An analytical model for alkaline membrane direct methanol fuel cell

International Journal of Heat and Mass Transfer 74 (2014) 376–390

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

An analytical model for alkaline membrane direct methanol fuel cell Hao Deng a, Jixin Chen b, Kui Jiao a,⇑, Xuri Huang c a

State Key Laboratory of Engines, Tianjin University, 92 Weijin Rd, Tianjin 300072, China Department of Mechanical Engineering, University of Michigan, 2350 Hayward St., Ann Arbor, MI 48109, USA c State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, 2 Liutiao Rd, Changchun 130023, China b

a r t i c l e

i n f o

Article history: Received 30 September 2013 Received in revised form 9 March 2014 Accepted 12 March 2014 Available online 12 April 2014 Keywords: Alkaline anion exchange membrane Direct methanol fuel cell Multiphase analytical model Performance

a b s t r a c t In this study, a multiphase analytical model is developed for alkaline anion exchange membrane direct methanol fuel cell (AAEM-DMFC). The model prediction agrees with experimental data reasonably. Modeling results show that the methanol feed concentration, operating temperature and membrane thickness are the three factors that most significantly affect the cell performance. The effect of reactant flow rate is insignificant in high flow rate range, and this effect enhances when the flow rates are low. In low current density range, the cell shows better performance with lower methanol feed concentrations, while this trend reverses in high current density range. A similar trend is also found for the operating temperature. A thinner membrane leads to a higher methanol crossover; however, it yields better performance in mid and high current density range. Water is mass transfer limited once membrane thickness is high enough, resulting in the decrease of limiting current density. The carbon dioxide bubbles produced in anode are removed faster at higher operating temperatures. When the anode of the cell faces up, the best performance can be achieved. Inclining the cell leads to lower cell performance, and the performance degradation becomes more significant with larger inclining angles. Ó 2014 Elsevier Ltd. All rights reserved.

3 O2 þ 6Hþ þ 6e ! 3H2 O 2

1. Introduction There are active researches in the past two decades focusing on the direct methanol fuel cell (DMFC), which is considered as an ideal candidate for portable electronic applications due to its convenient fuel storage and handling, high energy density and low operating temperature [1,2]. In the early 1950s, Palve first demonstrated that methanol can act as a fuel in aqueous electrolytes [3], since the development of solid polymer electrolytes (mainly perfluorinated cation exchange membranes), proton exchange membranes (PEMs) have been widely used for DMFC applications. Nowadays, PEM-DMFC still faces two major obstacles, namely, the relatively sluggish kinetics at the anode and methanol crossover from anode to cathode [4], which hinder its commercialization. The reactions occurring in the electrodes of a PEM-DMFC are: Anode oxidation:

CH3 OH þ H2 O ! CO2 þ 6Hþ þ 6e Cathode reduction: ⇑ Corresponding author. Tel.: +86 22 27404460; fax: +86 22 27383362. E-mail address: [email protected] (K. Jiao). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.03.035 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.

ð1Þ

ð2Þ

Overall reaction:

3 CH3 OH þ O2 ! CO2 þ 2H2 O 2

ð3Þ

In the electrode reaction at the PEM-DMFC anode, by consuming 1 mol of methanol, 6 mol of hydrogen ion and 6 mol of electron are produced; on the other hand, 1 mol of water needs to be consumed (needs effective delivery of water to the electrode), and 1 mol of CO2 is produced (needs effective removal of CO2 from the electrode), which may make the mass transport difficult. In addition, the methanol crossover from anode to cathode may also cause parasitic consumption of fuel, flooding of cathode and other problems lowering the performance [5]. Many mathematical models have been developed to study the heat and mass phenomena coupled with the electrochemical reactions [6–12]. Among these models, considerable attention has been devoted to analytical model, because it provides qualitative insights into the transport processes in the fuel cells based on fundamental considerations and appropriate assumptions [10–12]. For example, Rosenthal et al. [11] developed a one-dimensional analytical model for PEM-DMFC to study the effect of a variety of operating parameters (such as methanol feed concentration and

H. Deng et al. / International Journal of Heat and Mass Transfer 74 (2014) 376–390

377

Nomenclature a A C d D E EW F g i k K M n N P R Re s Sh T v V x

activity cell geometric area (m2) molar concentration (mol m3); gas constant; viscous drag coefficient diameter (m) mass diffusivity (m2 s1) potential (V); effective activation energy (J mol1) equivalent weight of the membrane (kg mol1) Faraday’s constant (96485.0 C mol1); force (N) acceleration of gravity (m s2) current density (A m2) Henry’s constant permeability (m2) molecular weight (kg mol1) stoichiometric coefficient of electrons in electrode reaction; molar number and pore number (mol) Flux (mol m2 s1) pressure (Pa); partial pressure of gas with zero dimension universal gas constant (8.314 J K1 mol1); cell resistivity (X m2); radius (m) Reynolds number volume fraction; entropy (J mol1 K1) Sherwood number temperature (K) velocity (m s1) voltage (V); volume (m3); partial molar volume (m3 mol1) position or coordinate (m)

Greek symbols K volumetric flow rate (m3 s1) a kinetic transfer coefficient b cell inclining angle (°) d thickness (m) e porosity g voltage loss (V) h contact angle (°) k water content in ionomer l dynamic viscosity (kg m1 s1) n electro-osmotic drag coefficient (H2O per OH) q density (kg m3) r membrane conductivity (S m1); surface tension coefficient (N m1)

operating temperature) on the cell performance. Their results suggest that increasing the methanol feed concentration results in higher methanol crossover and lower open circuit voltage (OCV). At higher methanol feed concentration, the OCV is not a monotonic function of the operating temperature, which only holds at lower methanol feed concentrations. Another one-dimensional analytical model was developed for liquid-feed PEM-DMFC by Kareemulla and Jayanti [12]. They used a multi-step reaction mechanism to describe the methanol electrochemical reaction at the anode, with Stefan–Maxwell equations to describe the multi-component diffusion in the cathode. Their results suggested that at high methanol feed concentration, oxygen depletes on the cathode side due to the excessive methanol crossover, which results in substantial mass transport loss. Although active research has been conducted in the PEM-DMFC theoretical modeling and fundamental understating of heat and mass transfer, the high cost of PEMs, platinumbased catalysts, substantial fuel crossover and sluggish reaction kinetics appear to be unavoidable, which limit its development and application.

/

average gas relative humidity

Subscripts and superscripts 0 intrinsic value, standard condition, reference a anode act activation process AAEM alkaline anion exchange membrane ACL anode catalyst layer ADL anode diffusion layer AFC anode flow channel bub bubble buo buoyancy c cathode cap capillary cell fuel cell cross crossover CC concentration vs. concentration CCL cathode catalyst layer CDL cathode diffusion layer CFC cathode flow channel CO2 carbon dioxide diss dissolved eff effective g gas h hydraulic H Henry’s law H2O water in inlet lq liquid water m membrane mol molecular Me methanol ohm ohmic out outlet O2 oxygen pore pore ref reference rs electrode reaction sat saturation tran transport process vis viscous resistance w water wv water vapor / potential

In recent years, researchers are turning their interest toward alkaline anion exchange membrane direct methanol fuel cell (AAEM-DMFC). It is known that the electrochemical reaction kinetics in alkaline electrolyte is faster than that in acidic media [13]. In fact, one of the first DMFCs developed by Justi and Winsel in 1955 was operated with alkaline aqueous electrolytes [14]. However, the research on alkaline DMFC had to be scaled down in 1980s due to the electrolyte poisoning caused by CO2 production of methanol oxidation and from air, which limited its application [15]. In order to reduce the formation of carbonate in the electrolyte caused by CO2, researchers solidified the alkaline media, namely, replaced the liquid electrolyte with solid electrolyte, so that air might be used in AAEM-DMFC. This direction can be reflected by an impressive growth in publications related to AAEMs recent years [16–20]. Xiong et al. [16] presented a new way to prepare AAEMs based on polyvinyl alcohol (PVA). They grafted quaternary ammonium groups as charge carriers onto the PVA backbone by using (2,3- epoxypropyl)trimethylammonium chloride. The conductivities of the cross-linked quaternized-PVA were in the order

