Experimental and numerical studies of micro PEM fuel cell

DOI 10.1007/s10409-011-0495-z

RESEARCH PAPER

Experimental and numerical studies of micro PEM fuel cell

Received: 2 September 2009/ Revised: 13 June 2010 / Accepted: 29 October 2010

©The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag Berlin Heidelberg 2011

Abstract A single micro proton exchange membrane fuel cell (PEMFC) has been produced using Micro-electro-mechanical systems (MEMS) technology with the active area of 2.5 cm2 _{and channel depth of about 500μm. A}

theoretical analysis is performed in this study for a novel MEMS-based design of a micro PEMFC. The model consists of the conservation equations of mass, momentum, species and electric current in a fully integrated finite-volume solver using the CFD-ACE+ commercial code. The polarization curves of simulation are well correlated with experimental data. Three-dimensional simulations are carried out to treat prediction and analysis of micro PEMFC temperature, cur-rent density and water distributions in two diffecur-rent fuel flow rates (15 cm3_{/min and 40 cm}3_{/min). Simulation results show}

that temperature distribution within the micro PEMFC is af-fected by water distribution in the membrane and indicate that low and uniform temperature distribution in the mem-brane at low fuel flow rates leads to increased memmem-brane wa-ter distribution and obtains superior micro PEMFC current density distribution under 0.4 V operating voltage. Model predictions are well within those known for experimental mechanism phenomena.

Keywords Micro PEMFC· MEMS · Simulation · Fuel flow rate

Nomenclature

A The x-dir. position in channel (m)

B The y-dir. position in channel (m)

R.-G. Peng (¬)· C.-C. Chung · C.-H. Chen

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, China e-mail: b68411@ms25.hinet.net

cref Reference molar concentration (kmol·m−3)

cR

C Molar concentration of hydrogen in catalyst layer (kmol·m−3₎

cR

L Molar concentration of hydrogen in channel (kmol·m−3₎

Deff Gas effective diffusivity (m2·s−1)

D Diffusivity (m2_·s−1₎

F Faraday constant (C·kmol−1₎

HC Flow channel height (m)

HG GDL thickness (m)

h Mixture enthalpy (J·kg−1₎

Jconv

C The mass flow rate from channels to GDL (kg·s−1₎

Jdiff

G The mass flow rate from GDL to catalyst layer (kg·s−1₎

j Net current density (A·m−2₎

je Exchange current density (A·m−2)

M Molecular weight (kg·kmol−1₎

p Absolute pressure (Pa)

q Heat flux (J·m−2₎

R Universal gas constant (kJ·kmol−1_·K−1₎

S Surface area (m2₎

S h Sherwood number

T Temperature (K)

U Fluid velocity (m·s−1₎

V Volume (m3₎

Y Fluid mass fraction

Greek symbols

α Mass transfer coefficient β Kinetic constant ε Porosity ρ Fluid density (kg·m−3₎ η Overpotential (V) κ Permeability (m2₎ μ Dynamics viscosity (kg·m−1_·s−1₎ σ Electrical conductivity (Ω−1_·m−1₎ τ Shear stress tensor (Pa)

τ Tortuosity

φ Concentration exponent

Superscripts conv Convection diff Diffusion K Reaction kinetics N Nerst R Molar tot Total Subscripts an Anode C Flow channel ca Cathode

con Concentration loss

e Exchange eff Effective value G GDL in Inlet L Catalyst layer 1 Introduction

The micro proton exchange membrane fuel cell (PEMFC) is expected to be a major source of portable electrical power because of its low-temperature operation, quick start-up, lightweight packing, small volume, and low pollution poten-tial. Micro-electro- mechanical systems (MEMS) technol-ogy offers advantages in manufacturing micro-scale materi-als and is used to make miniaturized electronic devices. Con-sequently, micro PEMFCs can be fabricated using MEMS technology for portable electronic power applications. A sil-icon substrate is used as the major material for a flow field plate. This study focuses on both MEMS fabrication and numerical simulation, which employs a silicon-MEMS tech-nology to manufacture flow channels for use in a single mi-cro PEMFC, and developing a three-dimensional model to elucidate its electrochemical properties in the membrane.

