Agriculture Reference
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respectively. The terms
C
m
and
C
im
are the concentrations in the mobile and
immobile water (μg cm
-3
), and
v
m
is the average pore-water velocity in the
mobile region (cm h
-1
). Also
x
is depth (cm) and
t
is time (h). It is also assumed
that the immobile water (Θ
im
) is located inside aggregate pores (interaggre-
gate) where solute transfer occurs by diffusion only. In Equation 8.2 α is a
mass transfer coefficient (h
-1
), which governs the transfer of solutes between
the mobile- and immobile-water phases in analogous manner to a diffusion
process.
The mobile-immobile concept represented by Equations 8.1 and 8.2 may be
generalized for the transport of reactive solutes. Incorporation of reversible
and irreversible retention for reactive solutes in Equations 8.1 and 8.2 yields:
∂
∂
+ρ
∂
m
m
2
m
−νΘ
∂
∂
m
C
t
S
t
∂
∂
C
x
C
x
m
m
mm
mim
Q
m
Θ
f
= Θ
D
−α
(
CC
−
)
−
(8.3)
∂
2
and
∂
∂
+−ρ
∂
im
im
C
t
S
t
im
CC
Q
mim
im
Θ
(1
f
)
=α −−
(
)
(8.4)
∂
where ρ is soil bulk density (g cm
-3
). Here the soil matrix is divided into two
regions (or sites) where a fraction
f
is a dynamic or easily accessible region and
the remaining fraction is a stagnant or less accessible region (see Figure 8.2).
The dynamic region is located close to the mobile phase, whereas the stag-
nant region is in contact with the immobile phase. Moreover,
S
m
and
S
im
are
the amounts of solutes sorbed in the dynamic and stagnant regions (μg per
gram soil), respectively. Also
Q
m
and
Q
im
are sink (or source) terms associ-
ated with the mobile and immobile water regions, respectively. Therefore,
Q
m
and
Q
im
represent rates of irreversible-type reactions. These terms must
be distinguished from
S
m
and
S
im
, which represent reversible sorbed solutes
in the dynamic and stagnant regions, respectively.
The mobile-immobile approach has been successful in describing the fate
of several pesticides in soils when linear and Freundlich reversible reactions
were considered (van Genuchten, Wierenga, and O'Connor, 1977). However,
it is often necessary to include kinetic rather than equilibrium reactions to
account for the degradation of pesticides in soils (Rao et al., 1979). The mobile-
immobile approach has been successfully used to describe heavy metal
transport in soils when adsorption was considered as a Langmuir kinetic
along with a first-order irreversible reaction (Selim and Amacher, 1988). The
mobile-immobile is approach has had only limited success when extended to
describe the transport and exchange of ions in soils for binary (Ca-Mg) and
ternary (Ca-Mg-Na) systems (for a review see Selim, 1992).
The mobile-immobile concept is commonly referred to as the two-
region model and is regarded as a mechanistic approach where physical
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