Understanding the dynamic behaviour of direct methanol fuel cells: Response to step changes in cell current

Available online at www.sciencedirect.comJournal of

www.elsevier.com/locate/jelechem

Journal of Electroanalytical Chemistry 609 (2007) 105–119

ElectroanalyticalChemistry

Understanding the dynamic behaviour of direct methanol fuelcells: Response to step changes in cell current

U. Krewer a,1, A. Kamat a, K. Sundmacher a,b,*

a Max-Planck-Institut (MPI) fur Dynamik komplexer technischer Systeme, Sandtorstraße 1, 39106 Magdeburg, Germanyb Otto-von-Guericke-Universitat Magdeburg, Lehrstuhl fur Systemverfahrenstechnik, Universitatsplatz 2, 39106 Magdeburg, Germany

Received 1 May 2007; accepted 15 June 2007Available online 29 June 2007

Abstract

This paper presents investigations on the dynamic behaviour of Direct Methanol Fuel Cells (DMFC). Experimental cell voltageresponses to step changes in cell current are analysed. Nonlinear DMFC models indicate that the anode reaction mechanism is the mainphysico-chemical phenomenon which causes anode overpotential overshooting, hence cell voltage overshooting. Since the models arestrongly nonlinear, linearised models underestimate the DMFC’s dynamic behaviour. The presented models correctly predict the influ-ence of operating conditions like current density level and current step size on the cell voltage response. Furthermore, the models indicatea low influence of the methanol distribution inside flow fields: Distribution has an influence on the cell voltage only in cells with very lowlocal methanol concentrations (<0.1 M).� 2007 Elsevier B.V. All rights reserved.

Keywords: DMFC; Analysis; Flow field influence; Reactor network

1. Introduction

Direct methanol fuel cells (DMFC) are seen as a poten-tial supplemental power source for portable electronicequipment which resolve the problem of short operatingtime[1–3]. However, the DMFC’s power density is lowerthan that of other fuel cell types and the DMFC voltageshows a continuous decrease during operation [4,5]; bothproblems are attributed to material problems. Despitethese difficulties, commercialisation of DMFCs is on theway. In order to optimise DMFC operation, an in-depthanalysis of the processes inside the DMFC and of the state

0022-0728/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.jelechem.2007.06.015

* Corresponding author. Address: Max-Planck-Institut (MPI) furDynamik komplexer technischer Systeme, Sandtorstraße 1, 39106 Mag-deburg, Germany. Tel.: +49 391 6110 350; fax: +49 391 6110 353.

E-mail address: [email protected] (K. Sundma-cher).

1 Present address: Samsung SDI CO. LTD, Energy Lab, CorporateR&D Center, 575, Shin-dong, Yeongtong-gu, Suwon-si, Gyeonggi-do443-391, Republic of Korea.

of both anode and cathode is helpful. A significant contri-bution to such understanding can be achieved by combina-tion of experimental studies and model based analysis.Here, steady-state investigations give basic information,while additional dynamic investigations help to separateand investigate the different processes inside the DMFC[6].

A dynamic investigation technique frequently applied toDMFCs is electrochemical impedance spectroscopy (EIS)[7–9]. EIS covers a wide time span as well as most processeswhich occur in the DMFC. However, quantitative interpre-tation and modelling of EIS of complete DMFCs have notbeen achieved yet. Experimental methods which do notrequire additional equipment as needed for EIS are mea-surements where step changes in input parameters like con-centration or current are applied to the DMFC and thecorresponding response of the DMFC voltage is analysed.Sundmacher and co-workers analysed the dynamicresponse of DMFCs when applying a step change of meth-anol concentration at the anode inlet [10–12]. Various stud-ies [5,13–15] investigated the dynamic behaviour of the

mailto:[email protected]

Nomenclature

As geometric electrode area of the DMFC,= 0.01 m2

ACSTRs geometric electrode area of a module, m2

cPt surface concentration of Pt, = 0.011 mol/m2

cRu surface concentration of Ru, = 0.121 mol/m2

cA;ijCH3OH methanol concentration inside the anode com-

partment of module ij, mol/m3

cA;inCH3OH methanol concentration of the inlet feed,

= 1000 mol/m3

cAC;ijCH3OH methanol concentration in the anode catalyst

layer of module ij, mol/m3

CAC anode double layer capacitance, F/m2

CCC cathode double layer capacitance, F/m2

dAC thickness of anode catalyst layer, = 35 · 10�6 m[34]

dAD thickness of anode diffusion layer, = 1.7 ·10�4 m [34]

dM thickness of (fully hydrated) Nafion� 105 mem-brane, = 10�4 m [34]

DCH3OH diffusion coefficient of methanol in water at333 K, = 3.187 · 10�9 m2/s, (calc. acc. [35], p.600)

DMCH3OH diffusion coefficient of methanol in membrane at

333 K, = 4.7 · 10�10 m2/s (own measurements)F Faraday constant, = 96485 C/molFA,in flow rate of flow entering the anode compart-

ment, m3/sFA,ij flow rate of flow leaving anode compartment

CSTR ij, m3/sgCO inhomogeneity/interaction factor for Frumkin/

Temkin adsorption on Pt, = 6.82gOH inhomogeneity/interaction factor for Frumkin/

Temkin adsorption on Ru, = 0.43h, i, j countericell cell current density, A/m2

iijcell cell current density of module ij, A/m2

kAD effective mass transport coefficient in anode dif-fusion layer,=DCH3OHð�ADÞ1:5=dAD, m/s

nM;ijCH3OH flux density of methanol inside the membrane of

module ij, mol/m2/srij

An reaction rate for anode reaction step n in moduleij

rA10 reaction rate constant for anode reaction step 1,= 8.75 · 10�6 m/s

rA20 reaction rate constant for anode reaction step 2,= 5.45 · 10�4 mol/m2/s

rA�20 reaction rate constant for backward reaction ofanode reaction step 2, = 3.11 · 104 mol/m2/s

rA30 reaction rate constant for anode reaction step 3,= 4.6 · 10�2 mol/m2/s

rijC cathodic reaction rate in module ij, mol/m2/s

rC0 cathodic reaction rate constant,= 1.1 · 10�5 mol/m2/s

R universal gas constant, = 8.314 J/mol/Kt time, sT cell temperature, = 333 KUh

0 standard cell voltage, 1.213 V (thermodynamiccalc.)

