Investigation of cell orientation effect on transient operation of passive direct methanol fuel cells

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 4 9 3 e6 5 0 7

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Investigation of cell orientation effect on transient operation of passive direct methanol fuel cells Guo Ting a, Jing Sun a,b, Hao Deng c, Xu Xie c, Kui Jiao c,*, Xuri Huang a,** a

Institute of Theoretical Chemistry, Jilin University, 2 Liutiao Rd, Changchun, 130023, China School of Computer Science, Jilin Normal University, 1301 Haifeng St, Siping, 136000, China c State Key Laboratory of Engines, Tianjin University, 92 Weijin Rd, Tianjin, 300072, China b

article info

abstract

Article history:

A transient model for passive direct methanol fuel cell (DMFC) is developed to investigate

Received 2 December 2015

the effect of cell orientation and operating condition. The results show that the passive

Received in revised form

DMFC with vertical orientation has better performance than the horizontal one, except the

18 February 2016

case of high current density, because a large amount of water produced in cathode is hard

Accepted 22 February 2016

to be removed in vertical orientation, which is easier for horizontal orientation due to

Available online 22 March 2016

gravity. The passive DMFC with horizontal orientation is sensitive to methanol crossover, and moderate current density or voltage is necessary to ensure high energy efficiency. The

Keywords:

anode micro-porous layer (MPL) plays an important role in reducing the rate of methanol

Passive direct methanol fuel cell

crossover by providing flow resistance. The MPL in cathode has a significant effect on water

Methanol crossover

transport by enhancing the water back-flow from cathode to anode, which prevents water

Micro-porous layer

removal. Therefore, the anode MPL and cathode MPL have different effects on horizontal

Cell orientation

orientation and vertical orientation. Additionally, the size of fuel tank can improve the

Fuel efficiency

energy density by providing more fuel, and the effect on fuel efficiency and energy effi-

Energy density

ciency is a bit obvious in vertical orientation than horizontal orientation. Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Direct methanol fuel cell (DMFC) has many advantages over conventional batteries: easier storage of liquid methanol fuel, higher energy density and cleaner recycling. These features make DMFC a promising power source for portable applications. The energy density of DMFC is up to 4800Whl
1in theory [1], but there is still challenge to increase the fuel and energy efficiencies, which attracted great attentions. Since active DMFCs need certain ancillary devices in operation, such as

pump and fan, making it complicated and unsuitable for portable applications, passive DMFCs with simpler design and operation are often considered to be a better choice [2e4]. In a passive liquid-feed DMFC, the fuel and oxygen supply is driven by concentration gradient (fuel supply may also be driven by gravity based on cell orientation), and design optimization is needed to ensure proper reactant delivery and product removal. Many experimental studies were carried out for this purpose to optimize the membrane thickness [5], electrode structure [6] and cell structure [7,8]. For example, Ward et al. [8] designed a tubular DMFC, and the power density was

* Corresponding author. Tel.: þ86 22 27404460; fax: þ86 22 27383362. ** Corresponding author. E-mail addresses: [email protected] (K. Jiao), [email protected] (X. Huang). http://dx.doi.org/10.1016/j.ijhydene.2016.02.114 0360-3199/Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

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Nomenclature a A Alg C Cg Cp E F h hlg I IP j K k kH _ m M MOR n nd N ORR Pc R s S t T u v

V x

Water activity Active reaction area, m2 Interfacial specific area between liquid and gas phase, m
1 Molar concentration, mol m
3 Gas constant Specific heat capacity, J kg
1 K
1 Effective activation energy, J mol
1 Faraday's constant Height, m; heat transport coefficient, W m
2 K
1; latent heat, J kg
1; horizontal orientation Interfacial transfer rate constant for methanol, m2 s
1 Current density, A m
2 Parasitic current density results from methanol crossover, A m
2 Reaction rate, A m
3; mass flux of reaction, kg m
2 s
1 Permeability of porous material, m2 Thermal conductivity, Wm
1 K
1; relative permeability Henry's constant Source term of liquid or gas mixture, kg m
3 s
1 Molecular weight, kg mol
1 Methanol oxidation reaction Amount of substance, mol Electro-osmotic drag coefficient Mol flux, mol m
2 s
1 Oxygen reduction reaction Capillary pressure, Pa Universal gas constant, 8.314 J K
1 mol
1 Liquid saturation Source terms, mol m
3 s
1; entropy, J mol
1 K
1 Time, min Temperature, K Velocity, m s
1 Vertical orientation Electrical potential, V Position or coordinate, m; or mole fraction

