Fundamentals of Mass Transfer

Abstract

Diffusion is the process by which molecules, ions, or other small particles spon-taneously mix, moving from regions of relatively high concentration into regions of lower concentration. This process can be analyzed in two ways. First, it can be described with Fick's law and a diffusion coeffìcient, a fundamental and scientific description used in the fìrst two parts of this book. Second, it can be explained in terms of a mass transfer coef-ficient, an approximate engineering idea that often gives a simpler description. It is this simpler idea that is emphasized in this part of this book. Analyzing diffusion with mass transfer coefficients requires assuming that changes in concentration are limited to that small part of the system's volume near its boundaries. For example, in the absorption of one gas into a liquid, we assume that all gases and liquids are well mixed, except near the gas-liquid interface. In the leaching of metal by pouring acid over ore, we assume that the acid is homogeneous, except in a thin layer next to the solid ore particles. In studies of digestion, we assume that the contents of the small intestine are well mixed, except near the villi at the intestine's wall. Such an analysis is sometimes called a "lumped-parameter model" to distinguish it from the "distributed-parameter model" using diffusion coefficients. Both models are much simpler for dilute solutions. If you are beginning a study of diffusion, you may have troubìe deciding whether to organize your results as mass transfer coefficients or as diffusion coefficients. I have this trouble too. The cliché is that you should use the mass transfer coeffìcient approach if the diffusion occurs across an interface, but this cliché has many exceptions. Instead of depending on the cliché, I believe you should always try both approaches to see which is better for your own needs. In my own work, I have found that I often switch from one to the other as the work proceeds and my objectives evolve. This chapter discusses mass transfer coefficients for dilute solutions; extensions to con-centrated solutions are deferred to Section 13.5. In Section 8.1, we give a basic definition for a mass transfer coefficient and show how this coefficient can be used experimentally. In Section 8.2, we present other common definitions that represent a thicket of prickly al-ternatives rivaled only by standard states for chemical potentials. These various definitions are why mass transfer often has a reputation with students of being a difficult subject. In Section 8.3, we list existing correlations of mass transfer coefficients; and in Section 8.4, we explain how these correlations can be developed with dimensional analysis. Finally, in Section 8.5, we discuss processes involving diffusion across interfaces, a topic that leads to overall mass transfer coeffìcients found as averages of more local processes. This last idea is commonly called mass transfer resistances in series.