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of 2–7  103 S cm1 at room temperature [17]. A number of other membrane materials have been reported for application in AAEMDMFC, such as polysiloxane containing quaternary ammonium groups [18], quarternized poly (phthalazinone ether sulfone ketone) [19] and quaternised polyethersulfone cardo [20]. Considerable attention has also been devoted to anode catalysts because the electro-oxidation of methanol in alkaline electrolytes is structure insensitive [21], thus non-precious-based anodic catalysts, such as Pd, Ag, and Co-based catalysts, become potential candidates to reduce the cost [22–24]. Fig. 1 shows the schematic diagram of an AAEM-DMFC. In the anode, methanol is oxidized, and CO2 and electrons are produced. In the cathode, oxygen is reduced to produce hydroxide ions with supplied electrons. Hydroxide ions are transferred through the membrane to the anode. In addition, water is produced and consumed in the anode and cathode, respectively. The reactions occurring in the electrodes of an AAEM-DMFC are: Anode oxidation:

CH3 OH þ 6OH ! CO2 þ 5H2 O þ 6e

ð4Þ

Cathode reduction:

3 O2 þ 3H2 O þ 6e ! 6OH 2

ð5Þ

and liquid water are therefore reversed to their diffusion, reducing the methanol crossover and flooding in cathode. The hydroxide in AAEM may be neutralized by the CO2 in air and released during methanol oxidation (although not as severe as in liquid electrolyte), which may lower the membrane conductivity and the catalyst activity. A comprehensive understanding of fundamental heat and mass transfer theories is therefore needed despite the high theoretical electrochemical kinetics and low theoretical methanol crossover. Nevertheless, most AAEM-DMFC research focused on the development of membrane and catalyst materials. There were few mathematical models for AAEM-DMFC in literature. In previous studies [25,26], the authors developed a three-dimensional half-cell steady-state and transient numerical model for AAEM hydrogen fuel cell, and investigated the gas and liquid transport characteristics in the gas diffusion layer (DL) and catalyst layer (CL) with different designs and under different step changes of operating conditions. However, to the best of the authors’ knowledge, there has not been a comprehensive analytical model for AAEM-DMFC in literature so far. In this study, a one-dimensional two-phase analytical model is therefore developed, taking into account the major mass transport phenomena and electrochemical reactions.

2. Model formulation

Overall reaction:

3 CH3 OH þ O2 ! CO2 þ 2H2 O 2

2.1. Physical problem

ð6Þ

Different from PEM-DMFC, Fig. 1 shows that in an AAEM-DMFC, the charge carrier in membrane is hydroxide ion and it moves from the cathode to the anode during operation, which reverses the direction to that in PEM-DMFC. The electro-osmotic drag for both methanol

The computational domain is shown in Fig. 1, which is segmented into seven regions, including the anode flow channel (AFC), anode diffusion layer (ADL), anode catalyst layer (ACL), AAEM (A201, Tokuyama, Japan), cathode catalyst layer (CCL), cathode diffusion layer (CDL) and cathode flow channel (CFC).

Fig. 1. Schematic diagram of an alkaline anion exchange membrane direct methanol fuel cell.

H. Deng et al. / International Journal of Heat and Mass Transfer 74 (2014) 376–390

379

Table 1 Base model parameters. Parameter

Value

Cell length Channel width Channel height DL thickness CL thickness Membrane thickness Geometric area Hydraulic diameter Porosities Contact angles of DL, CL Pore diameter of ADL Intrinsic permeabilities of DL, CL

0.1 m 1  103 m 1  103 m 2  104 m 1  105 m 28  106 m AADL, ACDL, AAFC, ACFC = 2  104, 2  104, 1  104, 1  104 m2 1  103 m eADL,ACL,CCL,CDL = 0.6, 0.3, 0.3, 0.6 h = 100° dpore,ADL = 7.78  105 m

Liquid water density Transfer coefficients of electrode reaction Faraday’s constant Universal gas constant Standard entropy change Methanol activity Water activity Reference methanol concentration Reference oxygen concentration Reference water concentration Effective activation energy of MOR and ORR [30,31] Reference temperature Reference exchange current densities of the anode and cathode Sherwood number [32] Total cell resistance (except membrane resistance) Membrane conductivity at 23, 40, 60 °C [37] Standard Henry’s constant [38] Gas constant for carbon dioxide [38] Acceleration of gravity Partial molar volume of the water

qlq = 1000 kg m3 aa = 0.5, ac = 0.5

Equivalent weight of A201 membrane [47] Density of dry A201 membrane [47] Molecular weight of oxygen, water and nitrogen Molecular volume [49] Liquid water activity [49]

The corresponding voltage losses in each region are also presented in Fig. 1. The flux of any species along the direction from anode to cathode is defined to be positive. The base model parameters are shown in Table 1.

K 0DL;CL ¼ 6:2  1012 ; 6:2  1013 m2

F = 96485 C mol1 R = 8.314 J K1 mol1 D^s ¼ 81:2 J mol1 K1 aMe, depends on methanol concentration aH2 O ¼ 1 CMe,ref = 1000 mol m3 C O2 ;ref ¼ 18:4 mol m3 C H2 O;ref ¼ 16000 mol m3 Ea;/0 ; Ec;/0 ¼ 58; 000; 67; 000 J mol1 Tref = 298 K ia,0,ref, ic,0,ref = 0.01,1  108 A m2 Sh = 2.3 Rother = 1.0  104 X m2 rm = 3.01, 4.15, 5.49 S m1 kH,CC,ref = 0.8317 C = 2400 g = 9.8 m s2 V w ¼ 18  106 m3 mol1 EW = 0.58824 kg mol1 qAAEM = 1092.7 kg m3 M O2 ;H2 O;N2 ¼ 32; 18; 28 g mol1 V O2 ;H2 O;N2 ;CO2 ¼ 16:3; 13:1; 18:5; 34 cm3 mol1 alq = 2.6

fixed to be zero, because they can be removed from the channel quickly.  For the gas phase in anode, only CO2 is considered, and water vapor is ignored in anode.

2.2. Assumptions 2.3. Voltage losses The analytical model is developed based on the following assumptions.  The cell operates in steady-state and isothermal conditions, and the non-isothermal effect is considered by using the related parameters corresponding to the operating temperature.  The transport in the through-plane direction (normal to the electrode) is primarily considered in this one-dimensional model, and the along-channel transport is considered as the secondary direction only with simplified mass transport analysis (described in the following subsections).  Only the diffusive mass transport is considered in the DL and CL, whereas in the channel the convective mass transport is also taken into account.  The CL is considered to be a surface because it is very thin, and this assumption was also widely used in previous modeling studies [11,27].  The crossed methanol from anode to cathode is assumed to be fully consumed immediately in the cathode.  The concentration of CO2 in the anode channel is fixed to be zero, and the amount of liquid water in the cathode channel is

The overall cell voltage is determined by the thermodynamic equilibrium voltage and various voltage losses:

V cell ¼ Ecell  ga  gc  gohm

ð7Þ

where Vcell is overall cell voltage; Ecell is thermodynamic voltage;

gohm is the ohmic loss; and ga and gc are the polarization losses of the anode and cathode, respectively. The polarization losses, ga and gc, determine the rate of electrochemical reaction in the anode and cathode, respectively, which is the sum of activation and transport losses on each side:

ga ¼ gaact þ gatran gc ¼ gcact þ gctran

ð8Þ ð9Þ

It should be noted that the voltage loss caused by methanol crossover is considered in the calculation of activation and transport loss in the cathode; namely, included in gc. More details can be found in the Section 2.5.

