Agriculture Reference
In-Depth Information
The reversible solute retention from the soil solution is represented by the
term, on the left side of Equation 9.1, while the irreversible solute removed
from soil solution is expressed by the term
Q
on the right side of Equation 9.1.
9.3 Boundary Condition at the Interface
An important boundary condition needed in the analysis of multilayered
soils is that at the interface between layers. It should be noted that both first-
type and third-type boundary conditions are applicable at the interface. Leij,
Dane, and van Genuchten (1991) showed that although the principle of sol-
ute mass conservation is satisfied, a discontinuity in concentration develops
when a third-type interface condition is used. On the other hand, a first-type
interface condition will result in a continuous concentration profile across
the boundary interface at the expense of solute mass balance. To overcome
the limitations of both first- and third-type conditions, a combination of first-
and third-type conditions was implemented. The first-type condition can be
written as:
C
=
C
II
xL
,
t
>
0
(9.2)
I
xL
−
+
→
→
1
1
where and denote that
x
=
L
1
is approached from the upper and lower layer,
respectively. Similarly, the third-type condition can be written as:
∂
∂
C
x
∂
∂
C
x
I
II
qC
−θ
D
=
qC
− θ
D
,
t
>
0
(9.3)
I
I
I
II
II
II
−
+
xL
→
xL
→
1
1
Incorporation of Equation 9.2 into Equation 9.3 yields:
∂
∂
C
x
∂
∂
C
x
I
II
θ
D
=θ
D
,
t
>
0
(9.4)
I
I
II
II
−
+
xL
→
xL
→
1
1
The boundary condition of Equation 9.4 was first proposed by Zhou and
Selim (2001) and resembles that for a second-type boundary condition as
indicated earlier by Leij, Dane, and van Genuchten (1991).
9.4 Equilibrium Retention Models
The form of solute retention reactions in the soil system must be identified if
prediction of the fate of reactive solutes in the soil using the CDE (Equation
9.1) is sought. The reversible term
(/t)
∂∂
is often used to describe the rate of
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