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

The nature of the processes controlling D W and D O is not precisely known, but
it is suspected that they are a combination of flow (GZ) and mass transfer (kAZ)
resistances. If we substitute GZ for each D, recognizing that G may be fictitious,
we obtain
1/k 2 = V FZ F/D V = V FLZ O(1/G WZ W + 1/G OZ O) = (V FL/G W)K OW + (V FL/G O)
= t WK OW + t O
By plotting 1/k 2 against K OW for a series of chemicals taken up by goldfish, Mackay
and Hughes (1984) estimated that t W was about 0.001 hours and t O 300 hours. This
is another example of probing the nature of series or “two-film” resistances using
chemicals of different partition coefficient as discussed in Chapter 7.
The times t W and t O are characteristic of the fish species and vary with fish size
and their metabolic or respiration rate, as discussed by Gobas and Mackay (1989).
The uptake and clearance equilibria and kinetics, i.e., bioconcentration phenomena,
of a conservative chemical in a fish are thus entirely described by K OW, L, t W, and t O.
The bioconcentration equation can be expanded as before to include uptake from
food with a D value D A, loss by egestion (D E) and loss by metabolism (D M), giving
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V FZ Fdf F/dt = D Vf W + D Af A – f F (D V + D M + D E)
A growth dilution D value D G defined as Z FdV F/dt can be included as an additional
loss term. This term can become very important for hydrophobic chemicals
for which the D V and D M terms are small. The primary determinant of concentration
is then how fast the fish can grow and thus dilute the chemical. It should be noted
that this treatment of growth is simplistic in that growth is assumed to be first order
and does not change other D values.
A mass balance envelope problem arises when treating the food uptake or
digestive process. The entire fish, including gut contents, can be treated as a single
compartment. In this case, the food uptake D value is simply the GZ product of the
food consumption rate and its Z value, i.e., G AZ A, subscript A applying to food. Z A
can be estimated as L AZ O, where L A is the lipid content of the food. Often, the
fugacity of a chemical in the food f A will approximate the fugacity in water. The
rate of chemical uptake into the body of the fish is then E AD Af A or D AEf A, where E A
is the uptake efficiency of the chemical. In reality, the gut is “outside” the epithelial
tissue of the fish, and it may be better to treat the fish as only the volume inside the
epithelium. In this case, the uptake D value is G AZ AE A. To avoid confusion, we
define two uptake D values, D AE, which includes the efficiency, and D A, which does
not. The same problem applies to egestion where we define D EE as including a
transport efficiency and D E, which does not.
The digestive process that controls E A and thus D AE is more complicated and
less understood than gill uptake. The first problem is quantifying the uptake efficiency,
i.e., the ratio of quantity of chemical absorbed by the fish to chemical
consumed. It is generally about 50% to 90%. Gobas et al. (1989) have suggested