Diffusion Mass Transfer in Fluid Systems

In this chapter we want to connect mass transfer coefficients, diffusion coefficients, and fluid flow. In seeking these connections, we are combining the previous chapter, which deals with mass transfer, with the first two sections of the book, which dealt with diffusion.

To find these connections, we will develop theories of mass transfer. These theories are rarely predictive, but they clarify the chemistry and physics which are involved. They are less predictive because they are most often for fluid–fluid interfaces whose geometry is not well known. They are much more successful for solid–fluid interfaces, which are much better defined. Unfortunately, fluid–fluid interfaces are much more important for mass transfer than fluid–solid interfaces are.

Before reviewing the common theories, we should identify exactly what we want to predict. Almost always, we want to predict the mass transfer coefficient k as a function of the diffusion coefficient D and the fluid velocity v. In many cases, convection will be forced, i.e., the velocity will be caused by mechanical forces like pressure drop imposed from outside the system. In occasional cases, convection will be free, the consequence of gravity driven flows often caused by the mass transfer itself. While we will discuss both cases, we will stress forced convection because it is more important and more common in chemical processing.