Environ. Sci. Technol. 2009 43, 9038–9042
Scaling up microbial fuel cells (MFCs) is inevitable when power outputs have to be obtained that can power electrical devices other than small sensors. This research has used a bipolar plate MFC stack of four cells with a total working volume of 20 L and a total membrane surface area of 2 m2. The cathode limited MFC performance due to oxygen reduction rate and cell reversal. Furthermore, residence time distribution curves showed that bending membranes resulted in flow paths through which the catholyte could flow from inlet to outlet, while leaving the reactants unconverted. The cathode was improved by decreasing the pH, purging pure oxygen, and increasing the flow rate, which resulted in a 13-fold power density increase to 144 W m-3 and a volumetric resistivity of only 1.2 mΩ m3 per cell. Both results are major achievements compared to results currently published for laboratory and scaled-up MFCs. When designing a scaled-up MFC, it is important to ensure optimal contact between electrodes and substrate and to minimize the distances between electrodes.
bution to a sustainable energy supply, however, we should also increase the scale of MFCs orders of magnitude beyond the currently studied lab-scale MFCs. The largest MFCs so far reported are on the 1 to 2 L scale, which have achieved power densities up to 0.03 kW m-3 (5, 6). According to a number of studies, this is a systematic effect; with increasing MFC size, the volumetric power density decreases (7, 8). In their review paper, Clauwaert et al. (9) analyze this effect in terms of a volume-based resistivity, being the product of the actual internal resistance of the reactor and actual volume of the reactor. In this way, a metric is defined that makes it possible to compare reactors of different volumes. They show that with increasing volume, the volume-based resistivity tends to increase. This resistivity can be analyzed in terms of a number of elements that all contribute to the total internal resistance, like anode and cathode overpotential, concentration overpotential, membrane resistance, and solution resistance. These contributions to internal resistance have been extensively studied, and strategies have been developed to lower them. However, little if any attention has been paid to the study of the scale dependency of these elements of internal resistance. This has been hampering a systematic scale up of the MFC. For increased insight, we must obtain more experience with larger scale MFCs. We therefore studied a MFC with a volume of 20 L, which is a factor of 10 larger than the largest MFCs reported so far. The MFC consisted of four single flat plate MFCs, each with a 0.5 m2 projected surface area. These single MFCs were stacked with bipolar plates to further reduce the ohmic resistance of the conducting materials. Parallel connecting of the MFCs is not useful as the large current obtained in this would lead to higher losses in the conducting materials (3). Stacking in series gives rise to another challenge, cell reversal, which is known to occur at higher current densities (10, 11). The objective of this paper is to increase experience with larger MFCs and obtain insight in the processes that influence the internal resistance of larger MFCs by performing more detailed analysis of the performance of the system. Therefore, each single MFC was equipped with an anode and cathode reference electrode. Flow characteristics of the MFCs were also studied using residence time distribution (RTD) measurements.
Introduction
Materials and Methods
Downloaded via DURHAM UNIV on July 9, 2018 at 15:43:36 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
Analysis and Improvement of a Scaled-Up and Stacked Microbial Fuel Cell ARJAN DEKKER,† A N N E M I E K T E R H E I J N E , †,‡ M I C H E L S A A K E S , ‡,§ H U B E R T U S V . M . H A M E L E R S , * ,† A N D C E E S J . N . B U I S M A N †,‡ Sub-Department of Environmental Technology, Wageningen University, Bomenweg 2, P.O. Box 8129, 6700 EV Wageningen, The Netherlands, Wetsus, Centre of Excellence for Sustainable Water Technology, Agora 1, P.O. Box 1113, 8900 CC Leeuwarden, The Netherlands, and MAGNETO special anodes B.V., Calandstraat 109, 3125 BA Schiedam, The Netherlands
Received July 2, 2009. Revised manuscript received August 28, 2009. Accepted September 8, 2009.
