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Numerical investigation on double gas diffusion backing layer functionalized on water removal in a proton exchange membrane fuel cell
Energy xxx (2016) 1e10
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Numerical investigation on double gas diffusion backing layer functionalized on water removal in a proton exchange membrane fuel cell Im Mo Kong a, Aeri Jung b, Young Sang Kim c, Min Soo Kim b, * a b c
Powertrain Research Center, Korea Automotive Technology Institute, Gwangju 62207, South Korea Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, South Korea Department of Eco-machinery System, Korea Institute of Machinery & Materials, Daejon 34103, South Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 October 2015 Received in revised form 18 October 2016 Accepted 16 November 2016 Available online xxx
Since flooding is a limiting factor of cell performance in a proton exchange membrane fuel cell (PEMFC), it is important to remove produced water effectively from GDL. In this study, a multi-layer GDL containing single micro porous layer (MPL) and double gas diffusion backing layer (GDBL) was introduced as a practical design and the effect of porosity and/or hydrophobicity of GDBL on water removal was investigated with one-dimensional steady-state model based on a capillary pressureesaturation relationship. The results shows that double GDBL with different porosity in a positive direction (GDBL with lower porosity near the MPL and GDBL with higher porosity near the flow channel) and/or different hydrophobicity in a negative direction (more hydrophobic GDBL near the MPL and less hydrophobic GDBL near the flow channel) enhances the water removal ability of the GDL compared with uniform single GDBL. Based on the results, the property arrangements of double GDBL were optimized to minimize the amount of liquid water remaining in GDL. It is expected that the amount of produced water remaining in ML-GDL can be reduced about 9.2% with optimized porosity arrangement and 5.6% with optimized hydrophobicity arrangement. © 2016 Published by Elsevier Ltd.
Keywords: Proton exchange membrane fuel cell Gas diffusion layer Water removal Porosity Hydrophobicity Contact angle
1. Introduction It is expected that hydrogen energy technologies will play an important role on a future energy economy and a fuel cell has received a significant attention due to its high electrical efficiency and clean energy conversion [1,2]. Among the various types of fuel cells, a proton exchange membrane fuel cell (PEMFC) has several advantages such as low operating temperature, quick response, and high fuel utilization efficiency [3]. In PEMFCs, placed between membrane electrode assembly (MEA) and gas supplying channels, the gas diffusion layer (GDL) plays important roles on water management, gas diffusion, electron transport and membrane electrode assembly (MEA) support. Among them, water management is an important issue for fuel cell performance because the produced water remaining inside GDL occupies the pore volume and excess water blocks the reactant
* Corresponding author. E-mail address: [email protected] (M.S. Kim).
gases to reach the reaction sites. This phenomenon is called as flooding and, in addition to flooding in channels [4], flooding in GDL is a limiting factor of fuel cell performance [5,6]. Therefore, the water removal ability and gas diffusion kinetics of GDL should be enhanced for high cell performance. Considering the operation condition of PEMFCs and the pore size of GDL, water transport in GDL is strongly dominated by capillary force, while viscous and inertial forces are negligible [7]. Based on the YoungeLaplace equation, the capillary pressure is related to the average pore diameter and hydrophobicity of the porous material, which can be replaced by porosity and contact angle. Therefore, the cell performance can be improved with optimized property of porosity and contact angle in GDL [8,9]. For this reason, conventional GDL is composed of micro porous layer (MPL) and gas diffusion backing layer (GDBL). Placed between the catalyst layer and gas diffusion backing layer (GDBL), MPL effectively removes the produced water from the catalyst layer where the fuel cell reaction occurs so that the reactant gases can reach the reaction sites through the relatively dry pores [10]. However, since the low porosity of MPL acts as a resistance for gas
http://dx.doi.org/10.1016/j.energy.2016.11.100 0360-5442/© 2016 Published by Elsevier Ltd.
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diffusion, the MPL should be coated on GDBL as thin as possible. Then, in order to investigate the effect of GDBL porosity on cell performance, many researchers have developed flow models in porous media [11e17]. In addition, Chu et al. [18] suggested GDBL with porosity gradient and investigated the effect of average porosity on the oxygen transport. Roshandel et al. [19] evaluated the effects on PEM fuel cell performance with porosity variation resulting from the compression pressure corresponding to assembly process. Zhan et al. [20,21] analyzed the distribution of liquid water saturation in GDL containing GDBL with uniform porosity, linear porosity gradient, and parabolic porosity distribution. In their researches, the effects of continuous distribution of GDBL porosity on gas diffusion and water removal were investigated based on a simplified one-dimensional model. Chen et al. [22] developed a two-phase flow model based on the multiphase mixture concept to investigate the transport characteristics of produced water passing through the cathode GDL containing GDBL with linear porosity gradient. Moreover, Huang et al. [23] predicts the enhancement of the water transport for linear porosity gradient in the cathode GDL with a three-dimensional, two-phase, nonisothermal model. With these efforts, numerically, it has been demonstrated that a GDBL with a linear porosity gradient is more favorable than that with uniform porosity for water removal from the catalyst layer to the flow channel. Hydrophobicity, which is represented by contact angle, is also an important parameter in terms of water management. It was found that GDL with proper hydrophobicity effectively removes the liquid water [24e30]. To date, various hydrophobic agents such as polytetrafluoroethylene (PTFE) [24e28] and fluorinated ethylene propylene (FEP) [29,30] have been employed to GDBL. Moreover, it was found that CF4 plasma treatment is also effective to make hydrophobic materials [31]. In general, a hydrophobic treatment is conducted by dipping a GDBL into the hydrophobic agent or spraying, brushing it on the GDBL. Then, hydrophobic agent permeates through the GDBL and it makes hydrophobic gradient in GDBL. Hence, some degree of hydrophobic gradient is an inevitable phenomenon, whether it is intended or not. For example, Kumar et al. [32] developed multistage PTFE treatment to enhance the mechanical and electrochemical durability of GDLs and observed a PTFE gradient in the GDL by adopting the treatment. However, considering the manufacturing difficulties, A GDL with intended linear gradient of property is more about hope than reality in the near future. Recently, in order to overcome the manufacturing difficulties of linear gradient of porosity and/or hydrophobicity, double GDBL structure was suggested [33e35]. For convenience, Kong et al. [33,34] prepared double GDBL by stacking conventional uniform GDBLs and investigated the effect of the double GDBL on water retention for self-humidified PEM fuel cell. On the other hand, Oh et al. [35] developed double GDBL by mixing two different fibers for each layer and observed that the cell performances was improved with double GDBL under various humidity conditions. However, despite the practicality and usefulness of double GDBL on water management, there have been little discussions on the optimal design of double GDBL for water removal. In this study, in order to improve the water removal ability of GDL, the optimal design of double GDBL was investigated with onedimensional steady-state model based on the capillary pressureesaturation relationship. As shown in Fig. 1, it was assumed that each layer has uniform porosity and contact angle. Also, total thickness of GDBL-1 and GDBL-2 was fixed, while the thickness ratio of each GDBL can be changed (if the thickness ratio of GDBL-1 is 20%, the thickness ratio of GDBL-2 is 80%). With this model, the effect of porosity and contact angle arrangements of double GDBL was investigated under varied thickness ratio of GDBL-1 (0e100%). Then, in order to minimize the amount of residual water in GDL,
Fig. 1. Schematic design of the GDL composed of single MPL and double GDBL.
