Journal of The Electrochemical Society, 151 共11兲 A1856-A1864 共2004兲

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0013-4651/2004/151共11兲/A1856/9/$7.00 © The Electrochemical Society, Inc.

Geometric Scale Effect of Flow Channels on Performance of Fuel Cells Suk-Won Cha,a,*,z Ryan O’Hayre,a,* Sang Joon Lee,b Yuji Saito,a,** and Fritz B. Prinza,** a

Rapid Prototyping Laboratory, Department of Mechanical Engineering and Department of Material Science and Engineering, Stanford University, Stanford, California 94305-3030, USA b Department of Mechanical and Aerospace Engineering, San Jose State University, San Jose, California 95192-0087, USA This paper studies the effect of flow channel scaling on fuel cell performance. In particular, the impact of dimensional scale on the order of 100 micrometers and below has been investigated. A model based on three-dimensional computational flow dynamics has been developed which predicts that very small channels result in significantly higher peak power densities compared to their larger counterparts. For experimental verification, microchannel flow structures fabricated with varying sizes in SU-8 photoepoxy have been tested with polymer electrolyte membrane electrode assemblies. The experimental results confirm the predicted outcome at relatively large scales. At especially small scales 共⬍100 ␮m兲, the model 共which does not consider two-phase flow兲 disagrees with the measured data. Liquid water flooding at the small channel scale is hypothesized as a primary cause for this discrepancy. © 2004 The Electrochemical Society. 关DOI: 10.1149/1.1799471兴 All rights reserved. Manuscript submitted October 14, 2003; revised manuscript received April 6, 2004. Available electronically October 8, 2004.

Fuel cell systems have been drawing increasing attention as a possible solution for improved power sources in stationary and portable power systems.1-5 Crucial for the successful implementation of fuel cells is an understanding of how design and manufacturing process parameters influence performance. Design parameters include electrolyte thickness, diffusion layer structure, and electrode and flow channel geometry. In polymer electrolyte membrane 共PEM兲 fuel cells, characterization of transport phenomena has been a critical issue due to its considerable impact on performance.6-20 Accordingly, flow field geometry has been intensively investigated for improved species transport.13-20 However, these investigations have so far not addressed the issues in small channels, specifically channels whose characteristic dimension is less than 0.5 mm. Generally, convective mass transport improves as flow velocity increases.21 Thus, we expect fuel cell performance to improve as the channel flow velocity increases. Increasing flow velocity is a somewhat Pyrrhic victory, considering that flow beyond the stoichiometric condition is ‘‘wasted.’’ However, reduction of channel dimensions provides an alternative route to increase flow velocity while maintaining constant gas stoichiometric number. Thus, employing smaller flow channels may lead to fuel cell performance improvement at little additional cost. This motivated us to investigate the scaling effect of flow channels, especially microchannels, on the performance of a fuel cell. To study microscale flow phenomena, it is necessary to have a suitable platform for rapid and cost-effective prototyping of fuel cells with microflow channels. Recent miniature fuel cell designs have leveraged micromachining and microfabrication technologies to build flow structures with fine features and exceptional accuracy.22-24 Silicon, which boasts the highest level of existing process development, has been a natural candidate material for microflow structures.23,24 However, issues still remain regarding the expense and long process cycle for silicon prototyping. An interesting parallel field of research has been the development of other microfluidic devices, especially for chemical and biological analysis. These include nonsilicon microchannel devices that favor low cost and rapid prototyping. Among several available technologies, one of the most successful has been the fabrication of structural channels by photosensitive polymers and ultrathick photoresist.25-30 Advances in photosensitive materials have enabled microchannel fabrication with high aspect ratio and fine feature