Because of the finiteness of fossil fuels and threats of climate change, there is a need to develop sustainable energy technologies that can power the world’s future economies and societies. The microbial fuel cell (MFC) is a new sustainable energy technology, which produces electricity directly from organic materials (1-3). The MFC consists of an anodic and a cathodic compartment. In the anodic compartment, organic matter is oxidized by microorganisms and converted to CO2, electrons, and protons. The electrons are used in the cathode to reduce, for example, oxygen to water. The MFC has been intensively studied in recent years, and as a result, the power density of lab-scale MFCs at the milliliter scale has been increased up to 1 kW m-3 (4). This would make a MFC competitive to anaerobic digestion with respect to power density (2). To make a substantial contri* Corresponding author phone: +31 317 483447; fax: +31 317 428108; e-mail:
[email protected]. † Wageningen University. ‡ Wetsus. § MAGNETO special anodes B.V. 9038
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 43, NO. 23, 2009
Research Setup. The stack consisted of four microbial fuel cells that were bipolar stacked (Figure 1) with 1 mm thick
FIGURE 1. Schematic overview of a bipolar stack with two anodes (A1-A2), two cathodes (C1-C2), and two membranes (m) (OM ) organic matter). Electrons only need to move the short distance through the bipolar plate to move from an anode to a cathode, for example, from A2 to C1. 10.1021/es901939r CCC: $40.75
2009 American Chemical Society
Published on Web 09/23/2009
titanium plates of 33 cm × 150 cm. These plates functioned as anode and cathode electrode and were coated with a mixed metal oxide (MMO) coating using a P -alloy component (12) (Magneto special anodes B.V., Schiedam, The Netherlands). This coating reduced the internal resistance and overpotentials of the anode (12) and cathode (13). Each cell had a projected surface area of 0.5 m2. The thickness of each anode and cathode compartment was 5 mm, which made the net working volume of the total stack 20 L, thus, 5 L for each individual cell. The bipolar plates were covered with two layers of titanium mesh coated with the MMO with a specific surface area of 1 m2 m-2, so the total surface area of an anode or cathode consisting of three layers of 0.5 m2 was 1.5 m2. The flow in the anodes and cathodes was distributed by two titanium rods, which created an s-shaped flow path from the inlet on the bottom of the cell to the outlet on the top of the cell. A RALEX cation exchange membrane (MEGA a.s., Praha, Czech Republic) was used. All anode and cathode potentials were measured versus reference electrodes (Ag/AgCl, 3 M KCl, ProSense QiS, Oosterhout, The Netherlands). The reference electrodes were connected via capillaries to the top of each anode and cathode compartment. The potential of these reference electrode was checked throughout the research versus a SCE (+0.241 V versus NHE). The potentials of anodes and cathodes were converted and expressed versus SCE. Startup and Operation. The four anodes of the stack were fed from the same anode recirculation vessel. This recirculation vessel was inoculated with a mixed culture anolyte from operating MFCs at our lab. A synthetic anode medium was continuously fed to the anode recirculation vessel with feed dosing pumps (Stepdos 08 RC) at a rate of 57 mL h-1. Excess anolyte could flow out through a water lock. The medium consisted of acetate, buffer, nutrients, and vitamins. The acetate concentration required in the medium was calculated from the produced current. To ensure that acetate depletion would not limit current production due to Coulombic efficiency losses, we mulitplied the calculated acetate concentration by a factor 1.5. A potassium phosphate buffer concentration of 20 mM was used for the anolyte. Furthermore, the anode medium always contained 10 mL L-1 of a macronutrient solution and 1 mL L-1 of micrometerutrient and vitamin solutions (6). The anode recirculation vessel was controlled at pH 7 with a 3 M sodium hydroxide solution (Endress & Hauser Liquisys M CPM223/253). The anode and cathode compartments had a flow rate of 20 L h-1, resulting in a total flow rate through the stack of 160 L h-1 during all experiments unless stated otherwise. All four cathodes were fed from the same cathode recirculation vessel. The volume of this recirculation vessel was 25 L, which was large enough to increase the time the catholyte spent in the recirculation vessel and therefore enhance the catholyte dissolved oxygen concentration. The catholyte in this vessel was actively aerated with air or pure oxygen using four porous Teflon cylinders. The catholyte pH was controlled during some experiments with 20 v/v % sulfuric acid (Endress & Hauser