the geometrical design of membraneless micro fuel cells: failure and success

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2010; 34:878–896Published online 1 September 2009 in Wiley InterScience(www.interscience.wiley.com). DOI: 10.1002/er.1615

The geometrical design of membraneless microfuel cells: Failure and success

Dewan Hasan Ahmed, Hong Beom Park, Kyung Heon Lee and Hyung Jin Sung�,y

Department of Mechanical Engineering, KAIST, 373-1 Guseong-dong Yuseong-gu, Daejeon 305-701, Korea

SUMMARY

A comprehensive numerical study of membraneless micro fuel cells with various geometries is carried out with the aimof reducing the mixing of the anode and cathode fluids and increasing their fuel utilization. Designs with blocks orobstacles in the main channel or a main channel with a wavy shape result in very little improvement in these propertiesor even in their deterioration. However, some designs with other types of channel cross-section exhibit much less mixingof the two fluids in the main channel. In particular, an octagonal cross-section is found to result in better performance.However, the difficulty of the micro fabrication of fuel cells with this design encourages us to test two other geometriesfor the cross-section: H-shaped and trident-shaped. The H-shaped cross-section exhibits much less mixing in the mainchannel and much higher fuel utilization. The fuel cell with a trident-shaped cross-section has two inlets for the anodeand cathode fluids and a third inlet for the proton-conducting fluid, and is found to be the best design in that the anodeand cathode fluids are more restricted to their respective electrodes (reaction surfaces). Further, in this design thereactants cover only 40% of the channel width, which is much less than in the other designs, and maximum fuelutilization is obtained. The failure and success cases will guide for future geometrical design of any micro fluidic deviceswhere mixing and non-mixing issues are the major concerns. The present numerical results are validated by comparisonwith literature data. Copyright r 2009 John Wiley & Sons, Ltd.

KEY WORDS: membraneless micro fuel cell; portable application; trident-shape; mixing width; depletion width; fuelutilization

1. INTRODUCTION

The development of membraneless micro fuel cellshas received much attention in recent years, inparticular to their geometries, reactant combination,

and composition, with the aim of increasing theirfuel utilization and cell performance. Membrane-less micro fuel cells are considered to be alterna-tive power sources for portable devices, especiallycell phones, laptops, global positioning systems,

*Correspondence to: Hyung Jin Sung, Department of Mechanical Engineering, KAIST, 373-1 Guseong-dong Yuseong-gu, Daejeon305-701, Korea.yE-mail: [email protected]

Contract/grant sponsor: Creative Research Initiatives of MEST/KOSEF

Received 27 May 2009

Revised 17 July 2009

Accepted 17 July 2009Copyright r 2009 John Wiley & Sons, Ltd.

cameras, and portable appliances for medicaldiagnostic and military applications. At present,the proton exchange membrane fuel cell (PEMFC)and the direct methanol fuel cell (DMFC) areconsidered to be candidates for portable micro fuelcells. However, PEMFCs and DMFCs both relyon a membrane, and so there are several problemsassociated with their operation, including watermanagement and carbon monoxide production,which could potentially lead to carbon monoxidepoisoning. Moreover, the attempt to miniaturizesuch fuel cells for use in portable devices gives riseto other problems, such as those associated with thewater removal process and reactant crossover [1].In addition, the geometrical aspects of such fuelcells, such as the channel shoulder width, are alsoa major concern in regard to the concentrationoverpotential [2,3]. In general, the membrane is theheart of existing fuel cells, and accounts foraround 15% of the total cost of the cell. Themembrane electrode assembly (MEA) comprisesthe electrodes and membrane, and accounts foraround 50% of the total cost [4]. Thus, thedevelopment of a membraneless micro fuel cellwould be of great benefit to portable devicetechnologies because such a cell would eliminateor reduce the above problems.

In contrast to PEMFCs and DMFCs, the op-eration of membraneless micro fuel cells is verysimple: the liquid fuel and oxidant are used asenergy sources and the liquid reactants (fuel andoxidant) flow side by side (in laminar fashion) in asingle channel without a membrane or any se-paration of the materials. In the opposing twosidewalls of the single channel two electrodes arepositioned, which is where the electrochemical re-actions take place to produce electricity. Mem-braneless micro fuel cells can greatly simplifymanufacturing of fuel cells and reduce overallcosts [5]. The advantages of this system are theremoval of nafion based or other membranes fromthe fuel cell, as well as the associated issues in-cluding fuel crossover, cathode flooding, andelectrolyte dry-out [6]. The technical aspects, effi-ciency, and performance of the membraneless mi-cro fuel cell have undergone gradual developmentwith the aim of penetrating the global market asan alternative power source for portable electronic

