Introduction

The extruder, shown schematically in Figure 1.1, is central to most melt processing operations. We can achieve considerable insight into the operation and design of single-screw extruders by remarkably simple models, despite the mechanical complexity. We begin this chapter by obtaining velocity, stress, and temperature distributions for flow in straight channels with parallel walls of “infinite” length. The infinite channel results are important in and of themselves, but we shall see here that they lead immediately to a model for the single-screw extruder as well. The results also provide an important framework for the modeling of flows in situations in which the walls are not parallel, which we address in Chapter 5.

Plane Channel

Stress Distribution

Let us suppose we have steady isothermal flow (i.e., the temperature is constant throughout the flow field and all ∂/∂ t = 0) between two infinite parallel planes, as shown in Figure 3.1. The flow is in the x direction. We assume for generality that there is a finite pressure gradient (∂ p/∂ x ≠ 0) and that the surface at y = 0 moves relative to the surface at y = H with a constant velocity V. We shall see subsequently that the results obtained here will form the foundation for the modeling of single-screw extrusion and the extrusion coating of flat sheets.