definition.28-30 We have found that microchannel structures based on such photopolymers can be successfully integrated into PEM fuel cells.31,32 With this technology, we have experimentally investigated the scaling effect of flow channels on fuel cell performance. In addition, computational flow dynamics 共CFD兲 modeling has been employed for comparison with experiment. In the following sections, we present a description of the flow channel scaling investigation and results from the model prediction. This is followed by details on microchannel fabrication and experimental results. Investigation on Size Scaling of Flow Channels The geometry of a fuel cell flow structure involves several dimensional parameters, e.g., flow channel pattern, channel and rib shape, and diffusion layer thickness. Practically, it is impossible to investigate the effects from all combinations of these parameters simultaneously. Usually, the investigation deals with a certain range of dimensions for a single flow channel pattern.13,14,16-18,20 In this paper, we investigated parallel flow patterns with square-shaped channels and ribs. Unlike interdigitated or serpentine flow channels, parallel flow patterns minimize species cross flow between channels.13-20 This allows more facile characterization of convective transport.14-16 Furthermore, because channels and ribs with square cross sections associate only a single dimension, we can define the ‘‘feature size’’ as the size of the channel width, which is the same as the channel depth, rib width, or rib depth. All other dimensions, such as the diffusion layer thickness, can remain constant. The scaling investigation can be conducted by observing the performance of flow channels by varying only this single feature size. The operating condition of the fuel cell associates several parameters as well, such as the gas stoichiometric number, cell temperature, and gas humidity. These parameters must remain constant for a fair comparison of performance at each feature size. Note that under constant gas stoichiometry conditions, small channels accommodate faster gas flow than large channels 共gas velocity ⬃1/feature size兲. In addition, the Reynolds number remains unchanged for all sizes of channels, as the changes of characteristic dimension and flow velocity cancel each other. This is a possible advantage of the proposed scaling observation because the physical behavior of the flow may be unchanged, not considering microflow effects to be discussed later. Numerical Procedures

* Electrochemical Society Student Member. ** Electrochemical Society Active Member. z

E-mail: [email protected]

In past decades, numerous fuel cell modeling studies have successfully integrated electrochemical reaction and transport phenom-

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2. Laminar flow is assumed. 3. Physical properties of electrode, catalyst, and membrane are isotropic and homogeneous. 4. Ionic conductivity of the membrane and catalyst layer is assumed to be constant. 5. Gas permeation and water permeation or drag through the membrane are ignored. 6. An isothermal condition is assumed for the entire computational domain. 7. Effects from gravity are neglected. 8. Water can exist only in the vapor phase. Governing equations.—A single set of governing equations has been employed for all domains 共flow channels, gas diffusion layer, and catalyst layer兲 similar to the approaches of Um et al.11 Continuity:

⳵ 共 ␧␳ 兲 ⫹ ⵜ • 共 ␧␳U兲 ⫽ 0 ⳵t

Momentum conservation:

⳵ 共 ␧␳U兲 ⫹ ⵜ • 共 ␧␳UU兲 ⳵t

⫽ ⫺␧ⵜp ⫹ ⵜ • 共 ␧␶ 兲 ⫹ Species conservation:

关1兴

␧ 2 ␮U ␬

关2兴

⳵ 共 ␧␳Y i兲 ⫹ ⵜ • 共 ␧␳UY i兲 ⳵t

⫽ ⵜ • 共 D ieffⵜY i兲 ⫹ M ia i⬘

jT F

关3兴

Charge conservation: ⵜ • iS ⫽ ⫺ⵜ • iI ⫽ ⵜ • 共 ␴ Seffⵜ␾ S兲 ⫽ ⫺ⵜ • 共 ␴ Ieffⵜ␾ I兲 ⫽ j T Electrochemical reaction:

冋 再 再

j T ⫽ j 0 exp

␣F 共 ␾ ⫺ ␾ I兲 RT S

关4兴



⫺ 共 1 ⫺ ␣ 兲F ⫺ exp 共 ␾ S ⫺ ␾ I兲 RT Figure 1. 共a兲 Cross section, 共b兲 side view, and 共c兲 isometric view of computational domain for fuel cell with straight channel. Geometry has been generated based on actual prototype design used in experimentation, including gas inlet and outlet. Physical dimensions are summarized in Table I.

ena with CFD.10-12,14,15,19,20 Moreover, some of these efforts have demonstrated modeling capability for three-dimensional 共3D兲 fuel cell geometries.14,15,19,20 Figure 1 shows a fuel cell geometry that was generated for this scaling investigation. The geometry incorporates the same dimensions as actual prototypes used in the experiments. Only half of the unit flow channel along the flow direction has been modeled because of the periodic geometry of the parallel channels. This significantly reduces the computational requirements. Flow inlet and outlet have been incorporated normal to the flow channels based on the actual fuel cell prototype configuration. The feature size of the model has been varied between 5-500 ␮m to investigate scaling effects over this range. The physical dimensions of the model geometry are summarized in Table I. Model assumptions.—The electrochemical reactions in the fuel cell are complicated, so the following common simplifying assumptions are made. 共Refer to similar assumptions in previous computational studies.兲10,11,20 1. An ideal gas mixture is assumed in the flow channels and the porous electrode.