Early in 2000, Lee et al. [1] used microfabrication tech-niques, such as deep silicon etching, photo masked electro-plating, physical vapor deposition, anodic bonding, and spin coating, on a silicon wafer to create flow channels. They pro-duced a milliwatt micro fuel cell using new techniques and materials that had a current density of 150 mA/cm2_.

Mean-while, Hsieh et al. [2] developed a new design and fabrica-tion process for a micro fuel cell flow field plate with a cross section of 5 cm2 _{and a thickness of 800μm. The novel}

de-sign had a reported power density of 25 mW/cm2 _{at 0.65 V,}

and the results obtained from tests on this fuel cell indicated a reliable and stable power output at ambient temperatures. Hsieh et al. [3] used the SU-8 photoresist microfabrica-tion process to fabricate micro PEMFC flow channels. Their work contributed to the low-cost mass-production of a small, flat single fuel cell with a power density of 30 mW/cm2 _at

0.35 V.

In 2006, Cha et al. [4] studied the transport phenom-ena on flow channels in the micro fuel cell. The channels

were constructed using a structural photopolymer and had 500μm, 100 μm, and 20 μm wide measures. The effects of the channel size and the gas diffusion layer thickness were then examined. It was found that a high pressure drop in very small channels improved the convection of air into the gas diffusion layer (GDL) and improved fuel cell performance at a low current density. The results signified that using a thin GDL improved the performance of the micro fuel cell. Hsieh et al. [5] investigated the operational parameters of a H2/air micro PEMFC with different flow configurations

us-ing impedance spectroscopy. The work considered a range of operating parameters for the backpressure and cell tempera-ture in order to determine how the flow configuration affects the performance of the micro fuel cells. Optimal operating conditions were adopted to test the micro PEMFC stack [6]. The results demonstrated that the effect of the operational pa-rameters on stack performance is similar to that on a single micro PEMFC.

For fuel cells with small dimensions, the influence on the mass transport or electrical conductivity is significant. Chiang and Chu [7] found that the membrane electrical con-ductivity increased when the aspect ratio channel was low. Shimpalee and Van Zee [8] investigated how serpentine flow fields with different channels/rib cross-sectional areas af-fected performance and species distributions for both au-tomotive and stationary conditions. The simulation results indicated that for a stationary condition, a narrow channel with a wide rib spacing improved performance; however, the opposite occurs when the automotive condition is applied. Matamoros and Bruggemann [9] adopted steady and three-dimensional models to determine the influence of geomet-ric parameters on cell performance under different humidity conditions. According to their results, anode and cathode liquid water saturation may affect species transport and the polymer electrolyte water content. Thus, one must simulta-neously calculate both water absorption and desorption via the polymer electrolyte and liquid water saturation in the an-ode and cathan-ode porous media in order to obtain an actual view of the ohmic and concentration losses in PEMFC per-formance.

Shimpalee et al. [10] examined different channel path lengths to determine the impact of flow path length on the temperature and current density distributions on PEMFC performance. According to their results, local tempera-ture, water content, and current density distributions be-come increasingly uniform under serpentine flow field de-signs with short path lengths or an increased number of channels. Liu et al. [11] developed an isothermal, steady-state, three-dimensional multi-component transport model for a PEMFC. Their results revealed the detailed distribution characteristics of oxygen concentration, local current den-sity, and cathode activation overpotential at different current densities.

Most previous simulation papers dealt with PEMFC flow channel configurations or water and thermal issues.