Greek letters a Kinetic transfer coefficient g Reaction order; water phase change rate, s
1 Thickness of porous layers, m d Porosity ε Voltage loss, V; fuel consumption efficiency h Contact angle,  q

significantly improved. For passive methanol supply, the methanol crossover is difficult to control and always considered to be the key to improve the fuel efficiency. Moreover, the micro-porous layer (MPL), acting as a methanol barrier in anode, is often considered to be effective in reducing the methanol crossover [9e11], and the MPL in cathode may also facilitate water transport from cathode to anode [12e14]. In addition, it was also experimentally shown that the vertical and horizontal

k l m r s

f u

Electrical conductivity, S m
1 Water content in ionomer Dynamic viscosity, kg m
1 s
1 Density, kg m
3 Surface tension coefficient, N m
1; Electrical potential, V Volume fraction of ionomer in catalyst layer

Subscripts and superscripts a Anode air Air ACL Anode catalyst layer ADL Anode diffusion layer AMPL Anode micro-porous layer c Cathode CCL Cathode catalyst layer CDL Cathode diffusion layer CMPL Cathode micro-porous layer ch Channel con Convection cond Condensation cross Crossover diff Diffusion drag Electro-osmotic drag ele Electronic equil Equilibrium evap Evaporation FT Fuel tank g Gas phase i Components i ion Ionic in Inlet condition l Liquid phase LD Liquid water-dissolved water phase change M Liquid methanol MEM Membrane MV Methanol vapor MW Membrane water op Operation condition reac Reaction ref Reference rev Reversible rib Rib ro Room condition sat Saturation vl Vapor to liquid phase change WV Water vapor

cell orientations may lead to significantly different operating characteristics and performance [15e19]. The multiphase transient transport processes are affected by cell orientation duo to gravity and buoyancy effects, such as the transport of CO2 bubble driven by buoyancy [20,21]. It was also experimentally found that passive DMFC with vertical orientation has longer discharging time and higher output voltage than horizontal orientation in low current density operation [22e25].

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Mathematical models were developed for passive DMFC to understand the heat and mass transfer processes, and many of them focused on steady-state operation [26e28]. In some models, special attentions were paid to the effect of MPL [29e32]. However, for a passive DMFC, since the methanol in fuel tank is continuously consumed, everything changes during operation, therefore, the important performance parameters, such as the fuel efficiency, energy efficiency and energy density, need to be evaluated for the whole operation process (fuel tank from full to empty), and transient models are needed [33e39]. In such transient models, the effects of electrode design, operating temperature, voltage, current density, methanol feeding concentration and other parameters were comprehensively studied [33e39]. However, another important factor, the cell orientation, which was experimentally found to have great impacts on the performance, was largely ignored in previous transient models. As mentioned above, to understand the cell orientation effect on the heat and mass transfer characteristics and

performance of passive DMFC, a transient multiphase model for passive liquid-feed DMFC incorporating the cell orientation effect is developed in this study. In addition, the role of anode and cathode MPLs, as well as the effect of operation conditions, are discussed with different cell orientations.

Model description Computational domain Two cell orientations, horizontal and vertical, are considered in this two-dimensional model, as shown in Fig. 1. The computational domain includes the methanol fuel tank (FT), anode diffusion layer (ADL), anode micro-porous layer (AMPL), anode catalyst layer (ACL), membrane (MEM), cathode diffusion layer (CDL), cathode micro-porous layer (CMPL) and cathode catalyst layer (CCL). The horizontal orientation means that the anode faces upward, and the gravity becomes

Vertical orientation Feed inlet

Horizontal orientation

Methanol Fuel Tank

Current Collectors

ADL AMPL CMPL CDL

h0

Air breathing

h0

Methanol Fuel Tank

Feed inlet

ADL

Ribs

Ribs

AMPL ACL Membrane CCL CMPL

Y

Y X

CDL

X

Ribs

a.

Current Collectors

Air breathing

Ribs

b.

ACL Membrane CCL

Current Collectors

Current Collectors

ADL AMPL ACL CCL CMPL CDL Membrane

Anode rib

Cathode rib

Anode channel

Cathode channel

y Symmetry boundary

c.

x

Fig. 1 e Schematic of a passive liquid-feed DMFC in horizontal orientation (a); in vertical orientation (b); and the computational domain (c).

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the direct driving force for methanol supply. The vertical orientation means that the fuel tank is placed on the side of cell. Oxygen is taken from ambient air passively into the cathode by diffusion. The cell geometries and operating conditions are shown in Table 1, and the correlative physicochemical properties are given in Table 2 [29,31,35,36,40e48].

NM;flux ¼

In ACL, the kinetics of methanol oxidation reaction (MOR) is [45,49].


