A Guide to Previous Work

In many cases, detailed solutions to diffusion problems can be adapted from calculations that have already been published, thus avoiding the mathematical detail presented in the earher sections in this chapter. These ealeulations involve the same differential equations, with relatively minor ehanges of boundary eonditions. They include elaborate but straightforward manipulations, like the integration of eoneentration profiles to find average concentrations. 

Even with these limitations, the published solutions ean be used to save eonsiderable effort. Besides individual papers, there are two important books that have eolleeted and eompared this literature. The first. Crank s The Mathematics of Diffusion (1975), dis-eusses aspeets of chemical reactions. The second, Carslaw and Jaeger s The Conduction of Heat in Solids (1986), must be used by analogy, but it includes a more complete selection of boundary conditions. The notation used in these books is compared with that used here in Table 3.5-1. 

In the remainder of this seetion we give examples illustrating how this literature can 

Example 3.5-1 Diffusion through a polymer film Imagine that we are studying a polymer film that is permeable to olefins like ethylene but mueh less permeable to ahphatie hydrocarbons. Such a film could be used for selectively separating the ethylene produced by dehydrogenation reactions. As part of our study, we use the diaphragm cell shown in 

Variable Our notation Crank s notation Carslaw and Jaeger analogue 

---