However, there are few complete computational models that consider the electrochemical properties of micro PEMFCs. In this study, a number of simulations are carried out, with-out considering the two-phase flow effect, to compare with the corresponding experimental results. We concentrate on investigating the effects of two different fuel flow rates, 15 cm3_{/min and 45 cm}3_{/min, on the polarization curve,}

tem-perature, current density, and water distribution in the mem-brane. Better understanding of the distributions of tempera-ture, current density, and water content in the micro PEMFC

can help to further improve its performance. 2 Model development

A micro PEMFC has several components. These include the end plate, the gasket, the GDL, the membrane electrode as-sembly (MEA), the flow field plate, and the current collector. Figure 1a schematically depicts the micro PEMFC. Figure 1b displays a single micro PEMFC that has been fabricated with all of the components.

a b

Fig. 1 a Scheme of micro PEMFC; b Picture of micro PEMFC

2.1 Basic assumptions

The following assumptions are utilized to simplify the sim-ulation conditions for this study. The simsim-ulations performed are based on a steady state laminar flow, which neglects the effects of gravity. The gases are considered to behave like an ideal gas with a uniform distribution in the inlet. The flows in the catalyst layer, gas diffusion layer, and channel flow field are in the gaseous phase, and the effects of vaporization and condensation are not considered. The Butler–Volmer equa-tion is used to describe the electrochemical reacequa-tions within the catalyst layer. The Nerst–Planck equation is used to de-scribe the transport of protons through the membrane. The polarization curve is based on Ohm’s law. The GDL, cata-lyst layer, and membrane are all isotropic porous media. The membrane is impermeable to gases and electrons. The phys-ical transport properties are considered to be constant in each domain.

2.2 Governing equations

The three-dimensional mathematical model consists of the conservation equations of mass, momentum, species, and current in a fully integrated finite-volume solver using the CFD-ACE+ commercial code. The conservation equations used are listed below. Further details can be found in the work of Mazumder and Cole [12].

2.2.1 In the gas channel

Based on the above assumptions, the conservation equations of continuity, momentum, and species in the gas flow chan-nel are follows:

Continuity equation ∂ρ

∂t + ∇ · (ρU) = 0. (1)

Momentum conservation equations: X-axis ∂ρu ∂t + ∇ · (ρUu) = − ∂p ∂x + ∇ · (μ∇u), (2) Y-axis ∂ρv ∂t + ∇ · (ρUv) = − ∂p ∂y + ∇ · (μ∇v), (3) Z-axis ∂ρw ∂t + ∇ · (ρUw) = − ∂p ∂z + ∇ · (μ∇w), (4)

whereρ is the fluid density, p is the pressure, and μ is the dynamic viscosity.

Species conservation equation ∂

∂t(ρYi)+ ∇ · (ρUYi)= ∇ · Ji, (5) where Yiis the mass fraction of the i-th species, and Jiis the diffusive flux.

Ji= ρDi∇Yi+ρYi_M Di∇M − ρYi  j Dj∇Yj −ρYiΔM_M  j DjYj, (6)

where M is the mixture molecular weight, and Diis the effec-tive mass diffusion coefficient of species i. The first term rep-resents the Fickian diffusion due to concentration gradients. The last three terms are correction terms necessary to satisfy the Stefan-Maxwell equations for multicomponent species i within the porous medium, and depend on the porosity, ε, and tortuosity,τ, of the medium

Di= Di,FSετ, (7)

Di,FS is the free stream diffusion coefficient of the i-th

species. It is common practice to use a tortuosity value of 1.5 in Eq. (7), resulting in the so-called Bruggeman model. The same value is adopted in the simulations due to lack of better information.

2.2.2 In the porous media

The continuity equation and momentum conservation equa-tions are as follows

∂ ∂t(ερ) + ∇ · (ερU) = 0, (8) ∂ ∂t(ερU) + ∇ · (ερUU ) = −ε∇p + ∇ · (ετ) + ε2_μU κ , (9)

whereε is the porosity, ρ is the fluid density, U is the fluid velocity vector, p is the pressure, τ is the shear stress ten-sor, μ is the dynamic viscosity, and κ is the permeability (the square of effective volume to the surface area ratio of a porous medium). The last term in Eq. (9) represents Darcy’s drag force imposed by the pore walls on the fluid, which leads to a significant pressure drop across the porous medium.