Eleven governing equations are solved to describe the mass and heat transfer processes. The governing equations are listed in Table 3, and the corresponding mass and energy source terms are shown in Table 4.

ref

ja ¼ ja e


 I KMEM DPl;c
a CM NM ¼
Deff M;MEM VCM þ nd;M
F ml dMEM

(1)

εsCM

!ga

εsCH2 O þ ð1
sÞεCWV þ uCMW

Cref M

!

Cref H2 O

(4)

ref

jc ¼ jc e

(2)

The total flux of methanol consumption includes two parts: electrochemical reaction and methanol crossover, which is expressed by:

Value 2.0  10
4

m

dMPL

0.2  10
4

m

dCL dMEM

0.1  10
4 1.75  10
4

m m

dch drib h0 Top Tro Pin g Cin M

5  10
4 5  10
4 1.0  10
3 303.15 293.15 P0 2000

m m m K K Pa mol m
3

Cin MV

Csat MV

mol m
3

Cin WV;a

Psat WV RT

mol m
3

Cin O2

0:21 

Cin WV;c

Psat WV RT

mol m
3

sa, sc

1.0, 0.1

e

Pg RT

Cref O2

!gc

a
e

aF RT hc



a þe

cF RT hc

!

IP ¼ 6FNM

(5)

(6)

where IP and NM represent the parasitic current density and the total molar flux of methanol crossover (Eq. (1)).

The water transport in the porous layers is driven by capillary pressure [45,50], which is defined as the difference between liquid pressure and gas pressure: Pc ¼ Pg
Pl ¼ scosqðε=KÞ0:5 JðsÞ JðsÞ ¼

(7)

1:417ð1
sÞ
2:12ð1
sÞ2 þ 1:263ð1
sÞ3 0 < qc  90+ 1:417s
2:12s2 þ 1:263s3 90+ < qc  180+ (8)

The capillary pressure is assumed to be continuous at the interface of two distinct porous layers due to the continuous of liquid pressure and gas pressure. As a result, liquid saturation jump [41,31] occurs at those interfaces (e.g. AMPL and ADL). Pc; ADL ¼ Pc; AMPL


Csat WV

ð1
sÞεCO2

Unit

dDL






1 1 T
Tref

The permeate methanol is oxidized in CCL, generating a socalled ‘parasitic’ current density:

 Table 1 e Cell geometric dimensions and operation parameters. Symbol





ERc

Liquid saturation jump


 I r KMEM DPl;c
a þ nd;H2 O
l F ml MH2 O dMEM

Diffusion layer thickness Microporous layer thickness Catalyst layer thickness Membrane thickness (Nafion 117) Channel width Rib width Height of fuel tank Operation temperature Room temperature Cathode inlet pressure Inlet methanol concentration at anode Inlet methanol vapor concentration at anode Inlet water vapor concentration at anode Inlet oxygen concentration at cathode Inlet water vapor concentration at cathode Inlet liquid saturation at anode or at cathode



1 1 T
Tref

  aa F ac F  e RT ha
e RT ha




The polymer electrolyte membrane allows for the transport of dissolved methanol and water. Generally, dissolved water and methanol permeate through membrane depends on diffusion, pressure gradient (convection) and electro-osmotic drag (EOD). The methanol crossover is assumed totally oxidized in CCL [13,44]. The flux of methanol and dissolved water through the membrane is expressed as follows:

Parameters



ERa

In CCL, the oxygen reduction reaction (ORR) gives [45,49]:

Transport in electrolyte

NMW ¼

(3)

Electrochemical kinetics and current balance

Governing equations


Deff MW VCMW

ia þ NM 6F

mol m
3


s cos qADL

εADL KADL

(9) 0:5


JðsADL Þ ¼ s cos qAMPL

εAMPL KAMPL

0:5 JðsAMPL Þ

(10)

Boundary and initial conditions As shown in Fig. 1, the boundary conditions of the two orientations are defined. For the horizontal orientation, the gravity is considered as a driving force for feeding methanol fuel, the detailed boundary condition can be found in our previous work [36]. The mainly difference between horizontal orientation and vertical orientation is the liquid pressure at anode inlet. While for vertical orientation, the height of methanol fuel tank, ht,y, is related to the reaction time and the location of anode inlet, the liquid pressure is the highest at the end of anode inlet, and lowest at the top of anode inlet:

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Pl ¼ P0 þ rght;y

(11)

The liquid saturation at anode inlet remains 1.0 (sin a ¼ 1:0) [43] in both two orientations, and the corresponding gas pressure is different according to Eq. (7). At the air inlet in cathode, the boundary condition of vertical orientation is the same as that of horizontal orientation, and the standard atmospheric condition (1 atm) of gas pressure, the constant value (sin c ¼ 0:1) [29] of liquid saturation, the different gas concentrations according to the standard atmospheric condition of fully humidified air. At the cathode air inlet, nature convection condition is defined (303.15 K of operating temperature, 10 K higher than the environmental

temperature, 293.15 K of the environmental temperature and the convection heat transfer coefficient is 10 W m
2 K
1). The cell operates at constant current density or voltage, and the setting of the vertical orientation is same as that in horizontal operation for the electro and ion transport. The steady-state simulation results at open circuit voltage are used as the initial conditions for the transient calculations.