Ucell cell voltage, V

VA volume of a CSTR in the active area of the an-ode compartment, m3

VCOL, (VDIS) volume of a CSTR in the collector (dis-tributor) area of the anode compartment, m3

VAC volume of anode catalyst layer in a DMFC,= As Æ dAC Æ �AC, m3

VAC,CSTR volume of anode catalyst layer in a module,m3

aA charge transfer coefficient for anode reactionstep 2, = 0.5

aC charge transfer coefficient for cathodic reaction,= 0.5

bCO (bOH) symmetry parameter for Frumkin/Temkinadsorption on Pt (Ru), = 0.5

�AC porosity of anode catalyst layer, = 0.81 [34]�AD porosity of anode diffusion layer, = 0.71 [34]gij

A anode overpotential of module ij, V

gijC cathode overpotential of module ij, V

jM ionic conductivity of membrane, = 0.0873 1/X/m (calc. acc. [36])

hijCO surface coverage of Pt with COads in module ij

hijOH surface coverage of Ru with OHads in module

ij

Superscripts

A anode compartmentA, in entering the anode compartmentAC anode catalyst layerAD anode diffusion layerCC cathode catalyst layerCSTR CSTR in active areaij counter for CSTRs and modules: i = row,

j = columnM membrane

Abbreviations

CSTR continuously operated stirred tank reactorDMFC direct methanol fuel cellOCV open circuit voltagepcd-DMFC DMFC with parallel channel design flow

fieldrd-DMFC DMFC with rhomboidal design flow fieldsd-DMFC DMFC with spot design flow field on anode

106 U. Krewer et al. / Journal of Electroanalytical Chemistry 609 (2007) 105–119

U. Krewer et al. / Journal of Electroanalytical Chemistry 609 (2007) 105–119 107

DMFC using experimentation of step input changes of cellcurrent. They found significant overshooting behaviour inthe cell voltage response. The studies of Argyropouloset al. [5,14] give a general overview of the DMFC’sresponse to step changes in current and to other loadchanging scenarios. They focus on investigating series ofload changes rather than analysing in-depth the principlecauses for cell voltage overshooting. A combination ofexperimental and model-based studies researching thecause for cell voltage overshooting has been presented in[15]. This study indicated both that anode reaction kineticshas a strong influence on the dynamic behaviour and that acorrect prediction of the DMFC’s dynamic behaviourrequires the use of quantitative reaction kinetics. If it is cor-rect that the anode reaction kinetics is the main cause forthe observed dynamic behaviour, overshooting analysisof DMFCs can be used to determine the state of the anodeduring DMFC operation.

Although experimental investigations on methanol oxi-dation are numerous [16–29], most of the previous findingsare qualitative and use only non-technical electrodes. Theirdirect application to the modelling of the entire DMFC isdifficult. Recent studies were able to determine quantitativereaction kinetics of methanol on an anode membraneassembly [26,27]. Since experimental conditions, set-upand the working electrode were close to that of a DMFC,the identified kinetics is suitable for integration intodynamic DMFC models.

To fully understand the dynamic response of the DMFCto step changes in current, analysis of the influence of cur-rent density level and operating conditions is essential.Also, due to the low flow rate applied in portable DMFCsystems, the methanol distribution within the anode flowfield may have an impact on the dynamic behaviour. Inprevious research [30], the residence time behaviour andconcentration distribution of three anode flow field designswere studied both experimentally and by 3D numericalflow simulations (computational fluid dynamics, CFD).In addition, reduced hydrodynamic models composed ofideal reactor networks were investigated. The use of CFDfor complete DMFC modelling including multi-step reac-tion mechanisms, leads to a highly complex set of equa-tions and the set-up and simulation are time consumingand may lead to instable or intractable models. Further-more, such models are typically not applicable to dynamicsimulations and control. The reduced models [30] have amore promising approach for modelling complete DMFCs,especially when focusing on dynamic aspects.

This work focusses on analysis of the DMFC behaviourwithin the first seconds after a step change in current isapplied and on identification of the causes of the observedcell voltage overshooting. It investigates the underlyingphysico-chemical phenomena as well as the effect of operat-ing conditions and anode flow fields. Simulation with phys-ico-chemical models give a deep insight into the interactionof the processes and the cause of overshooting; the here

presented experiments are conducted in parallel to identifymodel parameters and check the validity of the model. Theapplied models are a combination of the reduced hydrody-namic models being proposed in [30] with anode reactionkinetics identified in [26] and the basic dynamic model pre-sented in [15]. They correctly predict the experimentallyobserved influence of operating conditions on the cell volt-age response and highlight the influence of anode flow fielddesign and volume flow rate.

2. Experimental

2.1. Anode flow fields

There are four frequently applied flow field designs forliquid DMFCs, three of which are addressed in thisresearch: the parallel channel design, the rhomboidaldesign, the spot design and finally the meander design.The hydrodynamic behaviour of the first three flow fieldtypes has been experimentally and theoretically analysedin [30]. In order to study the flow field influence on thedynamic behaviour, these flow fields [30] are integrated intosingle cell DMFCs. The flow field geometry is displayed inFig. 1.

The parallel channel design and the rhomboidal designboth feature the same active area geometry: 42 channelsof width 2 mm, separated by 1 mm wide ribs. For produc-ing the spot design, the parallel channel design is modifiedby using interlaced ribs: Every 3 mm a gap of 2 mm inlength is machined into the ribs. As a result, the spot designenables a flow in horizontal and vertical direction, whilethe flow in the active area geometry of the parallel channeldesign and rhomboidal design can only proceed along thechannels. In all three designs, the active area has the outerdimensions of 86 mm · 125 mm, and the flow field’s depthis 2 mm. Parallel channel design and spot design both fea-ture an inlet distributor channel and a collector channel of6 mm width, which are used to supply the active areageometry with fuel. In the rhomboidal design, the distribu-tor and collector areas both have a triangular shape withcuboids of 1 mm width and length. This will guarantee amore homogeneous flow distribution to the single channels.In the previous research [30], the three flow field designswere hydrodynamically characterised and modelled byanalysing residence time distribution and concentrationdistribution within each flow field at different volumetricflow rates. The studies showed a homogeneous distributionprofile for the spot design, an inhomogeneous concentra-tion distribution for the parallel channel design, and aslightly inhomogeneous concentration distribution for therhomboidal design.

