In this chapter we turn our attention to problems involving fluid flow. Such problems are solved by using the mass and momentum balance equations derived in Chapter 2. We start by analyzing Newtonian fluids in simple geometries, such as flow between parallel plates, or flow in a tube. We use scaling to determine whether inertial or viscous effects dominate the problem, and we concentrate initially on viscous-dominated flows. These simple-geometry viscous results are useful building blocks for process modeling, especially in polymer processing where the fluid viscosity is very large. Several examples illustrate how this is done. We show how to formulate problems with free or moving boundaries, a situation that is common in materials processing, and we apply these ideas to some simple models of mold filling. Finally, we consider cases in which the inertial terms are dominant, and we provide basic tools for treating these problems.

NEWTONIAN FLOW IN A THIN CHANNEL

Consider flow in a channel whose thickness is much smaller than its width and length. A great many polymer processing operations involve this type of geometry, for reasons that can be understood by using the results from Chapter 4. Most plastic parts are intended to be inexpensive, which requires that they be produced in a short time, and cooling the polymer melt is the slowest part of the process because polymers are relatively poor conductors of heat.