Numerical Analysis of Closure Criteria for Spectral Viscoelastic Constitutive Equations Used in the Classical Melt Spinning Model

Abstract

The classical melt spinning model is reformulated to include a spectral rheological constitutive equation for an arbitrary number of modes composing the spectra of relaxation times and
modules. This resulting spectral spinning model requires a closure criterion to be applied in the iteration of the spinning initial condition of the total stress tensor, at the onset of the stretching zone. Thus this stress value must be distributed, at each one of the iterations, among the stress modes of the spectral viscoelastic rheological model, the sum of which shall be consistent with the total stress value. For this purpose different closure criteria are generated in the literature to carry out this stress distribution. Without loss of generality, in this work we study numerically this particular problem for the isothermal condition only. A new closure criterion is proposed and analyzed in relation to previous ones. In general it is found that two zones are clearly distinguished along the stretching flow: one, where numerical results of the process elongational viscosity are insensitive to the closure criterion used, and the other involving the counterpart situation.