冎 册兿 N

i⫽1



Yi i

关5兴

The last term in the species conservation equation represents the generation or consumption of species from electrochemical reaction. The charge conservation equation considers conduction of both electrons and protons in porous media. This is especially important in catalyst layers where the conductivity of both species is relatively high. The expression for the electrochemical reaction is a simplified form of the Butler-Volmer equation. This is a reasonable approximation as the backward current 共second exponential term兲 is negligible compared to the forward current density 共first exponential term兲 except at very low current densities. The effective diffusion coefficient is obtained from the Bruggman correlation to account for the effect of porosity and tortuosity in electrode and catalyst as D ieff ⫽ ␧ ␶ D i

关6兴

Boundary conditions.—The flow velocity and mass concentration of all gases were specified at the gas inlet 共denoted as I in Fig. 1.兲. Flow rates at inlets are described in Table I as the stoichiometric flow ratio at 1 A/cm2. At the gas outlet, a fixed pressure condition was assumed 共O in Fig. 1兲. Nonslip flow and isothermal conditions were applied at the walls 共W in Fig. 1兲. All the boundaries were assigned with no current flux except on the surface of the current collectors. A fixed potential condition was applied on the current collection area to represent the fuel cell loading condition 共C in Fig. 1兲. Symmetry wall conditions were imposed on the boundaries facing other unit flow channels 共S in Fig. 1兲.

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Table I. Physical parameters and properties of fuel cell model. Quantity

Value

Gas channel length, L Feature size, f Gas diffusion layer thickness, t g Catalyst thickness, t c Membrane thickness, t m Flow inlet 共or outlet兲 length, L i( ⫽ L o) Hydrogen diffusivity Oxygen diffusivity Faraday constant, F Ionic conductivity in catalyst layer, ␴ I,c Ionic conductivity in membrane, ␴ I,m Porosity of catalyst layer, ␧ c Porosity of gas diffusion layer, ␧ g Tortuosity of catalyst layer, ␶ c Tortuosity of gas diffusion layer, ␶ g Permeability of catalyst layer, ␬ c Permeability of gas diffusion layer, ␬ g Exchange current density at anode, j 0,a Exchange current density at cathode, j 0,c Transfer coefficient at anode, ␣ ,a Transfer coefficient at cathode, ␣ ,c Electronic conductivity of catalyst layer, ␴ S,c Electronic conductivity of gas diffusion layer, ␴ S,g Relative humidity of inlet gases Hydrogen inlet flow stoichiometric ratio 共at 1 A/cm2兲 Oxygen inlet flow stoichiometric ratio 共at 1 A/cm2兲 Outlet pressure

12 mm 5, 20, 50, 100, 200, and 500 ␮m 0.25 mm 0.05 mm 0.125 mm 1 mm 1.0 ⫻ 10⫺4 m2/s 2.6 ⫻ 10⫺5 m2/s 96,485 C/mol 4 S/m 8 S/m 0.28 0.4 4 3.3 1 ⫻ 10⫺13 m⫺2 1 ⫻ 10⫺13 m⫺2 5.0 ⫻ 108 A/m3 5.0 ⫻ 106 A/m3 0.5 0.75 53 S/m 53 S/m 100% 1.8 1.9 1 atm

Solution procedure.—A finite-volume method has been employed to solve the governing equations with a commercial flow solver 共CFDRC version 2002 from CFD Research Corp兲.33 Table I summarizes the physical properties and parameters used in the model. The convergence of an iterative solution was decided when the relative residual error between the iterations was less than 10⫺4 . After all the equations were solved, the average current density was obtained by integrating the local current density at the rib and gas diffusion layer interface as I⫽

1 A



A

iS • dA

关7兴

Experimental Flow channel fabrication.—Microflow channels were fabricated with photoresist using photolithography techniques. SU-8 series negative photoresist 共Microchem Corp.兲 was chosen for implementation in actual prototypes due to its well-established processing base and extensive usage in microfluidic devices.21-30 Three microflow channel prototypes were prepared with varying feature sizes: 5, 20, and 100 ␮m. The fabrication for each prototype follows a similar process flow. However, the exact type of SU-8 photoresist and exact process parameters are different for each feature size. Detailed processing guidelines have been documented by the photoresist vendor.34 Table II summarizes the actual fabrication parameters used in our process.

