Agriculture Reference
In-Depth Information
the soil, and are represented by a system of consecutive and concurrent
reactions similar to those given in Figure 9.1. The model is capable of han-
dling concurrent and consecutive solute interactions along the lines of sur-
face diffusion, and inter- or intra-organic matter diffusion, etc. Different
sites with varied degree of affinity to solutes are analogues to concepts of
solute retention via surface diffusion or intra-organic matter diffusion as
discussed by Pignatello and Xing (1996), among others. A basic assumption
of the second-order model is that there are a limited number of adsorp-
tion sites for solute on the soil; therefore, the reaction rates are functions
of both solute concentration in solution and the availability of adsorption
sites on the soil matrix. Denoting ϕ as the number of sites available for
solute adsorption, the associated retention mechanisms were (Selim and
Amacher, 1988):
SKC
e
=θ
(9.30)
∂
∂
=θ−+
S
t
k
kC
(
kkS
)
(9. 31)
1
2
irrk
∂
∂
S
t
irr
=
kS
(9.32)
irrk
Here ϕ is related to the sorption capacity (
S
max
) by:
S
max
=++
S
S
(9.33)
e
k
where ϕ
and
S
max
are the unoccupied (or vacant) and total sorption sites on
soil surfaces, respectively (μg solute per g soil). In addition,
S
max
was con-
sidered as an intrinsic soil property and is time invariant. The unit for
K
e
is
cm
3
μg
-1
,
k
1
is cm
3
μg
-1
h
-1
, and
k
2
and
k
irr
are assigned units of h
-1
.
At equilibrium, total amounts of atrazine adsorbed on the
S
e
and
S
k
sites are:
ω
+ω
C
C
SSSS
=+=
(9.34)
T
e
k
max
1
Here ω
[=(
K
e
+ K
k
)θ] is the affinity coefficient of the combined equilibrium
and kinetic adsorption, and
K
k
=
k
1
/
(
k
2
+ k
irr
)
.
Moreover, the mass balance
equation for batch reactions is then written as:
dC
dt
dS
dt
dS
dt
e
k
−θ
=ρ
+
(9.35)
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