GDBL properties were optimized. This study provides an inspiration on the design of double GDBL functionalized on water removal to prevent flooding, especially under high current densities. 2. Numerical model 2.1. Liquid water saturation and water flux As mentioned, water transport in GDL is strongly dominated by capillary force (multiplication of capillary pressure and active area). Then, the capillary pressure is defined as the difference in pressure across the interface between the non-wetting phase and the wetting phase. For the GDL, gas and liquid phases correspond to nonwetting phase and the wetting phase, respectively.
Pc ¼ Pnw Pw ¼ Pl Pg
(1)
In porous media, the capillary pressure is expressed as [13,14,20e23,36].
s cos q Pc ¼ JðSÞ ðK=3 Þ0:5
(2)
where s is surface tension (N m1), q is contact angle ( ), K is permeability (m2), 3 is porosity, and S is the liquid water saturation defined as the ratio of the pore volume occupied by water to the entire pore volume of (S ¼ Vl/Vp). If S ¼ 0, it means that the entire pore volume of GDL is fully dried. On the other hand, if S ¼ 1, it means that the entire pore volume of GDL is filled with water. Then, Leverett J-function, J(S) can be obtained as a dimensionless function of liquid water saturation.
JðSÞ ¼
1:417ð1 SÞ 2:120ð1 SÞ2 þ 1:263ð1 SÞ3 ðq < 90+ Þ ðq > 90+ Þ 1:417S 2:120S2 þ 1:263S3 (3) 90 ),
In hydrophobic GDL (q > liquid phase pressure is higher than gas phase pressure (Pc > 0) and the produced water is transported from catalyst layer to channel passing through the GDL. In recent years, various attempts have been made to relate the permeability to other more readily measurable properties and the most broadly known is the Kozeny-Carman relation [37]. Tomadakis and Robertson [37] also proposed a more comprehensive relation to predict the anisotropic permeability. Tamayol and Bahrami [38,39] related the permeability of porous media to the microstructure geometrical parameters. In addition, they modified their result to accommodate the effects of mechanical compression and PTFE contents. Among them, Kozeny-Carman equation is used in this study because of its simplicity and wide usage [20,21]. For random nonoverlapping fiber structures [37], the Kozeny-Carman
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equation becomes
K¼
3
3 d2 f
16kK ð1 3 Þ2
(4)
where df is fiber diameter (m), and kK is a Kozeny constant. Then, the water flux (m_ H2 O ) produced by the electrochemical reaction at the cathode is expressed as
m_ H2 O ¼ MH2 O
i 2F
(5)
Then, the relation of water flux and capillary pressure is given as [13,14,20e23].
MH2 O
i r Kkr ð1 þ 2aÞ ¼ l Vpc 2F ml
(6)
In this relation, it was assumed that all the product water is in liquid phase and the phase change of water inside the GDL is negligible. For liquid water, the relative permeability is known as a function of liquid saturation [20,21,36]. 3
kr ¼ S
(7)
Then, with the additional assumption that the water flux driven by electro-osmotic drag is balanced by backing diffusion [36], Eq. (6) is simplified to Eq. (8)
MH2 O
i r KS3 ¼ l Vpc 2F ml
(8)
3
Then, Q [mg] should be as small as possible for water removal at a fixed liquid water flux through GDL [20,21]. The minimum amount of water remaining in GDL (Qmin) is a function of porosity, contact angle (hydrophobicity), and thickness of GDBLs. In this study, the total thickness of GDBL was fixed to 300 mm.
dGDBL1 þ dGDBL2 ¼ 300
(12)
Qmin ¼ f ð3 GDBL1 ; 3 GDBL2 ; qGDBL1 ; qGDBL2 ; dGDBL1 Þ
(13)
For convenience, the porosity and contact angle were adjusted within the range of Eqs. (14) and (15), which are as follows.
0:5 3 0:9
120 q 140
(14)
(15)
2.3. Boundary conditions The saturation distribution in each layer is governed by Eq. (10). However, at the interface of layers, the saturation has a sudden change because of the change in material or structure properties while the capillary pressure is maintained continuously. Hence, liquid water saturation at the interface is derived from the continuity of the capillary pressure.
sMPL cos qMPL ðKMPL =3 MPL Þ
J 0:5 MPL
s cos qGDBL1 J Sx¼dMPL ¼ GDBL1 S 0:5 GDBL1 x¼dMPL ðKGDBL1 =3 GDBL1 Þ (16)
Substituting Eqs. (2)e(4) into Eq. (8), a one-dimensional steadystate model is obtained based on a capillary pressureesaturation relationship
sGDBL1 cos qGDBL1
ðKGDBL1 =3 GDBL1 Þ0:5
dS 1:417S3 4:240S4 þ 3:789S5 dx pffiffiffiffiffiffi i n 4ð1 3 Þ kK ¼ MH2 O 2F s cos qc 3 2 df
¼ (9)
The porosity (3) and contact angle (Wc) are uniform at each layer and the right hand side of Eq. (9) could be assumed as a constant for each layer. Then, integrating Eq. (9), an analytic solution is obtained.
1:417 4 4:240 5 3:789 6 S S þ S 4 5 6 pffiffiffiffiffiffi i n 4ð1 3 Þ kK xþC ¼ MH2 O 2F s cos qc 3 2 df
The liquid water saturation in porous media is defined as the ratio of the pore volume occupied by water to the entire pore volume. Then, the liquid water volume remaining in the GDL is an integral of the saturation in the GDL. Therefore, assuming that the density of liquid water is 1 g/cm3, the amount of liquid water remaining in GDL under steady conditions is calculated by Eq. (12).
ZdGDL 3 ðxÞSðxÞdx
ðKGDBL2 =3 GDBL2 Þ
J 0:5 GDBL2
Sx¼dMPL þdGDBL1
(17)
In general, a constant value is assigned for liquid saturation at channel [20,21,36] and, in this study, S ¼ 0.01 is assumed at the interface of GDL and gas channel to determine the integral constant which depends on the channel condition. In addition, other properties of each layer and predetermined values are listed in Table 1.
3.1. The effect of MPL on water removal
(10)
2.2. Liquid water remaining in GDL
0
sGDBL2 cos qGDBL2
3. Results and discussions
The value of integral constant, C, is obtained from the boundary condition of each layer.
