The processes we have considered thus far – extrusion, wire coating, and injection and compression molding – are dominated by shear between confined surfaces. By contrast, in fiber and film formation the melt is stretched without confining surfaces. It is still possible to gain considerable insight from very elementary flow and heat transfer models, but we must first parallel Section 2.2 and develop some basic concepts of extensional flow. The remainder of the chapter is then devoted to an analysis of fiber formation by melt spinning.
Our analysis of fiber spinning in this chapter will be based on an inelastic rheological model of the stresses. This rheological description appears to be adequate for polyesters and nylons, which comprise the bulk of commercial spinning applications, and our spinning model is essentially the one used in industrial computer codes. This is a process in which melt viscoelasticity can sometimes play an important role, however, and we will revisit the process in Chapter 10.
Uniaxial Extensional Flow
Consider a cylindrical rod of a very viscous polymer melt, as shown in Figure 7.1, with radius R and length L. We impose a stress σzz in the axial direction in order to stretch the rod; hence, R and L are both functions of time, but R2L is a constant for an incompressible melt. We assume that the rod draws down uniformly as it is stretched, so R is independent of z.