Agriculture Reference
In-Depth Information
9.2 Convection-Dispersion Equation
A two-layered soil column of length
L
is shown in Figure 9.1. The length
of each layer is denoted by
L
1
and
L
2
, respectively. To show heterogeneity,
each soil layer has specific, but not necessarily the same, water content, bulk
density, and solute retention properties. Only vertical, steady-state water
flow perpendicular to the soil layers (Figure 9.1) will be considered. The
convective-dispersive equation (CDE) governing solute transport in the
i
th
layer (see Figure 9.1) is given by Equation 9.1 (Selim, Davidson, and Rao 1977):
ρ
∂
∂
S
t
+θ
∂
∂
C
t
∂
∂
∂
∂
C
x
∂
∂
C
x
i
i
i
i
=
θ
D
−
q
−
Q
i
i
i
i
i
x
(9.1)
(0
≤≤ =
xLi
,
,2)
i
where (omitting the
i
):
C
= resident concentration of solute in soil solution (μg cm
-3
)
S
= amount of solute adsorbed by the soil matrix (μg g
-1
)
ρ = soil bulk density (g cm
-3
)
θ = volumetric soil water content (cm
3
cm
-3
)
D
= solute dispersion coefficient (cm
2
d
-1
)
q
= Darcy soil-water flow velocity (cm d
-1
)
Q
= a sink or source for irreversible solute interaction (μg cm
-3
d
-1
)
x
= distance from the soil surface (cm)
t
= t ime (d)
Soil Surface
x
Layer 1:
C
1
, θ
1
L
1
L
Layer 2:
C
2
, θ
2
L
2
FIGURE 9.1
A schematic diagram of a two-layered soil.
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