2.2. MEA manufacturing and operating conditions

The previously presented anode flow field designs wereintegrated into single cell DMFCs. The cathode flow field

Fig. 1. CAD drawings of the investigated flow field designs: parallelchannel design (a), spot design (b) and rhomboidal design (c).


geometry of the DMFCs with parallel channel or spotdesign anode compartment was identical to the parallelchannel design geometry. DMFCs with the rhomboidalanode flow field geometry used the same geometry alsofor the cathode compartment. In all cases, the media flowon anode and cathode side was countercurrent. As diffusionlayer PTFE-coated TORAY carbon paper (TGP-H-060)was used. The PTFE loading was between 20 and 25 mass%

with respect to the uncoated material. The diffusion layerscovered the complete anode and cathode flow field. Themembrane electrode assemblies (MEA) featured an activearea of 100 cm2. They were prepared from NAFION� N-105 membrane foil, onto which the catalyst layers wereapplied using an airbrush technique developed by ZSWUlm (Germany) [31]. The anode catalyst layer featured acatalyst loading of 5 mg/cm2 (unsupported) platinum ruthe-nium black (Alfa Aesar Johnson Matthey HiSPEC� 6000)and a NAFION� content of 15 mass% relative to the metalloading (i.e. 0.75 mg/cm2). The cathode catalyst layer hadthe same metal loading, but as catalyst unsupported plati-num black was used (Alfa Aesar Johnson Matthey HiS-PEC� 1000). NAFION� content was 10 mass% relativeto the metal loading (i.e. 0.5 mg/cm2). The DMFC wascompleted by gold-plated copper current collectors andstainless steel plates for bracing the whole sandwich struc-ture. A torque of 5 N m was exerted on the screws, whichhold together the steel back plates. After assembly, eachDMFC was activated and evaluated by operating the cell3 · 8 h using humidified hydrogen and air.

The measurements were conducted using the DMFCminiplant presented in [15]. The following operating condi-tions were adjusted:

� Anode
feed temperature: 333 K (equals whole DMFCtemperature),methanol feed concentration: 1 mol/dm3,pressure: 1.7 · 105 Pa.
� Cathode
feed temperature: 293 K,feed composition: dry air (dew point approx. 271 K),flow rate: 0.5 N m3/h,pressure: 1.7 · 105 Pa.
All steady-state measurements were conducted in galva-nostatic mode, and the mean cell voltage recorded between570 s and 600 s after applying a cell current density wasused as steady-state value for the polarisation curves. Anexact analysis of the strong impact of the time after whichsteady state is postulated on the polarisation curve is givenin [32]. All presented cell voltage responses were calculatedusing the mean values of at least two measurements toensure reproducibility. After each step change in current,OCV was maintained for 1 h.

3. Model

The motivation for the composition of the DMFCmodel design was previously addressed in the introduction.The DMFC model is a combination of lumped DMFCmodels and the hydrodynamic anode flow field models pre-sented in [30]. Cathode flow field effects are not covered bythe DMFC model. As depicted in Fig. 2, each hydrody-namic model consists of a network of CSTRs. The volumeof the active area CSTRs, VA,CSTR, the volume of distribu-

Fig. 2. CSTR network model of the parallel channel flow field (a), spotdesign flow field (b) and rhomboidal design flow field (c) acc. [30].

Fig. 3. Schematic representation of the 2-M model.


tor and collector CSTRs, VDIS and VCOL, as well as thefraction of flow entering each CSTR, ai, are as follows [30]:

� pcd-DMFC: VDIS = VCOL = 1.5 ml; VA,CSTR = 0.8 ml;a1 = a6 = 28%; a2 = a5 = 14%; a3 = a4 = 8%.� sd-DMFC: VDIS,i = VCOL,i = 0.5 ml; VA,CSTR = 1.7 ml;

a11 = a12 = 63%; a21 = a31 = 60%; a22 = a32 = 62%;aCOL1 = aCOL2 = 44%.� rd-DMFC: VDIS,1 = VCOL,3 = 2 ml; VDIS,2 = VCOL,2 =

1.2 ml; VDIS,3 = VCOL,1 = 0.4 ml; VA,CSTR = 0.8 ml;a1 = 15.2%; a2 = 24.8%; a3 = 35.6%; a4 = 19.3%;a5 = 38%.

To each anode flow field CSTR ij (row i and column j,grey CSTRs in Fig. 2) at the active area, a lumped DMFCmodel is assigned. The combination of CSTR ij andlumped DMFC model ij is referred to as module ij. The dis-tributor and collector CSTRs (white CSTRs in Fig. 2) arepure hydrodynamic elements and as such are not connectedto a lumped DMFC model. The lumped DMFC model is anonlinear mathematical model which accounts for the fol-lowing phenomena (see Fig. 3, module on top or bottom):

� Diffusive mass transport of methanol through the anodediffusion layer.� Oxidation of methanol in the anode catalyst layer.� Formation of the intermediates CO (adsorbed on Pt)

and OH (adsorbed on Ru) in the anode catalyst layer.� Electrochemical reduction of oxygen in the cathode cat-

alyst layer.� Methanol crossover.� Undesired electrochemical oxidation of methanol in the

cathode catalyst layer.

The following model assumptions hold for each module:

� The Ohmic drop in current collectors and electric con-nections are negligible.� The fuel cell is operated isothermally.� Oxygen and carbon dioxide do not diffuse in the PEM.� Oxygen is fed in excess to the cathode compartment, so

oxygen conversion is negligible and no oxygen mass bal-ance is formulated.� Water concentration on the anode side is assumed to be

constant, since it is an excess component in a liquidmixture.� The media on the anode side is a liquid phase mixture,

hence gas-phase formation by release of carbon dioxidebubbles is not taken into account.


� Due to the postulated instantaneous dissolution of car-bon dioxide after production, no carbon dioxide balanceis formulated.� Since the charge processes of the anode and cathode

double layers are faster than the mass transport pro-cesses and electrode reactions (see [15]), they are in aquasi-steady-state.� The anode compartment of the module is perfectly mixed.� Mass transport within the diffusion layers of the module

is fast, and thus it is in a quasi-steady-state.� Mass transport resistances in the catalyst layer of the

module are negligible due to the fact that the layer isthin (35 lm) in comparison to the diffusion layer(170 lm) and the PEM (100 lm). So the methanol con-centration in the catalyst layer of each module ishomogeneous.� Methanol which is transported to the cathode is instan-

taneously reacting with oxygen, hence its concentrationin the cathode catalyst layer is zero.� Experiments were carried out with zero pressure differ-

ence between the anode and cathode compartment,hence no pressure-driven transport through the mem-brane takes place.� At the investigated low to medium current densities,

methanol crossover due to electroosmotic drag is negli-gible when compared to methanol diffusive transport.� Mass transport in the membrane is always in a quasi-

steady-state. Previous studies showed that the dynamicsof mass transport has only a small impact on the cellvoltage response to step changes in cell current [15].� A reaction kinetic model with a three step reaction

mechanism is used to describe the electrochemical oxida-tion of methanol at the platinum–ruthenium catalyst. Itwas identified in former studies [26,27] which combinedhalf cell measurements and simulations. The proposedlumped mechanism accounts for methanol partial oxida-tion, for the oxidation of a Pt-adsorbed intermediate COand for that of a Ru-adsorbed intermediate OH:

ðPtÞ CH3OH!rA1CH3OHads ! � � � !�3Hþ�3e�

COads þHþ þ e�

ð1Þ

ðRuÞ H2O �rA2

rA�2

OHads þHþ þ e� ð2Þ

ðPt=RuÞ COads þOHads!rA3

CO2 þHþ þ e� ð3ÞThe following set of equations defines each module ij in

the active area of the DMFC:

dcA;ijCH3OH

dt¼ 1

V A;CSTR

Xh

F A;hcA;hCH3OH �

F A;ij

V A;CSTRcA;ij

CH3OH

� kADACSTRS

V A;CSTRðcA;ij

CH3OH � cAC;ijCH3OHÞ ð4Þ

dcAC;ijCH3OH

dt¼ kADACSTR

S

V AC;CSTRðcA;ij

CH3OH � cAC;ijCH3OHÞ �

ACSTRS

V AC;CSTRnM;ij

CH3OH

� ACSTRS

V AC;CSTRrij

A1 ð5Þ

dhijCO

dt¼ 1

cPt

ðrijA1 � rij

A3Þ ð6Þ

dhijOH

dt¼ 1

cRu

ðrijA2 � rij

A3Þ ð7Þ

dgijA

dt¼ 0 ¼ 1

CACiijcell þ

1

CACð�4Frij

A1 � FrijA2 � Frij

A3Þ ð8Þ

dgijC

dt¼ 0 ¼ � 1

CCCiijcell �

1

CCC6Frij

c �1

CCC6FnM;ij

CH3OH ð9Þ

rijA1 ¼ rA10 � exp½�bCOgCOðhij

CO � 0:5Þ� � cAC;ijCH3OH � ð1� hij

COÞð10Þ

rijA2 ¼ rA20 � exp

aAFRT

gijA

� �� exp½�bOHgOHðhij

OH � 0:5Þ�ð1� hijOHÞ

� rA�20 � exp �ð1� aAÞFRT

gijA

� �

� exp½ð1� bOHÞgOHðhijOH � 0:5Þ�hij

OH ð11Þrij

A3 ¼ rA30 � exp½ð1� bCOÞgCOðhijCO � 0:5Þ�hij

CO � hijOH ð12Þ

rijC ¼ �rC0 � exp

�ð1� aCÞFRT

gijC

� �ð13Þ

nM;ijCH3OH ¼

DMCH3OH

dMcAC;ij

CH3OH ð14Þ

U cell ¼ U h0 � gij

A þ gijC �

dM

jMiijcell ð15Þ

Eq. (4) represents the methanol mass balance in theanode compartment CSTR, Eqs. (5)–(7) are the mass bal-ances of methanol, the intermediate CO and the intermedi-ate OH in the anode catalyst layer respectively. Eqs. (8)and (9) are the quasi-steady-state charge balance on boththe anode and cathode sides. Eqs. (10)–(12) display thereaction rates of the previously presented anode reactionscheme, and Eq. (13) is a simplified Tafel-type cathode rateequation which assumes a constant oxygen concentrationin the catalyst layer. Finally, Eq. (14) represents the meth-anol crossover, and Eq. (15) describes the calculation of theoverall cell voltage Ucell. A detailed variable and parameterdeclaration is given in the nomenclature. The volume of thecatalyst layer of module ij, VAC,CSTR, is calculated asfollows:

V AC;CSTR ¼ V AC

number of active area CSTRsð16Þ

ACSTRS is the geometric electrode area of the module’s cata-

lyst layer:

ACSTRS ¼ AS

number of active area CSTRsð17Þ

The expressionP

hF A;hcA;hCH3OH (Eq. (4)) contains all flows h

entering the anode flow field CSTR ij. Its exact formulationhas to be taken from the set of equations for the respectiveflow field design model (see [30]). The same procedure isused for the volumetric flow rates leaving CSTR ij. Here,only the total flow leaving CSTR ij (F A;ij � cA;ij

CH3OH) isdisplayed.

Fig. 4. State variables of the 2-M model vs. cell current density. a: Ucell

(black, solid), g1A � g2

A (black, dash-dotted), g1C � g2

C (black, dashed), h1CO

(grey, solid), h2CO (grey, circles), h1

OH (grey, dashed), h2CO (grey, triangles). b:

cAC1CH3OH (black, solid), cAC2

CH3OH (black, dashed), i1cell (grey, solid) and i2

cell

(grey, dashed). Anode flow rate: 50 ml/min.


The cell voltage Ucell is identical for all modules. The cellcurrents of all modules are added to yield the total cell cur-rent AS icell (Kirchhoff’s node law):

ASicell ¼X

ij

ACSTRS iij

cell ð18Þ

Together, all lumped DMFC model elements constitute themembrane electrode assembly. The elements are electroni-cally interconnected via Eqs. (15) and (18). Due to differentmethanol concentrations in the single modules, the localanode overpotentials gij

A, the local current densities iijcell

and all other state variables will be different in eachmodule.

For all models presented in the following, the same setof parameters is used (see nomenclature): Whereas thetransport and material parameters are those of the DMFCmodel presented in [15], the original anode kinetic param-eters [26] were slightly modified to account for changes inthe experimental set-up by fitting to the experimentalbehaviour of the pcd-DMFC in the activation controlledand pseudo-Ohmic regions of the polarisation curve. Thesame procedure was used for the cathode reaction rateconstant.

4. Analysis

4.1. Model based analysis of basic steady state and dynamic

behaviour

This section presents an analysis of the basic processeswhich govern the behaviour of the DMFC model intro-duced above. The focus is on influence of the main statevariables on the DMFC’s steady state and dynamic behav-iour. It should be noted that the model was designed forusage at low to medium current densities, where cathodeside transport effects and anode side two phase flow haveless influence. Because the model does not account forthese two effects, model results should deviate from exper-imental results at high currents. However, analysis of theidealised DMFC behaviour predicted by the model is help-ful for understanding the principle dependence of theDMFC behaviour on factors like the methanol concentra-tion distribution over the active area or the current density.

Analysis of the basic processes inside the DMFC is donewith a DMFC model which contains two anode compart-ment CSTRs in series. Both CSTRs (VA,CSTR = 7.7 ml)are combined with a lumped DMFC model, respectively.The model will be referred to as 2-M model. Fig. 3 showsits schematic structure.

The dependence of the steady state of the model vari-ables on cell current density is illustrated in Fig. 4. Ascan be seen in Fig. 4a, the cell voltage, Ucell breaks downdue to a steep increase in anode overpotential gA. Thisincrease is caused by a kinetic limitation rather than a masstransport limitation because the methanol concentration inthe anode catalyst layer cAC

CH3OH (Fig. 4b) is well above zeroeven in the limiting current density region. Methanol con-

tributes indirectly to this limitation due to its influence onCO surface coverage, which in turn influences the OH sur-face coverage and the cell voltage (details see [32]). Fig. 4also illustrates the interaction between the two modules.While the methanol concentration of the second moduleis always slightly lower than that of the first module, thereis no visual difference between all other state variables andlocal current densities of the single modules over the wholerange of icell. This does not hold for high cell current den-sities, where the lower methanol concentration of the sec-ond module leads to a lower local cell current density.The resulting higher i1

cell in turn causes a decrease in the firstmodule’s methanol concentration, leading to similar over-potentials in both modules.