Figure 2 shows a brief process diagram. A uniform film of SU-8 photoresist was applied on a flat metal 共copper兲 substrate using a spin-coater 共Laurell WS-400A-6NPP-LITE兲. Next, the substrate plus SU-8 film was soft-baked on a hot plate 共Barnstead Dataplate 732A兲 to evaporate solvents from the photoresist. Two-step baking at low temperature 共65C°兲, then high temperature 共95C°兲, was employed to avoid thermal shock of the photoresist. Afterward, the film was exposed to ultraviolet light through a mask with the desired flow channel pattern using a commercial mask aligner 共Karl Suss MA-6 Contact Aligner兲. The intensity of the UV light was 15 mW/cm2. This exposure was followed by a postbake process on a hot plate for curing. Finally, the structure was rinsed with SU-8 developer 共Microchem Corp.兲 to dissolve uncured photoresist. Because the flow channels must be electrically conductive, the surfaces of the flow channels were covered with a thin gold film by dc sputter-deposition using a 2 in. gold target 共99.99% pure, Kurt J. Lesker兲 under an argon atmosphere of 1.5 Pa with 30 standard cubic centimeters per minute 共sccm兲 flow at 100 W power. The gold film was 2 ␮m thick. Figure 3 illustrates the microchannel details and the final prototype. The flow pattern was 14 mm long and 14 mm wide, including flow inlet and outlet. Thus, it provided a 1.96 cm2 active area. The actual flow channel length was 12 mm, due to the space occupied by the flow inlet and outlet trenches, which were 1 mm long and 14 mm wide. These broad inlet and outlet trenches ensured relatively uniform gas flow to each of the individual parallel channels. Gases were introduced normal to the flow field. In addition to

Table II. Typical process parameters for SU-8 microchannels. Channel feature size Photoresist type Spin speed Softbake time and temperature Exposure dose Postexposure bake time Develop time

5 ␮m SU-8 2005 3000 rpm 1 min at 65C°, then 2 min at 95C° 100 mJ/cm2 1 min at 65C°, then 1 min at 95C° 40 s

20 ␮m SU-8 2010 1000 rpm 1 min at 65C°, then 3 min at 95C° 130 mJ/cm2 1 min at 65C°, then 2 min at 95C° 2 min

100 ␮m SU-8 100 3000 rpm 10 min at 65C°, then 30 min at 95C° 600 mJ/cm2 1 min at 65C°, then 10 min at 95C° 7 min

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Figure 2. Fabrication process flow for SU-8 microchannels. Typical lithography processes were applied for patterning SU-8. In final step, a current collection layer 共preferably gold兲 was deposited by dc sputtering.

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Figure 4. Cell polarization curves for flow channels of various feature sizes obtained from calculation. Cell performance increases as channel size decreases.

the microchannel prototypes, a ‘‘500 ␮m’’ flow channel structure was fabricated from an aluminum block by conventional machining processes. Conductive gold film was deposited on the surface by the same process as used for the microchannel prototypes. Test.—The testing method of microflow channel performance is similar to that used for conventional fuel cells. Commercial membrane electrode assemblies 共MEAs兲 were obtained from BCS Technology 共Byran, TX兲. The MEAs were fabricated from Nafion 115 and carbon cloth electrodes with Pt/C catalyst. The platinum loading was 1 mg/cm2, and the active area was 14 ⫻ 14 mm 共1.96 cm2兲. During the test, the MEA was placed between two flow channel prototypes, sealed with thin silicon rubber gaskets, and mechanically clamped by two metal blocks. The metal blocks contained gas routing paths to provide hydrogen and air to the fuel cell. The metal blocks were compressed by an arbor press under constant load throughout the experiment. Note that the same MEA was used to measure the performance of all prototypes. This eliminated any discrepancies that could have arisen due to MEA variability between tests of each prototype. Humidified hydrogen and air were provided to the fuel cell. The inlet flow rate of hydrogen and air were regulated at 30 and 80 sccm, respectively, under atmospheric pressure. Both gases were fully saturated with water vapor at 50C°. Cell polarization curves were measured by a Solartron 1287 potentiostat. The concentration overvoltage was measured by the current interruption technique using a Gamry PC4/750 potentiostat. The voltage was recorded at a 1000 Hz sampling rate with the anode as reference electrode. In addition, electrochemical impedance spectroscopy 共EIS兲 was employed to measure ohmic resistance using the Gamry potentiostat. Sinusoidal signals of 100 kHz-0.1 Hz were applied with a 10 mV amplitude. Results and Discussion

Figure 3. 共a兲 Scanning electron microscopy 共SEM兲 image of SU-8 microchannels, showing 100 um wide ⫻100 um deep square channels in parallel flow configuration. Ribs have the same width as channels. 共b兲 Photograph of final prototype covered with gold film for current collection.

