Agriculture Reference
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velocity (
q
A
,
q
B
), porosity (Θ
A
, Θ
B
), solute concentration (
C
A
, C
B
), and disper-
sion coefficient (
D
A
,
D
B
). The two flow domains are related by an interaction
term Γ such that:
Γ=α−
(
C
AB
)
(8.72)
where α is the mass transfer coefficient between the two flow domains.
This two-domain model reduces to a capillary bundle model when α = 0
and it approaches the classic one-domain convective-dispersion equation as
α increases. The two-flow domain model can also be reduced to a mobile-
immobile model when
V
B
equals zero. The convective-dispersion equation
in each flow domain can be written as (Skopp, Gardner, and Tyler, 1981):
∂
C
t
2
C
x
∂
∂
C
x
α
Θ
∂
∂
A
A
A
=
D
−
v
−
(
CC
−
)
(8.73)
A
A
AB
∂
2
A
∂
∂
C
t
2
C
x
∂
∂
C
x
−
α
Θ
∂
∂
B
B
B
=
D
−
v
(
CC
−
)
(8.74)
B
B
B
A
2
B
The corresponding initial and boundary conditions associated with each
flow domain (
i
) can be expressed as:
C
i
= 0
(
t
= 0, 0 <
x
<
L
)
(8.75)
∂
∂
C
x
i
vC
= Θ
vC
D
(
xt
=<
,
t
)
(8.76)
i
o
i
i
i
p
∂
∂
C
x
i
0
= Θ
vC
D
(
xt
=>
0,
t
)
(8.77)
i
i
i
p
∂
∂
C
x
i
=
0(
xLt
=
,
≥
)
(8.78)
These conditions are similar to those described earlier for the transport of
a solute pulse (input) having a concentration
C
o
in a uniform soil having a
finite length
L
where a steady water flux
v
was maintained constant.
8.6.1 Experimental Evidence
The two-flow domain model, which may be referred to as a dual-porosity
concept, has been used in the solute transport literature to account for the
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