Q ¼ 0:1A
JGDBL1 Sx¼dMPL þdGDBL1
(11)
Fig. 2 shows the liquid water saturation distribution across the single GDBL with/without MPL. The given properties of GDBL and Table 1 Values of variables used in the modeling [34]. Parameters
Values
Thickness of GDL (MPL/GDBL) Kozeny constant Fiber diameter of GDBL Fiber diameter of MPL Porosity of MPL Saturation at channel Faraday constant Molecular weight of water Surface tension Kinematic viscosity Density of water Current density Area
350 (50/300) mm 6 9 mm 1 mm 0.5 0.01 96487 C mol1 18 g mol1 0.0725 N m1 3.5 107 m2 s1 1 g cm3 1 A cm2 1 cm2
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Fig. 2. Liquid water saturation in the direction of GDL thickness according to (a) porosity and (b) contact angle of GDBL without MPL, and according to (c) porosity and (d) contact angle of GDBL with MPL (default value: contact angle of GDBL ¼ 140 for (a) and (c), porosity of GDBL ¼ 0.8 for (b) and (d)).
MPL are listed in Table 1. The results shows that, regardless of MPL, the local liquid water saturation decreases with increased porosity and/or increased contact angle (high contact angle indicates high hydrophobicity) of GDBL. Since the amount of liquid water remaining in the GDL is an integral of the saturation in the GDL, the water flux through the GDL can be improved with higher porosity and contact angle of the GDBL as reported in the previous studies [19e31], although capillary pressure itself is increased with decreased porosity. Then, with the given ranges, the porosity of 0.9 and contact angle of 140 are best properties for the GDBL in the respect of water removal. In addition, when an MPL is placed between the catalyst layer and the GDBL, it was found that the liquid water saturation at the interface of the MPL/GDBL decreases remarkably. Since the liquid water saturation at the interface must satisfy the continuity of the capillary pressure, the liquid water saturation changes rapidly at the interface of MPL and GDBL (at d ¼ 50 mm) in the case of MPL coated single GDBL as shown in Fig. 2(c) and (d). In addition, small porosity and thin fiber diameter of MPL generates extremely low permeability of MPL and a very large capillary pressure gradient through the MPL. This makes the MPL effectively remove the produced water from the catalyst layer. However, local liquid water saturation in MPL increases, the farther the MPL is away from the interface of MPL/GDBL. Therefore, it should be noted that the MPL have to be coated on GDBL as thin as possible for sufficient gas diffusion as noted by Zhan et al. [20]. Fig. 3 shows the amount of residual water remaining in GDL with/without MPL. With MPL, as shown in Fig. 3, the amount of residual water was significantly
Fig. 3. The amount of liquid water remaining in GDL with/without MPL.
reduced and it implies that the water removal ability of GDL could be improved due to MPL as reported by Zhan et al. [20]. In their research, they found that liquid water volume remaining in the
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I.M. Kong et al. / Energy xxx (2016) 1e10
GDBL and the water flux through the GDBL can be improved by inserting MPL between catalyst layer and GDBL. When a MPL is placed between the catalyst layer and the GDBL, the liquid water saturation at the interfaces of the catalyst layer/MPL and MPL/GDBL decreases, while the liquid water flux through the GDBL increases. Also, with the increased porosity and decreased thickness of MPL, the saturation at the interface of the catalyst layer/MPL decreases. One remarkable thing is that, as shown in Fig. 2, the liquid water saturation distribution in MPL is almost unchanged even though the properties of GDBLs are changed. This is because the capillary pressure gradient in MPL is extremely higher than GDBL due to its higher hydrophobicity, lower porosity, and thinner fiber diameter. It makes the local liquid water saturation in MPL near the interface is almost unchanged regardless of GDBL property. 3.2. The effect of double GDBL 3.2.1. Double GDBL with different porosity In this study, a property arrangement in positive direction refers to lower value for GDBL-1 and higher value for GDBL-2, while a property arrangement in negative direction refers to higher value for GDBL-1 and lower value for GDBL-2. Fig. 4 shows the effect of double GDBL with different porosities on liquid water saturation distribution and the amount of water remaining each layer. In order to explore the directional effect of porosity arrangement, for convenience, two different porosity arrangements of 0.8/0.9 and 0.9/0.8 were introduced to GDBL-1/GDBL-2. In addition, in order to evaluate
the effect of thickness ratio of GDBL, the thickness of GDBL-1 was adjusted from 0 mm (this case is the same with the GDL composed of MPL and GDBL-2 without GDBL-1) to 300 mm (this case is the same with the GDL composed of MPL and GDBL-1 without GDBL-2). The properties of MPL used in the modeling are listed in Table 1. Since the total thickness of GDBL-1 and GDBL-2 was fixed to 300 mm, the corresponding thickness of GDBL-2 was decreased as the thickness of GDBL-1 was increased. Then, the effect of double GDBL with porosity arrangement in positive direction on liquid water saturation distribution in GDL and the amount of liquid water remaining in each layer are shown in Fig. 4(a) and (b), respectively. As the thickness of GDBL-1 was increased from 0 to 300 mm, the amount of liquid water remaining in GDBL-1 was increased and that in GDBL-2 was decreased, while the amount of liquid water remaining in MPL is almost unchanged. Then, the total amount of liquid water was decreased initially, and then started to increased. In addition, with double GDBL, the minimum amount of liquid water in GDL was lowered than single GDBL. Based on these results, it was concluded that the porosity arrangement in positive direction with proper thickness ratio of GDBL-1 and GDBL-2 helps water removal. In this case, the thickness of 115 mm (38.33% of total thickness of GDBL-1 and GDBL-2) was the best choice for the GDBL-1. Next, the effect of negative direction of porosity arrangement on liquid water saturation distribution in GDL and the amount of liquid water remaining in each layer are shown in Fig. 4(c) and (d), respectively. Similarly with result of the porosity arrangement in positive direction, as the thickness of GDBL-1 was increased from 5.0
εGDBL-1=0.8, εGDBL-2 =0.9 (δGDBL-1, δGDBL-2), μm
0.2
(0, 300)
(60, 240)
(120, 180)
(180, 120)
(240, 60)
(300, 0)
0.1
0.0
Residual water, Q (mg)
Liquid water saturation, S
0.3
5
εGDBL-1=0.8, εGDBL-2 =0.9
4.0
MPL GDBL-1 GDBL-2 Total
3.0 2.0 1.0 0.0
0
50
0
100 150 200 250 300 350
50
x (μm)
200
250
300
(b)
eGDBL-1=0.9, eGDBL-2 =0.8
S , n o it 0.6 a r u t a 0.4 s r te a w0.2 id u q i L
150
δGDBL-1 (μm)
(a) 0.8
100
(dGDBL-1, dGDBL-2), μm (0, 300)
(60, 240)
(120, 180)
(180, 120)
(240, 60)
(300, 0)
0.0
7.0
eGDBL-1=0.9, eGDBL-2 =0.8
) 6.0 g m ( 5.0 Q r, 4.0 e t a w 3.0 l a u 2.0 d i s e 1.0 R
MPL GDBL-1 GDBL-2 Total
0.0 0
50
100 150 200 250 300 350
x (μm) (c)
0
50
100
150
200
250
300
dGDBL-1 (μm) (d)
Fig. 4. The effect of porosity arrangement in positive direction (0.8/0.9 for GDBL-1 and GDBL-2, respectively) on (a) liquid water saturation distribution and (b) The amount of liquid water remaining in the GDL, and in negative direction (0.9/0.8 for GDBL-1 and GDBL-2, respectively) on (c) liquid water saturation distribution and (d) The amount of liquid water remaining in the GDL (according to the thickness of GDBL-1 changed from 0 mm (0%) to 300 mm (100%) with the same contact angle of 140 for GDBL-1 and GDBL-2).