devices. However, membraneless micro fuel cellsexhibit very low power density and low fuelutilization. In order to improve their performanceand power density, researchers have tested manyapproaches, in particular varying the oxidantand fuel compositions. For example, H2 dissolvedin H2SO4 and H2 dissolved in KOH have beentested as fuels in combination with O2 dis-solved in H2SO4 as the oxidant [7]; alternatively,HCOOH in H2SO4 has been tested as the fuelwith O2 dissolved in KMnO4 and H2SO4 as theoxidant [8]. Other studies have considered the useof vanadium redox [9], H2O2 [10], and CH3OH [11]as fuels with the aim of obtaining a higher powerdensity. However, oxygen dissolved in various sol-vents is the most common oxidant in membrane-less micro fuel cells. The use of dissolvedoxygen, which has a low diffusivity in aqueoussolutions, means that the mass transfer of oxidantto the cathode is a factor limiting cell perfor-mance. In practice, the low diffusivity of oxygen inaqueous solutions causes severe problems asso-ciated with the depletion of the reactants, espe-cially the oxidant, in the downstream region of thechannel. Jayashree et al. [1] suggested an air-breathing laminar flow-based microfluidic fuel cell,in which air is used directly as the oxidant. How-ever, all membraneless micro fuel cells developedto date have maximum power densities of only afew mWcm�2.

The performance of membraneless micro fuelcells is greatly affected by the geometrical shape ofthe channel because the mixing and depletion ofthe anode and cathode fluids (the fuel and oxidant,respectively) are major problems. The mixingwidth of the two streams depends mainly on theupstream flow conditions and the geometricalstructure of the channel. The operation of a microfuel cell begins to fail when the anode and cathodefluid streams become mixed to the point that oxi-dation and reduction are no longer restricted tothe appropriate electrodes [12]. The mixing widthcan be reduced by increasing the Peclet number Pe(Pe5UH/D), where U is the average velocity, H isthe height of the channel, and D is the diffusivityof the species [13]. Increasing U means increasingthe flow rate, which in turn increases the con-sumption of fuel and oxidant. One possible

THE GEOMETRICAL DESIGN OF MEMBRANELESS MICRO FUEL CELLS 879

Copyright r 2009 John Wiley & Sons, Ltd. Int. J. Energy Res. 2010; 34:878–896

DOI: 10.1002/er

method for reducing the mixing width is to opti-mize the geometry. In addition, the mixing widthalso depends on the height of the channel(Dz ¼ ðDHx=UÞ1=3), where x is the distance thatthe fluid has flowed downstream. The depletion ofreactants (fuel and oxidant) near the electrodes canbe quantified as the depletion width, and is an-other key problem downstream in the channel thatleads to a reduction in cell performance. The de-pletion width is also affected by the mixing of thetwo streams in the main channel. Moreover, thedepletion of reactants also depends on the fluidcompositions in the anode and cathode channels;this is especially true for systems with oxygendissolved in aqueous solution, as oxygen is muchless soluble in aqueous media than in air. Thegeometrical shape and structure of membranelessmicro fuel cells must therefore be designed to re-duce the mixing and depletion widths of the twostreams and to allow the two streams to flow inthin bands adjacent to their respective electrodeswith a steeper concentration gradient, becausethese properties increase the fuel utilization ofthe cell.

The objective of the present study is to obtain abetter geometry for membraneless micro fuel cellsthat result in higher fuel utilization. However, wehave found that many geometries worsen both themixing of the anode and cathode fluids in the mainchannel and the fuel utilization. Thus, we are ableto determine those geometrical features that arenot favorable for the performance of membrane-less micro fuel cells and in particular for theirmixing width and fuel utilization. Numericalsimulations of membraneless micro fuel cells withvarious geometries are performed with a three-dimensional model. First, we have carried outnumerical simulations of the fluid flow for thesegeometries and obtained results for the flowbehavior and distribution of the reactants in themain channel. Then we have carried out furthernumerical simulations of both the fluid flowand the chemical reactions of the reactants atthe reaction surfaces (electrodes). Based on theresults of these simulations, we propose two geo-metries for membraneless micro fuel cells. Thesimulation results are validated by comparisonwith literature data.

2. NUMERICAL SIMULATION

In membraneless micro fuel cells, the fuel andoxidant flow side by side in a channel, with mixingof the reactants occurring only by diffusion. Wedeveloped a three-dimensional model based on thefollowing assumptions: laminar flow, steady state,and isothermal flow. The chemical reactions of thereactants occur only at the reaction surfaces. Thefollowing governing equations, which includeconservation of mass, momentum transport, andspecies transport equations, are solved:

H � ðr~uÞ ¼ 0 ð1Þ

H � ðr~u~uÞ ¼ �HPþ H � ðmH~uÞ ð2Þ

H � ðrYi~uÞ ¼ H � ðJiÞ þ Pi ð3Þ

where Yi is the species mass fraction of species iand Pi is the net rate of production of species i bychemical reaction. The definition of Pi is

Pi ¼Mi

XNR

k¼1

P̂i;k

whereMi is the molecular weight of species i, P̂i;k isthe molar rate of creation or destruction of speciesi in reaction k which is controlled by Arrheniuskinetic expression.