Fig. 5 shows the dynamic behaviour of the 2-M modelfor a step change in current density from 520 A/m2 to260 A/m2 at an anode flow rate of 50 ml/min. The cell volt-age Ucell shows an overshoot. The cell voltage reaches itsmaximum 2 s after the step change in current due to nega-tive anode overpotential overshooting, g1

A and g2A. Cell

voltage overshooting in a similar order of magnitude wasalso observed in experiment [5,15], and it is the main targetof this research to understand such behaviour. Up to now,physico-chemical models which can predict similar

Fig. 5. Dynamic responses of the 2-M model to a step change in cellcurrent density from 520 A/m2 to 260 A/m2 at an anode flow rate of50 ml/min: Ucell (dash-dotted), g1

A (solid), g2A (dashed), i1

cell (solid grey), i2cell

(dashed grey).

0 2 4–2

–1

0

1x 10

–3

time, t /[s]

reac

tion

rate

s, r

i /[m

ol/m

2 /s]

a

b

Fig. 6. Responses of the first module to a step change in cell currentdensity from 520 A/m2 to 260 A/m2. (a) Reaction rate r1

A1 (dash-dotted),reaction rate r1

A2 (dashed), reaction rate r1A3 (solid). (b) Anode overpoten-

tial (solid), OH surface coverage (dashed) and CO surface coverage (dash-dotted).

0 5 10 15 200.48

0.5

0.52

0.54

0.56

time, t /[s]

cell

volta

ge,U

cell/[V

]

Fig. 7. Cell voltage responses of the nonlinear (solid) and linearised(dashed) sets of equations to a step change in current density from 520 A/m2 to 260 A/m2.


dynamic behaviour as observed in experiment did not exist.It can be concluded therefore that with the here presentedmodel a significant step to build a realistic dynamic modelhas been achieved.

Besides cell voltage overshooting, a further dynamiceffect is observed: The different anode methanol concentra-tions and states of the two modules cause minimally differ-ent slopes for g1

A and g2A within the first second. Since Ucell

is identical for both modules, giC as well as ii

cell (i 2 {1,2})compensate the differences between g1

A and g2A. Both i1

cell

and i2cell show overshoots within the first second. Since the

total current density of 260 A/m2 is fixed, Eq. (18) causesthe total current densities i1

cell and i2cell to be axially symmet-

ric to each other. They reach a steady state after 2 s whenthe cell voltage shows a maximum.

The observed pronounced cell voltage overshootingshould be attributed to the interaction between the fastchemisorption of water and the slow oxidation reactionsof methanol and CO. This is illustrated in Fig. 6, wherethe single reaction rates of the first module are displayedin Fig. 6a, and the OH and CO surface coverages as wellas the anode overpotential of the first module are displayedin Fig. 6b. In consequence of the quasi-steady-state anodecharge balance (Eq. (8)), a sudden decrease in cell currentat t = 0 causes an instantaneous drop in the fastest reactionrate, i.e. of rA2. This leads to a decrease in OH surface cov-erage and reaction rate rA3. The consumption of CO isreduced and the CO coverage slowly increases. This in turndecreases the reaction rate rA1, and the drop in rA3 and theOH coverage is slowed down and shows a negative over-shoot. Since the OH surface coverage is directly coupledto the anode overpotential via reaction step 2, the anodeoverpotential and the cell voltage show overshooting.

Fig. 7 shows a comparison of the cell voltage response ofthe nonlinear set of equations (Eqs. (4)–(15)) to that of thelinearised set of equations. In the latter case, the set ofequations was linearised around the initial steady state.Since only one set of equations was used for the linearisedmodel, the model consists of one module with an anode

volume of VA,CSTR = 15.2 ml. As can be seen in Fig. 7,overshooting of the cell voltage is much smaller for the lin-earised model. The DMFC model seems to be highly non-linear, so a linearisation of the model equations diminishessignificant contributions of the dominant dynamic pro-cesses. The interaction of the fast water chemisorption withthe two slow steps of methanol and CO oxidation shouldbe the main reason for the pronounced nonlinear behav-


iour of the model. Consequently using a linearised modellike a transfer function model, is not suitable for modellingthe dynamic behaviour of DMFCs.

4.2. Influence of flow field design on the steady-state

performance of DMFCs

Fig. 8 shows the simulated (a) and experimental (b)polarisation curves of the pcd-DMFC, the sd-DMFC andthe rd-DMFC at an anode flow rate of 50 ml/min. In con-trast to the models, where anode kinetic limitation deter-mines the limiting current behaviour (see Section 4.1),experimental limiting current densities and cell voltagesat high cell current densities are much lower. Effects notaccounted for by the model like anode side two phase floware responsible for the deviation, as explained in Section4.4.

The simulated polarisation curves of the three designsare identical except for small differences in the limiting cur-rent region. Similar findings were obtained for the experi-ments of the pcd-DMFC and sd-DMFC. The precedinginvestigations on the hydrodynamic behaviour of the threeflow field designs [30] highlighted that the DMFCs with thedifferent flow field designs strongly vary in the homogeneityof methanol distribution over the active area. It can there-fore be concluded that homogeneity of methanol distribu-tion seems to have a low impact on the DMFCpolarisation curves. However, the polarisation curve ofthe experimental rd-DMFC differs from that of the pcd-DMFC and sd-DMFC at current densities below the limit-

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Fig. 8. Polarisation curves of the pcd-DMFC (solid; squares), the sd-DMFC (dashed; triangles) and the rd-DMFC (dash-dotted; circles) at ananode flow rate of 50 ml/min. Simulated (a) and experimental results (b).

ing current density. The experimental polarisation curve ofthe rd-DMFC shows cell voltage values which are 50–70 mV lower than that of the experimental pcd- and sd-DMFC. Since this also occurs at OCV, the deviation isattributed to design specific properties of the rhomboidalflow field DMFC like the increased collector and distribu-tor areas, which caused additional methanol crossover.While the polarisation curve of the rd-DMFC is shiftedto lower cell voltages compared to the pcd-DMFC andsd-DMFC due to design properties, the limiting currentdensity of all three designs is similar. This indicates thatthe underlying reason for the low experimental limitingcurrent density was identical for all three designs. It canbe concluded that anode flow field design had a negligibleeffect on the experimental and simulated limiting current.In most cases the flow field design had also a low impacton the polarisation curves. The reason for the observedinsensitivity of the DMFC to flow field design is analysedin the following.