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H. Deng et al. / International Journal of Heat and Mass Transfer 74 (2014) 376–390

Table 2 Water transport parameters. Parameter Saturated water–vapor pressure [40]

Expression  Psat ¼ 2:1794 þ 0:02953ðT  273:15Þ  9:1837  105 ðT  273:15Þ2 þ 1:4454  107 ðT  273:15Þ log10 101325 (T in K)

Dynamic viscosity of liquid water [41]

llq ¼ 2:414  105  10T140

Liquid and gas permeability [45]

Klq = K0s4.0 lq , liquid Kg = K0(1  slq)4.0, gas

Liquid water diffusivity in porous media [46] Electro-osmotic drag coefficient [26,47] Liquid water diffusivity in membrane [26,47]

Dlq ¼  llq

K

lq

N m1 Pa

m2 m2 s1

dP cap dslq

n = 0.183k + 1.3, 0 6 k 6 19 8 > ð0:0051  T  k  1:44kÞ  1010 ; 0 6 k 6 14 > h > > <  0:006131k3  0:28926k2 þ4:513k23:2404Þ Deff w;AAEM ¼ > > ðT  303:15Þ þ 0:03337k3  1:3329k2 þ 17:928k > > : 79:826  1010 ; 14 6 k 6 19 (T in K) 8 > 0:605/3 þ 0:85/2  0:205/þ0:153Þ  ðT  313:15Þ > > < 3 2 k ¼ þ39:0/  47:7/ þ 23:4/ þ 0:117; 0 6 / 6 1:0 > > ð 0:00265/ þ 0:05795 Þ  ðT313:15Þ þ 1:5915ð/  1Þ > : þ14:817; 1:0 6 / 6 3:0 (T in K)

Water content [26,47]

a

Surrounding relative humidity

N/A m2 s1

N/A

þa

N/A

/ ¼ w;a 2 w;c aw,a = 1 + 2slq,a, anode aw,c = 1 + 2slq,c, cathode

Water activity

Pa kg m1 s1

247:8

(T in K) r = 0.0001676T + 0.1218, 273.15 K 6 T 6 373.15 K  0:5 P cap ¼ P g  P l ¼ r cos h Ke0 JðsÞ (  1:42 1  slq  2:12ð1  slq Þ2 þ 1:26ð1  slq Þ3 ; if h < 90 JðsÞ ¼ 1:42slq  2:12s2lq þ 1:26s3lq ; if h > 90

Surface tension coefficient [42] Capillary pressure [43,44]

Unit

N/A

Table 3 Methanol transport parameters. Parameter

Expression

Diffusion coefficient of methanol [48]

Deff Me;ADL ¼

Unit



2 eCO ADL

1:5

DMe;w

m2 s1

1:5 Deff Me;AAEM ¼ eAAEM DMe;W

Water volume fraction in AAEM [12] Partial molar volume of membrane [12]

20460 1 1 DMe;w ¼ 2:1  109 e R ðT 313Þ (R in J K1 mol1, T in K) eAAEM ¼ Vk

kþ

N/A

AAEM Vw

V AAEM ¼ qEW

m3 mol1

AAEM

where aa and ac are the transfer coefficients of the anode and cathode electrode reactions; F is the Faraday’s constant; R is the universal gas constant; and T is the operating temperature. ia and ic are the anode and cathode current density, respectively. ia is equal to the output current density i by neglecting the oxygen crossover, and ic = i + icross (in which icross is the inner current density caused by methanol crossover). ia,0 and ic,0 are the anode and cathode exchange current density corrected by the effects of the reactant concentrations in the CL and the operating temperature: E

eCO2 C Me;rs  a;/R 0 ia;0 ¼ ACL e eACL C Me;ref

2.4. Thermodynamic voltage

E

The thermodynamic (reversible) AAEM-DMFC cell voltage, Ecell, is calculated by the corrected Nernst equation [11,28]:

Ecell ¼

E0cell

8 9 D^s RT < aMe PCO2 = þ ðT  T 0 Þ  ln nF :aH2 O P32 ; nF O2

ð10Þ

where the first term on the right hand side represents the standardstate reversible fuel cell voltage (1.214 V at 25 °C and 1 atm). The second and third terms represent the effects of operating temperature and species concentration on the reversible voltage, respectively. The related parameters are shown in Table 1. 2.5. Polarization losses The electrochemical reaction rates are given by Butler–Volmer equations [29]:

   6aa F ga 6aa F ga ia 6aa F ga ¼ e RT  e RT ¼ 2 sinh ia;0 RT    4ac F gc 4ac F gc ic 4 a c F gc ¼ e RT  e RT ¼ 2 sinh ic;0 RT

ð11Þ ð12Þ

ic;0 ¼



1 1 T T ref

C O2 ;rs C H2 O;rs  c;/R 0 e C O2 ;ref C H2 O;ref



 ia;0;ref 

1 1 T T ref

ic;0;ref

ð13Þ ð14Þ

2 where eCO ACL and eACL are the ACL corrected (CO2 bubble effect) and intrinsic porosities, respectively; and their quotient is used to describe the CO2 bubble (released during methanol oxidation) effect on cell performance (Section 2.7). The reference methanol concentration in ACL (CMe,ref), reference oxygen and water concentrations in CCL (C O2 ;ref and C H2 O;ref Þ, effective activation energy for methanol oxidation reaction (MOR) and oxygen reduction reaction (ORR) (Ea;/0 and Ec;/0 Þ [30,31], reference temperature (Tref), and reference exchange current densities of the anode and cathode (ia,0,ref and ic,0,ref) are given in Table 1. According to Eqs. (11)–(14), the reactant concentrations in ACL and CCL (including CMe,rs, C O2 ;rs and C H2 O;rs Þ are the parameters needed to determine the polarization voltages (ga and gc), which leads to the following analysis of mass transport in AAEM-DMFC.

2.5.1. Methanol transport The flux of methanol in ADL is determined by the reaction and crossover rates:

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H. Deng et al. / International Journal of Heat and Mass Transfer 74 (2014) 376–390 Table 4 Oxygen transport parameters. Parameter

Expression

Diffusion coefficient of oxygen in CDL (oxygen feed case) [49]

Unit 0:101T

1:75

 DCDL O2 ;wv ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

m2 s1

1 M O þM H O 2 2



CDL=CFC C O ;rs þC O2 2 Psat þ RT 2



1 V 3O 2

1 þV 3H O 2

2

(T in K, M in g mol1, P in Pa and V in cm3 mol1) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Diffusion coefficient of oxygen in CFC (oxygen feed case) [49]

DCFC O2 ;wv ¼ 

0:101T 1:75 

Psat þC CFC O RT



2

(T in K, M in g mol Diffusion coefficient of oxygen in CDL (air feed case) [49]

1 M O þM H O 2 2 1

1

V 3O þV 3H 2

2O

, P in Pa and V in cm3 mol1) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

1 0:101T 1:75  M þM O2 N2 CDL=CFC C O ;rs þC O2 2 Psat þ RTþðP c -Psat Þ0:79 2

 DCDL O2 ;N2 ¼



1

1

V 3O þV 3N 2

DCFC O2 ;N2 ¼ 

0:101T 1:75 

1 MO þMN 2 2



Psat þC CFC O RTþðP c -P sat Þ0:79 2

1 V 3O 2

1 þV 3N 2

m2 s1

2 2

(T in K, M in g mol1, P in Pa and V in cm3 mol1) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Diffusion coefficient of oxygen in CFC (air feed case) [49]

m2 s1

2

m2 s1

2

(T in K, M in g mol1, P in Pa and V in cm3 mol1) Effective diffusion coefficient

Table 5 Carbon dioxide transport parameters. Parameter

Expression

Diffusion coefficient of CO2 [49]