The species conservation equation is estimated as ∂

∂t(ερYi)+ ∇ · (ερUYi)= ∇ · Ji+ ˙ωi, (10) where Yiis the mass fraction of the i-th species, Jiis the mass diffusion flux of the i-th species, and ˙ωiis the mass produc-tion rate of the i-th species in the gas phase. ˙ωiis due to the heterogeneous electrochemical reactions within the porous media.

The temperature field of each domain is acquired by solving the energy conservation equation, which is written as follows ∇ · (ερUh) = ∇ · q + ετ · ∇U − je S_V  effη + | j · j| σ , (11)

where h is the gas enthalpy, q is the heat flux comprised of contributions due to thermal conduction, je is the

ex-change current density, S is the reaction surface area, V is the medium volume,η is the electrode over-potential, j is the transfer current density, andσ is the electrical conductivity.

Reactant species undergo electrochemical reactions at the electrode catalyst layers. Hydrogen is oxidized at the an-ode, and the corresponding proton is reduced at the cathode.

These two reactions are driven by the potential difference, also called the activation over-potential, between the solid phase and the electrolyte phase. The Butler–Volmer equa-tion, which describes this phenomenon, is expressed as

j= je C_C ref  expβanF RT η  − expβ_{RT η}caF , (12) where C is the reactant molar concentration, Crefis the

ref-erence molar concentration,βanandβcaare the kinetic

con-stants determined from experimentally generated Tafel plots, andη is the over-potential between the solid and electrolyte phases of the electrode.

During the electrochemical reaction, the performance of the PEMFC drops when the reactant species concentra-tions are deficient on the reaction surfaces, especially when operating a PEMFC at a low operating voltage due to large amounts of water that can cause clogging. A concentration loss happens due to water clogging and bending channels. The total concentration loss is expressed as

ηton con= RT_2F  1+1_αlnC R C CR L , (13) where CR

C is the reactant molar concentration in flow

chan-nels, CR

Lis the reactant molar concentration in catalyst layers,

andα is the mass transfer coefficient expressing how varia-tions in electrical potential across reaction interfaces change the reaction rate. The value ofα depends on the reaction and electrode material.

One concentration loss, called the Nerst potential change due to reactant species depletion in catalyst layers, has the following form

ηN con= RT_2Fln CR C CR L . (14)

The second form by which a concentration contributes to concentration loss is via reaction kinetics. It has the fol-lowing form ηK con= RT 2αFln CR C CR L . (15) 2.3 Boundary conditions

The governing equations for the present micro PEMFC model are elliptic and partial differential equations. Hence, boundary conditions are required for all boundaries in the computational domain. The temperature of the outer sur-faces of flow patterns was maintained at 323 K. The condi-tions of the anode inlet included a temperature of 323 K and a pressure of 300 kPa with a 1.2 stoichiometric flow rate of 100 % H2. The conditions of the cathode inlet included a

temperature of 323 K and a pressure of 300 kPa with a 2.0 stoichiometric rate of 100 % O2. Each outer surface of the

flow pattern in the z-direction is assigned for a specific solid-phase overpotential. This value is set to zero on the anode side, and the total over-potential is set on the cathode side. A co-current flow direction is applied in this investigation.

2.4 Solution strategy

Simulations are solved using the commercial computational package CFD-ACE+. The results are regarded to be con-verged, since the normalized residual of each parameter (such as temperature, pressure, and gases velocity) is less than 10−4_{. The physical and chemical properties of the}

mem-brane in this model are those determined by Mazumder and Cole [12]. The membrane permeability is 1.8×10−18_{, the}

porosity is 0.28, and the tortuosity is 5. The diffusivity of gases is calculated using Stefan Maxwell equations with a Bruggeman correction applied to account for the poros-ity and tortuosporos-ity in the porous media GDL, catalyst layers, and membrane. Tables 1 and 2 show the dimensions and properties of the flow field plate, membrane, electrode ma-terial properties, and the initial operating conditions used in the numerical simulation. The component parameters and transport properties used in this study were obtained from Mazumder and Cole [12] and Springer et al. [13].

