Environmental Engineering Reference
In-Depth Information
k
1
(Ce) (Ci)
CO
2
k
2
k
3
CO
2
→ Organic C
k
4
↑
F
4
CA
HCO
3
-
→HCO
3
-*
Phytoplankton cell
−
. The
δ
13
C of the actively trans-
Fig. 9
Schematic presentation of the active transport of HCO
3
−
*
) is assumed to be the same as that of HCO
3
−
ported carbon (HCO
3
in the medium.
Data
source
Yoshioka (
1997
)
k
3
Ci
F
4
X
=
(5.25)
−
: The transported carbon has the same
δ
13
C value
(2)
Active transport of HCO
3
−
as HCO
3
, as depicted in the scheme shown in (Fig.
9
). The overall fractiona-
tion equation is substantially different from Eq. (
5.19
), although the steady-
state for Ci is denoted by a similar term as Eq. (
5.16
), which can be written
as:
(∆
k
1
+
1
)(∆
k
3
+
1
)(
1
−
X
) + (∆
k
1
+
1
)(∆
k
2
+
1
)
X
(∆
k
3
+
1
)(
1
−
f
) + (∆
k
1
+
1
)(∆
k
3
+
1
)(∆
k
4
+
1
)
f
α =
(5.23)
−
dissociation process.
Note that
f
and
X
are the same as those in the active transport of CO
2
.
Considering that the second- and third-order terms of
Δ
k
i
are negligible, and
Δ
k
1
=
Δ
k
3
, then
α
can be approximated as follows:
where
Δ
k
4
denotes the fractionation in the CO
2
—HCO
3
α =
1
+ ∆
k
1
(
1
−
f
) + (∆
k
2
− ∆
k
1
)(
1
−
f
)
Ci
Ce
− ∆
k
4
f
(5.24)
When
f
=
1,
α
becomes:
α =
1
+ (∆
k
2
− ∆
k
1
)
k
3
Ci
F
4
(5.25)
− ∆
k
4
which implies that the overall fractionation decreases by (
Δ
k
1
+
Δ
k
4
) when
all carbon derives from the active transport of
HCO
3
−
(
F
=
1
)
,
compared to
the passive diffusion model (Eq.
5.15
). It can be deduced from (Eq.
5.24
) that
all fractionation steps, including overall fractionation would be affected by
f
.
The difference between (Eqs.
5.19
and
5.24
) or (
Δ
k
1
+
Δ
k
4
) corresponds to the
difference in
δ
13
C values between
CO
2
AND HCO
3
−
.
These equations indicate that
the overall fractionation from [CO
2
]
aq
to organic carbon may be less than unity
under some conditions (Yoshioka
1997
).
From a reanalysis of Hinga's data (Hinga et al.
1994
) one gets that the active trans-
port of CO
2
for
S. costatum
can contribute ~ 30-40 % of the total carbon influx. The
relative contribution of active transport can reach 25-35 %, without any change in
CO
2
demand for an uptake of 10 % of the total carbon mediated by
β
-carboxylation