The species mass flux is given by

Ji ¼ �rDiHYi ð4Þ

where D is the diffusion coefficient.In this study, formic acid and oxygen dissolved

in sulfuric acid solution are chosen as the fuel andoxidant, respectively. Reactions occur at both re-action surfaces (anode and cathode). The oxida-tion of formic acid on its reaction surface (theanode) is

2HCOOH! 2CO2 þ 4Hþ þ 4e�

The reduction of oxygen on the cathode reactionsurface is

O2 þ 4Hþ þ 4e� ! 2H2O

Only the forward reactions are considered in thesesimulations, and the rate coefficients are assumed

D. H. AHMED ET AL.880


DOI: 10.1002/er

to have an Arrhenius form

k ¼ Ae�Ea=RT ð5Þ

where A is the pre-exponential constant, Ea is theactivation energy, and R is the gas constant. Thepre-exponential constant and activation energy forthe formic acid oxidation and oxygen reductionreactions depend on temperature and also on theoperating potential [14–19]. For formic acid oxi-dation, the pre-exponential constant and activa-tion energy are assumed to be 15 000 s�1 and48.57 kJmol�1, respectively [14]. For oxygenreduction, the pre-exponential constant and acti-vation energy are assumed to be 9320 s�1 and11.03 kJmol�1, respectively [18].

The details of the boundary conditions in thismodel are given in Table I. In the present study,0.5M HCOOH in 0.1M H2SO4 is used as the fuel[8], dissolved O2 in 0.1M H2SO4 is used as theoxidant [11]. The fuel, oxidant, and proton-con-ducting fluid are introduced into the main channelvia the three inlets of the trident-shaped geometry.

The above governing equations are solved by usingthe finite volume method with appropriateboundary conditions. The velocity–pressure couplingis tracked by using SIMPLEC algorithm andCFD-ACE1 is used to solve the problem. Inall these case studies, the minimum number of cellsis 400 000, which is sufficient to fulfill the conver-gence criterion.

3. RESULTS AND DISCUSSION

Firstly, the numerical model was validated: wecarried out numerical simulations for a mainchannel with a square cross-section [12]. Figure 1shows the distributions of formic acid and oxygen6mm downstream of the first mixing point.Figure 1(a) shows the mass fractions of formicacid that has not undergone chemical reaction andof formic acid and oxygen that have undergonechemical reaction 6mm downstream of the firstmixing point reported by Bazylak et al. [12].Figure 1(b) shows the corresponding distributionsobtained in the present study. There are somediscrepancies between the distributions of thereactants in the two sets of data, which are dueto the use of different values for the variousphysical parameters. In general, however, theagreement is acceptable. The fuel utilization weobtained for this square cross-section is approxi-mately 4%, which is close to the value of 3%reported by Bazylak et al. [12]. Note that the fuelutilization is defined as the ratio of consumption offuel in the cell to the flow of fuel at the inlet.

The major concerns of the present study are toobtain a better geometrical design with less anodeand cathode fluid mixing in the main channel andbetter fuel utilization. First, we have carried outnumerical simulations for conventional rectan-gular channel cross-sections with various aspectratios (width/height) and Reynolds numbers (withconstant inlet velocity5 0.01m s�1). The resultsare shown in Figure 2: the mixing between theanode and cathode decreases for increases in theaspect ratio and the velocity. However, conven-tional rectangular channel cross-sections do notprovide better fuel utilization and have small re-action surface areas. The fuel utilization for aspect

Table I. Physical parameters and boundary conditions.

Parameter Value

Velocity at fuel inlet 0.01m s�1

Velocity at oxidant inlet 0.01m s�1

Velocity at proton-conducting fluid inlet

0.01m s�1

Diffusivity 5� 10–10m2 s�1

Length of the main channel 10mmWidth of the main channel 0.5mmActivation energy for formicacid oxidation

