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

larger in mass and volume, but only a factor of 30 0.33 or about 3 in radius. The colloid
diffusivity will thus be about one-third that of the dissolved molecule. But if 90%
of the chemical is sorbed, the colloidal diffusion rate will exceed that of the dissolved
form. As a result, is necessary to calculate and interpret the component diffusion
processes, since it may not be obvious which route is faster.
7.7 DIFFUSION BETWEEN PHASES: THE TWO-RESISTANCE CONCEPT
7.7.1 Derivation Using Concentrations
So far in this discussion, we have treated diffusion in only one phase, but in
reality, we are most interested in situations where the chemical is migrating from
one phase to another. It thus encounters two diffusion regimes, one on each side of
the interface. Environmentally, this is discussed most frequently for air-water
exchange, but the same principles apply to diffusion from sediment to water, soil to
water and to air, and even to biota-water exchange.
An immediate problem arises at the interface, where the chemical must undergo
a concentration “jump” from one equilibrium value to another. The chemical may
even migrate across the interface from low to high concentration. Clearly, whereas
concentration difference was a satisfactory “driving force” for diffusion within one
phase, it is not satisfactory for describing diffusion between two phases. When
diffusion is complete, the chemical’s fugacities on both sides of the interface will
be equal. Thus, we can use fugacity as a “driving force” or as a measure of “departure
from equilibrium.” Indeed, fugacity is the fundamental driving force in both cases,
but it was not necessary to introduce it for one-phase systems, because only one Z
applies, and the fugacity difference is proportional to the concentration difference.
Traditionally, interphase transfer processes have been characterized using the
Whitman Two-Resistance mass transfer coefficient (MTC) approach (Whitman,
1923), in which departure from equilibrium is characterized using a partition coefficient,
or in the case of air-water exchange, a Henry’s law constant. We derive the
flux equations for air-water exchange using the Whitman approach and following
Liss and Slater (1974), who first applied it to transfer of gases between the atmosphere
and the ocean, and Mackay and Leinonen (1975), who applied the same
principles to other organic solutes. We will later derive the same equations in fugacity
format. Unfortunately, the algebra is lengthy, but the conclusions are very important,
so the pain is justified.
Figure 7.6 illustrates an air-water system in which a solute (chemical) is diffusing
at steady-state from solution in water at concentration C W (mol/m 3 ) to the air at
concentration C A mol/m 3 , or at a partial pressure P (Pa), equivalent to C ART. We
assume that the solute is transferred relatively rapidly in the bulk of the water by
eddies, thus the concentration gradient is slight. As it approaches the interface,
however, the eddies are damped, diffusion slows, and a larger concentration gradient
is required to sustain a steady diffusive flux. A mass transfer coefficient, k W, applies
over this region. The solute reaches the interface at a concentration C WI, then abruptly
changes to C AI, the air phase value. The question arises as to whether there is a
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