Flow of Polymeric Liquid in Complex Geometry

The flow geometry encountered in many polymer processing operations of industrial importance is often far more complex than that in cylindrical or slit dies. As will be shown in the following chapters, the industry manufactures polymeric products using very complex flow geometries. For instance, the fiber industry produces “shaped fibers,” which have cross sections that are noncircular. What is most intriguing in the production of shaped fibers is that a desired fiber shape is often produced by spinneret holes whose cross-sectional shape is quite different from that of the final fiber produced. Hence, an important question may be raised as to how one can determine, from a sound theoretical basis, the cross-sectional shape of spinneret holes that will produce a fiber with a desired cross-sectional shape. In extrusion and injection molding, a polymeric liquid invariably passes through a large cross section before entering into a small cross section, and such a flow is referred to as “entrance flow.” The entrance flow of polymeric liquids, due to their viscoelastic nature, is quite different from that of Newtonian liquids. Similarly, the flow behavior of viscoelastic polymeric liquids near the exit of a die, commonly referred to as “exit flow,” is quite different from that of Newtonian liquids. A better understanding of the unique characteristics of both entrance and exit flows of viscoelastic polymeric fluids is essential for successful design of extrusion dies and molds, as well as to solve difficult technical problems related to a particular processing operation. Before presenting specific polymer processing operations in following chapters, in this chapter we consider the flow of polymeric liquids through complex geometry: (1) fully developed flow through a rectangular channel with uniform channel depth; (2) fully developed flow through a rectangular channel with a moving channel wall; (3) flow through a rectangular channel with varying channel depth; (4) flow in the entrance region of a rectangular die having constant cross section; (5) flow through a tapered die; (6) flow in the exit region of a cylindrical or slit die; (7) flow through a slit die having side holes; and (8) flow through a coat-hanger die.