Agriculture Reference
In-Depth Information
At steady state the flux of CO
2
gas must equal the net flux of dissolved CO
2
and
carbonate species, therefore
F
GC
=
F
LC
=
F
LH
2
CO
3
∗
+
F
LHCO
3
−
+
F
LCO
3
2
−
(
3
.
34
)
where H
2
CO
3
∗
represents CO
2
(aq)
+
H
2
CO
3
.
The fluxes of the uncharged solutes, CO
2
and H
2
CO
3
, are given by equations
of the type
D
LA
δz
L
(C
LA
−
C
LA0
)
F
LA
=−
(
3
.
35
)
The fluxes of charged solutes depend on the diffusion potential arising from
differences in the mobilities of individual ions, as well as on an ion's own
concentration gradient (Equation 2.21). The effect of diffusion potentials will be
important if the carbonate species are a large part of the total ion concentration,
as they often will be. Therefore we have for the net flux of ion B
F
LB
=−
D
LB
d
C
LB
d
z
+
Z
B
C
LB
D
LB
D
L
i
d
C
L
i
/
d
z
Z
i
2
D
L
i
C
L
i
(
3
.
36
)
where subscript
i
refers to all the co- and counter-ions in solution and
Z
B
and
Z
i
are the ionic charges. This gives
D
LB
δz
L
(C
LB0
−
C
LB
)
+
Z
B
2
(C
LB
+
C
LB0
)D
LB
Φ
F
LB
≈−
(
3
.
37
)
where
D
L
i
d
C
L
i
/
d
z
Z
i
2
D
L
i
C
L
i
Φ
=
There is an equation of this type for each of the ions present.
The principal cations and anions in floodwaters are generally Ca
2
+
,Cl
−
,
HCO
3
,CO
2
−
3
and OH
−
. Therefore we have five equations of type (3.37) for
the fluxes of the five charged species, Equation (3.33) for CO
2
gas and Equa-
tion (3.35) for H
2
CO
3
∗
. These seven equations contain six unknowns—the con-
centrations of H
2
CO
3
∗
and the five ions in solution at the interface—and these
are found with the following six equations: Equation (3.34), Equations (1)-(3)
in Table 3.3, and
F
LCa
2
+
=
0and
F
LCl
−
=
0—i.e. no net flux of Ca
2
+
and Cl
−
across the interface, their concentration gradients being balanced by their diffu-
sion potential gradients.
Note that charge balance between the diffusing ions is inherent in Equa-
tion (3.37). Note also that the movement of H
+
ions formed in the carbonate
equilibria is allowed for in the movements of the various conjugate acid-base
pairs present: H
2
CO
3
-HCO
3
−
,
HCO
3
−
-CO
3
2
−
and H
2
O-OH
−
. For each mol
of CO
2
entering or leaving the water, 1mol of H
+
is added or removed at the
