Agriculture Reference
In-Depth Information
flow,
when a solute, if dispersion is ignored, moves in a porous medium or
is displaced through the soil like a piston. Dispersion is a passive process
in response to water flow. Therefore, dispersion is effective only during
fluid flow, so that for a static water condition or when water flow is near
zero, molecular diffusion is the dominant mixing process for solute trans-
port in soils. A longitudinal dispersion coefficient (
D
L
) and transverse dis-
persion coefficients (
D
T
) are needed to describe the dispersion mechanism.
Longitudinal dispersion refers to that in the direction of water flow and (
D
T
)
refers to dispersion in directions perpendicular or transverse to the direc-
tion of flow. Longitudinal dispersive transport can be described by an equa-
tion similar to Equation 3.14 for diffusion:
∂
∂
C
z
=
−Θ
(3.23)
U
D
m
L
Separate studies investigated the effects of the soil water content Θ (Laryea
et al., 1982; Smiles and Philip, 1978; Smiles et al., 1978) and the water flux q
(Smiles and Gardiner, 1982; De Smedt and Wierenga, 1984) on
D
L
. A linear
relationship between unique
D
L
and
v
, where
v
is referred to as the pore-
water velocity and is given by (
q
/Θ), is commonly used:
D
=D
o
+λ
v
(3.24)
L
where
D
o
is the molecular diffusion coefficient in water. The term λ is a
characteristic property of porous media known as the
dispersivity
(cm).
Dispersivity values λ vary from a few centimeters for uniformly packed (dis-
turbed) laboratory soil columns to several meters for field-scale experiments.
Large values of λ are also reported for well-aggregated soils. In practice, an
empirical parameter
D
rather than
D
L
is often introduced to simplify the flux
equation (Boast, 1973). Moreover, because
D
o
<<
D
L
,
D
L
or simply
D
= λν, or a
more general formula (see Bear, 1972):
DD
=
λ
n
(3.25)
=
v
L
is often used, where
n
is an empirical constant with a common range of 1.0 to
1.2 (Yasuda et al., 1994; Montero et al., 1994; Jaynes, Bowman, and Rice, 1988).
Therefore,
D
versus ν may not be strictly linear and the dispersivity λ is not
velocity dependent (Gerritse and Singh, 1988).
Several modifications of
D
vs. ν are found in the literature by introducing
the tortuosity coefficient τ of Equation (3.17), including that by Brusseau (1993):
D=
D
τ+λ
n
(3.26)
v
o
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