48.57 kJmol�1

Pre-exponential constant forformic acid oxidation

15 000 s�1

Activation energy for oxygenreduction

11.03 kJmol�1

Pre-exponential constant foroxygen reduction

9320 s�1

Operating temperature 300KDensity of HCOOH 1220 kgm�3

Density of H2SO4 1800 kgm�3

Density of O2 1.429 kgm�3

Density of H2O 1000 kgm�3

Viscosity of HCOOH 0.00157 kgm�1 s�1

Viscosity of H2SO4 0.0267 kgm�1 s�1

Viscosity of O2 2.5� 10�6 kgm�1 s�1

Viscosity of H2O 1.0� 10�3 kgm�1 s�1



DOI: 10.1002/er

ratio (AR)5 10 obtained from the numericalsimulation is 7.41%, which is close to the value of8% reported by Bazylak et al. [12]. Figure 3(a)shows the formic acid distribution across thechannel at different positions along the channel fora channel aspect ratio of 1.25. These results showthat the mixing of the anode and cathode fluidsgradually increases as the flow proceeds down-stream. Hence, the mixing width gradually in-creases along the channel (see Figure 3(b)). Themixing width is calculated along the width for themass fraction of fuel with the range of0.0025–0.9975. In such circumstances, the anodeand cathode fluids are not restricted to their re-spective zones, which results in a sharp decrease incell performance. We have performed a series ofnumerical simulations with various geometries inan attempt to improve fuel utilization and reducethe mixing of the anode and cathode fluids. In thefollowing sections, we discuss several geometriesthat fail to reduce the mixing of the anode andcathode fluids in the main channel. We believe thatthe reduction of mixing is the primary concern forattempts to increase the fuel utilization and

performance of membraneless micro fuel cells. Thenumerical simulations for the various geometriesare carried out with only two fluids that flow sideby side in a laminar fashion. Thus, we have fo-cused mainly on the mixing of the anode andcathode fluids. However, to determine the fuelutilization, we have also carried out numerical si-mulations with detailed chemical reactions on thereaction surfaces.

As shown in Figure 3(b), the mixing widthgradually increases along the channel, so our firstattempt is to reduce the mixing width and to re-strain further mixing of the anode and cathodefluids in the main channel until the exit. We havetested the insertion of blocks into the middle of thechannel at positions upstream of the main channel,even though micro fabrication of some of thesedesigns may be difficult. The upstream gaps be-tween the blocks (lateral) are slightly greater thanthe mixing width, which has been calculated fromthe results in Figure 3(b). We have also testedvarious block shapes such as inclined-flat edge,inclined-sharp edge, parallel single block, and in-clined parallel combination. Figure 4 shows that

Formic acid w/o chemical reaction

Oxygen with chemical reaction

Formic acid with chemical reaction

(a)

(b)

Figure 1. Reactant distributions with and without chemical reaction for a membraneless micro fuel cell with aconventional geometry and a square cross-section: (a) Bazylak et al. [12] and (b) present study.



DOI: 10.1002/er

the mixing widths obtained with these designs arenot convincing to those obtained with AR5 10.These results are attributed to the flow disturbancegenerated by the blocks. The shapes of the blocksare not the main factor in this increased dis-turbance in the main channel. This conclusion hasbeen confirmed by placing multiple obstacles in thechannel, such as parallel blocks and the inclinedparallel combination, for which the formic aciddistribution is worst at a position 2mm upstreamfrom the outlet, as shown in Figure 5. Figure 6shows the formic acid distributions across thechannel at various positions along the channel inthe presence of multiple parallel blocks. The re-sults show that each block results in significant

mixing of the anode and cathode fluids in the mainchannel. Downstream near the exit, there is sig-nificant mixing of the anode and cathode fluids,with significant reactant crossover in the mainchannel.

To obtain more details about the effects ofinserting blocks into the main channel, we havedesigned a main channel with periodic conver-gence and divergence sections and inserted diamond-shaped blocks (see Figure 7). The lateral gapbetween the two diamond blocks is selected byconsidering Figure 3(b). Each periodic convergencesection is placed immediately after the diamondblocks in order to increase the velocity of the fluidsnear the wall region. However, the mixing of the

CH

CO

OH/C

i ,HC

OO

HC

HC

OO

H/C

i ,HC

OO

H

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

AR = 1.25

(a)

Re = 0.048

Re = 0.48

Re = 4.8

W/W0 W/W0

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

AR = 5

(c)

Re = 0.018

Re = 0.18

Re = 1.8

AR = 2.5

(b)

Re = 0.031

Re = 0.31

Re = 3.1

0 0.2 0.4 0.6 0.8 1

AR = 10

(d)

Re = 0.0099

Re = 0.099

Re = 0.99

Figure 2. HCOOH mole fraction distributions for main channels with various aspect ratios.



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L/ L0

Mix

ingw

idth

, µm

0 2 4 6 8 1050

150

250

350

(b)

W/W0

CH

CO

OH/C

i,HC

OO

H

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

L/ L0 = 6.5 L/ L0 = 3.5

L/ L0 = 10L/ L0 = 0

(a)

Figure 3. (a) HCOOH distributions across the channel at different positions along the channel and (b) mixingwidth variation along the channel.