Model results.—Current-voltage 共I-V兲 curves obtained from the fuel cell model are shown in Fig. 4. Clearly, the performance increases as the channel size decreases. Interestingly, the smaller channels not only extend the limiting current, but also improve the performance in the linear region at the middle of the I-V curve. This indicates that the transport voltage loss may significantly affect the linear region. In Fig. 5, the same I-V data from Fig. 4 is rearranged to show voltage vs. feature size at various current densities. The figure shows that as the channel size decreases, cell voltage increases at all current density levels. In other words, the efficiency of the fuel cell and

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Figure 5. Figure 4 rearranged to plot voltage vs. feature size. At a given constant current density, output voltage increases as channel size decreases.

the fuel utilization level increase accordingly. This model result bolsters our earlier hypothesis that the employment of smaller flow channels increases fuel cell performance. Because the rib size in

Figure 6. Calculated oxygen concentration in fuel cell model at different overpotential 共␩兲 levels. Diagrams show cross section of fuel cell in the middle of the channel 共at L ⫽ 7 mm兲 with cathode side on top.

Figure 7. Peak power density of fuel cells from the model prediction 共〫兲 along with calculated pressure drop in the flow channels 共䉱兲. The model predicts that the peak power density increases with decreasing feature size, and the ‘‘penalty’’ resulting from pressure drop is small compared to the power gain.

microscale channels can be smaller than the gas diffusion layer thickness, the reactant concentration is more uniformly distributed across the whole diffusion layer. This eliminates inefficiencies that would normally be caused by obstructed ‘‘dead zones’’ under the dividing ribs. Similar results have been reported in other flow patterns.13 The dead zone effect is illustrated by the oxygen concentration profiles in the diffusion layer 共Fig. 6兲. At low overpotential (␩ ⫽ 0.2 V兲, the oxygen concentration is uniform in the diffusion layer for channels of all sizes. However, at high overpotential (␩ ⫽ 0.8 V兲, oxygen is deficient under ribs of the ‘‘500 ␮m’’ channels. Interestingly, in Fig. 6, even though the oxygen concentration is uniform near the catalyst layer for both the ‘‘100 ␮m’’ and ‘‘20 ␮m’’ channels, the oxygen concentration is higher near the catalyst layer for the 20 ␮m channels. This observation suggests that in relatively small channels, the performance improvement does not come solely from the reduced dead zone effect. One possible explanation is that higher flow velocity in smaller channels facilitates the convective mass transport of oxygen at the cathode side, which decreases the limiting current. From Fig. 6, the oxygen concentration in the flow channels near the gas diffusion layer surface is significantly higher for smaller channels, e.g., comparing the 500 and 20 ␮m channels. This could confirm the theory that performance improves due to flow velocity improvements in smaller channels. However, it turns out that the contribution from increased flow velocity may be relatively low compared to the contribution from the reduced dead zone effect 共see Appendix兲. A more plausible explanation is that due to the increased flow resistance in small channel prototypes, convective flow penetrates more deeply into the surface of the gas diffusion layer. From the model result, a reasonable flow velocity vector could be observed in the gas diffusion layer right underneath the flow channels. Essentially, this phenomenon reduces the ‘‘effective gas diffusion layer thickness’’ 共even though the real gas diffusion layer thickness remains constant兲, thus significantly improving performance. As the channel size decreases, the associated increase in pressure loss becomes a concern. However, considering that microchannel designs would most likely be adopted in miniature fuel cells, the active areas should be small and the absolute length scales relatively short. Accordingly, the model indicates that the penalty encountered in terms of pressure drop would be less significant than the benefits provided by enhanced flow through the microchannels. Figure 7 shows the peak power density and the pressure drop on the cathode side obtained from the model. The pressure drop has been converted to power density by the following relation

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Figure 9. Comparison of peak power density from the CFD model 共〫兲 and experiment 共䊐兲. Below 100 um, discrepancy between model and experiment can be observed.

Figure 8. 共a兲 Experimental cell polarization curves for the SU-8 microchannels and 共b兲 IR corrected curves of 共a兲. Ohmic loss has been measured from EIS and subtracted from 共a兲. Performance peaks at ‘‘100 ␮m’’ channel and decreases for smaller channels.

W 共 W/cm2 兲 ⫽

⌬p 共 Pa兲 ⫻ A f共m2 ) ⫻ V 共 m/s兲 A a 共cm2 )

关8兴

Here, W, ⌬p, A a , V, and A f represent the pressure drop loss, pressure drop between gas inlet and outlet, flow inlet area, flow velocity at inlet, and active area, respectively. This power is equivalent to the power consumption of a pump that provides air to the fuel cell assuming 100% pump efficiency. If high-pressure air is not readily available to fuel cell systems 共which is a common situation兲, this power must be provided by the fuel cell. When the calculated peak power density and pressure drop of the cell are compared, the loss associated with the pressure drop is significantly smaller than the increase in peak power due to channel size reduction. Experimental results.—In contrast to the model findings, the experimental cell polarization curves reveal surprising results, as shown in Fig. 8a. Figure 8b shows the same polarization curves after the ohmic loss is corrected. It turns out that the change of ohmic loss for each channel is negligible throughout the measured current density regime. This result can possibly support the assumption made that the membrane presents a constant ionic conductivity. The polarization curves reveal that the cell performance peaks for the 100 ␮m experimental channels and gradually decreases with further reductions in feature size. This is clearly shown in Fig. 9, when the trend of peak power density from each feature size is compared between experiment and model. The experimental results do not agree with the model predictions, especially for feature sizes less than 100 ␮m. This discrepancy could be explained by water condensation in the cathode. In the experimental prototypes, the volume of

