Agriculture Reference
In-Depth Information
of H
3
O
+
and OH
−
are anomalously large because they move by a proton jump
mechanism in which protons are passed between favourably orientated water
molecules (Glasstone
et al
., 1941).
However, in bulk diffusion, ions cannot move independently of each other
because electrical neutrality must be maintained. Consequently there is an electric
potential between diffusing ions such that the faster ions tend to be slowed down
by the slower ones and vice versa. The flux of a particular ion is therefore the
sum of the diffusion due to its own concentration gradient and that due to the
gradient of the diffusion potential arising from differences in the mobilities of the
ions present. This is expressed by the Nernst-Planck equation along the
x
-axis:
F
LA
=−
D
LA
d
C
LA
d
x
Z
A
C
LA
F
RT
d
ψ
d
x
+
(
2
.
19
)
where
F
is the Faraday,
Z
A
is the charge of ion A and
ψ
is the potential. If A
is present in only small concentrations, the diffusion potential term is much less
important than the concentration gradient term, and can be ignored. However, if
A is a large part of the total ionic strength, and ions are present with differing
mobilities, the diffusion potential will be important. Vinograd and McBain (1941)
used the condition of no net flux of charge:
Z
i
F
L
i
=
0
(
2
.
20
)
where subscript
i
refers to a particular species and
Z
i
is its charge, to express
the term d
ψ/
d
x
in terms of the ionic concentrations gradients, giving
D
LA
d
C
LA
d
x
Z
A
C
LA
D
LA
D
L
i
d
C
L
i
/
d
x
Z
i
2
D
L
i
C
L
i
F
LA
=−
+
(
2
.
21
)
Equation (2.21) shows that the greater
Z
A
,C
LA
and
D
LA
, and the smaller d
C
LA
/
d
x
,
the greater will be the effect. But the effect is small for ions with similar mobili-
ties and for ions whose concentrations are small compared with the total solution
concentration.
A further point is that a significant proportion of many of the cations in solu-
tion in submerged soils may be complexed with organic ligands (Chapter 3).
The diffusion coefficients of the complexed ions will be smaller than the corre-
sponding free ions. Table 2.4 compares self-diffusion coefficients of chelated and
unchelated Fe
3
+
and Zn
2
+
. Table 2.5 gives the diffusion coefficients in aqueous
solution of other uncharged solutes important in submerged soils, and diffusion
coefficients in air.
The Soil Moisture Content,
θ
L
andBulkDensity,
ρ
In submerged soils there tends to be a gradient of bulk density with depth as
a result of the settling of disturbed sediment. As a result, the bulk density is