Table 1 Dimensions, properties and parameters for the numerical

model

Channel length/mm 14

Channel width/mm 0.3

Channel depth/μm 500

Rib width/mm 0.7

Diffusion layer thickness/mm 0.4

Catalyst layer thickness/mm

Anode 0.018

Cathode 0.026

Membrane thickness/mm 0.035

Total reaction area/cm2 _2.5

Effective diffusivity (Bruggeman model) τ = 5

For membrane Bruggeman model for τ = 1.5

diffusion and catalyst layer

Membrane permeability/m2 _1.8×10−18

Diffusion and catalyst layer _{1.76×10−11}

permeability/m2

Membrane porosity 0.28

Diffusion and catalyst porosity 0.4

Air and fuel side pressure/Pa 3.03×105

Transfer coefficient _0.5

(Tafel constants) at anode Reference current density at

9.23×108 anode ((A·m−3_)(m3_(kg·mol·H

2)−1)1/2)

Transfer coefficients (Tafel _1.5

constants) at cathode Reference current density at

1.05×106 cathode ((A·m−3_)(m3_(kg·mol·H

2)−1)1/2)

Diffusion and catalyst layer ₅₃

conductivity/(Ωm)−1

Table 2 Operating conditions for the numerical model

H2at fuel inlet/(cm3·min−1) 15 and 40

Anode gas 100 % H2

O2at fuel inlet/(cm3·min−1) 15 and 40

Cathode gas 100 % O2

Operating pressure/Pa 1.01×105

Operating temperature/K 323

2.5 Experimental

A micro PEMFC is set up to obtain the polarization curves. The end plate is made of acrylic, and its size is 45 mm×45 mm×13 mm. The gasket isolates and prevents gas leakage; it is made of silica gel and has a thickness of 1 mm. The GDL used herein is a standard carbon pa-per (CARBEL CL GDL) with a thickness of 0.4 mm. The MEA (thickness: 0.035 mm, catalyst loading of the anode and cathode: 0.5 mg/cm2 _{Pt) is a commercial product. The}

micro PEMFC reaction area is 2.5 cm2_.

Silicon is used as the material of the substrate in the an-ode and cathan-ode flow field plates. The flow field plates are formed using MEMS technology. Figure 2 depicts the pro-cedure for fabricating the silicon wafer. A 4-inch diameter silicon wafer is used as the substrate in the investigation.

Fig. 2 Silicon wafer etching process

The contaminants on the surface of the silicon wafers at the start of the MEMS process or those that are accumulated in the middle of the process must be removed during process-ing. The purpose is to obtain high-performance and highly reliable semiconductor devices as well as diffusion and de-position tubes. It also serves to prevent equipment contam-ination, especially under a high temperature oxidation. Sil-icon wafers undergo Radio Corporation of America (RCA) cleaning as a standard procedure before they undergo high-temperature processing steps (i.e., oxidation, diffusion, and

chemical vapor deposition (CVD)) in semiconductor manu-facturing.

A spinner is used to dry the wafer after RCA cleaning. Next, 200 nm silicon nitride is deposited by low-pressure chemical vapor deposition (LPCVD); one side of the sili-con wafer is polished, and the silisili-con substrate is then spin-coated with a resistive layer 7μm thick at various rotating speeds.

Next, the silicon substrate is soft baked. Soft baking is a process where almost all of the solvents are removed from the photoresist coating. Ultraviolet light with a g line is used for the exposure process. After exposure has been com-pleted, heat is again applied for approximately 2–3 minutes for post exposure baking. Development is done in the vitrics to form micro flow channels.