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0.2
0.1
(δGDBL-1, δGDBL-2), μm (0, 300) (120, 180) (240, 60)
0.0 0
Liquid water saturation, S
0.3
5.0
θGDBL-1=120°, θGDBL-2 =140°
50
(60, 240) (180, 120) (300, 0)
θGDBL-1=120°, θGDBL-2 =140°
4.0 3.0
MPL GDBL-1 GDBL-2 Total
2.0 1.0 0.0 0
100 150 200 250 300 350
50
100
150
200
x (μm)
δGDBL-1 (μm)
(a)
(b)
θGDBL-1=140°, θGDBL-2 =120° (δGDBL-1, δGDBL-2), μm
0.2
Residual water, Q (mg)
Liquid water saturation, S
0.3
(0, 300)
(60, 240)
(120, 180) (240, 60)
(180, 120) (300, 0)
0.1
0.0
5.0
250
300
? GDBL-1=140°, ? GDBL-2 =120°
) g 4.0 m ( Q3.0 ,r e t a w2.0 l a u d i 1.0 s e R
MPL GDBL-1 GDBL-2 Total
0.0
0
50
100 150 200 250 300 350
0
50
x (μm)
100
150
200
250
300
dGDBL-1 (μm)
(c)
(d)
Fig. 5. The effect of contact angle arrangement in positive direction (120 /140 for GDBL-1 and GDBL-2, respectively) on (a) liquid water saturation distribution and (b) The amount of liquid water remaining in the GDL, and in negative direction (140 /120 for GDBL-1 and GDBL-2, respectively) on (c) liquid water saturation distribution and (d) The amount of liquid water remaining in the GDL (according to the thickness of GDBL-1 changed from 0 mm (0%) to 300 mm (100%) with the same porosity of 0.8 for GDBL-1 and GDBL-2).
0 to 300 mm, the amount of liquid water remaining in GDBL-1 was increased and that in GDBL-2 was decreased. However, as shown in Fig. 4(c), the liquid water saturation in GDBL-1 was extremely increased so that the total amount of liquid water in GDL became larger than single GDBL. Therefore, double GDBL with porosity arrangement in negative direction with proper thickness ratio of GDBL-1 and GDBL-2 helps water retention. In fact, the effect of double GDBL with porosity arrangement in negative direction was verified experimentally in the previous researches [32,33]. In the researches, the cell showed a better performance with a modified GDL containing double GDBL with porosity arrangement in negative direction under low humidity conditions. However, the cell performance was worse under sufficiently humidified conditions, where water removal is more important than water retention. The result of this study is coincided with the result of Zhan et al. [20,21]. In their research, for the GDLs with the same equivalent porosity, they compared the effects of linear gradient and parabolic gradient. Then, they concluded that linear gradient is more effective than parabolic gradient. Based on the result of present study, the result is reasonable because linear gradient has parabolic gradient has combination effect of positive direction and negative direction of porosity. 3.2.2. Double GDBL with different hydrophobicity Since the degree of hydrophobicity can be represented by the contact angle (one of the measurable parameter) [24e32], in this study, contact angle was used to evaluate the effect of
hydrophobicity. Fig. 5 shows the effect of double GDBL with different contact angles on liquid water saturation distribution and the amount of water remaining each layer. In order to explore the directional effect of contact angle arrangement, for convenience, two different contact angle arrangements of 120 /140 and 140 / 120 were introduced to GDBL-1/GDBL-2. The thickness of GDBL-1 was also adjusted from 0 mm to 300 mm. As shown in Fig. 2, with single GDBL, water removal ability of GDL was improved with increased porosity and/or contact angle (hydrophobicity). In Fig. 4, water removal ability of GDL was improved with porosity arrangement of double GDBL in positive direction. Then, Fig. 5 shows similar trends but different tendency in property direction compared with the result shown in Fig. 4. In the case of contact angle, water removal ability of GDL was enhanced with the contact angle arrangement in negative direction. These results are reasonable in terms of capillary pressure. The liquid water in a porous media flows to the region where lower capillary pressure formed. In a porous media, capillary pressure is a function of porosity, contact angle, and liquid water saturation and can be expressed as
Pc ff ð3 ÞgðqÞJðSÞ
f ð3 Þ ¼
ð1 3 Þ 3
(18)
(19)
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I.M. Kong et al. / Energy xxx (2016) 1e10
gðqÞ ¼ cosðqÞ
(20)
JðSÞ ¼ 1:417S 2:120S2 þ 1:263S3
(21)
7
Then, as shown in Fig. 6, the capillary pressure decreases with increase of porosity and decrease of contact angle. Since relatively higher capillary pressure in GDBL-1 and lower capillary pressure in GDBL-2 helps water removal, double GDBLs with a porosity arrangement in positive direction and/or contact angle arrangement in negative direction were effective on improving water removal ability of GDL. 3.3. Optimization As mentioned, the amount of liquid water remaining in GDL should be as small as possible for effective water removal. Fig. 7 shows the minimum amount of water remaining in the GDL, Qmin, with optimized thickness ratio of GDBLs at each porosity and/ or contact angle arrangements. It was found that when the porosity of GDBL-2 was 0.9, Qmin appears regardless of contact angle arrangements. It means that, in order to maximize the water removal ability of GDL, the porosity of GDBL near the gas flow channel should be maximized. Also, when the porosity of GDBL-1 was smaller than that of GDBL-2 (porosity arrangement in positive direction), Qmin was minimized when the contact angles of GDBL1and GDBL-2 are maximized. Next, when the porosity of GDBL-1 was similar to that of GDBL-2 (single GDBL), Qmin was minimized when the difference of contact angles were maximized. Lastly, when the porosity of GDBL-1 was larger than that of GDBL-2 (porosity arrangement in negative direction), Qmin with the contact arrangement of 140 /130 and 140 /120 is the same as the result of 140 /140 except near the range where the porosity of GDBLs are the same. It was because porosity arrangement in negative direction significantly reduces water removal ability of GDL so that the Qmin appears when the thickness of GDBL-1 is 300 mm (single GDBL with GDBL-1). Based on the results shown in Fig. 7, the optimization can be classified into two cases; when the porosity of GDBL-2 is fixed to 0.9, and when the porosity of GDBL-1 and GDBL-2 are the same. Fig. 8(a) shows the minimum amount of liquid water remaining in GDL according to the varied porosity of GDBL-1, with a fixed porosity of 0.9 for GDBL-2. The corresponding thickness of GDBL-1 is shown in Fig. 8(b). The result shows that Qmin was remarkably changed between the porosity range of 0.8 and 0.9 for GDBL-1.