Liquisys M CPM223/253). A potassium phosphate buffer concentration of 20 mM was used in all experiments. The temperature of the complete system was controlled at 30 ( 1 °C. During the startup period, the external resistance was gradually lowered from 1000 to 4 Ω to increase the current density. Residence Time Distribution. To analyze the flow characteristics, we executed residence time distribution (RTD) experiments. This is a relatively underexposed subject in MFC research, while in PEMFC research flow characteristics are an important design factor of which optimization leads to significant performance improvements (14, 15). This concept of residence time can be applied to all inert compounds injected to a flow system. The time that such a compound
spends in a system is called the residence time (t). A distribution of residence times is caused by axial dispersion of fractions of the injected compound, which is the effect of flow velocity profiles, radial mixing, and radial molecular diffusion (16). The inert compound used was a 10 mL of 1 M KCl solution. The profile was determined by measuring the conductivity at the outlet with a conductivity meter (WTW cond 340i). According to our calculations, salt diffusion through the membrane did not significantly influence the measurements. The salt diffusion coefficient of the membrane used was mmol NaCl cm-2 h-1 mol-1 L. The maximum salt concentration that has passed the measuring point at the outlet was 0.01 mol L-1, and the membrane surface area was 0.5 m2. As a result, 0.05 mmol NaCl would diffuse through the membrane in 30 min. This is only 0.5% of the injected 10 mmol KCl. By injecting the KCl solution simultaneously at the anode and cathode side of the MFC, the concentration difference between both sides was lower, and the effect of salt diffusion through the CEM was further minimized. From the RTD profiles, the average hydraulic residence time (HRT) was calculated with eq 1. average HRT )
∫
∞
0
tf(t)dt
(1)
where f(t) is the fraction of inert mass that left the system at a certain time between t and t + dt. During all RTD experiments, dt was 1 s. Polarization Experiments. Power density versus current density was determined by polarization experiments. The polarization curve was obtained by manually applying external resistances from the open cell voltage (OCV) down to 1 or 2 Ω. During each polarization experiment, the external resistance was lowered and current density increased until cell reversal. After one of the cells of the stack reversed, the polarization was aborted. For each external resistance step, a stabilization period of 30 min was maintained to get a stable performance: the stack voltage did not decrease anymore at the applied external resistance. The current was calculated with Ohm’s law and the power with the calculated current and measured voltage. Acetate Measurements. The concentration of acetate was determined by taking a duplicate sample at the end of each stabilization period during a polarization experiment at the inlet and outlet of the MFC stack. The samples were centrifuged, diluted 20 times with 3 v/v % formic acid, and analyzed with by gas chromatography (HP 5890A) (12).
Results and Discussion Before inoculation, the MFC did not produce significant power. A maximum power density of 0.35 W m-3 was attained. Therefore, the contribution of other than microbiological processes to power production is negligible. An acetate concentration of 20 mM was used, and the anode and cathode had a pH of 7. The sixth day after inoculation, the stack attained a stable maximum cell voltage of 3.1 V with an external resistance of 1000 Ω. To increase the current and power density, we gradually lowered the external resistance. After 26 days, a power density of 6.1 W m-3 at a current density of 0.11 A m-2 and stack voltage of 2.2 V was achieved with an external resistance of 40 Ω, which was stable for 24 h. Cell Reversal Limited Stack Performance. The 34th day after startup a polarization experiment was executed that resulted in a maximum power density of 11 W m-3 at a current density of 0.3 A m-2 and stack voltage of 1.5 V (Figure 2a). The measured average anode acetate inlet concentration was 19 mM. The average cathode oxygen inlet concentration was 5.7 mg L-1 as a result of air purging, and the uncontrolled cathode pH was 9.6. VOL. 43, NO. 23, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
9039
FIGURE 2. (a) Polarization experiment of the stack. Maximum power density was 11 W m-3. (b) Performance of the individual cells. Cell 2 shows cell reversal at a current density of 0.35 A m-2.
FIGURE 3. Anode and cathode potential of cells 2 and 4 during the polarization experiment show that the cathode was the limiting factor and that reversal of cell 2 was caused by the cathode.