To show the effect of concentration distribution within aflow field on cell current density distribution, the localmethanol concentrations in the catalyst layer of eachdesign – the pcd-DMFC (a), the sd-DMFC (b) and therd-DMFC (c) – and the respective local current densitiesare presented in Table 1. The sequence of the single mod-ules is identical to the sequence of the active area CSTRsof the flow field networks in Fig. 2. The values are obtainedat conditions, where methanol concentration differencesover the flow field are large: icell = 520 A/m2, FA,in =2 ml/min.

Modules with methanol concentrations above a certainlevel show the following trend: Lower concentrations leadto higher current densities, see e.g. modules 11 and 12 ofthe pcd-DMFC. This behaviour originates from methanolcrossover: A lower concentration causes lower methanolcrossover and a lower absolute cathode overpotential. Sincethe anode overpotential is insensitive to methanol concen-tration for medium to high methanol concentrations andsince the cell voltage is the same for all modules, the cellcurrent density rises with decreasing concentration. Onthe other hand, modules with very low concentration levelsshow an inverse dependence, i.e. lower concentrations leadto lower cell current densities. This dependence should beattributed to the steep increase of anode overpotential withdecreasing methanol concentration at high overpotentials(see Section 4.1); since the cell voltage is the same for allmodules, cell current density decreases with decreasing con-centration. The critical concentration at which the concen-tration influence on cell current density is inversed isindependent of the flow field design: below 222 mol/m3

(module 22) for the pcd-DMFC, below 230 mol/m3 (mod-ule 32) for the sd-DMFC, and below 227 mol/m3 (module33) for the rd-DMFC.

Modules with a comparably low methanol concentra-tion of 88 mol/m3 (pcd-DMFC, modules 23 and 24) obtaina current density similar to that of modules with four timeshigher concentration (e.g. pcd-DMFC, module 11 and 16).

Table 1Local methanol concentration in the catalyst layer and the correspondinglocal current densities at FA,in = 2 ml/min and icell = 520 A/m2: pcd-DMFC (a), sd-DMFC (b), rd-DMFC (c)

Column j

1 2 3 4 5 6

(a) pcd-DMFC

cAC;1jCH3OH mol m�3 512 400 284 284 400 512

i1jcell A m�2 522 549 569 569 549 522

cAC;2jCH3OH mol m�3 395 222 88 88 222 395

i2jcell A m�2 550 572 515 515 572 550

cAC;3jCH3OH mol m�3 296 104 18 18 104 296

i3jcell A m�2 568 532 299 299 532 568

Column j

1 2 3

(b) sd-DMFC

cAC;1jCH3OH mol m�3 529 363 178

i1jcell A m�2 476 518 534

cAC;2jCH3OH mol m�3 443 294 161

i2jcell A m�2 498 530 531

cAC;3jCH3OH mol m�3 344 230 155

i3jcell A m�2 521 537 529

Column j

1 2 3 4 5 6

(c) rd-DMFC

cAC;1jCH3OH mol m�3 426 499 479 376 352 442

i1jcell A m�2 511 493 498 523 528 507

cAC;2jCH3OH mol m�3 256 370 338 188 159 280

i2jcell A m�2 543 524 531 543 537 540

cAC;3jCH3OH mol m�3 137 265 227 75 53 162

i3jcell A m�2 530 542 544 479 440 538

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Fig. 9. Response of Ucell (black) and h1OH (grey) of the 2-M model to step

changes in current density at 50 ml/min and different current densitylevels: Step from 390 A/m2 to 260 A/m2 (dash-dotted), step from 520 A/m2 to 390 A/m2 (solid), step from 1520 A/m2 to 1390 A/m2 (dashed).


In contrast to this, in modules with methanol concentra-tions of 18 mol/m3 (pcd-DMFC, module 33 and 34), thecurrent density has dropped to approximately half of thecurrent density at 88 mol/m3. This illustrates, that the influ-ence of local methanol concentration on cell performance isnegligible over a wide concentration range, whereas verylow concentrations show a stronger effect on the local cellcurrent density and on the steady-state performance of aDMFC model. Hence, a significant difference in perfor-mance between the three DMFC models can only beexpected in the limiting current region. There, less homoge-neous flow distribution, as observed for the pcd-DMFC,causes an earlier cell voltage breakdown.

4.3. Influence of current density level and magnitude

of the step change on the dynamic behaviour

Fig. 9 displays the principle influence of current densitylevel on the dynamic behaviour of the DMFC model. Itshows three cell voltage responses of the 2-M model to step

changes in current density of 130 A/m2: Steps in the activa-tion controlled region (dash-dotted), pseudo-Ohmic region(solid), and high current density region (dashed). The cellvoltage responses differ significantly from region to region:While the cell voltage shows pronounced overshoots at lowcell current densities, the overshoot is smaller in thepseudo-Ohmic region. For high cell current densities noovershoot is observed. The different responses are causedby a change in dynamic behaviour of the anode kinetics,i.e. of the anode overpotential, with current density: Lowcurrent densities cause low anode overpotentials, highmethanol concentrations and overshooting OH surfacecoverage, whereas high current densities cause low metha-nol concentrations, high anode potentials and no OH sur-face coverage overshooting (see also Section 4.1). It can beconcluded that high anode overpotentials decrease thedynamic response of the cell voltage to step changes in cellcurrent.

Such a decrease in cell voltage overshooting withincreasing current density level has also been reported inliterature [15]. In the cited work, dynamic experiments withlarge step changes in current density were conducted; theywere carried out at negligible methanol residence timeinside the anode compartment. The same trend of currentdensity level influence can be found in the following stud-ies. These investigations present smaller step changes incurrent in order to avoid disturbance of the voltage signalby gaseous carbon dioxide. Such disturbances wereobserved for large steps in current density and for high cur-rent densities [14,15]. Furthermore, the here presentedinvestigations were conducted at higher residence times,so that current density level and the influence of flow fielddesign can be studied in parallel. Fig. 10 shows simulated(a,c,e) and experimental (b,d,f) cell voltage responses ofthe three DMFC designs to step changes in current densityof 130 A/m2: pcd-DMFC (a,b), sd-DMFC (c,d), rd-DMFC(e,f). All models predict a slightly smaller voltage overshootfor step changes from 650 A/m2 to 520 A/m2 (dashed) thanfor step changes from 520 A/m2 to 390 A/m2 (dash-dotted).The simulated voltage responses to the same step change incurrent are strongly similar for the different flow field

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Fig. 10. Simulated (a,c,e) and experimental (b,d,f) cell voltage responses to different step changes in current density at an anode flow rate of 50 ml/min:pcd-DMFC (a,b), sd-DMFC (c,d), rd-DMFC (e,f). Steps from 520 A/m2 to 260 A/m2 (solid), from 520 A/m2 to 390 A/m2 (dash-dotted), and from 650 A/m2 to 520 A/m2 (dashed).


designs. This is expectable due to the discussed insensitivityof cell voltage to methanol concentration inhomogeneity athigh concentration levels (see Section 4.2). Quantitativecomparison of the experimental responses is difficult, sincethe minimum time interval between recording two mea-surement points is one second; as a result, the experimentalcurve is too coarse to determine the exact cell voltageresponse and overshoot height. However, experiment andsimulation show a similar overshoot height and similartrend of current density level influence. The latter is mar-ginally visible for the pcd-DMFC, whereas it is more pro-nounced for the sd-DMFC and rd-DMFC.