Numerical implementation The two-dimensional computational domain includes 7000 grid cells. There are 10 cells across the ADL, AMPL, ACL, MEM,

Table 2 e Physicochemical properties. Parameters

Symbol

Porosity, permeability, contact angle of DL [40,29,31] Porosity, permeability, contact angle of MPL [36,41,41] Porosity, permeability, contact angle of CL [29,42,43] Nafion volume fraction in CL Permeability of MEM [42] Methanol diffusion in Nafion [44]

εDL, KDLqDL εMPL, KMPL, qMPL εCL, KCL, qCL u KMEM DM,MEM

Methanol diffusion in liquid water [42] Methanol vapor diffusion in gas [45]

DM,l DMV,g

Water vapor diffusion in gas [45]

DWV,g

O2 diffusion in gas [45]

DO2 ;g

Value 0.8, 1.0  10
12 m2, 0.4, 2.5  10
13 m2, 0.4, 2.0  10
14 m2, 0.1 2.0  10
18 m2
2436

110 140 95 

1 1 333
T

m2 s
1 4:9  10
10 e 1.58  10
9e0.02623(T
298) m2 s
1
6:954  10
6 þ 4:5986  10
8 T þ 9:4979  10
11 T2
2:334 T 2:56  10
5 307:15 m2 s
1
1:775  10
5

1:823
1


1

Viscosity of gas phase [46] Viscosity of liquid phase [46] Electro-osmotic drag coefficient of water [45]

mg ml nd;H2 O

2.03  10 kg m s 4.05  10
4 kg m
1 s
1

Electro-osmotic drag coefficient of methanol [45]

nd,M

nd;H2 O xM

Evaporation, condensation rate constant for water [43] Interfacial transfer rate constant for methanol [42] Specific interfacial area between liquid and gas [42] Heat transfer coefficient of nature convection [36] Gas constant for carbon dioxide [47] Henry law constant for CO2 [47]

gevap, gcond hlg Alg h Cg kH;CO2

Henry law constant for methanol [45] The saturation pressure of methanol vapor [48]

kH,M log10 Psat WV

m2 s
1

T 273:15


5

m2 s
1

2:5 22 l

1 s
1 0.001 m
2 s
1 105 m
1 10 W m
2 K
1 2400
Cg

!

1 1 T
Tref

0:8317e 0.096e0.0451(T
273.15)
2:1794 þ 0:02953ðT
273:15Þ
9:1837  10
5 ðT
273:15Þ þ 1:4454  10
7 ðT
273:15Þ Pa

Psat MV Vrev

kH,MxM Pa

Anode and cathode transfer coefficient [35] Anode reference exchange current density

aa, ac

0.5, 0.5

Cathode reference exchange current density

jc

The saturation pressure of methanol vapor [42] Theoretical voltage [43]

in 1:214
1:4  10
4 ðT
298:15Þ
0:5  RT 6F  logðPg Þ V

ref

ja

3:8  105 e

Reaction order Reference concentration methanol, water and oxygen Effective activation energy of MOR and ORR [36] Surface tension [42] Equivalent weight of ionomer [43] Liquid water density [42] Membrane density [41] Latent heat of water evaporation [47] Latent heat of methanol evaporation [47] Standard entropy change of MOR and ORR [47]

ref

ga, gc ref ref Cref M , CH2 O , CO2

Ea, Ec s EW rl rMEM DhWV DhMV DSMOR, DSORR



Ea R

 1 1 353
T



Ec R



A m
3

1 1 353
T

9:0  105 e A m
3 0.5, 1.0 100, 56000, 36.5 mol m
3 35570, 73200 J mol
1 0.0644 N m
1 1.1 kg mol
1 1000 kg m
3 1980 kg m
3 2.094  106 J kg
1 1.403  106 J kg
1 16.66,
65.24 J mol
1 K
1

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Table 3 e Governing equations. Conservation equations V$ðkeff ele Vfele Þ þ Sele ¼ 0 V,ðkeff ion Vfion Þ þ Sion ¼ 0

Electron Proton Liquid pressure Gas pressure Methanol in liquid Methanol in vapor

v vt ðrl εsÞ


 l _ ¼ V$ rl Kk ml VPl þ ml

v vt ðrg εð1


sÞÞ ¼ V$ rg



v vt ðεsCM Þ v vt ðεð1

¼
V$

!

