Diffusion Mass Transfer in Fluid Systems

Diffusion causes convection. To be sure, convective flow can have many causes. For example, it can occur because of pressure gradients or temperature differences. However, even in isothermal and isobaric systems, diffusion will always produce convection. This was clearly stated by Maxwell in 1860: “Mass transfer is due partly to the motion of translation and partly to that of agitation.” In more modern terms, we would say that any mass flux may include both convection and diffusion.

This combination of convection and diffusion can complicate our analysis. The easier analyses occur in dilute solutions, in which the convection caused by diffusion is vanishingly small. The dilute limit provides the framework within which most people analyze diffusion. This is the framework presented in Chapter 2.

In some cases, however, our dilute-solution analyses do not successfully correlate our experimental observations. Consequently, we must use more elaborate equations. This elaboration is best initiated with the physically based examples given in Section 3.1. This is followed by a catalogue of flux equations in Section 3.2. These flux equations form the basis for the simple analyses of diffusion and convection in Section 3.3 that parallel those in the previous chapter.

After simple analyses, we move in Section 3.4 to general mass balances, sometimes called the general continuity equations. These equations involve the various coordinate systems introduced in Chapter 2. They allow solutions for the more difficult problems that arise from the more complicated physical situation.