Asymptotic analysis for fiber drawing processes

In fiber drawing, axial tension is applied to long, thin viscous threads to increase their length and consequently reduce their cross-sectional area. This process is used to manufacture rods and threads of glass and polymer such as optical fibers and filaments for textiles. Drawing is described mathematically using the Trouton model for extensional flow in a long, narrow cylinder. This leading-order description gives simple expressions for fiber radius and one-dimensional axial velocity in the long, slender limit. In this paper we determine the next-order corrections, showing that they can be an order of magnitude larger than previously assumed.