TABLE 1. Volumetric Resistivity of the Four Cells Before and After Improvements cell
cathode 3
3
resistivity (mΩ m ) number 1 2 3 4
resistivity (mΩ m )
after improvements
before improvements
after improvements
before improvements
after improvements
8.1 12.3 8.1 8.8
1.6 1.3 1.6 1.4
6.6 10.5 7.5 7.8
1.3 1.1 1.4 1.2
81.8 85.6 91.6 88.3
81.0 85.7 89.3 84.6
Despite the fact that all cathodes were fed the same cathode solution and all anodes were fed the same anode solution, there was a performance difference between the individual MFCs (Figure 2b). Cell 2 had the worst performance and, therefore, had the largest impact on the decrease of stack voltage and power density. At a current density of 0.35 A m-2, the cell reversed so that the common stack current could only be produced by cell 2 at the expense of total stack voltage. The volumetric resistivities of the cells in the stack calculated from the slope of the individual polarization curves in Figure 2b are shown in Table 1. The resistivities calculated from Figure 2a are the “before improvements” values in Table 1, which means that they were the resistivities before the stack was improved. The cathode resistivity always contributed over 80% to the total volumetric resistivity. Cell Reversal Caused by the Cathode. Potentials of individual cathodes were measured versus an Ag/AgCl reference electrode during the polarization experiment. Cells 1, 3, and 4 showed similar behavior, while cell 2 was different. To illustrate the performance difference, the anode and cathode polarization of cells 2 and 4, which were the worst and best performing cells, are shown in Figure 3. 9040
9
contribution (%)
before improvements
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 43, NO. 23, 2009
In all cells, the cathodes were limiting power production. Although all cathodes were fed the same catholyte at the same flow rate, they did not show similar behavior. To investigate why the cathodes were limiting and why they showed different behavior, we studied the impact of higher reactant concentrations and flow characteristics of the cathodes. Residence Time Influenced Cathode Performance. The cathode and thus the oxygen reduction reaction have been limiting the performance during this research as shown in Figure 3 by the steeper slope for the cathodes. Both a higher proton and higher oxygen concentration had a positive effect on current density. We found that decreasing the cathode pH from 7 to 4 almost doubled the current density from 0.45 to 0.8 A m-2 at the maximum power density with an oxygen concentration of 5.8 mg L-1. Furthermore, increasing the oxygen concentration from 5.8 to 34.7 mg L-1 by pure oxygen purging resulted in an increased current density from 0.8 to 2.8 A m-2 at the maximum power density with a catholyte inlet pH of 4. The reactant concentrations were thus rate limiting. Because the oxygen concentration, pH, and buffer concen-
FIGURE 4. RTD curves of cathodes 2 and 4 that had an average HRT of 511 and 288 s, respectively. tration of the catholyte was identical for all cathodes, it does not explain the performance difference between the individual cathodes. Also, unequal flow rate cannot explain the difference because all cathodes had the same flow rate of 20 L h-1. To study the reason for the unequal performance, we anaylyzed the residence time distribution (RTD) curves. The RTD curves (Figure 4) show the fractions of the injected mass that had a certain residence time between 0 and 1500 s. The RTD curves of cathode 2 and cathode 4 are presented because they were the worst and best performing cells. In general, the residence time of cathode 4 was much shorter than that of cathode 2. The RTD curve of cathode 4 consists of two peaks that seem to be the result of two preferential flow paths through which the majority of the catholyte flowed from the inlet to outlet. The first peak of cathode 2 seems to be the result of a preferential flow path through which a minor part of the catholyte can flow more rapidly to the outlet. The major part of the catholyte from cathode 2 had a much longer residence time. From the RTD curves, the average HRT was calculated with eq 1. The average HRT of cathode 2 was 511 s and cathode 4 was 288 s. Furthermore, the average HRT of cathode 1 was 410 s and cathode 3 was 400 s. The average HRTs combined with the results of the polarization experiment at day 34 show a relation between the average HRT and cathode performance. Shorter average HRTs resulted in better cathode performance, although there was no correlation between the average cathode HRT and cathode internal resistance. Furthermore, the data in Table 1 shows that the cathode is limiting MFC performance due to a contribution of over 80% to the total volumetric resistivity. Thus, to obtain higher power densities from the MFC stack, we need to improve the performance of the cathodes. Despite the fact that cathode and anode compartments were identically designed and constructed and the flow rate was equal during all RTD experiments, large differences between the average HRTs were found. This inevitably led