the flow channel is directly proportional to feature size. This means that the same amount of water occupies more area in smaller channels. Thus, the flooding area in flow channels may increase inversely proportional to feature size. As stated earlier, the model used in this paper does not capture this issue because it assumes only singlephase flow. However, the model results may still be valid for hightemperature fuel cells, e.g., solid oxide fuel cells, that truly associate only single-phase flow. The pressure drops measured from the experiments may be enhanced by the two-phase flow when compared to model estimation, even though, due to the instability of two-phase flow and small fuel cell size, the measured pressure fluctuates greatly in time. Roughly, the measured pressure drop for 100 ␮m channels, 0.2-0.5 psi 共or 1-3 mW/cm2 from Eq. 8兲, is 2-3 times higher than that of the model estimation. Interestingly, 5 and 20 ␮m channels showed similar pressure drops at 1-2 psi 共or 5-10 mW/cm2兲. This result may suggest that significant flow travels through the gas diffusion layer. In addition, these values are even smaller then that of the model estimation, which suggests that permeability of the actual gas diffusion layer is higher than the model value. For further investigation on flooding, the transport voltage loss has been obtained for 5, 20, and 100 ␮m channels using the current interruption method.35 The decoupling of activation loss and the transport voltage loss is a challenging task, so a predetermined time constant 共50 ms兲 was used to measure the partially coupled activation and the transport overvoltage. Because the purpose of this paper was to observe trends but not exact values, this provided enough qualitative information on concentration effects. In addition, use of a single MEA enabled a direct comparison without perfect decoupling because the discrepancy of activation overvoltage between prototypes should be minimized. Figure 10 shows that the transport voltage loss increases rapidly for smaller channels as the current density increases. This is in agreement with the observed trends from IRcorrected cell polarization curves. Note that at low current density 共100 mA/cm2兲, the overvoltage of the 5 ␮m channel is smaller than that of the 20 or 100 ␮m channels. Because the difference in overvoltage is so small 共in the order of 0.01 V兲, it may be difficult to claim the validity of the data despite the fact that the data has been obtained from multiple test sets with negligible error range, as shown in Fig. 10. However, the possible implication is that smaller channels may benefit from the reduced effective gas diffusion layer thickness at low current density when flooding is not a serious issue in the flow channels. As discussed in the model results section, convective gas flow penetrates deeper into the diffusion layer in smaller channels. Due to the water blocking in flow channels, the gas may penetrate even deeper in the experiments, especially for smaller channels. This may explain the higher voltage output at low

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Figure 10. Transport voltage loss of 5 共䊐兲, 20 共䉭兲, and 100 um 共X兲 channels obtained by current interruption method. Transport voltage loss increases as channel size decreases below 100 ␮m.

current density in extremely small 共5 ␮m兲 channels, as shown in Fig. 8b. In our past experiments, the 20 ␮m channel prototype has exhibited better performance than the 100 ␮m channel prototype when dry oxidant was supplied to retard flooding.31 Thus, we may expect similar trends for other nonflooding operating conditions, such as at low current density. This effect may be observed by monitoring peak power density while varying flow rate. Figure 11 shows the experimental results for the effect of airflow rate on peak power density. The peak power density has been measured with various microflow channel prototypes 共feature sizes of 5, 20, 100, and 500 ␮m兲 at varying inlet air flow rates of 20, 40, 80, 120, and 160 sccm. In the figure, performance increases for all feature sizes as the flow rate increases. In addition, as expected from previous observations, increased flow rate may impede flooding, and so the optimum power point shifts toward smaller channel size. Interestingly, due to this decreased flooding effect, the experimental condition becomes more similar to the modeling condition. Therefore, the trends of peak power density follow the trend from the model prediction more closely as the flow rate increases. Thus, further experiments employing high temperature membranes are suggested to possibly confirm

Figure 11. Effect of flow rate on peak power density. Peak power density has been experimentally measured at inlet air flow rates of 20, 40, 80, 120, and 160 sccm 共equivalent to 0.49, 0.97, 1.94, 2.9, and 3.9 A/cm2 stoichiometric inlet air flow rate, respectively兲. Power density peak 共dotted area兲 shifts toward smaller feature sizes as flow rate increases.