W/W0

CH

CO

OH/C

i,HC

OO

H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Inclined - flat edge (IFE)

Inclined - sharp edge (ISE)

Inclined parallel combination (IPC)

Parallel single block (PSB)

AR 10

Figure 4. HCOOH mole fraction distributions when blocks with various shapes are inserted into the main channel.



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W/W0

CH

CO

OH/C

i,HC

OO

H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Parallel - multi blocks

AR 10

Inclined parallel combination

-multi blocks

Figure 5. HCOOH mole fraction distributions when multiple blocks are inserted into the main channel.

W/W0

CH

CO

OH/C

i,HC

OO

H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

L/L0 = 7.99

L/L0 = 0

L/L0 = 3.99

L/L0 = 1

Figure 6. HCOOH mole fraction distributions at various positions along the channel when multiple parallel blocks areinserted into the main channel.



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anode and cathode fluids worsens and becomessevere for higher numbers of diamond blocks. Thedetails of the results of the simulations with various

block shapes and combinations are shown inFigure 8. It is true that the mixing width narrowsimmediately after each block, but the upstream

Figure 8. HCOOH distributions in the main channel for: (a) inclined flat edge (IFE); (b) inclined sharp edge (ISE);(c) inclined parallel combination (IPC); (d) 5 diamond blocks (5DB); and (e) 10 diamond blocks (10DB).

W/W0

CH

CO

OH/C

i,HC

OO

H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 diamond blocks

5 diamond blocks

AR10

Figure 7. HCOOH mole fraction distributions when various numbers of diamond blocks are inserted into the mainchannel.



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position of the block causes some disturbance (ascan be seen in Figures 8(a–e), which allows mixingand results in reactant crossover.

We have also tested a main channel with a wavy(top view) shape and two inserted hexagonal-shaped blocks to encourage the anode and cathodefluids to move toward their respective walls. Theblocks are placed in the main channel at variousdistances from the first mixing point (gaps of 0.05,0.1, 0.15, and 0.2mm or gap to total channellength ratios of 0.027, 0.055, 0.083, and 0.111, re-spectively). However, the results (see Figure 9) donot indicate any improvement in mixing in thisdesign; indeed, there is not much variation in theformic acid distribution across the channel for thedifferent gap positions. Furthermore, multiplepentagonal shape obstacles (blocks) are insertedinto the wavy-shaped main channel. The resultsworsen as the flow proceeds downstream (seeFigure 10). Thus, inserting blocks or obstacles intothe main channel does not result in any improve-ment in the mixing of the anode and cathodefluids. The blocks and obstacles increase the dis-turbance of the fluid flow in the main channel,

which causes significant mixing of the anode andcathode fluids. We conclude that it is of no valueto insert blocks or obstacles in membraneless mi-cro fuel cells even for main channels with a peri-odical convergence–divergence or wavy shape.

After the failure to improve performance byinserting blocks or obstacles into the main chan-nel, we have tested various channel cross-sections.Numerical simulations are carried out for mainchannels with butterfly shapes and compared withthe results for the case with a rectangular channelcross-section with AR5 10. The results show (seeFigure 11) a much better formic acid distributionacross the channel than was found with AR5 10;Butterfly Shape 2 (BS 2) and Butterfly Shape 3 (BS 3)exhibit better anode fluid distributions than thatof AR5 10. Furthermore, numerical simulationsare carried out with hexagonal shapes (similar tothe butterfly shape) and obtained much better for-mic acid distributions across the channel than ob-tained with AR5 10. The results (see Figure 12)show that the mixing of the anode and cathodefluids in the main channel can be controlled to asignificant extent by varying the hexagonal shape.

W/W0

CH

CO

OH/C

i,H

CO

OH

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Gap-total length ratio

0.111

Gap-total length ratio0.083



No obstacle

Figure 9. HCOOH mole fraction distributions for various gaps between the channel entrance and the block in a curvedmain channel.



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However, Hexagonal 3 results in the best formicacid distribution across the channel, as can beseen in Figure 12. Figure 13 shows the formic acid

distribution results of the numerical simulations forthe butterfly and hexagonal shapes. It is clear thatthe hexagonal shape reduces the mixing width.

W/W0

CHCOOH/C

i,HCOOH

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Before1st

obstacle

After1st

obstacle

After2nd

obstacle

After3rd

obstacle

After4th

obstacle

After5th

obstacle

Figure 10. HCOOH mole fraction distributions after each obstacle in a curved main channel.

W/W0

CHCOOH/C

i,HCOOH

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

BS 1

BS 2

BS 3

AR 10

Figure 11. HCOOH mole fraction distributions for various butterfly shapes.