Fig. 7. The effect of porosity arrangements on the amount of liquid water remaining in the GDL with (a) the same contact angle and (b) the contact angle arrangement in negative direction for GDBL-1 and GDBL-2.
10
1.0 Pc ,high
Pc ,high
0.8
6
g(θ)
f(ε)
8
4 2
0.6 0.4 0.2
Pc ,low
Pc ,low
0.0
0 0.1
0.4
0.7
1.0
90
120
150
ε
θ
(a)
(b)
180
Fig. 6. The effect of (a) porosity and (b) contact angle on the capillary pressure in a porous media.
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3.4
εGDBL-2=0.9
2.7
(θGDBL-1, θGDBL-2) (120°, 120°)
(130°, 130°)
2.6
(140°, 140°)
(140°, 130°)
(140°, 120°)
(130°, 120°)
2.5 2.4
3.0 2.8 2.6
2.3
2.4
2.2
2.2 0.5
0.6
0.7
0.8
εGDBL-1=εGDBL-2
3.2
Qmin (mg)
Qmin (mg)
2.8
(θGDBL-1, θGDBL-2)
0.5
0.9
(120°, 120°)
(130°, 130°)
(140°, 140°)
(140°, 130°)
(140°, 120°)
(130°, 120°)
0.6
0.7
(a)
150
0.9
εGDBL-1=εGDBL-2
250
(120°, 120°)
(130°, 130°)
(140°, 140°)
(140°, 130°)
(140°, 120°)
(130°, 120°)
δGDBL-1 (μm)
δGDBL-1 (μm)
300
(θGDBL-1, θGDBL-2)
200
0.8
(a)
εGDBL-2=0.9
250
0.9
εGDBL
εGDBL-1
300
0.8
100 50
200 150 (θGDBL-1, θGDBL-2)
100
(140°, 130°) (140°, 120°)
50
(130°, 120°) 0
0 0.5
0.6
0.7
0.8
0.9
εGDBL-1
0.5
0.6
0.7
εGDBL
(b)
(b)
Fig. 8. Properties of double GDBL for (a) Minimum amount of liquid water remaining in GDL and (b) corresponding thickness of GDBL-1 for this, with a fixed porosity of 0.9 for GDBL-1.
Fig. 9. Properties of double GDBL for (a) Minimum amount of liquid water remaining in GDL and (b) corresponding thickness of GDBL-1 for this, with the same porosities of GDBL-1 and GDBL-2.
When the porosity of GDBL-1 was below 0.8, the change in Qmin is negligible. Since low porous layer increases the risk of flooding, the higher porosity of GDBL-1 is better for gas diffusion. As shown In Fig. 8(a), the lowest Qmin appeared when the porosity of GDBL-1 is 0.82 and contact angles are 140 /140 for GDBL-1/GDBL-2. In this case, the optimized thicknesses are 120 mm (40% of total thickness of GDBLs) for GDBL-1 and 180 mm for GDBL-2, respectively. With this optimized arrangement, Qmin was lowered by 9.2% compared with the lowest value of Qmin in MPL coated single GDBL (with 3GDBL ¼ 0.9, qGDBL ¼ 140 ). Next, Fig. 9(a) shows the minimum amount of liquid water remaining in GDL according to the varied porosity of GDBLs, when the porosity of GDBL-1 and GDBL-2 are the same. The
corresponding thickness of GDBL-1 is shown in Fig. 9(b). Although the contact angle arrangement was less effective on water removal compared with porosity arrangement, contact angle arrangement is still important and necessary. When the porosities of GDBL-1 and GDBL-2 are the same (3GDBL-1 ¼ 3GDBL-2), the lowest Qmin appeared when the contact angle arrangement is 140 for GDBL-1 and 120 for GDBL-2, respectively. Therefore, in order to find out GDBL properties for Qmin, the difference of contact angles should be maximized. In addition, the optimized Qmin appeared where 3GDBL1 ¼ 3GDBL-2 ¼ 0.9 with thicknesses of 203 mm (67.67% of total thickness of GDBLs) for GDBL-1 and 100 mm for GDBL-2, respectively. With this optimized arrangement of contact angle, Qmin was lowered by 5.6% compared with the lowest value of Qmin in MPL
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I.M. Kong et al. / Energy xxx (2016) 1e10
coated single GDBL (with
3GDBL
¼ 0.9, qGDBL ¼ 140 ).
4. Conclusions In this study, in order to improve the water removal ability of GDL, double GDBL structure was introduced. With one-dimensional steady-state model based on the capillary pressureesaturation relationship, the effect of porosity and contact angle arrangements of double GDBL was investigated under varied thickness ratio of GDBL-1 (0e100%). Since relatively higher capillary pressure in GDBL-1 and lower capillary pressure in GDBL-2 helps water removal, double GDBLs with a porosity arrangement in positive direction and/or a contact angle arrangement in negative direction were effective on improving water removal ability of GDL. In terms of water removal, the optimized porosity, contact angle and thickness of GDBLs are 0.82, 140 , 120 mm for GDBL-1 and 0.9, 140 , 180 mm for GDBL-2, respectively. If the porosity of GDBL-1 and GDBL-2 are the same, the optimized arrangement becomes 0.9, 140 , 203 mm for GDBL-1 and 0.9, 120 , 97 mm for GDBL-2, respectively. The result of this study provides an inspiration on how to design the property of double GDBL functionalized on water removal. Acknowledgements This work was supported by the Brain Korea 21 Plus Project (F14SN02D1310)of Seoul National University. This research was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2013R1A2A1A01014589). Nomenclature
Q C
Faraday constant (C mol1) molecular weight (g mol1) current density (A cm2) active area (cm2) Leverett J-function saturation capillary pressure (Pa) permeability (m2) relative permeability Kozeny constant porosity fiber diameter (m) volume (m3) flux (kg s1 m1) GDL thickness directional distance (mm) thickness(mm) surface tension (N m1) density (kg m3) dynamic viscosity (Pa s) kinematic viscosity (m2 s1) contact angle ( ) effective diffusion coefficient of water through membrane liquid water remaining in GDL (mg) integral constant
Subscript nw w l g P
non-wetting phase wetting phase liquid gas pore
F M i A J S Pc K kr kK 3
df V q x
d s r m n q a
H2O GDBL MPL
9
water gas diffusion backing layer micro porous layer
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performance of a PEM fuel cell. Electrochim Acta 2004;49(24):4149e56. [31] Pai YH, Ke JH, Huang HF, Lee CM, Jyh-Myng Z, Shieu FS. CF4 plasma treatment for preparing gas diffusion layers in membrane electrode assemblies. J Power Sources 2006;161(1):275e81. [32] Kumar JFR, Radhakrishnan V, Haridoss P. Enhanced mechanical and electrochemical durability of multistage PTFE treated gas diffusion layers for proton exchange membrane fuel cells. Int J Hydrogen Energy 2012;37(14):10830e5. [33] Kong IM, Choi JW, Kim SI, Lee ES, Kim MS. Experimental study on the selfhumidification effect in proton exchange membrane fuel cells containing double gas diffusion backing layer. Appl Energy 2015;145:345e53. [34] Kong IM, Jung A, Kim MS. Investigations on the double gas diffusion backing layer for performance improvement of self-humidified proton exchange membrane fuel cells. Appl Energy 2016;176:149e56.