Kkg mg VPg

_g þm





eff l
Kk ml VPl CM
DM VCM !


sÞCMV Þ ¼
V$




Kkg mg VPg

þ SM !

CMV
Deff MV VCMV

þ SMV

!

Water vapor

v vt ðεð1


sÞCWV Þ ¼
V$




Kkg mg VPg

! CWV
Deff WV VCWV

!

Oxygen

v vt ðεð1


sÞCO2 Þ ¼
V$




Kkg mg VPg

CO2
Deff O2 VCO2

þ SO 2

!

Carbon dioxide

v vt ðεð1


sÞCCO2 Þ ¼
V$

Membrane water content

v vt ðuCMW Þ

Energy

v vt ðεsrl Cp;l T

CCL, CMPL and CDL along the x direction, respectively, and 100 along the y direction. We have already tested grid independency for agreement. A model code for governing equations and boundary conditions is self-written by C language, and then use the software Fluent to solve the conservation equations for model implementation. The second order upwind scheme is used to solve the conservation equations. The iteration criterion for the converged results at each time step is 10
8 for all the variables, with a 0.1 s time step size.




Kkg mg VPg

þ SWV

!

CCO2
Deff CO2 VCCO2

! þ SCO2

¼ V$ðDeff MW VCMW Þ þ SMW þ εð1
sÞrg Cp;g TÞ þ Vðεsrl Cp;l ul T þ εð1
sÞrg Cp;g ug TÞ ¼ V,ðkeff VTÞ þ ST

The energy efficiency [51,52] is defined as the useful energy divided by the total theoretical amount of energy. Z IVðtÞdt henergy ¼

ðh0 C0
ht Ct ÞLHVM

(15)

where LHVM is the lower heating value of methanol, LHVM¼6.381  105 J mol
1, and V(t) is the voltage. It is noted that the passive DMFC is sensitive to operation conditions, especially the cell operation orientations, the details are presented below.

Results and discussion Effect of cell orientations To validate the transient model of passive DMFC, the polarization curves and transient cases with different orientations comparing the present model simulation results and the experimental data in Refs. [22], are shown in Fig. 2. The predicted results reasonably agree with the experimental results. Four major parameters are examined to evaluate the performance of the fuel cell: power density, methanol usage efficiency (husage), fuel efficiency (hfuel), energy efficiency (henergy) and energy density, respectively. To relate the amount of fuel used for electrochemical reaction at each time step, the methanol usage efficiency [33,51,52] is defined as: husage ¼

SM;reac SM;cross þ SM;reac þ SM;vl

(12)

The fuel efficiency [51,52] is used to measure the amount of fuel used for useful energy in total: Z hfuel ¼

jM ¼

jM dt ðh0 C0
ht Ct ÞMCH3 OH

IMCH3 OH 6F

(13)

(14)

In this section, the role of cell orientation (horizontal and vertical) is examined to investigate its effects on the species transport and cell performance. As shown in Fig. 3a, the passive DMFC with horizontal orientation always has higher power density, and it is more apparent at higher current densities. A lower current density always corresponds to a longer operating time. The passive DMFC with horizontal orientation shows better discharging performance at high current densities. With a decreased current density, the methanol fuel consumption rate decreases, and the passive DMFC with vertical orientation has longer discharging time. With a higher current density, the methanol crossover rate is lower due to more methanol fuel usage for electrochemical reaction, and the amount of methanol crossover with horizontal orientation always exceeds that of vertical orientation (Fig. 3b and c). The variation of oxygen concentration in CCL and water outlet flux are shown in Fig. 3d and e, the oxygen concentration is higher at a lower current density with vertical orientation (due to stronger natural convection), and the produced water is easy to be removed, which make the passive DMFC with vertical orientation last longer. Due to the effect of gravity on methanol supply, the passive DMFC with

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Table 4 e Mass and energy source terms for governing equations. Parameters

Expression

Effective diffusion coefficient of methanol (m2 s
1) Deff M

Effective diffusion coefficient of species (m2 s
1)

General generation rate of mass in gas phase (kg m
3 s
1)

Mole generation rate of species (mol m
3 s
1)

