We now turn our attention to the application of Fick's Laws for the solution of problems of interest to materials engineers. In this brief chapter the groundwork is laid through a discussion of the kinds of boundary conditions that can be applied.

Introduction

In the next few chapters we will build on our understanding of solutions to Fick's Laws, by learning how to apply them to a large variety of problems involving diffusion. This process involves a number of well-defined steps. These steps are required in order to turn a general statement of a problem into a framework which can be solved mathematically. The procedure we will adopt is generally applicable to all problems involving the solution of partial differential equations such as Fick's Laws. As we discussed in the last chapter, these equations fall under the general category of what are called ‘boundary-value problems’. That is, we need to solve a differential equation (such as Fick's Second Law), subject to certain bounds.