The photoresist is hard-baked for about 1minute, and the silicon substrate is later examined development. The cav-ities of the flow structure are patterned by wet etching. Re-active ion etching (RIE) is conducted to etch a silicon nitride layer of 300μm width. RIE is an etching technology that is used in microfabrication. It uses chemically reactive plasma to remove material that is deposited on wafers. Plasma is generated under low pressures in an electromagnetic field. The silicon nitride layer, however, was too thin to enable the fuel to flow from the inlet to the outlet. Hence, the exposed silicon wafer was etched to pattern micro PEMFC channels in an aqueous solution of 45% KOH at 80◦_{C. The etching}

depth of the channel is 500μm. The depth of the flow chan-nels is expected to favor gas uniformity, water management, and reduced flow resistance. The resist is then removed from the silicon substrate. The final step employs phosphoric acid to remove the remaining silicon nitride at 180◦_C.

The shapes of the three serpentine channels, which have channel and rib widths of 0.3 mm and 0.7 mm, respectively, are used for both the anode and cathode flow fields. The channels are etched on the sides of the anode and cathode, and the depth of each channel is 500μm. The holes for the feeding fuel are made by drilling from the rear side. The oversized flow field plates have an area of 2.5 cm2_{, and a}

sil-icon wafer 4 inches in diameter is used to make four such flow field plates. Figure 3 shows the silicon substrate after etching.

Current collectors provide an electrical pad for electri-cal transmission to the external load. Unlike metal, the sil-icon wafer is not considered to be an ideal current collector material because of its high resistance. The silicon wafer is only used as a fuel carrier in this investigation. There-fore, the alternative design includes an MEA and GDL sand-wiched between current collectors, which are made of brass foil. Consequently, the use of silicon substrates as flow field plates can be reduced since electrons do not pass through them. The advantage of this novel design is that no Au elec-troplate is required on top of the silicon wafer.

Fig. 3 Silicon substrate after etching process 3 Results and discussion

The results of our numerical simulations were validated with experimental data, and the governing equations were solved using CFD-ACE+ to obtain the polarization curves. The experimental micro PEMFC using MEMS technology was based on a silicon substrate. A single micro PEMFC is as-sembled to obtain the polarization curve. Two different fuel flow rates were compared in this investigation. The polariza-tion curves of hydrogen and oxygen were supplied at base operating conditions of fuel flow rates of 15 cm3_{/min and}

40 cm3_{/min, respectively, as shown in Figs. 4 and 5.}

Fig. 4 Comparison of simulation with experiment polarization

curves (fuel flow rate at 15 cm3_/min)

The relative difference of the current densities in the numerical data is better than that of the experimental data. Since the effect of water flooding was neglected in the simu-lation of the cathode side in a single phase model, the numer-ical values appear to be over-predicted. This explains why

Fig. 5 Comparison of simulation with experiment polarization

curves (fuel flow rate at 40 cm3_/min)

the numerical data are better than the experimental ones. However, the simulation results help to elucidate the phe-nomena observed in the micro PEMFC.

When the fuel flow rate of H2/O2 was provided at

15 cm3_{/min, the current density was 1 170 mA/cm}2 _{at 0.4 V}

in the simulation. When the fuel flow rate was provided at 40 cm3_{/min, the current density was 693 mA/cm}2 _{at 0.4 V.}

Figure 6 shows two polarization curves for each fuel flow rate. The experiment was performed at ambient pressure and temperature. Pure humidified hydrogen and dry oxygen are fed into the micro PEMFC. As the fuel flow rate increases, the cell performance worsened. Increasing the fuel tempera-ture accelerated the electrochemical reactions and increased the amount of liquid water produced. The decreasing of performance from the experimental results indicate that in-creasing the gas flow rate will easily degrade the humidity of MEA in a cathode and the diffusion of the gas; besides, it will carries away the heat generated by the micro fuel cell more easily. Thus, internal flooding was not obvious. A low fuel flow rate yielded better performance than that obtained with high fuel flow rates.

