Environmental Engineering Reference
In-Depth Information
!
1
1
þ
exp
RT
ð
E
anode
E
KA
Þ
j
¼
j
max
(1
:
11)
where j
max
is the maximum current density (A/m
2
), E
KA
is the anodic
acceptor potential for the half-maximum-rate (V), R is the ideal gas constant
(8.3145 J/mol K), F is the Faraday constant (96,485 Coulomb/mol), and T is the
temperature (298.15 K). Equation (1.11) shows that j =0.5 j
max
when
E
anode
=E
KA
.
Figure 1.7 shows properties of the Monod and Nernst-Monod expressions
in dimensionless forms that are easy to compare: the dimensionless Monod
expression is S
a
*/(1+S
a
*), where S
a
*=S
a
/K
Sa
; the dimensionless Nernst-Mo-
nod expression is 1/(1+exp(
*)), where the dimensionless local potential is
*=F/RT(E
anode
E
KA
). The two dimensionless equations saturate to 1 as the
respective variables on the horizontal axis increase. The dimensionless Monod
expression has two reference points (Fig. 1.7a): at S
a
*=0, the expression equals
zero, because the rate of substrate utilization equals zero when there is no
substrate; at S
a
*=1, S
a
equals K
Sa
, and the Monod expression gives the half
of the maximum rate of 0.5. In contrast, the Nernst-Monod expression has only
one reference point (Fig. 1.7b): at
* =0,E
anode
equals E
KA
and the Nernst-
Monod expression gives half of the maximum rate of 0.5.
We consider an example using Eq. (1.11) to understand the relationship
between voltage and current in an MFC with the following parameters: a single
adjustable external resistor R
useful
(), an anode surface area A =25cm
2
(0.0025 m
2
), and j
max
= 1 mA/cm
2
(10 A/m
2
). E
rxn
for an O
2
MFC is often
around 800 mV, and we used 250 mV to approximate inefficiencies due to non-
anode processes; thus, E
rxn
= 800-250 = 550 mV. We define the anode kinetic
loss
anode
(mV) as
anode
¼
E
anode
E
donor
(1
:
12)
1.0
1
0.8
0.8
0.6
0.6
1/2 max
1/2 max
0.4
0.4
0.2
0.2
0.0
0
0
1
2
3
4
5
-5 -4 -3 -2 -1 0 1 2 3 4 5
η
*
S
a
*
(a)
(b)
Fig. 1.7 Plots of dimensionless forms of (a) the Monod and (b) the Nernst-Monod equations