DADL CO2 ;w

¼



e

Unit CO2 ADL

1:5

m2 s1

DCO2 ;w

previous models for DMFC [1,5,6,9]. To calculate NAAEM Me , it is assumed that the variation of methanol concentration in AAEM is linear and the crossover methanol is consumed completely and   instantaneously C AAEM=CCL ¼ 0 , thus, Eq. (17) can be simplified to Me the following expression:

0:5

DCO2 ;w ¼ 7:4 

ða MH O Þ T 10-15 llq V 0:62 lq CO ;mole 2

Viscous drag coefficient [50] Reynolds number [50]

NADL Me ¼

(M in g mol1, T in K, l in kg m1 s1 and V in cm3 mol1) C v is ¼ 64 Re

NAAEM ¼ Me N/A

Deff Me;AAEM dm



! i n C Me;rs F 2C AAEM w

ð18Þ AFC=ADL

Re ¼

qlq dpore;ADL v CO2 ;bub;b llq

i þ NAAEM Me 6F

AAEM To calculate CMe,rs, it is needed to determine N ADL Me ; N Me ; C Me

N/A

C AAEM w

and according to Eqs. (15), (16) and (18). Therefore, two additional equations are needed: one can be given by considering the water mass transport in AAEM-DMFC to obtain a relation between

ð15Þ

where NADL Me is the diffusion flux of methanol in ADL without considering the convective transport:

NADL Me ¼

m2 s1

1:5 Deff DO2 O2 ¼ e

  Deff Me;ADL C AFC=ADL  C Me;rs Me dADL

C AAEM and CMe,rs (Section 2.5.2); and another can be derived by the w following boundary conditions to yield a relation between C AFC=ADL Me and NADL Me :

ð16Þ

where Deff Me;ADL is the effective diffusion coefficient of methanol in AFC=ADL

is the methanol concentraADL; dADL is the ADL thickness; C Me tion at the interface of AFC and ADL; CMe,rs is the methanol concentration in the ACL. It should be pointed out that by considering the CL as a surface [11,27], the diffusive transport inside CL is neglected in this model. N AAEM is the crossover flux of methanol through the Me membrane, contributed by diffusion and electro-osmotic drag:

NAAEM ¼ Me

 Deff Me;AAEM



dm Z dm 0

 i 1 C Me;rs  C AAEM=CCL n Me F C AAEM dm w

C AAEM Me dx

ð17Þ

where Deff Me;AAEM is the effective diffusion coefficient of methanol in is the methanol AAEM; dm is the membrane thickness; C AAEM=CCL Me concentration at the interface of AAEM and CCL; n is the electroosmotic drag coefficient of water; C AAEM is the average water conw is the average methanol concentracentration in AAEM; and C AAEM Me tion in AAEM. Because of the similar molecular structures and chemical properties of water and methanol, it is assumed that the electro-osmotic drag of methanol is proportional to the methanol molar fraction in water. This assumption was also widely used in

Fig. 2. Force analysis diagram of single CO2 bubble: buoyancy, gravity, viscous resistance, added mass force and Basset force. b is the inclined angle, and b = 0° means that the anode faces up.

H. Deng et al. / International Journal of Heat and Mass Transfer 74 (2014) 376–390

 1  in C AFC C Me;a þ C out Me ¼ Me;a  2  out ADL Ka C in Me;a  C Me;a ¼ AADL  eADL  N Me AFC=ADL

C Me

¼ C AFC Me 

dh AADL NADL 2ShDMe;w AAFC Me

ð19Þ

0.6

ð20Þ

0.5

ð21Þ

where C AFC Me is the average methanol concentration in AFC, assumed to be half of the total methanol concentrations at the anode inlet out and outlet (C in Me;a and C Me;a Þ. Ka is the volumetric flow rate of methanol solution. The second term on the right hand side of Eq. (21) represents the methanol concentration loss caused by convective transport, and DMe,w is the diffusion coefficient of methanol in liquid water. The geometric area of ADL and anode channel (AADL and AAFC), porosity of ADL (eADL), hydraulic diameter (dh), and Sherwood number (Sh [32]) are given in Table 1. 2.5.2. Water transport The analysis of mass transport for water in AAEM-DMFC is similar to that for methanol. The related equations are given in the following:

5i þ NAAEM w 6F eff   Dw;ADL AFC=ADL ¼ Cw  C ACL NADL w w dADL    Deff Psat i w;AAEM n ¼ C ACL þ C CCL NAAEM w  w w F dm RT i 5icross NCDL ¼ þ þ NAAEM w w 2F 6F AAEM icross ¼ 6FNMe   Deff w;CDL CDL=CFC NCDL ¼ C CCL w  Cw w dCDL   1 Psat AAEM CCL ¼ C ACL þ þ C Cw w w 2 RT

NADL ¼ w

ð22Þ

¼

C AFC w

¼0

0.3 0.2 0.1 0.0 0.000

0.005

0.010

0.015

0.020

0.025

0.030

Current density, A cm-2 Fig. 3. Comparison between the model prediction and the experimental data in [57] when the cell operates at a temperature of 80 °C and a pressure of 1 atm. Anode: methanol solution without added alkali (1 M at 5.0 ml min1); cathode: humidified oxygen (100 ml min1).

Table 6 Base case. Value

ð24Þ

Methanol feed concentration Membrane thickness Operating temperature Anode flow rate (methanol aqueous)

2M 28 lm 60 °C 1.0 ml min1 (equivalent anode stoichiometric ratio is 16.08 at 0.3 A cm2) 5.0 ml min1 (equivalent cathode stoichiometric ratio is 2.44 at 0.3 A cm2) 0° (anode faces up)

ð25Þ ð26Þ

Cathode flow rate (fully humidified oxygen)

ð27Þ

Angle between the throughmembrane direction and the vertical direction

ð28Þ

sat in Eq. (28), C ACL and PRT þ C CCL can be used to represent the water w w concentration in ACL and CCL, respectively. In addition, the calculated results suggest that the water vapor concentration is less than liquid water in CCL for about three orders of magnitude. To determine the relation between C AAEM and CMe,rs, two addiw tional equations from the following boundary conditions are needed:

C AFC=ADL w CDL=CFC Cw

0.4

Operating parameter

AFC=ADL CCL crossover, N AAEM ; C ACL and C CDL=CFC are the liquid Me ; C w w ; Cw w water concentrations at the interface of AFC and ADL, ACL, CCL and the interface of CDL and CFC, respectively. It should be noticed that in this model, the transport of water vapor in anode is neglected, because the anode is almost fully flooded in an operating AAEM-DMFC, and the amount of liquid water is much higher than water vapor. On the other hand, the transport of water vapor is considered in cathode for this model. At phase equilibrium, if liquid water presents in cathode, the water vapor is saturated. Therefore,

 1  in ¼ C w;a þ C out w;a 2   out ADL Ka C in w;a  C w;a ¼ AADL  eADL  N w

Experimental data [57] Model prediction

ð23Þ

eff eff where Deff w;ADL ; Dw;AAEM and Dw;CDL are the effective diffusion coefficients of liquid water in ADL, AAEM and CDL, respectively; dCDL is the thickness of CDL; Psat is the saturated water–vapor pressure determined by temperature; icross is the internal current density caused by methanol crossover, proportional to the flux of methanol

C AFC w

Cell voltage, V

382

ð29Þ ð30Þ ð31Þ ð32Þ

where C AFC is the average liquid water concentration in AFC, asw sumed to be half of the total liquid water concentrations of anode out inlet and outlet (C in w;a and C w;a Þ. The liquid water concentration loss caused by convective transport (Eq. (31)) is neglected. C CDL=CFC is w fixed to be zero because liquid water in CFC can be removed from such short straight channel quickly by air. Finally, the water concentration in CCL is the sum of liquid water concentration and water–vapor concentration in CCL:

C H2 O;rs ¼ C CCL w þ

Psat RT

ð33Þ

2.5.3. Oxygen transport Similar to methanol and water, the oxygen concentration in CCL (C O2 ;rs Þ can be calculated by the following transport equations and boundary conditions:

i þ icross 4F   DCDL O2 CDL=CFC CDL NO2 ¼ C O2 ;rs  C O2 dCDL Pc  Psat Pc  P sat in C O2 ;c ¼ ðoxygenÞ or  0:21 ðairÞ RT RT   1 in C O2 ;c þ C out C CFC O2 ¼ O2 ;c 2  

NCDL O2 ¼ 

out CDL Kc C in O2 ;c  C O2 ;c ¼ ACDL  eCDL  N O2

C CDL=CFC ¼ C CFC O2  O2

dh ACDL CFC

2ShDO2 ACFC

NCDL O2

ð34Þ ð35Þ ð36Þ ð37Þ ð38Þ ð39Þ

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where DCDL O2 is the effective diffusion coefficient of oxygen in CDL; CDL=CFC is the oxygen concentration at the interface C O2 CFC; C in O2 ;c is the oxygen concentration of cathode inlet

of CDL and

determined by the pressure of cathode inlet (Pc, 1 atm) and saturated water–vaC CFC O2

por pressure (Psat); is the average oxygen concentration in CFC, assumed to be half of the total oxygen concentrations at the cathout ode inlet and outlet (C in O2 ;c and C O2 ;c Þ; and Kc is the volumetric flow rate of the mixture of oxygen and water vapor. The second term on the right hand side of Eq. (39) represents the oxygen concentration

loss caused by convective transport. DCFC O2 is the diffusion coefficient of oxygen in water–vapor in CFC. The geometric area of CDL and CFC (ACDL and ACFC) and porosity of CDL (eCDL) are given in Table 1. 2.6. Ohmic loss The last term, gohm, on the right-hand-side of Eq. (7) represents the ohmic losses caused by the membrane resistance and other resistance:



gohm ¼ i Rother þ

dm



rm

ð40Þ

where Rother is the total resistance in fuel cell except the membrane resistance; rm is the membrane conductivity, which primarily depends on temperature and water content. Recently, Duan et al. [33] measured the ionic conductivity of A201 membrane (disassembled from MEA) at different temperatures and water activities. Their results show that the membrane conductivity increases with water content as well as temperature, however, yields a low value (5–7 mS cm1) because the OH mobility is about 4 times higher than HCO 3 form [34], while the membranes studied in their experiment are all converted into HCO 3 form due to the difficulty to measure the conductivity of the AAEM in the pure OH form. In the direct alcohol fuel cells (DAFCs), presently, alkali (typically the KOH and NaOH) is often added to the fuel solution to enhance the ionic conductivity of the membrane [35]. The ionic conductivity of A201 membrane was reported to be about 29 mS cm1 recently [3,36]. An et al. [37] measured the ionic conductivity of A201 membrane in 5.0 M NaOH solution from 23 to 60 °C, and showed that the ionic conductivity increases almost linearly with temperature (from 30.1 to 54.9 mS cm1), which is close to the values reported in [3,36]. Therefore, in this model, the membrane ionic conductivities reported by An et al. [37] at different temperatures are used (Table 1). In addition, since the anode is always flooded in an operating AAEM-DMFC, the membrane is always considered to be fully humidified in this study. 2.7. Carbon dioxide bubble effect Through the methanol oxidation in anode, CO2 is produced, and the CO2 is removed through two ways: dissolved in liquid water, and forming bubbles. It should be noted that CO2 bubbles will disturb the flow in ADL and ACL, and hinder the methanol transport to the catalyst sites. Thus, a correction for the porosities of ADL and ACL is needed for the effect of CO2 bubbles. This effect in CDL and CCL can be neglected for two reasons. First, the amount of CO2 production of methanol oxidation in cathode (due to crossover) and the CO2 in air is negligible by comparing with the amount of CO2 in anode; and second, the cathode is often not fully flooded, resulting in much easier CO2 removal. 2.7.1. Anode diffusion layer The expressions of ADL porosity corrected for the effect of CO2 bubbles are given by the following equations:

2 eCO ADL ¼

V ADL eADL  V ADL CO2 ;bub 4 3 pR nADL 3 CO2 ;bub;ADL pore

V ADL CO2 ;bub ¼ nADL pore ¼

ð41Þ

V ADL

ð42Þ

AADL eADL 1 4

ð43Þ

pd2pore;ADL

ADL Pa V ADL CO2 ;bub ¼ nCO2 ;bub RT

nADL CO2 ;bub

ð44Þ

C ADL CO2 ;bub V ADL ADL

e

¼

ð45Þ

ADL 2 where eCO ADL is the ADL porosity after correction; V CO2 ;bub is the total volume of CO2 bubbles in ADL, which is corresponding to the radius of CO2 bubble (RCO2 ;bub;ADL , assumed to be the same for all the bub  ADL bles in ADL) and number of pores in ADL nADL pore ; nCO2 ;bub and

C ADL CO2 ;bub are the molar number and concentration of CO2 bubbles in ADL, respectively. The volume of ADL (VADL) and the diameter of pore in ADL (dpore,ADL) are given in Table 1. ADL 2 To calculate eCO ADL , the relation between C CO2 ;bub and RCO2 ;bub;ADL is needed. It can be obtained from the following equations based on the mass transport of CO2 and Henry’s law [38]:

NADL CO2 ¼  NADL CO2

¼

i 6F

ð46Þ

NADL CO2 ;diss

NADL CO2 ;diss ¼ NADL CO2 ;bub ¼

þ

N ADL CO2 ;bub

ð47Þ

CO2 1:5  DADL CO2 ;w ADL C AFC=ADL CO2 ;diss 1 d ADL 2  CO2 ;bub C ADL CO2 ;bub

e

v

kH;CC ¼ kH;CC;ref e

C



1 1 T T ref



¼

 C ADL CO2 ;diss

C ADL CO2 ;diss C ADL CO2 ;bub



ð48Þ ð49Þ ð50Þ

where NADL ADL, including two parts: the CO2 CO2 is the CO2 flux in   and the CO2 flux in bubble flux dissolved in liquid water NADL CO2 ;diss ADL form (NADL CO2 ;bub Þ. DCO2 ;w is the diffusion coefficient of CO2 in liquid water. It is assumed that CO2 in AFC can be removed quickly   C ADL CO2 ;diss ¼ 0 , and the variation of CO2 concentration in ADL is lin-

ear. Thus, the average CO2 concentration dissolved in liquid water   ADL can be defined as the and in a bubble form C ADL CO2 ;diss and C CO2 ;bub corresponding concentrations in the middle of ADL, and the relation between them is established by Henry’s law [38]. v CO2 ;bub is the movement velocity of CO2 bubble towards the anode flow channel. kH,CC is the Henry’s constant determined by temperature. The standard Henry’s constant (kH,CC,ref) and gas constant (C) [38] are given in Table 1. v CO2 ;bub needs to be determined before the relation between C ADL CO2 ;bub and RCO2 ;bub;ADL can be derived according to Eqs. (46)–(50), while this is done by a force analysis of single CO2 bubble, as shown in Fig. 2. b is the inclined angle, and b = 0° means that the anode faces up. It can be observed from Fig. 2 that a single CO2 bubble bears five forces: buoyancy, gravity, viscous drag, added mass force, and basset force [39]. In steady-state operation, the CO2 bubbles are produced and removed at the same rate, and therefore the added mass force and basset force can be neglected. Moreover, the gravity can be neglected because the density of gas is much smaller than liquid. The following expression therefore holds based on a force balance:

F buo  F v is ¼ 0

ð51Þ

where Fbuo is the buoyancy and Fvis is the viscous resistance. They can be calculated by the following equations [39]:

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4 3 pR q g 3 CO2 ;bub;ADL lq 1 F v is ¼ C v is qlq pR2CO2 ;bub;ADL v 2CO2 ;bub;b 2

F buo ¼

ð52Þ ð53Þ

where the liquid water density (qlq) and acceleration of gravity (g) are given in Table 1. Cvis is the viscous resistance coefficient. v CO2 ;bub;b is the vertical movement velocity of CO2 bubble. The relation between v CO2 ;bub;b and v CO2 ;bub is given by:

v CO ;bub ¼ v CO ;bub;b e0:5 ADL cos b 2

compare with. However, for AAEM fuel cell with A201 membrane operating with ethanol, the addition of alkali in ethanol showed significant performance improvement [58]. Nevertheless, to represent the state-of-the-art performance of AAEM-DMFC, in the following calculations, methanol solution with NaOH as the fuel is considered. In this study, five operating or design parameters and different cell orientations are considered to study the cell performance

ð54Þ

2

where e0:5 ADL is tortuosity factor considering the effect of geometrical structure of DL on the CO2 bubble motion.

V ACL eACL  V ACL CO2 ;bub

ð55Þ

V ACL

ACL Pa V ACL CO2 ;bub ¼ nCO2 ;bub RT

kH;CC ¼ C ACL CO2 ;diss

¼

ð56Þ

C ACL CO2 ;bub V ACL ACL

e

C ACL CO2 ;diss 2C ADL CO2 ;diss

CO2 ACL

0.4

0.2

0.5 M

ð58Þ

C ACL CO2 ;bub ¼

0.6

ð57Þ

ð59Þ

(a)

V ACL CO2 ;bub

where e is the ACL porosity after correction; is the total volume of CO2 bubbles in ACL, which is proportional to the molar number of CO2 bubbles in ACL. The volume of ADL (VADL) and the ACL porosity before correction (eACL) are given in Table 1. The CO2 concentration dissolved in liquid water in ACL is assumed to be uniform, and then the average CO2 concentration dissolved in liquid water in ACL is twice as large as that in ADL. 2.8. Transport parameters The base model parameters, water, methanol, oxygen and carbon dioxide transport parameters are given in Tables 1–5 [12,26,30–32,37,38,40–50], respectively. It should be noticed that in this model, the Bruggeman correlation is used with an exponent of 1.5 to calculate the effective diffusion coefficient and electric/ionic conductivity in the porous electrode. Although the value of the exponent depends on the microstructure of the porous media, ranging from 1.2 to 4.5 [51,52], only the value of 1.5 was widely used in previous fuel cell models [1,6,9,11,12,53,54]. Recent experimental measurements and theoretical studies on the effective transport properties of fuel cell electrodes also showed reasonable agreement with the Bruggeman correlation with an exponent of 1.5 [55,56]. 3. Results and discussion Fig. 3 shows the comparison between the present analytical model prediction and the experimental data in [57] (which also adopts the A201 membrane). It can be observed that the model prediction agrees with the experimental data reasonably. It should be noted that the experiment used 1 M methanol without added alkali as the anode fuel to better evaluate the tolerance for methanol crossover, while the addition of alkali to the fuel solution can enhance the conductivity of the hydroxide in both the alkaline membrane and electrodes. That is the reason that the cell performance shown in Fig. 3 is low due to the large ohmic resistance. Although significant performance improvement can be obtained by adding alkali in supplied methanol, it is difficult to find the related experimental data for AAEM-DMFC with A201 membrane to

1.0 M

2.0 M

4.0 M

0.4

0.5

0.0 0.0

0.1

0.2

0.3

Current density, A cm-2

0.8

Crossover current density, A cm-2

nACL CO2 ;bub

Increasing methanol feed concentration (0.5 M, 1.0 M, 2.0 M, 4.0 M)

0.6

0.4

0.2

0.0 0.0

(b)

0.1

0.2

0.3

0.4

0.5

Current density, A cm-2

0.5 Cathode polarization loss 0.4

Voltage loss, V

2 eCO ACL ¼

Cell voltage, V

2.7.2. Anode catalyst layer In Section 2.7.1, C ADL CO2 ;diss is calculated. Thus, the corrected ACL porosity is given by the following equations:

0.8

0.3

Anode polarization loss Ohmic loss

0.2 0.1 Increasing methanol feed concentration (0.5 M, 1.0 M, 2.0 M, 4.0 M)

0.0

(c)

0.0

0.1

0.2

0.3

0.4

0.5

Current density, A cm-2 Fig. 4. Effect of methanol feed concentration on (a) cell performance; (b) methanol crossover current density; and (c) voltage losses (polarization losses of anode and cathode, ohmic loss) when the cell operates at a temperature of 60 °C and a pressure of 1 atm. Anode: methanol soluiton with NaOH (0.5, 1.0, 2.0 and 4.0 M at 1.0 ml min1); cathode: humidified oxygen (5.0 ml min1).

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Decreasing membrane thickness (150 μm, 100 μm, 60 μm, 40 μm, 28 μm)

0.6

0.4

0.2

0.0 0.0

0.1

0.2

0.3

0.6

0.4

0.2

0.0 0.0

0.4

0.1

(c)

Current density, A cm-2

0.2

0.3

0.4

0.3

0.4

-2

Current density, A cm

0.4 Decreasing membrane thickness (150 μm, 100 μm, 60 μm, 40 μm, 28 μm)

15

0.3

Water concentration in CCL, mol L-1

Crossover current density, A cm-2

(a)

Increasing membrane thickness (28 μm, 40 μm, 60 μm, 100 μm, 150 μm)

0.8

Methanol concentration in ACL, mol L-1

Cell voltage, V

0.8

0.2

0.1

0.0 0.0

(b)

0.1

0.2

0.3

12

9

6

3

Increasing membrane thickness (28 μm, 40 μm, 60 μm, 100 μm, 150 μm)

0 0.0

0.4

0.1

(d)

-2

Current density, A cm

0.2 -2

Current density, A cm

0.5 Cathode polarization loss

Voltage loss, V

0.4 0.3 0.2

Anode polarization loss

ohmic loss

0.1 Decreasing membrane thickness (150 μm, 100 μm, 60 μm, 40 μm, 28 μm)

0.0 0.0

(e)

0.1

0.2

0.3

0.4

-2

Current density, A cm

Fig. 5. Effect of membrane thickness (28, 40, 60, 100 and 150 lm) on (a) cell performance; (b) methanol crossover current density; (c) methanol concentration in ACL; (d) water concentration in CCL; and (e) voltage losses (polarization losses of anode and cathode, ohmic loss) when the cell operates at a temperature of 60 °C and a pressure of 1 atm. Anode: methanol solution with NaOH (2.0 M at 1.0 ml min1); cathode: humidified oxygen (5.0 ml min1).

under different working conditions. They are the methanol feed   concentration C in Me;a , operating temperature (T), membrane thickness (dm), and volumetric flow rates of methanol (Ka) and oxygen (Kc). Moreover, the cell performance with oxygen/air is compared. The base case condition is summarized in Table 6, and the results from the calculations are discussed in the following subsections.

3.1. Methanol feed concentration To investigate the effect of methanol feed concentration, 0.5, 1.0, 2.0 and 4.0 M methanol solutions with NaOH are considered, and the polarization curves are shown in Fig. 4. It can be observed from Fig. 4(a) that the open circuit voltage (OCV) slightly decreases with the increment of methanol feed concentration, although not readily noticeable due to the small scale of Fig. 4(a). This result

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with methanol feed concentration is insignificant, and only the temperature effect on membrane conductivity is considered in this study. For 0.5, 1.0 and 2.0 M methanol solutions, the mass transport losses can be observed at high current densities, while it is insignificant for 4.0 M methanol solution. This results suggest that the reaction is not mass transfer limited once the methanol feed concentration becomes high enough. Similar trends were also reported in [59] for an AAEM-DMFC based on a different membrane.