Comparison of the experimentally obtained dynamicbehaviour of the three DMFC designs reveals a furtherinfluencing factor, the state of the respective DMFC. Incontrast to the experimental cell voltage responses of thepcd-DMFC and sd-DMFC, the responses of the rd-DMFCshow only minor or no overshooting behaviour within thefirst 5 s. The deviation of the rd-DMFC behaviour from

that of the two other designs and from that predicted bythe model is attributed to the non-ideal realisation of therd-DMFC design (Section 4.2). The low experimental cellvoltage of the rd-DMFC is equivalent to higher anodepotential or cathode overpotential; a higher anode overpo-tential in turn diminishes the dynamic behaviour of theDMFC as shown at the beginning of this section.

Repetition of dynamic measurements showed that thedynamic response itself was highly reproducible, whereasthe exact steady-state cell voltage level of repeated experi-ments could vary by several mV. The latter one is a phe-nomenon observed generally for DMFCs [4,33]. Hence,the quantitative evaluation of the dynamic response itselfis seen to be more reliable to interpret the state of the anodethan evaluation of the steady-state behaviour.

Also presented in Fig. 10 is the influence of the magni-tude of the step change in current on the dynamic DMFCresponse. The step from 520 A/m2 to 260 A/m2 and thestep from 520 A/m2 to 390 A/m2 have the same initial

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Fig. 11. Influence of anode flow rate on the simulated (a) andexperimental (b) polarisation curve of the pcd-DMFC. Anode flow ratein simulation: 1 ml/min (triangles), 2 ml/min (squares), 5 ml/min (dash-dotted), 50 ml/min (solid), 100 ml/min (dashed). Anode flow rate inexperiment: 50 ml/min (squares), 100 ml/min (diamonds).


current density, but the step size in the latter case is half ofthe size of the step to 260 A/m2. In modelling as well as inthe experiments, increasing the step size twofold leads tomuch higher cell voltage overshooting within the first 5 s.While the experimental rd-DMFC again shows only minorovershooting and therefore deviates from simulation, thesimulations of the pcd-DMFC and sd-DMFC are in accor-dance with the experimental results. The finding ofincreased voltage overshooting with increased current stepsize correlates also with the experimental findings of thepreliminary studies [15]. In-depth analysis of the shape ofthe cell voltage responses to a step change in current den-sity from 520 A/m2 to 260 A/m2 shows strong similaritiesbetween experiment and simulation. All simulated cell volt-age responses are in a steady state after 5 s. The experimen-tal voltages also decrease rapidly within the first 4–5 s.However, this period is followed by a slow cell voltagedecay for about 15 s. This decay attributed to slow changesin methanol crossover flux which influence the cathodeoverpotential. Argyropoulos et al. [14] found in their exper-iments voltage changes which even lasted for about oneminute. While overshooting and initial rapid decay is cor-rectly predicted by the model, the dynamic methanol cross-over effect is not reproduced due to the model assumptionof a quasi-steady-state methanol profile in the membrane.As discussed in previous studies [15], the effect of transportthrough the membrane on the cell voltage response islimited to slightly smoothing the cell voltage response.Furthermore, additional modelling of the membranedynamics would unnecessarily complicate the here pre-sented research which targets on analysis of the reasonsfor overshooting and effects of operating conditions.

It can be concluded that the three models show the samedependence of the cell voltage response on cell current den-sity level and current step size as the experiments. The pcd-DMFC and sd-DMFC models correctly predict overshootheight and, except for the membrane transport effect, alsothe relaxation time.

4.4. Influence of anode flow rate

Fig. 11 shows the simulated (a) and experimental (b)polarisation curves of the pcd-DMFC at different anodeflow rates. In the simulation results of the pcd-DMFC, adecrease in anode flow rate decreases the limiting currentdensity. Major reason for this limitation is a decrease inmethanol concentration in the anode catalyst layer (detailssee Section 4.1). A similar dependence of limiting currentdensity on volumetric flow rate is observed in experimentFig. 11b. However, the limiting current densities obtainedin experiment are much lower than those simulated. In Sec-tion 4.2, it was already demonstrated that flow field designhas no influence on the experimental limiting current den-sity of the here presented DMFCs; this indicates that theobserved experimental limitation is caused either by pro-cesses within the anode, or by processes on the cathodeside. Since Fig. 11b showed that the experimental limiting

current density increases with increasing anode flow rate,the limitation in cell current density is caused by processeson the anode side. Less than 3% of the methanol fed intothe anode compartment is consumed in the anode catalystlayer at 50 and 100 ml/min. Since the resulting gradient inmethanol concentration should be sufficient to achieve cur-rent densities higher than that observed in experiment, it isconcluded that gaseous carbon dioxide blocks furthermethanol transport to the anode catalyst sites and thuscauses the observed low limiting current density.

Fig. 12 presents the simulated (a,c,e) and experimental(b,d,f) cell voltage responses to a step change in currentdensity at various anode flow rates. Initial steady-statevoltage (icell = 520 A/m2) and final steady-state voltage(icell = 260 A/m2) are evaluated to get information aboutthe principle dependence of the steady-state performanceof all three DMFCs (pcd-DMFC = a–b, sd-DMFC = c–d, rd-DMFC = e–f) on anode flow rate. The experimentalresults show an increase of cell voltage level with anodeflow rate; this behaviour is identical to that observed forthe pcd-DMFC in Fig. 11b and is attributed to gaseousCO2 removal effects. The pcd-DMFC and the rd-DMFCshow similar dependence of cell voltage level on flow ratewhile the performance of the sd-DMFC is less dependenton anode flow rate. Since the pcd-DMFC and rd-DMFChave an identical flow field geometry at the active area, asimilarly strong influence of carbon dioxide bubbles onthe anode side mass transport can be assumed. The sd-

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Fig. 12. Simulated (a,c,e) and experimental (b,d,f) cell voltage responses to step changes in current density from 520 A/m2 to 260 A/m2: pcd-DMFC (a,b),sd-DMFC (c,d), rd-DMFC (e,f). Anode flow rates: 1 ml/min (triangles), 2 ml/min (squares), 5 ml/min (dash-dotted), 50 ml/min (solid), 100 ml/min(dashed).