8 D ε1:5 s1:5 > > > M;l > > < ðε þ uÞ ¼ ε 1:5 1:5 þ u > > ðD ε s Þ ðDM;MEM u1:5 Þ > M;l > > : DM;MEM

AMPL; ADL ACL MEM

1:5 1:5 Deff i;g ¼ Di;g ε ð1
sÞ i : O2 ; WV; MV; CO2 8 ðADL AMPLÞ
MH2 O SWV ; > > < MH2 O ð
SWV
SLD Þ; ðACLÞ _l¼ m ð
SWV
SLD Þ; ðCCLÞ M > > : H2 O ðCDL CMPLÞ
MH2 O SWV ; 8 M S þM S ; ðADL AMPLÞ H O WV M MV > 2 > > > > > j > a < MH2 O SWV þMM SMV þMCO2 ; ðACLÞ 6Fð1 þ kH;CO2 Þ _g¼ m > > > MH O SWV þMO SO þMCO SCO ; > ðCCLÞ 2 2 2 2 2 > > > : MH2 O SWV ; ðCDL CMPLÞ 8
S ; ðADL AMPLÞ MV < SM ¼ j :
a
SMV
S drag;M þ Sdiff;M þ Scon;M ; ðACLÞ 6F Psat
P

SMV ¼ Alg hlg sð1
sÞ MVRT MV ; ðADL AMPL ACLÞ 8 > PWV
Psat > WV > 
; ðPWV > Psat <
gcond εð1
sÞ WV Þ ADL AMPL ACL RT SWV ¼ CDL CMPL CCL > > PWV
Psat >
g WV : ; ðPWV < Psat evap εs WV Þ RT 8r MEM > ðlACL
lequil Þ; ACL < EW SLD ¼ > : rMEM ðlCCL
lequil Þ; CCL EW j j Sdrag;H2 O ¼ nd;H2 O Fa , Sdrag;M ¼ nd;M Fa Sdiff;H2 O ¼ Deff MW

ACL CCCL MW
CMW dMEM dCL ,

CCL ACL rl KMEM Pl
Pl

Electron and proton generation rate (A m
3)

Heat generation rate (W m
3)

Sdiff;M ¼ Deff M

ACL CCCL M
CM dMEM dCL

PCCL
PACL

l l Scon;H2 O ¼ MH O ml dMEM dCL , Scon;M ¼ KMEM ml dMEM dCL CM 2 8 8 IP > <
jc ; CCL < CCL 4F SO 2 ¼ SCO2 ¼ 6Fð1 þ kH;CO2 ÞdCL : > : 0; CMPL; CDL 0 CMPL CDL 8 j a > > > SLD
6F
Sdrag;H2 O þ Sdiff;H2 O þ Scon;H2 O ; ðACLÞ > > > > < j SMW ¼ ðnd;H2 O;CCL
nd;H2 O;ACL Þ a ; ðMEMÞ > F > > > > > > : SLD þ jc
Ip þ Sdrag;H O
Sdiff;H O
Scon;H O ; ðCCLÞ 2 2 2 6F 3FdCL 8 8 ja ; ðACLÞ ja ; ðACLÞ > > > > > > < < Ip Ip Sion ¼
jc þ ; ðCCLÞ Sion ¼
jc þ ; ðCCLÞ > > d dCL CL > > > > : : 0; ðOthersÞ 0; ðOthersÞ 8 > I2 > >
SWV DhWV
SMV DhMV þ eff ; ðADL AMPLÞ > > > ss > > > > 
> > I2 I2 T > > > > ð
SWV
SLD ÞDhWV
SMV DhMV þ eff þ eff þ ja ha
DSMOR 6F ; ðACLÞ > ss sMEM > > > > > < I2 ; ðMEMÞ ST ¼ eff > > sMEM > > > 
> > > Ip DSMOR T I2 I2 T > > ð
RWV
SLD ÞDhWV þ
; ðCCLÞ þ eff þ jc hc
DSORR > eff > 4F 6F dCL > ss sMEM > > > > > > I2 > > > :
RWV DhWV þ eff ; ðCDL CMPLÞ ss

horizontal orientation always has lower methanol efficiency (due to higher methanol crossover), which is shown in Fig. 3f. As shown in Fig. 4, the cell operates at constant voltages of 0.2 V, 0.3 V and 0.4 V. Compared with the constant current

density cases, the slope of the power density curves change more smoothly for all the cases, the power density at the end of discharging decreases with the increment of cell voltage. The vertical cases always have longer discharging time

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Fig. 2 e Comparison of the present numerical prediction and the experimental data [22] in horizontal and vertical orientation with methanol feed concentrations of 2 M. The cell operates at 303 K and 1 atm with 5.55 £ 10¡2 m height of fuel tank. (a) Polarization curves and (b) transient cell voltage with a constant current density of 22.2 mA cm¡2 and 33.3 mA cm¡2 in horizontal orientation; (c)transient cell voltage with a constant current density of 22.2 mA cm¡2 and 33.3 mA cm¡2 in vertical orientation.

