The stretching of a viscoplastic thread of liquid

The problem of stretching a viscoplastic (yield-stress) thread of a liquid hanging vertically is considered. The length of the thread at later times and the time at which it ruptures is determined. A Lagrangian coordinate system is used to analyze the extension of the thread as it sags under its own weight, with negligible inertial effects. The biviscosity model has been used to characterize viscoplastic fluids; the Newtonian and Bingham models can be recovered as limiting cases. The Bingham limit is of special interest.