to the conclusion that the volumes were not equal in practice. Because the membrane was the only flexible part of the MFC stack, the conclusion was drawn that the membrane could bend toward an anodic or cathodic side. A membrane bended toward the cathodic side resulted in a smaller cathode and larger anode volume. At equal flow rates this causes a shorter average HRT for the cathode than for the anode. The MFC design allowed the membranes to move 3 mm. This could result in a volume change of 1.5 L and a difference between the residence times of 270 s at a flow rate of 20 L h-1. The difference between cathode 4 and cathode 2 was 223 s, so this membrane movement can explain these differences well. With equal flow rates and identical inlet reactant concentrations, one would expect that the cathode with the highest average HRT has the largest conversion of reactants into products and thus the best performance. Our results show the opposite: in a situation where the membrane was bended toward the anodic side and thus the cathodic side had a larger volume, this additional volume resulted in a lower performance. This additional volume gives room for a preferential flow path through which part of the catholyte can flow to the outlet. This path does not force the catholyte through the electrodes, so a large fraction of the reactants leave the MFC unconverted, while the reactants are depleted at the electrode. When the membrane is bended toward the cathodic side, against the cathode electrodes, the catholyte is forced to flow through the electrodes, resulting in a more efficient conversion of the reactants. Therefore, it is crucial that new scaled-up MFCs are designed in such a way that the catholyte and anolyte is forced to flow through the electrodes to maximize the conversion of reactants and thus improve performance. Improving Cathode Performance Resulted in a 13-fold Increase in Power Density. To overcome the challenges posed by the different average HRTs and the limiting oxygen reduction reaction, we improved the cathode performance by four means: (1) by fixing the membrane to avoid membrane movement, (2) by acidifying the catholyte to pH 4 with sulfuric acid, (3) by purging with pure oxygen, which resulted in an oxygen concentration of 34.7 mg L-1, and (4) by increasing the flow rate to 40 L h-1. This resulted in better cathode performance, although the cathode performance was still limiting MFC power output. The volumetric resistivity of the cell and cathode and the contribution of the cathode after improvement are shown in Table 1. This volumetric resistivity decreased on average by a factor of 6 after improvements. The contribution of the cathode to the total resistivity was still over 80% of the total resistance before and after the improvement. The MFC was able to produce 144 W m-3 at a current density of 2.8 A m-2 and stack voltage of 1.5 V (Figure 5a). At open circuit conditions, the stack voltage was 4.06 V. Cell 4 attained an open cell voltage (OCV) of 1.03 V, which was
FIGURE 5. (a) Polarization experiment of the stack where a power density of 144 W m-3 was achieved. (b) Performance of individual cells. VOL. 43, NO. 23, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
9041
the highest of the stack, and cell 3 attained an OCV of 1.00 V, which was the lowest (Figure 5b). The volumetric resistivity of the individual cells after the adjustments and under these conditions of this scaled-up MFC stack was reduced from on average from 9.3 to 1.2 mΩ m3 (Table 1). According to Clauwaert et al. (9), a major challenge is to scale up MFCs while maintaining a low volumetric resistivity. Our study shows that it is possible to have a scaled-up MFC with volumetric resistivity comparable to or lower than reported for 0.5 L scale systems. We have illustrated that high power densities can be attained with scaled-up MFCs (Figure 5a), even though cathode performance was still limiting. Oxygen reduction at a Pt catalyst under acidic conditions was chosen as the cathode reaction in this study because it was the most practical way of operation in the scaled-up MFC. There should be a further search into electron acceptors and catalysts that are sustainable, have a high potential, and are practical for larger systems. The polarization experiment was aborted when cell reversal occurred due to the anode of cell 1 (Figure 5b). This was most likely caused by the fact that the MFC had not operated at a current density higher than 1.3 A m-2 when this polarization experiment was executed. The biomass was thus not accustomed to producing a much higher current density of 2.8 A m-2. Therefore, the anode potential increased rapidly when a current density was reached that was too high to be produced by the biomass of anode 1. The combined OCV for the improved stack was 4.06 V. These OCVs are the highest thus far reported for oxygen reduction cathodes. In previous research (8), lower OCVs were attained in stacks that were fed from the same recirculation vessel. Ionic shortcut currents were stated to be the cause of these lower OCVs, and therefore, stacks should be fluidically isolated. Our findings do not support this conclusion. According to our results, stacks do not have to be fluidically isolated in all cases to avoid voltage losses due to shortcut currents. According to our results, a simple inverse logarithmic relation between MFC size and power density as proposed by a previous paper (7) does not apply. Obviously, when MFCs are scaled up, new challenges will arise that limit power production that have not been encountered in small laboratory setups.