DMFC has a more homogeneous flow distribution andmay permit better gas removal. The better gas removalresults in a lower impact of gaseous carbon dioxide onthe steady-state performance of the sd-DMFC at low cur-rent densities. MEA and cell designs with further improvedcarbon dioxide removal may minimise CO2 influence onthe polarisation curve, and may eventually lead to aninverse dependence of cell voltage on flow rate as observedin [14]. Those studies reported that an increase in flow rateleads to higher methanol crossover and as a result todecreasing cell voltage.

A decrease in cell voltage with increasing anode flowrate is also visible in the simulations of all three DMFCdesigns for anode flow rates above 5 ml/min. However,the simulation results at anode flow rates of 1 and 2 ml/min and a current density of 520 A/m2 show the oppositebehaviour (Fig. 12a,c,e): A decrease in cell voltage withdecreasing flow rate. At such flow rates, the prevailing

low anode methanol concentration causes a high sensitivityof anode potential to changes in anode flow rates, henceto changes in anode methanol concentration as discussedin Section 4.1. At low flow rates, also the simulated cellvoltages of the three DMFC designs show a divergence.As discussed in Section 4.2, homogeneity of methanol con-centration distribution depends on the flow field design,and the difference in methanol distribution between thedesigns causes the polarisation curves of the differentdesigns to diverge from each other at high anode poten-tials. Since the pcd-DMFC shows a more inhomogeneousconcentration profile, it shows a stronger dependence onflow rate than the other designs (Fig. 12a,c,e).

Experiment and simulation show the same dependenceof the dynamic behaviour of DMFCs on anode flow rate.At anode flow rates above 5 ml/min, the simulated cellvoltage reaches a maximum 1–2 s after the step change incurrent, and a new steady state is established after 5–6 s.


While the curves at 50 ml/min (solid) and 100 ml/min(dashed) are roughly identical, cell voltage overshootingat 5 ml/min (dash-dotted) is slower and has a lower height.This was observed in all experiments. The models predictthe same dependence of DMFC behaviour on anode flowrate. The difference in the cell voltage responses between5 ml/min on the one hand and 50–100 ml/min on the otherhand is not caused by diffusion effects, since diffusionwould have an effect only at longer time scales. The causelies in the level of methanol concentration in the anode cat-alyst layer. At low anode flow rates like 5 ml/min, the pre-vailing low methanol concentration level causes a highanode overpotential which is sensitive to methanol concen-tration changes. As discussed in Section 4.3, high anodeoverpotentials lead to less dynamic responses of the anodeand cell voltage to changes in current density. Very low vol-umetric flow rates result in a further decrease in cell voltageovershooting as seen for simulation results at 2 ml/min,and they eventually lead to a complete disappearance ofthe phenomenon of overshooting as observed for anodeflow rates of 1 ml/min.

Finally, Fig. 13 presents a comparison between the cellvoltage responses of the three models for low volumetricflow rates (2 and 5 ml/min). While Fig. 12 illustrated thenegligible differences between the designs at 50 and100 ml/min, Fig. 13 highlights the differences occurring atlower volumetric flow rates. At an anode flow rate of5 ml/min, the pcd-DMFC voltage overshoot is 7 mV smal-ler than the one of the sd-DMFC, while the rd-DMFCvoltage overshoot is only 3 mV smaller than that of thesd-DMFC. The same trend holds at 2 ml/min. There, thedeviation of the overshoot heights is even more pro-nounced. Obviously, the different flow field designs havea significant influence on the cell voltage response at suchlow volumetric flow rates. Underlying effect is the sensitiv-ity of the cell voltage to low local methanol concentrations:The more inhomogeneous the concentration distributionover a flow field, the higher is the probability that someof the modules have such low methanol concentrations,that the resulting high local anode overpotentials show aless pronounced dynamic behaviour. This tendency can

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Fig. 13. Zoom of cell voltage responses to a step change in current densityfrom 520 A/m2 to 260 A/m2 for the three DMFC models. pcd-DMFC(grey), sd-DMFC (light grey), rd-DMFC (black). Anode flow rates: 2 ml/min (squares), 5 ml/min (dash-dotted).

be seen when comparing the DMFC designs: The pcd-DMFC has the most inhomogeneous distribution of meth-anol as shown in Table 1 and as a result shows the leastdynamic behaviour, while the sd-DMFC has the mosthomogeneous methanol distribution (Table 1) and showsthe strongest dynamic behaviour.

The strong influence of modules with low methanol con-centrations on the dynamic behaviour is also directly visi-ble in the cell voltage response of the pcd-DMFC at2 ml/min. The step change in current density causes higheranode methanol concentrations within the whole flow field.While the concentration change only slightly influencesmost of the modules, the modules with the lowest methanolconcentration (modules 33 and 34, Table 1) react to theconcentration increase with a decrease of local anode over-potential and an increase of local current density for morethan 20 s. Since this causes a behaviour similar to the oneobserved at a volumetric flow rate of 1 ml/min (Fig. 12),the other local anode overpotentials are buffered. Hence,the overall cell voltage increases with time even afterovershooting.

5. Conclusions

This paper presented in-depth investigations on thedynamic behaviour of DMFCs. Experimental cell voltageresponses to step changes in cell current were analysed.The presented nonlinear models suggest that the anodereaction mechanism is the main physico-chemical phenom-enon which causes anode overpotential overshooting,hence cell voltage overshooting. Since the models arestrongly nonlinear, linearised models underestimate thedynamic behaviour. The models predicted a decreasingdynamic behaviour with increasing anode potential; as aresult, step changes in current at low flow rates or high cur-rent density levels cause low cell voltage overshooting ornone at all. In addition, voltage overshooting decreasedwith decreasing step size in current density. All trends werevalidated by experiments.

Furthermore, three flow field designs [30] were com-pared experimentally and via modelling with respect totheir influence on DMFC performance. The models sug-gested a low influence of methanol distribution within flowfields: Only cells with extremely low local methanol concen-trations (<0.1 M) in the anode catalyst layer showed aninfluence on the cell voltage. In such cases, the models pre-dicted a diminished overshooting of the cell voltageresponse to steps in cell current. The same impact of localmethanol concentrations on the cell voltage response wasobserved in experiments when operating at low anode flowrates.

The here presented experiments showed an influence ofgaseous carbon dioxide on the steady-state behaviour.Since the presented studies focussed on analysing the basicphenomena responsible for overshooting, the model didnot account for two-phase flow. Models which intend toquantitatively predict the steady state and dynamic experi-


mental DMFC results should also account for gaseous car-bon dioxide inside the anode flow field and diffusion layer.

The presented analysis contributed to understanding thedynamic behaviour of DMFCs. The results as well as themodels may be useful for development of diagnostic tools,which determine the state of the DMFC and the concentra-tion level inside the anode catalyst layer.

Acknowledgement

The authors thank Dipl.-Ing. Matthias Pfafferodt forsupporting this article.

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Documents

Understanding the dynamic behaviour of direct methanol fuel cells: Response to step changes in cell current