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These outcomes encouraged us to attempt furtherimprovements in design. Although Hexagonal 3results in the best formic acid distribution acrossthe channel, the micro fabrication of this geometryis not easy. Thus, we have considered a mainchannel with an octagonal cross-section, whichshould be much easier to fabricate. The resultsof the simulations for AR5 10, Hexagonal 3,and the octagonal cross-section are shown inFigure 14. The results for the octagonal cross-sec-tion are much better than those for the Hexagonal 3design and far better than those for AR5 10. Thusthe octagonal cross-section is the best design ofthose tested to this point for membraneless microfuel cells. The interfacial area of reactants andcross-section area occupied by each reactant are themajor criteria to minimize the mixing width of thismicro fluidic device.

Even though the micro fabrication of a mainchannel with an octagonal geometrical cross-sectionshould be much easier than of one with a Hexagonal3 design, we have continued our search for a betterdesign with easy micro fabrication that decreases themixing width and increases fuel utilization. Finally,we chose an H-shaped cross-section. The geometry

of a main channel with an H-shaped cross-section isshown in Figure 15. Figure 15(a) shows a top viewof this design, which consists of two inlets for theanode and cathode fluids and one outlet. A cross-sectional view is shown in Figure 15(b). There is asmall passage that connects the anode and cathodefluid channels. The fuel utilizations of the fuel cellswith AR5 10, octagonal, and H-shaped cross-sec-tions are shown in Figure 16. The H-shaped cross-section provides higher fuel utilization than theother two designs. We also believe that theH-shaped design is easier to fabricate. The formicacid distributions across the channel for these threedesigns are shown in Figure 17. The formic aciddistribution at W/Wo5 1 is almost zero, whichindicates that the chemical reactions occur on thereaction surfaces. However, the H-shaped cross-section does not offer significant improvement overthe formic acid distribution across the channel(halfway up) obtained for the octagonal cross-section. However, the H-shaped design does exhibithigher fuel utilization, which can be attributed to thehigher concentration gradient near the reactionsurface. The details of this design can be found inPark et al. [20].

W/W0

CHCOOH/C

i,HCOOH

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hexagonal 1

Hexagonal 2

Hexagonal 3

AR 10

Figure 12. HCOOH mole fraction distributions for various hexagonal shapes.



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After various trial-and-error attempts to furtherimprove the design, we have tested a design formembraneless micro fuel cells with three inlets andone outlet (the trident shape). A top view of theproposed trident-shaped cross-section is shown inFigure 18(a). Figure 18(b) shows a cross-sectionalview of the main channel, where the reactions occuron the sidewalls (AB and CD). The top two inlets(left and right) are for the cathode and anode fluids,respectively, and the bottom inlet is for the proton-conducting fluid. There are two small passages: oneconnects the anode fluid and the proton-conductingfluid, and the other connects the cathode fluid andthe proton-conducting fluid. A solid block islocated inside the main channel, which prevents thefuel and oxidant from coming into direct contact.The sidewalls (see Figure 18(b)) can be used aselectrodes in membraneless micro fuel cells. In thepresent model, we have only considered the case inwhich the surface reactions occur on these two

sidewalls. However, the reaction surface area canalso be increased by using surfaces such as AE, CF,EP, PQ, FS, ST, BK, DN, etc. (see Figure 18(b)) asreaction surfaces. Figure 19 shows the formic aciddistributions with respect to height and width,which were obtained from numerical simulationscarried out with chemical reactions. Figure 19(a)shows that formic acid is uniformly distributedwith respect to height through the small narrowpassage that connects the anode fluid and proton-conducting fluid channels. Figure 19(b) shows theformic acid distribution along the line y-y (as shownin Figure 18(b)), and indicates that formic acidcovers a maximum of 40% of the width, which ismuch less than the values obtained for all the othergeometrical designs tested in this study.

The performance of membraneless micro fuelcells is influenced significantly by the fluid velocityin the channel and the reaction area. To determinethe effects of fluid velocity on the performance of

Figure 13. HCOOH distributions for various main channel cross-sections: (a) Butterfly Shape 1 (BS 1); (b) ButterflyShape 2 (BS 2); (c) Butterfly Shape 3 (BS 3); (d) Hexagonal 1; (e) Hexagonal 2; and (f) Hexagonal 3.



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W/W0

CH

CO

OH/C

i,HC

OO

H

00 0.2 0.4 0.6 0.8 1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hexagonal 3

Octagonal

AR 10

Figure 14. HCOOH mole fraction distributions for various channel cross-sections.

Figure 15. Schematic diagrams of a membraneless fuel cell with an H-shaped cross-section: (a) top view and (b) cross-sectional view.



DOI: 10.1002/er

this design, we have carried out simulations withvarious inlet velocities for all three inlets (anode,cathode, and proton-conducting fluids). Figure 20

shows the fuel utilizations for various inlet veloci-ties. At lower velocities, the reactants diffuse largerdistances in the channel, are better distributed over

0

2

4

6

8

10

12

14

Fue

l util

izat

ion,

%

AR = 10 Octagonal H-shape

Figure 16. Fuel utilizations for various channel cross-sections.

