A mathematical model for spinning viscoelastic molten polymers.

A mathematical model for spinning viscoelastic materials is proposed. This work can be considered the continuation of some previous papers by A. Prastaro, which treated the case of newtonian materials. The viscoelastic system, as more differs from the newtonian as the elastic component is present; thus the viscoelastic mathematical model can be not be inferred from the analysis of the previous paper; on the contrary the viscoelastic model includes, as particular case, the newtonian model. The spinning process was analysed by adding the rheological equation for viscoelastic materials to the set of simultaneous partial differential equations describing a general molten spinning process. We gave the steady-state numerical solutions, i.e. the filament croos-section $ A(z)$, filament temperature $ T(z)$ and filament tension $ F(z)$, as function of position $ z$ and we related them to the parameters which influence the process of spinning: material parameters and spinning conditions parameters. We related the yarn birefringence $ \Delta n$ to the same parameters also. Moreover, we proposed to investigate which bounds impose the spinnability criterion on the viscoelastic paramaters and which conditions realize the maximum yarn production with fixed denier and section.