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Numerical investigation on double gas diffusion backing layer functionalized on water removal in a proton exchange membrane fuel cell Im Mo Kong a, Aeri Jung b, Young Sang Kim c, Min Soo Kim b, * a b c
Powertrain Research Center, Korea Automotive Technology Institute, Gwangju 62207, South Korea Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, South Korea Department of Eco-machinery System, Korea Institute of Machinery & Materials, Daejon 34103, South Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 October 2015 Received in revised form 18 October 2016 Accepted 16 November 2016 Available online xxx
Since flooding is a limiting factor of cell performance in a proton exchange membrane fuel cell (PEMFC), it is important to remove produced water effectively from GDL. In this study, a multi-layer GDL containing single micro porous layer (MPL) and double gas diffusion backing layer (GDBL) was introduced as a practical design and the effect of porosity and/or hydrophobicity of GDBL on water removal was investigated with one-dimensional steady-state model based on a capillary pressureesaturation relationship. The results shows that double GDBL with different porosity in a positive direction (GDBL with lower porosity near the MPL and GDBL with higher porosity near the flow channel) and/or different hydrophobicity in a negative direction (more hydrophobic GDBL near the MPL and less hydrophobic GDBL near the flow channel) enhances the water removal ability of the GDL compared with uniform single GDBL. Based on the results, the property arrangements of double GDBL were optimized to minimize the amount of liquid water remaining in GDL. It is expected that the amount of produced water remaining in ML-GDL can be reduced about 9.2% with optimized porosity arrangement and 5.6% with optimized hydrophobicity arrangement. © 2016 Published by Elsevier Ltd.
Keywords: Proton exchange membrane fuel cell Gas diffusion layer Water removal Porosity Hydrophobicity Contact angle
1. Introduction It is expected that hydrogen energy technologies will play an important role on a future energy economy and a fuel cell has received a significant attention due to its high electrical efficiency and clean energy conversion [1,2]. Among the various types of fuel cells, a proton exchange membrane fuel cell (PEMFC) has several advantages such as low operating temperature, quick response, and high fuel utilization efficiency [3]. In PEMFCs, placed between membrane electrode assembly (MEA) and gas supplying channels, the gas diffusion layer (GDL) plays important roles on water management, gas diffusion, electron transport and membrane electrode assembly (MEA) support. Among them, water management is an important issue for fuel cell performance because the produced water remaining inside GDL occupies the pore volume and excess water blocks the reactant
* Corresponding author. E-mail address: [email protected] (M.S. Kim).
gases to reach the reaction sites. This phenomenon is called as flooding and, in addition to flooding in channels [4], flooding in GDL is a limiting factor of fuel cell performance [5,6]. Therefore, the water removal ability and gas diffusion kinetics of GDL should be enhanced for high cell performance. Considering the operation condition of PEMFCs and the pore size of GDL, water transport in GDL is strongly dominated by capillary force, while viscous and inertial forces are negligible [7]. Based on the YoungeLaplace equation, the capillary pressure is related to the average pore diameter and hydrophobicity of the porous material, which can be replaced by porosity and contact angle. Therefore, the cell performance can be improved with optimized property of porosity and contact angle in GDL [8,9]. For this reason, conventional GDL is composed of micro porous layer (MPL) and gas diffusion backing layer (GDBL). Placed between the catalyst layer and gas diffusion backing layer (GDBL), MPL effectively removes the produced water from the catalyst layer where the fuel cell reaction occurs so that the reactant gases can reach the reaction sites through the relatively dry pores [10]. However, since the low porosity of MPL acts as a resistance for gas
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diffusion, the MPL should be coated on GDBL as thin as possible. Then, in order to investigate the effect of GDBL porosity on cell performance, many researchers have developed flow models in porous media [11e17]. In addition, Chu et al. [18] suggested GDBL with porosity gradient and investigated the effect of average porosity on the oxygen transport. Roshandel et al. [19] evaluated the effects on PEM fuel cell performance with porosity variation resulting from the compression pressure corresponding to assembly process. Zhan et al. [20,21] analyzed the distribution of liquid water saturation in GDL containing GDBL with uniform porosity, linear porosity gradient, and parabolic porosity distribution. In their researches, the effects of continuous distribution of GDBL porosity on gas diffusion and water removal were investigated based on a simplified one-dimensional model. Chen et al. [22] developed a two-phase flow model based on the multiphase mixture concept to investigate the transport characteristics of produced water passing through the cathode GDL containing GDBL with linear porosity gradient. Moreover, Huang et al. [23] predicts the enhancement of the water transport for linear porosity gradient in the cathode GDL with a three-dimensional, two-phase, nonisothermal model. With these efforts, numerically, it has been demonstrated that a GDBL with a linear porosity gradient is more favorable than that with uniform porosity for water removal from the catalyst layer to the flow channel. Hydrophobicity, which is represented by contact angle, is also an important parameter in terms of water management. It was found that GDL with proper hydrophobicity effectively removes the liquid water [24e30]. To date, various hydrophobic agents such as polytetrafluoroethylene (PTFE) [24e28] and fluorinated ethylene propylene (FEP) [29,30] have been employed to GDBL. Moreover, it was found that CF4 plasma treatment is also effective to make hydrophobic materials [31]. In general, a hydrophobic treatment is conducted by dipping a GDBL into the hydrophobic agent or spraying, brushing it on the GDBL. Then, hydrophobic agent permeates through the GDBL and it makes hydrophobic gradient in GDBL. Hence, some degree of hydrophobic gradient is an inevitable phenomenon, whether it is intended or not. For example, Kumar et al. [32] developed multistage PTFE treatment to enhance the mechanical and electrochemical durability of GDLs and observed a PTFE gradient in the GDL by adopting the treatment. However, considering the manufacturing difficulties, A GDL with intended linear gradient of property is more about hope than reality in the near future. Recently, in order to overcome the manufacturing difficulties of linear gradient of porosity and/or hydrophobicity, double GDBL structure was suggested [33e35]. For convenience, Kong et al. [33,34] prepared double GDBL by stacking conventional uniform GDBLs and investigated the effect of the double GDBL on water retention for self-humidified PEM fuel cell. On the other hand, Oh et al. [35] developed double GDBL by mixing two different fibers for each layer and observed that the cell performances was improved with double GDBL under various humidity conditions. However, despite the practicality and usefulness of double GDBL on water management, there have been little discussions on the optimal design of double GDBL for water removal. In this study, in order to improve the water removal ability of GDL, the optimal design of double GDBL was investigated with onedimensional steady-state model based on the capillary pressureesaturation relationship. As shown in Fig. 1, it was assumed that each layer has uniform porosity and contact angle. Also, total thickness of GDBL-1 and GDBL-2 was fixed, while the thickness ratio of each GDBL can be changed (if the thickness ratio of GDBL-1 is 20%, the thickness ratio of GDBL-2 is 80%). With this model, the effect of porosity and contact angle arrangements of double GDBL was investigated under varied thickness ratio of GDBL-1 (0e100%). Then, in order to minimize the amount of residual water in GDL,
Fig. 1. Schematic design of the GDL composed of single MPL and double GDBL.
