Agriculture Reference
In-Depth Information
discussed in Chapter 1, most reactive solute behavior is of the nonlinear
type with
b
≤ 1.
3.3 Initial and Boundary Conditions
Solutions of the above CDE yield the concentration distribution of the amount
of solute in soil solution (
C
) and that retained by the soil matrix (
S
) with
time and space in soil (
z
,
t
). In order to arrive at such a solution, the initial
and boundary conditions that accurately describe the experimental condi-
tions must be specified. Several boundary conditions are identified with the
problem of solute transport in porous media. First-type (Dirichlet) boundary
conditions for a solute pulse input may be described as:
C
=
,
z
=
0,
t
<
C
t
(3.41)
o
p
C
=
0,
z
=
0,
t
≥
t
p
(3.42)
where
C
o
(Μg cm
-3
) is the concentration of the solute species in the input pulse.
The input pulse application is for a duration
t
p
(
h
), which is then followed by
solution that is free of solute. These boundary conditions describe a tracer
solution applied at a specified rate from a perfectly mixed inlet reservoir
to the surface of a finite or semi-infinite soil profile. These Dirichlet bound-
ary conditions were used by Lapidus and Amundson (1952) and Clearly and
Adrian (1973) and assume that the concentration itself can be specified at the
inlet boundary. This situation is not usually possible in practice.
Third-type boundary conditions are commonly used and account for
advection plus dispersion across the interface of solute at concentration
C
o
.
For a continuous input at the soil surface, we have
∂
∂
C
z
>
(3.43)
=−
D
+
vC
,
z
=
0,
t
0
vC
o
and for a third-type pulse-input we have
∂
∂
C
z
=−
D
+
vC
,
z
=
0,
t
<
(3.44)
vC
t
o
p
∂
∂
C
z
=−
D
+
vC
,
z
=
0,
t
≥
0
t
p
(3.45)
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