the model prediction. Also, employing EIS can help identify the transport resistance by flooding. Such EIS studies are currently under investigation by the authors. Smaller channels may associate lower electric resistance, as the electron path from the catalyst layer to the current collector is shorter for small channels. However, this effect is not prominent due to the reduced performance of small channels in the experiment. It is worthwhile to discuss further the characteristics of microchannel flow, because the physical behavior may be different from flows in large regular fuel cell flow channels. As mentioned earlier in this paper, the Reynolds number for the flow in the microchannel prototypes is independent of the channel size, because the scaling of channel size and flow velocity cancel out. Under the experimental and model conditions, the Reynolds number is estimated to be around 10, ensuring that the flow condition is laminar. However, the Knudsen number of the flow varies for individual channel sizes; it is 0.013, 0.0033, and 0.0007 for 5, 20, and 100 ␮m channels, respectively. When the Knudsen number is less than 0.01, flow is considered to be in the continuum region.36 Thus, the continuum hypothesis is valid for all channels except the 5 ␮m channels. When the Knudsen number is between 0.01 and 0.1, the slip flow category applies, which may increase the flow rate. However, as even the 5 ␮m channels stand at the boundary of continuum flow and slip flow, the slip effect is almost negligible.36 Finally, a dimensional discrepancy may exist between model and experiment. Due to the deformation of the gas diffusion layer, or even the roughness of its surface, the actual experimental geometry of channels may not exactly match that of the model. However, the relative scaling trend observed in the experiment is still valid, accepting that the channel size for maximum peak power can shift based on the actual channel size.

Conclusions We have presented observations on microflow channel scaling effects in fuel cells with gaseous hydrogen/air reactants. A 3D computational model predicted that devices with smaller channels would have improved performance in terms of both power density and efficiency. In addition, the net pressure drop should be relatively small for certain applications, especially miniature fuel cells, which benefit from short absolute length scales. This presents a relative advantage for using microchannels in small fuel cells. Appreciable performance has been measured from microchannel flow fields that were fabricated directly from photopolymer material. Photopatterned structures with high aspect-ratio facilitated rapid prototyping and high-resolution features even for channels as small as 5 ␮m. Experimental results verified that microflow channels do enhance gas transport, in agreement with numerical predictions. However, a discrepancy between model expectations and experimental data was observed for channels smaller than 100 ␮m due to flooding in the cathode that resulted from the constraints in the experimental conditions. Water management represents a significant challenge. Liquid water has disadvantageous scaling implications because of high capillary forces and thus low mobility for removal. In any real fuel cell system, a delicate balance between convective improvement and flooding concerns must translate to an optimal flow geometry. This optimal flow geometry may change, depending on the operating condition target for the fuel cell device 共i.e., depending on the operating humidity, design temperature, and gas flow rate兲. Nevertheless, completely passive ambient fuel cells 共using no humidification兲 may be good candidates for realizing the full benefits of microchannel scaling, because they tend to operate not at peak power, but at higher voltage and lower current density on the polarization curve. Utilization of capillary forces in microchannels as a capillary pump or adaptation of other scaled-down components, such as extremely thin gas diffusion layers, may provide additional routes to improve the cell performance. These topics are left for future research along with the investigation of flooding or two-phase flow phenomena in

Journal of The Electrochemical Society, 151 共11兲 A1856-A1864 共2004兲 microflow channels. These subjects offer a unique opportunity as their effect can be highly amplified. Acknowledgments

Sh ⫽

␳ O2 兩 x⫽X,y⫽C共 x 兲 ⫽ ¯␳ O2 兩 x⫽0,y⫽flow

channel



⫽ ¯␳ O2 兩 x⫽0,y⫽flow

channel



Stanford University assisted in meeting the publication costs of this article.

Appendix Consider a simple half-cell fuel cell geometry consisting of a cathode compartment as shown in Fig. A-1. Here, the catalyst layer is assumed to be infinitely thin but is assumed to consume oxygen and generate water vapor. Oxygen transport is considered for only one direction 共y axis兲 for the convenience of the analytical estimation of scaling.12 In addition, current density is assumed uniform along the x direction. Then, the oxygen mass flux into the catalyst layer 共at y ⫽ C in Fig. A-1兲 is, by Faraday’s law M O2 I