GDBL properties were optimized. This study provides an inspiration on the design of double GDBL functionalized on water removal to prevent flooding, especially under high current densities. 2. Numerical model 2.1. Liquid water saturation and water flux As mentioned, water transport in GDL is strongly dominated by capillary force (multiplication of capillary pressure and active area). Then, the capillary pressure is defined as the difference in pressure across the interface between the non-wetting phase and the wetting phase. For the GDL, gas and liquid phases correspond to nonwetting phase and the wetting phase, respectively.
Pc ¼ Pnw Pw ¼ Pl Pg
(1)
In porous media, the capillary pressure is expressed as [13,14,20e23,36].
s cos q Pc ¼ JðSÞ ðK=3 Þ0:5
(2)
where s is surface tension (N m1), q is contact angle ( ), K is permeability (m2), 3 is porosity, and S is the liquid water saturation defined as the ratio of the pore volume occupied by water to the entire pore volume of (S ¼ Vl/Vp). If S ¼ 0, it means that the entire pore volume of GDL is fully dried. On the other hand, if S ¼ 1, it means that the entire pore volume of GDL is filled with water. Then, Leverett J-function, J(S) can be obtained as a dimensionless function of liquid water saturation.
JðSÞ ¼
1:417ð1 SÞ 2:120ð1 SÞ2 þ 1:263ð1 SÞ3 ðq < 90+ Þ ðq > 90+ Þ 1:417S 2:120S2 þ 1:263S3 (3) 90 ),
In hydrophobic GDL (q > liquid phase pressure is higher than gas phase pressure (Pc > 0) and the produced water is transported from catalyst layer to channel passing through the GDL. In recent years, various attempts have been made to relate the permeability to other more readily measurable properties and the most broadly known is the Kozeny-Carman relation [37]. Tomadakis and Robertson [37] also proposed a more comprehensive relation to predict the anisotropic permeability. Tamayol and Bahrami [38,39] related the permeability of porous media to the microstructure geometrical parameters. In addition, they modified their result to accommodate the effects of mechanical compression and PTFE contents. Among them, Kozeny-Carman equation is used in this study because of its simplicity and wide usage [20,21]. For random nonoverlapping fiber structures [37], the Kozeny-Carman
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equation becomes
K¼
3
3 d2 f
16kK ð1 3 Þ2
(4)
where df is fiber diameter (m), and kK is a Kozeny constant. Then, the water flux (m_ H2 O ) produced by the electrochemical reaction at the cathode is expressed as
m_ H2 O ¼ MH2 O
i 2F
(5)
Then, the relation of water flux and capillary pressure is given as [13,14,20e23].
MH2 O
i r Kkr ð1 þ 2aÞ ¼ l Vpc 2F ml
(6)
In this relation, it was assumed that all the product water is in liquid phase and the phase change of water inside the GDL is negligible. For liquid water, the relative permeability is known as a function of liquid saturation [20,21,36]. 3
kr ¼ S
(7)
Then, with the additional assumption that the water flux driven by electro-osmotic drag is balanced by backing diffusion [36], Eq. (6) is simplified to Eq. (8)
MH2 O
i r KS3 ¼ l Vpc 2F ml
(8)
3
Then, Q [mg] should be as small as possible for water removal at a fixed liquid water flux through GDL [20,21]. The minimum amount of water remaining in GDL (Qmin) is a function of porosity, contact angle (hydrophobicity), and thickness of GDBLs. In this study, the total thickness of GDBL was fixed to 300 mm.
dGDBL1 þ dGDBL2 ¼ 300
(12)
Qmin ¼ f ð3 GDBL1 ; 3 GDBL2 ; qGDBL1 ; qGDBL2 ; dGDBL1 Þ
(13)
For convenience, the porosity and contact angle were adjusted within the range of Eqs. (14) and (15), which are as follows.
0:5 3 0:9
120 q 140
(14)
(15)
2.3. Boundary conditions The saturation distribution in each layer is governed by Eq. (10). However, at the interface of layers, the saturation has a sudden change because of the change in material or structure properties while the capillary pressure is maintained continuously. Hence, liquid water saturation at the interface is derived from the continuity of the capillary pressure.
sMPL cos qMPL ðKMPL =3 MPL Þ
J 0:5 MPL
s cos qGDBL1 J Sx¼dMPL ¼ GDBL1 S 0:5 GDBL1 x¼dMPL ðKGDBL1 =3 GDBL1 Þ (16)
Substituting Eqs. (2)e(4) into Eq. (8), a one-dimensional steadystate model is obtained based on a capillary pressureesaturation relationship
sGDBL1 cos qGDBL1
ðKGDBL1 =3 GDBL1 Þ0:5
dS 1:417S3 4:240S4 þ 3:789S5 dx pffiffiffiffiffiffi i n 4ð1 3 Þ kK ¼ MH2 O 2F s cos qc 3 2 df
¼ (9)
The porosity (3) and contact angle (Wc) are uniform at each layer and the right hand side of Eq. (9) could be assumed as a constant for each layer. Then, integrating Eq. (9), an analytic solution is obtained.
1:417 4 4:240 5 3:789 6 S S þ S 4 5 6 pffiffiffiffiffiffi i n 4ð1 3 Þ kK xþC ¼ MH2 O 2F s cos qc 3 2 df
The liquid water saturation in porous media is defined as the ratio of the pore volume occupied by water to the entire pore volume. Then, the liquid water volume remaining in the GDL is an integral of the saturation in the GDL. Therefore, assuming that the density of liquid water is 1 g/cm3, the amount of liquid water remaining in GDL under steady conditions is calculated by Eq. (12).
ZdGDL 3 ðxÞSðxÞdx
ðKGDBL2 =3 GDBL2 Þ
J 0:5 GDBL2
Sx¼dMPL þdGDBL1
(17)
In general, a constant value is assigned for liquid saturation at channel [20,21,36] and, in this study, S ¼ 0.01 is assumed at the interface of GDL and gas channel to determine the integral constant which depends on the channel condition. In addition, other properties of each layer and predetermined values are listed in Table 1.
3.1. The effect of MPL on water removal
(10)
2.2. Liquid water remaining in GDL
0
sGDBL2 cos qGDBL2
3. Results and discussions
The value of integral constant, C, is obtained from the boundary condition of each layer.