because of the lower methanol crossover rate. Generally, the characteristics of mass transport are greatly influenced by the cell operation orientations, and also have similar trend by increasing the current density or decreasing the voltage. Fig. 5 shows the comparison of cell performance with different orientations. For the constant current density cases, the highest fuel efficiency is achieved at 30 mA cm
2 in horizontal orientation, and the highest energy efficiency and energy density are both achieved at 10 mA cm
2 in vertical orientation. While for the constant cell voltage cases, all the important parameters achieve the highest values under vertical operation condition (the highest fuel efficiency is 80.43% with 0.2 V; the highest energy efficiency and energy density are 36.04% and 3.38  108 J m
3 with 0.3 V, respectively). Increasing the current density or deceasing the voltage are able to increase the methanol usage, but shorten the working

time and lead to more methanol fuel left in the storage (decrease the fuel efficiency lower according to Eq. (13)). However, a moderate current density and cell voltage make the cell achieve the highest energy efficiency and energy density by keeping a longer operation time and more useful energy. It is worth noting that the vertical orientation always performs better than the horizontal orientation. Fig. 6 shows the transport processes driving methanol crossover versus time at 20 mA cm
2. The flux of methanol crossover in different orientations both decrease almost linearly during operation; the diffusion transport and electroosmotic drag play the same important role in methanol crossover, and the value in vertical orientation is lower than horizontal orientation; the convection methanol transport has little effects on methanol crossover in both vertical orientation and horizon orientation. So it is obvious that the

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Fig. 3 e Evolution of (a) power density; (b) methanol crossover through membrane; (c)methanol concentration in ACL; (d) oxygen concentration in CCL; (e) water outlet flux and (f) methanol efficiency with different current densities in horizontal and vertical orientations. The cell operates at 303 K and 1 atm with 2 M initial methanol feed concentration and 1 £ 10¡3 m height of fuel tank.

methanol usage for electrochemical reaction in vertical orientation is higher than horizontal orientation. The evaporation rate of vertical orientation is higher than horizontal orientation with stronger nature convection, although the evaporation rate is relatively low with low methanol concentration. As shown in Fig. 7, the different flow behaviors with different orientations lead to different methanol

distribution. The liquid is driven by inlet liquid pressure and the electrochemical reaction consumption. It is interesting to note that the flow direction is from the end of inlet to the bottom due to the higher liquid pressure at the end of inlet in the vertical orientation, and which is almost paralleled in the horizontal orientation. The distribution of methanol concentration is similar to the liquid flow direction and the

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Fig. 4 e Evolution of (a) power density; (b) methanol crossover through membrane; (c) methanol concentration in ACL; (d) oxygen concentration in CCL; (e) water outlet flux and (f) methanol efficiency with different cell voltages in horizontal and vertical orientations. The cell operates at 303 K and 1 atm with the initial operation condition of 2 M initial methanol feed concentration and 1 £ 10¡3 m height of fuel tank.

methanol concentration in ADL, AMPL and ACL is gradually diminishing.

Effect of MPL in different orientations For the comparison of the effects of MPL with different orientations, four cases are defined: ‘acMPL’, ‘aMPL’, ‘cMPL’ and

noMPL. ‘acMPL’ stands for both anode and cathode MPL and ‘noMPL’ means that no MPL is used. The ‘aMPL’ and ‘cMPL’ have anode MPL and cathode MPL, respectively. Fig. 8 depicts the response time of power density with different cell structures in horizontal and vertical orientations. For the horizontal cases, the ‘acMPL’ case has the similar performance to the ‘aMPL’ case; and the discharging

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cathode MPL can decrease the methanol convective transport, the effects is not obvious. While for the vertical cases, the ‘cMPL’ case achieves the worst cell performance with shorter discharging time and higher methanol crossover rate; the ‘aMPL’ case performs a little better than the ‘noMPL’ case; the ‘acMPL’ case has the best performance with the longest discharging time and lowest methanol crossover rate. Because the water produced in cathode is hard to be removed, which is the main problem affecting the cell performance in vertical orientation. The anode hydrophobic MPL mitigates the methanol crossover successfully, and the cathode MPL prevents water outlet by enhancing the water back-flow from the cathode to anode. Generally, the performance of passive DMFC with anode MPL shows better performance with higher fuel efficiency, energy efficiency and energy density, due to the slightly higher voltage and similar operation time for both horizontal and vertical orientations.