关A-1兴

4F

In the diffusion layer, the oxygen mass flux is calculated by Fick’s law as

eff j O2 兩 x⫽X,y⫽E ⫽ ⫺D O

␳ O2 兩 x⫽X,y⫽C ⫺ ␳ O2 兩 x⫽X,y⫽E

关A-2兴

HE

2

Between flow channel and gas diffusion layer, the convective oxygen flux may be expressed by j O2 兩 x⫽X,y⫽E ⫽ ⫺h m共 ␳ O2 兩 x⫽X,y⫽E ⫺ ¯␳ O2 兩 x⫽X,y⫽flow

M O2 I H E

关A-4兴

eff 4F D O

2

␳ O2 兩 x⫽X,y⫽E ⫽ ¯␳ O2 兩 x⫽X,y⫽flow

channel

M O2 I 1



关A-5兴

4F h m

The average oxygen concentration in the flow channel decreases as oxygen is consumed along the channel. Considering the oxygen mass flux at the inlet and oxygen consumption for the control volume within the dotted boundary, we have

u inH C共 ¯␳ O2 兩 x⫽0,y⫽flow

channel

⫺ ¯␳ O2 兩 x⫽X,y⫽flow

channel 兲





X

M O2 IX

共 j O2 兩 y⫽E兲 dx ⫽

4F

0

关A-6兴

From Eq. A-4, A-5, and A-6, we find

␳ O2 兩 x⫽X,y⫽C ⫽ ¯␳ O2 兩 x⫽0,y⫽flow

channel



M O2 I 4F



关A-8兴

D O2

X u inH C



1 hm



HE eff DO

2



关A-7兴

h m is determined from the Sherwood number by the relation

M O2 I 4F M O2 I



X u inH C





D O2 X

4FD O2 u inH C

HC ShD O2



HE D O2 ␧ ␶

⫹ ␪ CHC ⫹ ␪ DH E



冊 关A-9兴

where ␪ C ⫽ 1/Sh and ␪ D ⫽ 1/␧ ␶ The denominator of the first term in the parentheses on the right-hand side is a constant because the scaling of flow velocity and channel size cancel each other out. Thus, the first term may be treated as a constant for a fixed X position. The second term in the parentheses represents the contribution of convection on the oxygen concentration at the catalyst layer. It suggests that the decrease of channel size, H C , increases the oxygen concentration. Thus, smaller channels improve cell performance by enhanced convection. Decrease of the gas diffusion layer thickness, H E , also improves the cell performance by increasing the diffusion flux, which is represented by the third term in the parentheses. Reducing the rib size is equivalent to decreasing the effective gas diffusion layer thickness. Thus, this simple 1D model agrees with the observations from the 3D model presented earlier. To clearly understand the situation, it is worthwhile to estimate the relative degree of contribution from the convection vs. diffusion fluxes by comparing ␪ C and ␪ D . Using the Sherwood number ⫽ 2.693 for square channels21 and common values for other parameters, ␪ C /␪ D is estimated to be 0.1. However, this ratio could even reach 0.01, for low-porosity conditions during flooding. Thus, the contribution from the change of effective gas diffusion layer thickness may be the most significant effect on cell performance improvement.

关A-3兴

channel 兲

where h m is the convection mass transfer coefficient. Because the oxygen fluxes in Eq. A-1, A-2, and A-3 must be the same 共steady-state condition兲, we obtain these relations ␳ O2 兩 x⫽X,y⫽C ⫽ ␳ O2 兩 x⫽X,y⫽E ⫺

h mH C

Using this relation and Eq. 6, Eq. A-7 becomes

This work was supported by Honda R&D Co., Ltd., Stanford University, and a Stanford graduate fellowship.

j O2 兩 x⫽X,y⫽C ⫽

A1863

List of Symbols a⬘ a A D F hm i I j0 jT M p R t T U Y

stoichiometric coefficient of electrochemical reaction water activity total current collection area, m2 mass diffusivity of species, m2/s Faraday number, 96,485 C/mol convection mass transfer coefficient, m/s charge flux, A/m2 average current density, A/m2 exchange current density, A/m3 current density, A/m3 mixture molecular weight, kg pressure, Pa gas constant, 8.314 J/mol K time, s temperature, K velocity vector, m/s species mass fraction

Greek ␣ ␤ ␧ ␩ ␬ ␭ ␮ ␳ ␴ ␶ ⌽

transfer coefficient concentration exponent porosity overvoltage, V permeability, m⫺2 membrane water contents, H2 O/mol SO⫺ 3 viscosity, kg/m s density, kg/m3 conductivity, S/m tortuosity phase potential, V

Subscripts i I m S

species ionic phase membrane solid phase

Superscripts eff effective value sat saturation value

References

Figure A-1. Schematic of PEM fuel cell cathode for flux balance calculations.

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