Environmental Engineering Reference
In-Depth Information
Assuming E
KA
= E
donor
+ 100 mV [31], combining Eqs. (1.7), (1.11), and
(1.12) yields
V
cell
¼
jR
useful
ð
25 cm
2
Þ¼
400
anode
(1
:
13)
!
1
1
þ
exp
½
RT
ð
anode
100mV
Þ
j
¼
j
max
1000 mV
(1
:
14)
1 V
We calculate power density as P=jV
cell
and obtain Fig. 1.8 after solving Eqs.
(1.13) and (1.14) simultaneously.
An increase in j from 0 to 9 A/m
2
gradually decreases V
cell
from 550 to about
390 mV (Fig. 1.8). Between current density values of 1 and 9 A/m
2
, V
cell
changes
almost linearly with current, which is consistent with many observations [28].
Above j=9A/m
2
, V
cell
decreases rapidly due to the saturation response of the
biofilm. Under electrical potential saturation, factors other than the electrical
potential (e.g., electron donor and pH) limit the electrical current. Such rapid
change in the voltage is observed in experimental MFCs [36, 42]. A key lesson
from Fig. 1.8 is the trade-off between V
cell
and j, and power density is one way to
evaluate this trade-off. Because of an increase in current density under relatively
stable V
cell
, power density increases rapidly and reaches a maxima of 3.6 W/m
2
around 9 A/m
2
—3.6W/m
2
is near the currently observed maximum power
density for an MFC [43]. The maxima occurs around 16 , which would be the
operating external resistance achieving the best power density for this particular
example.
The Nernst-Monod equation describes how the potential controls the rate of
generation of electrons by ARB respiration, but the electrons from respiration
must be transported to the anode surface from wherever the ARB are located in
the biofilm. Components in the extracellular matrix of the anode biofilm are
600
4.0
3.5
500
3.0
400
2.5
300
2.0
1.5
200
1.0
100
0.5
0
0.0
0
5
10
j
(A/m
2
)
Fig. 1.8 The relationships among the current density j (A/m
2
), the useful voltage that is
actually harvested V
cell
(mV), and power density (W/m
2
) for an MFC example with a single
variable resistor R ()