W/W0

CH

CO

OH/C

i,HC

OO

H

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

H shape

Octagonal shape

AR 10

Figure 17. HCOOH mole fraction distributions for various channel cross-sections.



DOI: 10.1002/er

the reaction surface, and have sufficient time forchemical reaction. At higher inlet velocities, on theother hand, fewer reactant molecules impinge uponthe reaction surface, and hence the fuel utilizationdecreases significantly. A similar trend in fuel utili-zation as a function of inlet velocity was observedby Bazylak et al. [12]. However, this design exhibitsmuch higher fuel utilization than can be achievedwith the conventional rectangular channel cross-section, especially at low inlet velocities. Furtherdetails of this geometrical design can be found inAhmed et al. [21].

4. CONCLUSIONS

In this study we have tested many different designsfor membraneless micro fuel cells with the aims of

reducing the mixing of the anode and cathodefluids in the main channel and increasing the fuelutilization. To assess the mixing in these membra-neless micro fuel cells we have carried outnumerical simulations of fluid flow. However, todetermine the fuel utilization of the membranelessmicro fuel cells we have also carried out numericalsimulations that accounted for the chemicalreactions. The insertion of blocks or obstaclesinto the main channel has found not to reduce themixing width of the anode and cathode fluids.Indeed, the insertion of blocks or obstaclesincreases the turbulence and number of distur-bances in the main channel, and hence increasesthe mixing and reactant crossover. On the otherhand, channel cross-sections, such as butterfly,hexagonal, and octagonal, are found to exhibit lessmixing of the anode and cathode fluids. In fact,

Anodefluid inlet

Protonconducting fluid inlet

Cathodefluid inlet

Outlet

(a)

(b)

B

W0

H0

c

d a

h

b

ca

C AF

D

E

N K

y y

Cathodefluid

Protonconducting fluid

Anodefluid

P QS

RU

T

z

yx

Cathodeelectrode

Anodeelectrode

Figure 18. Membraneless micro fuel cell with a trident-shaped: (a) top view and (b) cross-sectional view.



DOI: 10.1002/er

H/ H0

CHCOOH/C

i,HCOOH

0 0.2 0.4 0.6 0.8 10.0E+00

1.5E-02

3.0E-02

4.5E-02

6.0E-02

(a)

W/W0

CHCOOH/C

i,HCOOH

0 0.2 0.4 0.6 0.8 10.0E+00

1.5E-01

3.0E-01

4.5E-01

(b)

Figure 19. Formic acid distributions: (a) parallel to the reaction surface and (b) normal to the reaction surface.

Inlet velocity, m/s

Fue

lutil

izat

ion,

%

0 0.05 0.1 0.15 0.2 0.25 0.30

10

20

30

40

50

60

Present study

Bazylak et al. [12]

Figure 20. Fuel utilizations for various velocity conditions.



DOI: 10.1002/er

hexagonal and octagonal channel cross-sections inmembraneless micro fuel cells exhibit much betterperformance with regard to mixing than theconventional rectangular channel cross-section(AR5 10). However, in order to improve the easeof micro fabrication, we have also investigatedmembraneless micro fuel cells with an H-shapedchannel cross-section and found a higher fuelutilization than with the conventional rectangular(AR5 10) or octagonal channel cross-sections.Furthermore, the best cross-section for membra-neless micro fuel cells has found to be the tridentshape (top view). In this fuel cell with a trident-shaped cross-section, three inlets are used for theanode, cathode, and proton-conducting fluids.Small narrow passages connect the anode andproton-conducting fluids and also the cathode andproton-conducting fluids. The reactants cover only40% of the channel width, which is much less thanfor other membraneless micro fuel cell designs.Furthermore, a maximum fuel utilization of 51%with an inlet velocity of 0.01m s�1 is obtained,which is much higher than previously reportedvalues for other designs. We believe that the failureand success cases for this study will not only guideto improve further of the geometrical design formembraneless micro fuel cell and also any othermicro fluidic devices designing issues where mixingand non-mixing issues are the major concerns.

NOMENCLATURE

A 5 pre-exponential constant (s�1)C 5 concentration (mol m�3)D 5 diffusion coefficient (m2 s�1)d 5 height of the anode or cathode

fluid channel (mm)Ea 5 activation energy (kJmol�1)H 5 height (mm)Ho 5 total height (mm)h 5 height of the proton-conducting

fluid channel (mm)L 5 length (mm)Lo 5 total length (mm)M 5molecular weight (kg mol�1)n 5 temperature exponent

P 5 net rate of production of speciesby chemical reactions (kg (m3 s)�1)

Pe 5Peclet numberR 5 gas constant (8.314 J (molK)�1)T 5 temperature (K)U 5 velocity (m s�1)W 5width (mm)Wo 5 total width (mm)x 5 distance (mm)Y 5 species mass fraction

Greek symbol

m 5 viscosity (N sm�2)

ACKNOWLEDGEMENTS

This work was supported by the Creative ResearchInitiatives of MEST/KOSEF.

