McKay, Donald. "Front matter" Multimedia Environmental Models ...

5. Diffusion within soils, and from soil to air.
6. Absorption of chemical by fish and other organisms by diffusion through the gills,
following the same route traveled by oxygen.
7. Transfer of chemical across other membranes in organisms, for example, from air
through lung surfaces to blood, or from gut contents to blood through the walls of
the gastrointestinal tract, or from blood to organs in the body.
Armed with these D values, we can set up mass balance equations that are similar
to the Level II calculations but allow for unequal fugacities between media.
To address these tasks, we return to first principles, quantify diffusion processes
in a single phase, then extend this capability to more complex situations involving
two phases. Chemical engineers have discovered that it is possible to make a great
deal of money by inducing chemicals to diffuse from one phase to another. Examples
are the separation of alcohol from fermented liquors to make spirits, the separation
of gasoline from crude oil, the removal of salt from sea water, and the removal of
metals from solutions of dissolved ores. They have thus devoted considerable effort
to quantifying diffusion rates, and especially to accomplishing diffusion processes
inexpensively in chemical plants. We therefore exploit this body of profit-oriented
information for the nobler purpose of environmental betterment.
©2001 CRC Press LLC
7.3 MOLECULAR DIFFUSION WITHIN A PHASE
7.3.1 Diffusion As a Mixing Process
In liquids and gases, molecules are in a continuous state of relative motion. If
a group of molecules in a particular location is labeled at a point in time, as shown
in the upper part of Figure 7.2, then at some time later it will be observed that they
have distributed themselves randomly throughout the available volume of fluid.
Mixing has occurred.
Since the number of molecules is large, it is exceedingly unlikely that they will
ever return to their initial condition. This process is merely a manifestation of mixing
in which one specific distribution of molecules gives way to one of many other
statistically more likely mixed distributions. This phenomenon is easily demonstrated
by combining salt and pepper in a jar, then shaking it to obtain a homogeneous
mixture. It is the rate of this mixing process that is at issue.
We approach this issue from two points of view. First is a purely mathematical
approach in which we postulate an equation that describes this mixing, or diffusion,
process. Second is a more fundamental approach in which we seek to understand
the basic determinants of diffusion in terms of molecular velocities.
Most texts follow the mathematical approach and introduce a quantity termed
diffusivity or diffusion coefficient, which has dimensions of m2/h,
to characterize this
process. It appears as the proportionality constant, B, in the equation expressing
Fick’s first law of diffusion, namely
N = –B A dC/dy