Effect of methanol feeding condition in different cell orientations

Fig. 5 e Comparison of current density and voltage results on fuel efficiency, energy efficiency and energy density in horizontal and vertical orientations. The cell operates at 303 K and 1 atm with the initial operation condition of 2 M initial methanol feed concentration and 1 £ 10¡3 m height of fuel tank.

time of ‘noMPL’ case is a little shorter than ‘cMPL’ case. The main reason is that the anode MPL plays an important role in decreasing the rate of methanol crossover by an increased resistance at the DL/MPL or MPL/CL interface, although the

The effect of methanol feeding concentration on cell performance is shown in Fig. 9. It is obvious that the cell voltage and discharging time increase with the increment of methanol concentration. The discharging time of 3M case in vertical orientation is similar to 4M case in horizontal orientation (Fig. 9a), which shows the significance role of cell operation orientation. With an increasing methanol concentration, the methanol crossover is more serious, and the methanol efficiency decreases (Fig. 9b and c). However, the methanol efficiency in vertical orientation is always higher than that in horizontal orientation. The energy density is the highest for the 4M case in vertical orientation. It is also noted that the highest energy efficiency is about 12.3%, which is much lower than the energy efficiency of 48.4% (2M case in vertical orientation) due to the deviation of working power density from theoretical energy. Fig. 10 shows the effects of the fuel tank height on different cell operation orientations. The liquid pressure in anode inlet is controlled by the fuel tank height, which has different

Fig. 6 e Evolution of different mechanisms of methanol crossover through membrane in horizontal orientation (a) and vertical orientation (b). The cell operates at 303 K and 1 atm with 2 M initial methanol feed concentration and 1 £ 10¡3 m height of fuel tank at 20 mA cm¡2.

Fig. 7 e Distributions of velocity vector of liquid in ADL and methanol concentration in ADL/AMPL/ACL in horizontal orientation (a) and vertical orientation (b). The cell operates at 303 K and 1 atm with 2 M initial methanol feed concentration and 1 £ 10¡3 m height of fuel tank at 20 mA cm¡2.

Fig. 8 e Effect of different cell structures (acmpl, ampl, cmpl and nompl) on (a) evolution of power density; (b) evolution of methanol crossover; (c) evolution of methanol efficiency and (d) fuel efficiency, energy efficiency and energy density. The cell operates at 303 K and 1 atm with the initial operation condition of 2 M initial methanol feed concentration and 1 £ 10¡3 m height of fuel tank at 20 mA cm¡2 in horizontal and vertical orientations.

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Fig. 9 e Effect of methanol concentration in horizontal and vertical orientations on evolution of (a) power density; (b) methanol crossover through membrane(c) methanol efficiency and (d) fuel efficiency, energy efficiency and energy density. The cell operates at 303 K and 1 atm with the initial operation condition of 2 M initial methanol feed concentration and 1 £ 10¡3 m height of fuel tank.

effects on different orientation. Increasing the fuel tank height makes the discharging time longer. The horizontal orientation shows slightly higher voltage and shorter discharging time than that of vertical orientation due to the lower voltage loss. The fuel efficiency and energy efficiency

have no obvious change in the horizontal orientation, but slightly increase in vertical orientation. The energy density increases significantly for both orientations. Above all, the fuel tank height has more obvious effects in the vertical orientation.

Fig. 10 e Effect of the height of fuel stank in horizontal and vertical orientations on (a) evolution of power density and (b) fuel efficiency, energy efficiency and energy density. The cell operates at 303 K and 1 atm with the initial operation condition of 2 M initial methanol feed concentration and 1 £ 10¡3 m height of fuel tank at 20 mA cm¡2.

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Conclusion In this work, we present a transient multiphase model for passive DMFC to investigate the effect of cell orientation and operation condition. It is found that the cell orientation has great effects on cell performance. The passive DMFC with horizontal orientation performs better at high current density due to lower methanol crossover. With the decrement of current density, more fuel is wasted for methanol crossover, and the discharging time of the passive DMFC with vertical orientation exceeds the horizontal orientation gradually. The fuel efficiency is improved by appropriately increasing the current density or decreasing the cell voltage because of the more fuel usage for electrochemical reaction. The highest energy efficiency and energy density are obtained at moderate current density or cell voltage. The anode MPL plays an important role in improving the fuel efficiency, energy efficiency and energy density by decreasing the methanol crossover. The cathode MPL could enhance the water back-flow from cathode to anode, which causes the difficulty to remove the product water in cathode. Therefore, the anode MPL is more important to improve cell performance, and the MPL in cathode leads to the worst performance of the passive DMFC with vertical orientation. With an increased methanol feeding concentration, the performance is improved in vertical orientation, and the 3M case in vertical orientation is similar to the 4M case in horizontal orientation due to serious methanol crossover in horizontal orientation. Generally, the energy density is increased with an increasing methanol concentration for all the cases, and both the fuel efficiency and energy efficiency are decreased. The size of fuel tank has more obvious effects on cell performance in vertical orientation than horizontal orientation.

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

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