Cell voltage, V

0.8

0.6

0.4

0.2 40 oC

23 oC

60 oC -1

0.0

0.1

0.2

0.3

0.4

Cell voltage, V

(a)

Current density, A cm-2

Increasing operating temperature (23 oC, 40 oC, 60 oC)

0.3

0.6

0.4

0.2

0.2

0.0

(a)

0.0

0.1

0.2

0.3

0.4

-2

Current density, A cm

0.1

0.25

0.0 0.0

0.1

(b)

0.2

0.3

0.4

-2

Current density, A cm

Cathode polarization loss 0.4

0.3 Ohmic loss 0.2

-1

0.1 ml min

-1

1.0 ml min

Methanol concentration in ACL, mol L-1

Crossover current density, A cm

Anode polarization loss

0.20

-1

5.0 ml min

0.15

0.10

0.05

0.00 0.0

(b)

0.1

Increasing operating temperature (23 oC, 40 oC, 60 oC)

0.0

(c)

0.0

0.1

0.2

0.3

0.4

-2

Current density, A cm

Fig. 6. Effect of operating temperature on (a) cell performance; (b) methanol crossover current density; and (c) voltage losses (polarization losses of anode and cathode, ohmic loss) when the cell operates at a pressure of 1 atm and temperatures of 23, 40 and 60 °C. Anode fuel: methanol solution with NaOH (2.0 M at 1.0 ml min1); cathode: humidified oxygen (5.0 ml min1).

corresponds to the fact that increasing the methanol feed concentration causes greater methanol crossover (Fig. 4(b)), and thus results in a larger polarization loss in the cathode (Eq. (12)), as shown in Fig. 4(c). On the other hand, the cell shows better performance as the current density increases at higher methanol feed concentration. Because increasing the methanol feed concentration leads to a higher ACL methanol concentration and a lower concentration loss in the anode (Fig. 4(c)). Moreover, the ohmic loss remains unchanged (Fig. 4(c)), because the water content variation

0.2

0.3

0.4

Current density, A cm-2

0.1

Crossover current density, A cm-2

-2

0.4

Voltage loss, V

0.1 ml min -1 1.0 ml min -1 5.0 ml min

0.8

0.0

0.4 -1

0.1 ml min

-1

1.0 ml min

-1

5.0 ml min

0.3

0.2

0.1

0.0 0.0

(c)

0.1

0.2

0.3

0.4

Current density, A cm-2

Fig. 7. Effect of volumetric flow rate of methanol solution on (a) cell performance; (b) methanol concentration in ACL; and (c) methanol crossover current density when the cell operates at a temperature of 60 °C and a pressure of 1 atm. Anode: methanol solution with NaOH (2.0 M at 0.1, 1.0 and 5.0 ml min1); cathode: humidified oxygen (5.0 ml min1).

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3.2. Membrane thickness To investigate the effect of membrane thickness, the thicknesses of 28, 40, 60, 100 and 150 lm are chosen, and the corresponding polarization curves are shown in Fig. 5. Fig. 5(a) shows that decreasing the membrane thickness produces better performance in the mid and high current density range, because the ohmic loss primarily depends on the membrane thickness (Eq. (8)). The crossover current density increases with the

-1

1.25 ml min

Cell voltage, V

0.8

-1

5.0 ml min -1 10.0 ml min

0.6

0.4

decrement of the membrane thickness (Fig. 5(b)), and correspondingly, the methanol concentration in anode and water concentration in cathode are decreased and increased with thinner membranes, respectively, due to the enhanced methanol and water crossover from anode to cathode (Fig. 5(c) and (d)). As a result, as shown in Fig. 5(e), for a thinner membrane, the ohmic loss is decreased, and the anode polarization loss is slightly increased because more methanol crosses to the cathode. For the cathode polarization loss (including the crossover loss), when the membrane thickness is decreased, the cathode polarization loss is increased in low current density range due to the enhanced methanol crossover; however, in mid and high current density range, the cathode polarization loss is decreased, because the methanol crossover becomes less significant (Fig. 5(b)), and more water from the anode can participate in the reaction in cathode (Fig. 5(d)). Fig. 5(a) and (e) even show that increasing the membrane thickness may cause significant mass transport loss in cathode, leading to lower limiting current density. To summarize, decreasing the membrane thickness generally improves the performance, although it also causes greater methanol crossover. 3.3. Operating temperature

0.2

The operating temperature is an important factor affecting the performance. Its effects on the cell performance, methanol crossover and voltage losses (polarization losses of anode and cathode, ohmic loss) are shown in Fig. 6. It can be noticed from Fig. 6(a) that

0.0 0.0

(a)

0.1

0.2

0.3

0.4

Current density, A cm-2

0.5

0.9

Cathode polarization loss

Anode polarization loss Ohmic loss

0.2 0.1

Increasing oxygen volume flow rate -1 (1.25, 5.0, 10.0 ml min )

0.0 0.0

(b)

0.1

0.2

0.3

Cell voltage, V

Voltage loss, V

0.4 0.3

Humidified oxygen feed Humidified air feed

0.8 0.7 0.6 0.5 0.4 0.3 0.2

0.4

Current density, A cm-2

(a)

0.00

0.04

0.08

0.12

0.16

0.20

Current density, A cm-2

26.4 Humidified air feed

22.8 21.6 1.2 0.0 0.0

(c)

Humidified pure oxygen feed

0.3

Decreasing oxygen volume -1 flow rate (10.0, 5.0, 1.25 ml min )

24.0

Voltage loss, V

Oxygen concentration -1 -3 in CCL, 10 mol L

0.4 25.2

Cathode polarization loss 0.2 Anode polarization loss 0.1

Ohmic loss 0.1

0.2

0.3

0.4

Current density, A cm-2

Fig. 8. Effect of volumetric flow rate of humidified oxygen on (a) cell performance; (b) voltage losses (polarization losses of anode and cathode, ohmic loss); and (c) oxygen concentration in CCL when the cell operates at a temperature of 60 °C and a pressure of 1 atm. Anode: methanol solution with NaOH (2.0 M at 1.0 ml min1); cathode: humidified oxygen (1.25, 5.0 and 10.0 ml min1).

0.0

(b)

0.00

0.04

0.08

0.12

0.16

0.20

Current density, A cm-2

Fig. 9. Effect of humidified oxygen/air on (a) cell performance; and (b) voltage losses (polarization losses of anode and cathode, ohmic loss) when the cell operates at a temperature of 60 °C and a pressure of 1 atm. Anode: methanol solution with NaOH (1.0 M at 1.0 ml min1); cathode: humidified oxygen/air (5.0 ml min1).

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in low current density range, the output voltage is slightly higher with a lower operating temperature, and as the current density increases, a higher operating temperature shows apparent improvement on the output voltage. This is caused by three changes when the operating temperature increases: more methanol crossover (Fig. 6(b)), enhanced electrode kinetics and lower membrane ohmic resistance (Fig. 6(c)), resulting in higher polarization loss in cathode (more methanol crossover), lower polarization loss in anode and lower ohmic loss. The improvement of cell voltage as the current density increases is a clear indication of enhanced electrode kinetics both in the anode and cathode. To summarize, a higher operating temperature enhances the electrode kinetics and membrane conductivity, although it also promotes methanol crossover.

