Agriculture Reference
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velocity and aggregate sizes. Equation 8.8 was extended to include a reactive
solute with a retardation factor
R
(van Genuchten and Dalton, 1986; Parker
and Valocchi, 1986):
22
im
2
(1
−
FavR
DR
)
(
)
m
DDF
=
+
(8.10)
2
15
e
where
R
im
is the retardation factor associated with the immobile phase,
R
is
an overall retardation factor (Θ
R
=
Θ
im
R
im
+
Θ
m
R
m
). Similar effective disper-
sion coefficients were obtained for rectangular aggregates with half width
of
a
l
as:
22
im
2
(1
−
Fa vR
DR
)
(
)
m
l
DDF
=
+
(8.11)
2
3
e
An overall
D
can also be derived from empirical first-order mass trans-
fer where uniform solute distribution in the immobile water phase may
be assumed. This was carried out by De Smedt and Wierenga (1984), who
derived an expression for
D
for nonreactive solutes for long columns as:
)
22
+
Θ−
α
(1
Fv
m
DDF
=
(8.12)
and for reactive solutes (van Genuchten and Dalton, 1986) as:
22
im
2
(1
−
FavR
R
)
(
)
m
l
DDF
=
+
(8.13)
2
α
Comparing Equations 8.8 and 8.12 an equivalent first-order transfer coef-
ficient (α
t
) for spherical aggregates is thus obtained:
15
DF
a
(1
−Θ
)
e
α=
(8.14)
t
2
This equation can also be used using moment analysis (Valocchi, 1985) and
has been used in solute transport (Selim, Schulin, and Flühler, 1987; Selim
and Amacher, 1988). Similar α expressions were obtained for a rectangular
aggregate as:
3(1)
2
DF
a
−Θ
e
α=
(8.15)
l
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