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

fraction of the total volume that is fluid, and thus is accessible to diffusion. It can
be argued that the tortuousity factor, F Y, is related to void fraction, v, raised possibly
to the power –0.5; therefore, in total, we can postulate that the effective diffusivity
in the porous medium, B E, is related to the molecular diffusivity, B, by
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B E = BF A/F Y = Bv 1.5
Such a relationship is found for packings of various types of solids, as discussed
by Satterfield (1970). This equation may be seriously in error since (1) the effective
diffusivity is sensitive to the shape and size distribution of the particles, (2) there
may also be “surface diffusion” along the solid surfaces, and (3) the solute may
become trapped in “cul de sacs” or become sorbed on active sites. At least the
equation has the correct property that it reduces to intuitively correct limits that B E
equals B when v is unity, and B E is zero when v is zero. There is no substitute for
actual experimental measurements using the soil or sediment and solute in question.
For soils, it is usual to employ the Millington–Quirk (MQ) expression for diffusivity
as a function of air and water contents. An example is in the soil diffusion
model of Jury et al. (1983).
The MQ expression uses air and water volume fractions v A and v W and calculates
effective air and water diffusivities as follows:
B AE= B Av A 10/3 /(vA + v W) 2
B WE= B Wv W 10/3 /(vA + v W) 2
where B A and B W are the molecular diffusivities, and B AE and B WE are the effective
diffusivities. Inspection of these equations shows that they reduce to a similar form
to that presented earlier. If v W is zero, B AE is proportional to v A to the power 1.33
instead of 1.5.
Occasionally, there is confusion when selecting the concentration driving force
that is to be multiplied by B E. This should be the concentration in the diffusing
medium, not the total concentration including sorbed form. In sediments, the pore
water concentration may be 0.01 mol/m 3 , but the total sorbed plus pure water, i.e.,
bulk concentration, is 10 mol/m 3 . B E should then be multiplied by 0.01 not 10. In
some situations (regrettably), the total concentration (10) is used, in which case B E
must be redefined to be a much smaller “effective diffusivity,” i.e., by a factor of
1000. The problem is that diffusivity is then apparently controlled by the extent of
sorption.
In sediments, it is suspected that much of the chemical present in the pore or
interstitial water, and therefore available for diffusion, is associated with colloidal
organic material. These colloids can also diffuse; consequently, the diffusing chemical
has the option of diffusing in solution or piggy backing on the colloid. From
the Stokes–Einstein equation, the diffusivity B is approximately inversely proportional
to the molecular radius. A typical chemical may have a molecular mass of
200 and a colloid an equivalent molar mass of 6000 g/mol, i.e., it is a factor of 30