These experimental results indicate that the fuel flow rate markedly affects cell performance. However, a high fuel flow rate dries out the membrane, which increases electri-cal resistance. A fuel flow rate of 15 cm3_{/min generates the}

worst performance.

Figure 7 shows the polarization curves for the two fuel flow rates. The results indicate that low fuel flow rates have higher limiting current densities, around half, compared with high fuel flow rates. This result demonstrates that the output current density is dictated by fuel flow rates, and a superior performance is achieved when applying a low fuel flow rate relative to the fuel permeability in the membrane. Low fuel

flow rates enable more fuel to permeate into the membrane and increase cell electrochemical reaction. Thus, a low fuel flow rate provides the ideal performance for the fuel cell. In addition, the temperature and water distributions of the membrane also affect micro fuel cell performance.

Fig. 6 Comparison of fuel flow rate polarization curves of

experi-ment data

Fig. 7 Comparison of fuel flow rate polarization curves of

simula-tion data

Figure 8 shows the distributions of the local current density in the membrane at an operation voltage of 0.4 V at fuel flow rates of 15 cm3_{/min and 40 cm}3_{/min. For}

over-all current density distributions, the local current density in-creased from the inlet toward the outlet, leading to a low tem-perature distribution. The local current density distributions

relative to the temperature are shown in Figs. 9. The results show that uniform temperature distributions (Fig. 9a) lead to a higher current density (Fig. 8a) because the higher fuel permeability enables fuel to reach the membrane faster and enhances the electrochemical reaction. Moreover, a more uniform temperature distribution in micro PEMFC provides lower proton conduction resistance and a more active elec-trochemical reaction from midstream to downstream along the flow channels. The phenomenon of a gradually increas-ing local current density distribution appears to be significant from the midstream to downstream. This leads to unifor-mity of the temperature distribution as well as an increase in the cell current density. In this regard, we used a micro PEMFC that had a small dimension of MEA (only 2.5 cm2₎

in this study. Owing to this, the worst performance caused by higher fuel flow rates could result in an increase in hot spots in the membrane that can damage the membrane structure. Consequently, a uniform temperature distribution is impor-tant to membrane proton conductivity and an increase in cell performance. This is verified by the experimental results in Fig. 6.

The uniformity of temperature distribution is important for minimizing the material stresses on MEA so that its life-time could be extended. We tried to discover how the inside temperature of a micro PEMFC is affected by electrochemi-cal reaction. The temperature distributions in the membrane surface of the micro PEMFC at the nominal operating con-dition, 0.4 V, are shown in Fig. 9. Figure 9 displays the dis-tributions of temperature in the membrane at fuel flow rates of 15 cm3_{/min and 40 cm}3_{/min. Figure 9a shows a more}

uni-form temperature distribution in the membrane at a fuel flow rate of 15 cm3_{/min. The temperature slightly decreased with}

an increase in the current density because the higher elec-trochemical reaction rate can produce more water, thus wet-ting the membrane and increasing proton conduction. An enhanced cell performance is observed. The simulations showed in Fig. 9b illustrate a high and non-uniform tem-perature distribution in the membrane at a fuel flow rate of 40 cm3_{/min. The temperature approaches 360 K from the}

in-let region to the midstream of the membrane, and then drops to around 350 K along the flow path. High temperatures may dry the membrane and increase proton conduction resistance. The lowest temperature is distributed in the middle of the flow channels. This could be due to the existence of low temperatures, as a result of water accumulation, at the exit region. We thus find that the uniformity of temperature dis-tribution indeed influences the electrochemical reaction rate. Low fuel flow rates can cause uniform temperature distri-butions, from which we can obtain a better micro PEMFC performance.

