Agriculture Reference
In-Depth Information
considered are large enough to average microscale variations, the soil can be
treated as quasi-homogeneous and Fick's first law can be applied to the system
as a whole. The term
C
in Equation (2.16) is then the concentration of the
diffusate in the whole soil system; that is, 'all those ions or molecules that are in
or pass through a mobile phase during a period that is short in comparison with
the time of the diffusion process' (Nye, 1979). Solutes that do not interchange
completely between the solid and solution within this time frame, i.e. a matter
of hours, are treated as having a rate of reaction and are dealt with by adding a
source or sink term to the appropriate form of the continuity equation.
Following from this definition, the diffusive flux of a solute through the solution
and solid in the
x
direction is given by (Tinker and Nye, 2000, Equation 4.17)
=−
D
L
f
L
θ
L
d
C
L
d
x
−
D
L
f
S
θ
S
d
C
S
F
(
2
.
17
)
d
x
where
D
L
is the diffusion coefficient of the solute in free solution,
θ
L
is the
fraction of the soil volume occupied by solution,
θ
S
is the fraction of the soil
volume occupied by soil solid,
f
L
and
f
S
are the impedance factors for the liquid
and solid phase, respectively, and
C
L
and
C
S
are the amounts of solute per unit
volume of liquid and solid phase, respectively.
The first term on the right-hand side of Equation (2.17) represents diffusion
exclusively in solution; the second term represents the additional diffusion that
occurs as a result of mobility on the soil solid.
The concentration of the solute in the solid is expressed in terms of the amount
per unit weight of solid,
S
S
,by
θ
S
C
S
=
ρS
S
where
ρ
is the weight of dry solid
per unit soil volume. By definition,
F
=−
D
d
C/
d
x
. Substituting for
F
and
θ
S
C
S
in Equation (2.17) and rearranging gives
D
L
f
L
θ
L
+
d
C
L
d
C
f
S
ρ
d
S
S
d
C
L
D
=
(
2
.
18
)
In the following sections I discuss the components of the diffusion coefficient so
defined in turn. Note all the components of
D
are altered by flooding the soil.
As well as increasing the cross-sectional area for diffusion, represented by
θ
L
,
flooding affects the geometry and tortuosity of the soil pore network, represented
by
f
L
and
f
S
, and solute sorption on the soil solid, represented by d
C
L
/
d
C
.
The Diffusion Coefficient in Free Solution,
D
L
Table 2.3 gives the self-diffusion coefficients of some important ions in sub-
merged soils and Figure 2.2 shows the values for the elemental ions plotted
against ionic potential (
|
z
|
/r
where
|
z
|
is the absolute ionic charge and
r
the
crystal ionic radius). As the ionic potential increases the hydration layer of water
molecules around the ion increases, and therefore the mobility tends to decrease.
Also, at the same ionic potential, cations diffuse faster than anions. The mobilities