3.7. Effect of CO2 bubbles Since the CO2 bubbles may hinder the methanol transport to the catalyst sites, and a correction for porosities of ADL and ACL is needed. Fig. 10 illustrates the effect of CO2 bubble on the effective porosities of ADL and ACL. Fig. 10(a) shows that the current density and operating temperature determine the significance of CO2 bubble effect. It can be observed that the effective porosities of ADL and ACL decrease with the current density, and the effect becomes minor as the current density increases, because the amount of CO2

0.56

3.6. Effect of oxygen/air Fig. 9 compares the effect of supplied oxygen and air. It can be observed from Fig. 9(a) that the cell shows better performance with oxygen, due to a smaller cathode polarization voltage loss shown in Fig. 9(b), resulted from a larger oxygen concentration in CCL. The ohmic loss and anode polarization voltage loss for the two cases are similar (Fig. 9(b)). Moreover, it should be noted that 1.0 M methanol solution with NaOH is considered for the comparison, because for the humidified air condition, the volumetric flow rate of 5.0 ml min1 for air is not suitable for the 2.0 M of supplied methanol solution (severe methanol crossover consumes too much oxygen).

Increasing operating temperature (23 oC, 40 oC, 60 oC)

Corrected ACL porosity

0.24

0.0

(a)

0.1

0.2

0.3

0.4

Current density, A cm-2

-5

3.0x10

60 oC

40 oC

23 oC

-5

Bubble radius, m

2.5x10

-5

2.0x10

-5

1.5x10

-5

1.0x10

-6

5.0x10

0.0 0.0

(b)

0.1

0.2

0.3

0.4

-2

Current density, A cm

-3

1.6x10

60 oC

-1

To investigate the effect of the volumetric flow rate of pure oxygen (fully humidified), the flow rates of 1.25, 5.0 and 10.0 ml min1 are compared in Fig. 8. It can be noticed from Fig. 8(a) that the effect of volumetric flow rate of oxygen on cell performance is similar to the volumetric flow rate of methanol solution: insignificant at high flow rates but enhanced when the flow rate is low. Fig. 8(b) shows the variations of voltage losses. It can be seen that the effect of oxygen flow rate on ohmic loss and anode polarization loss is minor, while the variation of cathode polarization loss shows the same trend with cell performance. These results can be attributed to the variation of oxygen concentration in CCL (Fig. 8(c)). The gas diffusion coefficient is much greater than the liquid diffusion coefficient, resulting in an insignificant change of oxygen concentration in CCL with the current density. Therefore, the oxygen diffusion limitation appears only when the oxygen flow rate is very low.

0.32

0.28

Bubble velocity, m s

3.5. Volumetric flow rate of oxygen

Porosity

3.4. Volumetric flow rate of methanol solution To investigate the effect of the volumetric flow rate of methanol solution, the flow rates of 0.1, 1.0 and 5.0 ml min1 are compared in Fig. 7. It can be seen from Fig. 7(a) that the variation of cell performance corresponding to the volumetric flow rate of methanol solution is insignificant at high flow rates, while this effect enhances when the flow rate is low due to the limited diffusive transport. The decrease of limiting current density with the volumetric flow rate is a clear indication of ineffective methanol mass transport, corresponding to the fact that the methanol concentration in ACL is reduced with the volumetric flow rate of methanol solution (Fig. 7(b)). The effect of volumetric flow rate of methanol solution on methanol crossover is similar to that on methanol concentration in ACL, which is becomes insignificant at high flow rates (Fig. 7(c)). Similar trends were also reported for a PEM-DMFC [60].

Corrected ADL porosity

0.60

-3

1.2x10

40 oC -4

8.0x10

23 oC -4

4.0x10

0.0

(c)

0.0

0.1

0.2

0.3

0.4

Current density, A cm-2

Fig. 10. (a) Effect of CO2 bubble on the effective porosities of ADL and ACL; (b) variation of bubble radius in ADL with current density; and (c) variation of bubble velocity in ADL with current density when the cell operates at temperatures of 23, 40 and 60 °C and a pressure of 1 atm. Anode: methanol solution with NaOH (2.0 M at 1.0 ml min1); cathode: humidified oxygen (5.0 ml min1).

H. Deng et al. / International Journal of Heat and Mass Transfer 74 (2014) 376–390

production and bubble radius strongly depend on the current density (Fig. 10(b)). However, as the current density increases, the bubble motion in ADL becomes faster (Fig. 10(c)) due to a linear correlation between bubble velocity and radius (Eqs. (52) and (53)), and weakens the effect of CO2 bubble on the porosities of ADL and ACL. Moreover, Fig. 10(a) shows that a higher operating temperature leads to less significant effect of CO2 bubble on the effective porosities of ADL and ACL, due to the enhanced removal rate of CO2 bubble (Fig. 10(c)). 3.8. Effect of cell orientation To investigate the effect of cell orientation on cell performance, the inclining angles (b) of 0°, 30°, 60° and 90° (0° means that the anode faces up, refer to Fig. 2) are compared in Fig. 11. It can be observed from Fig. 11(a) that a smaller value of b is preferred for a better cell performance, and this effect becomes more significant when b enlarges to 90°. The buoyancy is the only force devoted to the removal of CO2 bubble (Fig. 2), so that a larger value of b is associated with a slower motion of CO2 bubble, leading to the CO2 accumulation in ADL and ACL and hindering the methanol transport to the catalyst sites, and therefore a larger anode polarization voltage loss (Fig. 11(b)). It should be noted that when the inclining angle becomes greater than 90°, the buoyancy changes to a resistance rather than a driving force for the removal of CO2 bubble.

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4. Conclusion In this study, a one-dimensional two-phase analytical model has been developed for AAEM-DMFC, which considers the primary transport phenomena and electrochemical reactions. A reasonable agreement between the model prediction and previous experimental data in the literature is obtained. The effects of five operating and design parameters on the cell performance are investigated, including the methanol feed concentration, volumetric flow rates of methanol solution and oxygen, membrane thickness, and operating temperature. The oxygen/air effect and the effects of CO2 bubbles corresponding to different cell orientations are also analyzed. The methanol feed concentration, operating temperature and membrane thickness are the three variables that affect the cell performance most significantly. The effect of reactant flow rate is insignificant in high flow rate range, and this effect enhances when the flow rates are low. In low current density range, the cell shows better performance with lower methanol feed concentrations, while this trend reverses in high current density range. A similar trend is also found for the operating temperature. A thinner membrane leads to a higher methanol crossover; however, it yields better performance in mid and high current density range. Water is mass transfer limited once membrane thickness is high enough, resulting in the decrease of limiting current density. The carbon dioxide bubbles produced in anode are removed faster at higher operating temperatures. When the anode of the cell faces up, the best performance can be achieved. Inclining the cell leads to lower cell performance, and the performance degradation becomes more significant with larger inclining angles.

β=0°

0.8

β=30°

Conflict of interest

Cell voltage, V

β=60°

0.6

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, ‘‘An analytical model for alkaline membrane direct methanol fuel cell’’.

β=90°

0.4

0.2

Acknowledgments

0.0

(a)

0.0

0.1

0.2

0.3

0.4

This research is supported by the National Natural Science Foundation of China (Grant No. 51276121), the National Basic Research Program of China (973 Program) (Grant No. 2012CB932800), and the Natural Science Foundation of Tianjin (China) (Grant No. 12JCYBJC30500).

Current density, A cm-2

0.5 Cathode polarization loss 0.4

Voltage loss, V

References 0.3 Anode polarization loss 0.2 Ohmic loss 0.1 Decreasing β (90°, 60°, 30°, 0°)

0.0

(b)

0.0

0.1

0.2

0.3

0.4

-2

Current density, A cm

Fig. 11. Effect of cell orientation (b = 0°, 30°, 60° and 90°, 0° means that the anode faces up) on (a) cell performance; (b) voltage losses (polarization losses of anode and cathode, ohmic loss) when the cell operates at a temperature of 60 °C and a pressure of 1 atm. Anode: methanol solution with NaOH (2.0 M at 1.0 ml min1); cathode: humidified oxygen (5.0 ml min1).

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