that is required for pinching. For non-zero Reynolds numbers, we show that the dynamics is subtly influenced by inertia and the pinching location is selected by a competition between three distinct mechanisms. In particular, for a thread with initially uniform radius and a spatially uniform environment but with a non-uniform initial temperature profile, pinching can occur either at the hottest point, at the points near large thermal gradients or at the pulled end, depending on the Reynolds number.

This is a joint work with Jonathan Wylie (City U, HK), Huaxiong Huang (York U, Canada) and Robert M. Miura (NJIT, USA).