Modelling of the Melt Spinning Process

Textile spinning is the manufacturing process for synthetic yarns and fibers. There are two main processes, depending on whether the liquid state is achieved by raising the temperature (melting) or using a solvent. During the spinning process, the molten or dissolved polymer undergoes a mainly elongational and unidirectional flow. If the polymer is molten, solidification of the filament can be achieved either by gradual cooling (e.g. with an air jet) or by sudden quenching. In both cases, around a hundred filaments are produced simultaneously. These filaments are then assembled, after solidification, to form yarns using a sizing agent that ensures adhesion between the filaments and gives the yarn dimensional stability and dyeing properties. This article deals solely with the thermomechanical study, for one filament, of the flow between extrusion from the die plate and solidification. The aim of this study is to define the thermomechanical quantities (draw ratio, elongational stress, temperature profile, etc.) that will condition the structure of the filament and hence its properties.

The various products resulting from the spinning process are subject to very severe dimensional constraints. Textile fibers, for example, are intended to be dyed, assembled into yarn and then woven. The stability of the process in the industrial sense (absence of breakage, regularity of diameter, etc.) is therefore essential for subsequent operations. Many filaments are produced simultaneously, and the breakage of a filament in the liquid state is very restrictive for the operator, who must then discard or recycle the incomplete spool and restart the process. Nevertheless, under certain operating conditions, there are also instability phenomena in the hydrodynamic sense, which are a major limitation of the process. Under weakly anisothermal conditions and at relatively high draw rates, hydrodynamic instability is observed. In this case, the flow is unsteady and periodic in time.

Modeling gives us a key to understanding these instability problems, which are the main limitation of the process. The approach is a classic one, since it boils down to constructing a system of differential equations (the model) to describe the velocity, stress and temperature fields inside the polymer during flow. While the expression of the conservation of matter and the equilibrium of the forces involved poses little problem, the same cannot be said of the polymer behavior law linking elongational stress to strain intensity. Classically, it is observed that these polymeric products have a viscoelastic type of behavior, and while this is fairly well known for shear flow, it is much trickier to characterize in elongational flow. These equations naturally give rise to dimensionless numbers quantifying the intensity...