Water management also affects the performance of mi-cro PEMFCs. To study the effects of water distribution on a micro PEMFC, Fig. 10 presents the water distribution in the membrane at an operation voltage of 0.4 V at fuel flow rates of 15 cm3_{/min and 40 cm}3_{/min. At a fixed}

over-potential, the water concentration increased from the inlet to the outlet. The results show that a lower fuel flow rate can

Fig. 8 Distributions of current density in the membrane at

oper-ation voltage 0.4 V: a Fuel flow rates at 15 cm3_{/min; b Fuel flow} rates at 40 cm3_/min

Fig. 9 Distributions of temperature in the membrane at operation

voltage 0.4 V: a Fuel flow rates at 15 cm3_{/min; b Fuel flow rates at} 40 cm3_/min

Fig. 10 Distributions of water in the membrane at operation

volt-age 0.4 V: a Fuel flow rates at 15 cm3_{/min; b Fuel flow rates at} 40 cm3_/min

Fig. 11 Distributions of water content in the membrane at

oper-ation voltage 0.4 V: a Fuel flow rates at 15 cm3_{/min; b Fuel flow} rates at 40 cm3_/min

increase the electrochemical reaction and the quantity of wa-ter produced. The results also indicate that the concentration of water is at a maximum at the outlet gas channel region ad-jacent to the membrane because the consumption of oxygen produces water via an electrochemical reaction. The oxygen concentration is the lowest in this region. When the water diffuses backward from the membrane to the gas channel, water accumulates in the outlet gas channel. The higher fuel flow rate results in a more rapid exhaustion of water. Less water accumulates as the flow rate is increased, implying that a higher proton conduction resistance leads to worse cell per-formance.

Water content is given as the ratio of the number of wa-ter molecules to that of charge (SO−

3H+) sites. This ratio

in-dicates how well the membrane is hydrated and is the key to reducing membrane electrical resistance. Furthermore, maintaining a uniform distribution of membrane water con-tent can extend the micro PEMFC lifetime because the uni-form distribution reduces the uni-formation of local hot spots and flooding that stress and damage the MEA. Figure 11 shows the distributions of water content in the membrane at an operation voltage of 0.4 V at fuel flow rates of 15 cm3_/min

and 40 cm3_{/min. The membrane water content in this study}

was lower than 6 since no liquid water was formed. The re-sults show that the current density increased, and the mem-brane water content also increased for these two different fuel flow rates. The results also found that a higher water content occurred when the fuel flow rate was 15 cm3_/min.

This may be due to the gradual increase in current density distributions compared with that found with a fuel flow rate of 40 cm3_{/min. The membrane water content in the fuel flow}

rate of 15 cm3_{/min reached 2–5 from the midstream to the}

downstream of the flow channels. The water content for the cell with a fuel flow rate of 40 cm3_{/min only reached 0–3}

in all flow channels. These results suggest that the water content distribution is based on a fuel reaction utilizing rate. The cell with a fuel flow rate of 15 cm3_{/min has a higher}

membrane water content at 0.4 V operating voltage due to the higher water production rate from the electrochemical reaction. The water content is linearly related to the pro-ton conductivity such that a higher membrane water content leads to high proton conductivities. This decreases the over-potential caused by ohmic loss. Thus, the micro PEMFC performance is improved.

4 Conclusions

Portable consumer electronic products require a small, lightweight power supply with high capacity. The micro PEMFC satisfies these requirements. The current study em-ploys MEMS technology to etch flow fields on a silicon sub-strate. The reaction area of this single micro PEMFC is 2.5 cm2_{. A single micro PEMFC was successfully}

fabri-cated, and its performance was analyzed with a 3-D

math-ematical model. The model simulates temperature, current density, and water distributions at two different fuel flow rates. The simulation results show that a low and uniform temperature distribution in the membrane at low fuel flow rates can increase membrane water distribution and increase micro PEMFC performance.

Acknowledgments The authors would like to thank National

Sci-ence Council for financially supporting this research under Contract No. NSC98-2221-E-009-162. Nano Device Laboratories, Center for High-performance Computing, Center for Nanotechnology Re-search Center in Chiao-Tung University are also commended for fabrication and measurement support.

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