REFERENCES

1. Jayashree RS, Gancs L, Choban ER, Primak A, Natarajan D,Markoski LJ, Kenis PJA. Air-breathing laminar flow-basedmicrofluidic fuel cell. Journal of American Chemical Society2005; 127:16758–16759.

2. Ahmed DH, Sung HJ. Effects of channel geometricalconfiguration and shoulder width on PEMFC performanceat high current density. Journal of Power Sources 2006;162:327–339.

3. Ahmed DH, Sung HJ. Design of deflected membraneelectrode assembly in PEMFCs. International Journal ofHeat and Mass Transfer 2008; 51:5443–5453.

4. Tsuchiya H, Kobayashi O. Mass production cost of PEMfuel cell by learning curve. International Journal ofHydrogen Energy 2004; 29:985–990.

5. La OGS, In HJ, Crumlin E, Barbastathis G, Horn YS.Recent advances in microdevices for electrochemical energyconversion and storage. International Journal of EnergyResearch 2007; 31:548–575.

6. Morse JD. Micro-fuel cell power sources. InternationalJournal of Energy Research 2007; 31:576–602.

7. Cohen JL, Volpe DJ, Westly DA, Pechenik A, Abruna HD.A dual electrolyte H2/O2 planar membraneless microchannelfuel cell system with open circuit potentials in excess of 1.4V.Langmuir 2005; 21:3544–3550.

8. Choban ER, Markoski LJ, Wieckowski A, Kenis PJA.Microfluidic fuel cell based on laminar flow. Journal ofPower Sources 2004; 128:54–60.

9. Ferrigno R, Stroock AD, Clark TD, Mayer M,Whitesides GM. Membraneless vanadium redox fuel cellusing laminar flow. Journal of American Chemical Society2002; 124:12930–12931.

10. Chen F, Chang MH, Hsu CW. Analysis of membranelessmicrofuel cell using decomposition of hydrogen peroxide



DOI: 10.1002/er

in a Y-shaped microchannel. Electrochimica Acta 2007;52:7270–7277.

11. Cohen JL, Westly DA, Pechenik A, Abruna HD. Fabrica-tion and preliminary testing of a planar membranelessmicrochannel fuel cell. Journal of Power Sources 2005;139:96–105.

12. Bazylak A, Sinton D, Djilali N. Improved fuel utilizationin microfluidic fuel cells: a computational study. Journal ofPower Sources 2005; 143:57–66.

13. Chang MH, Chen F, Fang NS. Analysis of membranelessfuel cell using laminar flow in a Y-shaped microchannel.Journal of Power Sources 2006; 159:810–816.

14. Kemp TJ, Waters WA. The mechanisms of oxidation offormaldehyde and formic acid by ions of chromium (VI),vanadium (v) and cobalt (III). Proceedings of the RoyalSociety of London, Series A, Mathematical and PhysicalSciences 1963; 274(1359):480–499.

15. Jiang J, Kucernak A. Nanostructured platinum asan electrocatalyst for the electrooxidation of formicacid. Journal of Electroanalytical Chemistry 2002; 520:64–70.

16. Tripkovic AV, Popovic KDJ, Lovic JD, Markovic NM,Radmilovic V. Formic acid oxidation on Pt/Ru nanoparticles:temperature effects. Materials Science Forum 2005;494:223–228.

17. Younis LB. Modelling of hydrogen oxidation withincatalytic packed bed reactor. Journal of the Energy Institute2006; 79(4):222–227.

18. Anderson AB, Roques J, Mukejee S, Murthi VS,Markovic NM, Stamenkovic V. Activation energies for oxygenreduction on platinum alloys: theory and experiment. Journalof Physical Chemistry B 2005; 109:1198–1203.

19. Mustain WE, Kepler K, Prakash J. CoPdx oxygenreduction electrocatalysts for polymer electrolyte mem-brane and direct methanol fuel cells. Electrochimica Acta2007; 52:2102–2108.

20. Park HB, Ahmed DH, Lee KH, Sung HJ. An H-shapeddesign for membraneless micro fuel cells. ElectrochimicaActa 2009; 54:4416–4425.

21. Ahmed DH, Park HB, Sung HJ. Optimal geometricaldesign for improved fuel utilization in membraneless microfuel cell. Journal of Power Sources 2008; 185:143–152.



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the geometrical design of membraneless micro fuel cells: failure and success

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