A numerical approximation to the solution of the conservation equations is obtained using the FIDAP computational fluid dynamics software package. FIDAP allows for determination of the location of the two free surfaces of the filament simultaneously with the velocity, concentration, and temperature fields within it.
The simulations reveal the presence of a recirculation region in the bore of the filament under typical fiber spinning conditions. This recirculation region leads to larger than expected fiber dimensions initially in the draw zone and a more rapid decrease to the final fiber size along the draw zone than predicted by the one-dimensional approximation to the conversation equations (the thin filament analysis).
The simulations also indicate that mass transfer is confined to a thin region near the external surface of the filament. The extent of this region and the concentration profile within it are predicted well by a mass transfer boundary layer analysis. Additionally, the predicted extent of the region agrees well with experimental data obtained for a polyethylene-dodecanol filament.