  For flow-enhanced crystallization in fiber spinning, the viscoelastic
two-phase fiber models by Doufas et al. (J. Non-Newton. Fluid Mech., 2000) and
Shrikhande et al. (J. Appl. Polym. Sci., 2006) are state of the art. However,
the boundary conditions associated to the onset of crystallization are still
under discussion, as their choice might cause artificial boundary layers and
numerical difficulties. In this paper we show that the model class of ordinary
differential equations is singularly perturbed in a small parameter belonging
to the semi-crystalline relaxation time and derive asymptotically justified
boundary conditions. Their effect on the overall solution behavior is
restricted to a small region near the onset of crystallization. But their
impact on the performance of the numerical solvers is huge, since artificial
layering, ambiguities and parameter tunings are avoided. The numerics becomes
fast and robust and opens the field for simulation-based process design and
material optimization.
