Page 533 - Bird R.B. Transport phenomena

Chapter 1

iusivity and the Mechanisms

§17.1 Pick's law of binary diffusion (Molecular Mass Transport)
§17.2 Temperature and pressure dependence of diffusivities
§17.3° Theory of diffusion in gases at low density

§17.4° Theory of diffusion in binary liquids
§17.5° Theory of diffusion in colloidal suspensions
§17.6° Theory of diffusion of polymers
§17.7 Mass and molar transport by convection
§17.8 Summary of mass and molar fluxes
§17.9° The Maxwell-Stefan equations for multicomponent diffusion in
gases at low density

In Chapter 1 we began by stating Newton's law of viscosity, and in Chapter 9 we began
with Fourier's law of heat conduction. In this chapter we start by giving Fick's law of dif-
fusion, which describes the movement of one chemical species A through a binary mix-
ture of A and В because of a concentration gradient of A.
The movement of a chemical species from a region of high concentration to a region
of low concentration can be observed by dropping a small crystal of potassium perman-
ganate into a beaker of water. The KMnO begins to dissolve in the water, and very near
4
the crystal there is a dark purple, concentrated solution of KMnO . Because of the con-
4
centration gradient that is established, the KMnO diffuses away from the crystal. The
4
progress of the diffusion can then be followed by observing the growth of the dark pur-
ple region.
In §17.1 we give Fick's law for binary diffusion and define the diffusivity % AB for the
pair A-B. Then we discuss briefly the temperature and pressure dependence of the diffu-
sivity. After that we give a summary of the theories available to predict the diffusivity
for gases, liquids, colloids, and polymers. At the end of the chapter we discuss the trans-
port of mass of a chemical species by convection, thus paralleling the treatments in
Chapters 1 and 9 for momentum and heat transfer. We also introduce molar units and
the notation needed for describing diffusion in these units. Finally, we give the
Maxwell-Stefan equations for multicomponent gases at low densities.
Before starting the discussion we establish the following conventions. For multicom-
ponent diffusion, we designate the species with lower-case Greek letters a, /3, y,... and
their concentrations with the corresponding subscripts. For binary diffusion we use the
capital italic letters A and B. For self-diffusion (diffusion of chemically identical species)

513