Acknowledgments We thank MAGNETO special anodes B.V. for supplying the MFC stack and Delta Triqua for the equipment. We thank Vinnie de Wilde for his advice and assistance. Wetsus is funded by the Dutch Ministry of Economic Affairs, the city of Leeuwarden, the Province of Fryslaˆn, the European Union
9042
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 43, NO. 23, 2009
European Regional Development Fund and by the EZ/ KOMPAS program of the “Samenwerkingsverband NoordNederland”.
Literature Cited (1) Logan, B. E.; Hamelers, B.; Rozendal, R.; Schro¨der, U.; Keller, J.; Freguia, S.; Aelterman, P.; Verstraete, W.; Rabaey, K. Microbial fuel cells: Methodology and technology. Environ. Sci. Technol. 2006, 40, 5181–5192. (2) Rabaey, K.; Verstraete, W. Microbial fuel cells: Novel biotechnology for energy generation. Trends Biotechnol. 2005, 23, 291– 298. (3) Rozendal, R. A.; Hamelers, H. V. M.; Rabaey, K.; Keller, J.; Buisman, C. J. N. Towards practical implementation of bioelectrochemical wastewater treatment. Trends Biotechnol. 2008, 26, 450–459. (4) Fan, Y.; Hu, H.; Liu, H. Enhanced Coulombic efficiency and power density of air-cathode microbial fuel cells with an improved cell configuration. J. Power Sources 2007, 171, 348– 354. (5) Freguia, S.; Rabaey, K.; Yuan, Z.; Keller, J. Sequential anodecathode configuration improves cathodic oxygen reduction and effluent quality of microbial fuel cells. Water Res. 2008, 42, 1387– 1396. (6) Ter Heijne, A.; Hamelers, H. V. M.; Buisman, C. J. N. Microbial fuel cell operation with continuous biological ferrous iron oxidation of the catholyte. Environ. Sci. Technol. 2007, 41, 4130– 4134. (7) Dewan, A.; Beyenal, H.; Lewandowski, Z. Scaling up microbial fuel cells. Environ. Sci. Technol. 2008, 42, 7643–7648. (8) Ieropoulos, I.; Greenman, J.; Melhuish, C. Microbial fuel cells based on carbon veil electrodes: Stack configuration and scalability. Int. J. Energy Res. 2008, 32, 1228–1240. (9) Clauwaert, P.; Aelterman, P.; Pham, T. H.; De Schamphelaire, L.; Carballa, M.; Rabaey, K.; Verstraete, W. Minimizing losses in bio-electrochemical systems: The road to applications. Appl. Microbiol. Biotechnol. 2008, 79, 901–913. (10) Aelterman, P.; Rabaey, K.; Pham, H. T.; Boon, N.; Verstraete, W. Continuous electricity generation at high voltages and currents using stacked microbial fuel cells. Environ. Sci. Technol. 2006, 40, 3388–3394. (11) Oh, S. E.; Logan, B. E. Voltage reversal during microbial fuel cell stack operation. J. Power Sources 2007, 167, 11–17. (12) Ter Heijne, A.; Hamelers, H. V. M.; Saakes, M.; Buisman, C. J. N. Performance of non-porous graphite and titanium-based anodes in microbial fuel cells. Electrochim. Acta 2008, 53, 5697–5703. (13) Ioroi, T.; Yasuda, K. Platinum-iridium alloys as oxygen reduction electrocatalysts for polymer electrolyte fuel cells. J. Electrochem. Soc. 2005, 152, A1917–A1924. (14) Karimi, G.; Baschuk, J. J.; Li, X. Performance analysis and optimization of PEM fuel cell stacks using flow network approach. J. Power Sources 2005, 147, 162–177. (15) Park, J.; Li, X. Effect of flow and temperature distribution on the performance of a PEM fuel cell stack. J. Power Sources 2006, 162, 444–459. (16) Nauman, E. B. Residence time theory. Ind. Eng. Chem. Res. 2008, 47, 3752–3766.
ES901939R