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

If the fish is growing, there will be growth dilution, which can be included as
an additional loss rate constant k G, which is the fractional increase in fish volume
per hour.
At steady-state conditions, the left side is zero, and
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C F = (k 1C W + k AC A)/(k 2 + k M + k E)
Gobas (1993) has suggested correlations for these rate constants as a function of
fish size. The mass balance around the fish can be deduced and the important
processes identified. The rate constant k 1 is much larger than k A, typically by a factor
of 5000. Thus, uptake from water and food become equal when C A is about 5000
times C W, which corresponds to a K OW of about 10 5 and 5% lipid. For lower K OW
chemicals, uptake from water dominates whereas, for higher K OW chemicals, uptake
from food dominates.
8.9.3 Equations in Fugacity Format
We can rewrite the bioconcentration equation in the equivalent fugacity form as
V FZ Fdf W/dt = D V(f W – f F)
where D V is a gill ventilation D value analogous to k 1 and applies to both uptake
and loss. This form implies that the fish is merely seeking to establish equilibrium
with its surrounding water. The corresponding uptake and clearance equations are
f F = f W(1 – exp[–D Vt/V FZ F)]
f F = f FO exp(–D Vt/V FZ F)
The following expressions relate the rate constants and D values, showing that
the two approaches are ultimately identical algebraically.
k 1 = D V/V FZ W
k 2 = D V/V FZ F
K FW = Z F/Z W
As was discussed earlier, Z F can be approximated as LZ O, where L is the volume
fraction lipid content of the fish, and Z O is the Z value for octanol or lipid. K FW is
then LK OW, where L is typically 0.05 or 5%.
From an examination of uptake data, Mackay and Hughes (1984) suggested that
D V is controlled by two resistances in series, a water resistance term D W, and an
organic resistance term D O. Since the resistances are in series,
1/D V = 1/D W + 1/D O