Agriculture Reference
In-Depth Information
Subject to the appropriate initial and boundary conditions, the above sys-
tem of Equations 9.30 to 9.35 was solved using finite-difference approxima-
tion methods (for details see Ma and Selim, 1994).
The above formulation is now extended to mixed soils or geological media.
Specifically, each soil in the mixed system has its distinct set of solute reten-
tion parameters. The simplest case is that for a mixed system composed of
only two different soils with the designation
r
and
m
. If one assumes that
soils
r
and
m
compete concurrently for the retention of solute present in the
solution phase,
S
max
can be expressed as:
S
=
f S
[
]
+
(1
−
f
)[
S
]
(9.36)
max
max
r
max
m
where [
S
max
]
r
and [
S
max
]
m
represent the sorption capacity for soils
r
and
m
,
respectively. Here the dimensionless parameter
f
represents the fraction of
soil
r
to that of the soil (on a mass per unit bulk volume basis). This param-
eter is necessary in order to account for the proportion of each compartment
per unit bulk volume of the soil. Based on second-order formulation, we can
express
S
max
for each respective compartment as:
[
S
max
=φ++
]
[]
[] []
S
S
(9.37)
r
r
er
kr
[
S
]
=φ +
[]
[] []
S
+
S
(9.38)
max
m
m
em
km
Consequently, the amounts of solute sorbed by all equilibrium type sites are
Sf S
=
[] (1
+
−
f
)[
S
]
(9.39)
e
e
r
e
m
or more explicitly we have:
S
=λθ
C
where
λ=
fK
[
]
φ +− φ
(1)[]
fK
em m
(9.40)
e
e
rr
Similarly, the amount of solute sorbed by the kinetic sites of both
r
and
m
soils is
Sf
=
[] (1
S
+
−
f
)[
S
]
(9.41)
k
k
r
k
m
where
∂
[]
S
t
kr
∂
=θ φ− +
[]
kC
{[
k
][]}[]
k
S
(9.42)
1
r
r
2
r
irr
r
k
r
∂
[]
S
km
=
[]
k
θ φ− +
C
{[
k
]
[
k
]}[]
S
(9.43)
1
m
m
2
mirr
mk
m
∂
t
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