Q ¼ 0:1A
JGDBL1 Sx¼dMPL þdGDBL1
(11)
Fig. 2 shows the liquid water saturation distribution across the single GDBL with/without MPL. The given properties of GDBL and Table 1 Values of variables used in the modeling [34]. Parameters
Values
Thickness of GDL (MPL/GDBL) Kozeny constant Fiber diameter of GDBL Fiber diameter of MPL Porosity of MPL Saturation at channel Faraday constant Molecular weight of water Surface tension Kinematic viscosity Density of water Current density Area
350 (50/300) mm 6 9 mm 1 mm 0.5 0.01 96487 C mol1 18 g mol1 0.0725 N m1 3.5 107 m2 s1 1 g cm3 1 A cm2 1 cm2
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Fig. 2. Liquid water saturation in the direction of GDL thickness according to (a) porosity and (b) contact angle of GDBL without MPL, and according to (c) porosity and (d) contact angle of GDBL with MPL (default value: contact angle of GDBL ¼ 140 for (a) and (c), porosity of GDBL ¼ 0.8 for (b) and (d)).
MPL are listed in Table 1. The results shows that, regardless of MPL, the local liquid water saturation decreases with increased porosity and/or increased contact angle (high contact angle indicates high hydrophobicity) of GDBL. Since the amount of liquid water remaining in the GDL is an integral of the saturation in the GDL, the water flux through the GDL can be improved with higher porosity and contact angle of the GDBL as reported in the previous studies [19e31], although capillary pressure itself is increased with decreased porosity. Then, with the given ranges, the porosity of 0.9 and contact angle of 140 are best properties for the GDBL in the respect of water removal. In addition, when an MPL is placed between the catalyst layer and the GDBL, it was found that the liquid water saturation at the interface of the MPL/GDBL decreases remarkably. Since the liquid water saturation at the interface must satisfy the continuity of the capillary pressure, the liquid water saturation changes rapidly at the interface of MPL and GDBL (at d ¼ 50 mm) in the case of MPL coated single GDBL as shown in Fig. 2(c) and (d). In addition, small porosity and thin fiber diameter of MPL generates extremely low permeability of MPL and a very large capillary pressure gradient through the MPL. This makes the MPL effectively remove the produced water from the catalyst layer. However, local liquid water saturation in MPL increases, the farther the MPL is away from the interface of MPL/GDBL. Therefore, it should be noted that the MPL have to be coated on GDBL as thin as possible for sufficient gas diffusion as noted by Zhan et al. [20]. Fig. 3 shows the amount of residual water remaining in GDL with/without MPL. With MPL, as shown in Fig. 3, the amount of residual water was significantly
Fig. 3. The amount of liquid water remaining in GDL with/without MPL.
reduced and it implies that the water removal ability of GDL could be improved due to MPL as reported by Zhan et al. [20]. In their research, they found that liquid water volume remaining in the
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I.M. Kong et al. / Energy xxx (2016) 1e10
GDBL and the water flux through the GDBL can be improved by inserting MPL between catalyst layer and GDBL. When a MPL is placed between the catalyst layer and the GDBL, the liquid water saturation at the interfaces of the catalyst layer/MPL and MPL/GDBL decreases, while the liquid water flux through the GDBL increases. Also, with the increased porosity and decreased thickness of MPL, the saturation at the interface of the catalyst layer/MPL decreases. One remarkable thing is that, as shown in Fig. 2, the liquid water saturation distribution in MPL is almost unchanged even though the properties of GDBLs are changed. This is because the capillary pressure gradient in MPL is extremely higher than GDBL due to its higher hydrophobicity, lower porosity, and thinner fiber diameter. It makes the local liquid water saturation in MPL near the interface is almost unchanged regardless of GDBL property. 3.2. The effect of double GDBL 3.2.1. Double GDBL with different porosity In this study, a property arrangement in positive direction refers to lower value for GDBL-1 and higher value for GDBL-2, while a property arrangement in negative direction refers to higher value for GDBL-1 and lower value for GDBL-2. Fig. 4 shows the effect of double GDBL with different porosities on liquid water saturation distribution and the amount of water remaining each layer. In order to explore the directional effect of porosity arrangement, for convenience, two different porosity arrangements of 0.8/0.9 and 0.9/0.8 were introduced to GDBL-1/GDBL-2. In addition, in order to evaluate
the effect of thickness ratio of GDBL, the thickness of GDBL-1 was adjusted from 0 mm (this case is the same with the GDL composed of MPL and GDBL-2 without GDBL-1) to 300 mm (this case is the same with the GDL composed of MPL and GDBL-1 without GDBL-2). The properties of MPL used in the modeling are listed in Table 1. Since the total thickness of GDBL-1 and GDBL-2 was fixed to 300 mm, the corresponding thickness of GDBL-2 was decreased as the thickness of GDBL-1 was increased. Then, the effect of double GDBL with porosity arrangement in positive direction on liquid water saturation distribution in GDL and the amount of liquid water remaining in each layer are shown in Fig. 4(a) and (b), respectively. As the thickness of GDBL-1 was increased from 0 to 300 mm, the amount of liquid water remaining in GDBL-1 was increased and that in GDBL-2 was decreased, while the amount of liquid water remaining in MPL is almost unchanged. Then, the total amount of liquid water was decreased initially, and then started to increased. In addition, with double GDBL, the minimum amount of liquid water in GDL was lowered than single GDBL. Based on these results, it was concluded that the porosity arrangement in positive direction with proper thickness ratio of GDBL-1 and GDBL-2 helps water removal. In this case, the thickness of 115 mm (38.33% of total thickness of GDBL-1 and GDBL-2) was the best choice for the GDBL-1. Next, the effect of negative direction of porosity arrangement on liquid water saturation distribution in GDL and the amount of liquid water remaining in each layer are shown in Fig. 4(c) and (d), respectively. Similarly with result of the porosity arrangement in positive direction, as the thickness of GDBL-1 was increased from 5.0
εGDBL-1=0.8, εGDBL-2 =0.9 (δGDBL-1, δGDBL-2), μm
0.2
(0, 300)
(60, 240)
(120, 180)
(180, 120)
(240, 60)
(300, 0)
0.1
0.0
Residual water, Q (mg)
Liquid water saturation, S
0.3
5
εGDBL-1=0.8, εGDBL-2 =0.9
4.0
MPL GDBL-1 GDBL-2 Total
3.0 2.0 1.0 0.0
0
50
0
100 150 200 250 300 350
50
x (μm)
200
250
300
(b)
eGDBL-1=0.9, eGDBL-2 =0.8
S , n o it 0.6 a r u t a 0.4 s r te a w0.2 id u q i L
150
δGDBL-1 (μm)
(a) 0.8
100
(dGDBL-1, dGDBL-2), μm (0, 300)
(60, 240)
(120, 180)
(180, 120)
(240, 60)
(300, 0)
0.0
7.0
eGDBL-1=0.9, eGDBL-2 =0.8
) 6.0 g m ( 5.0 Q r, 4.0 e t a w 3.0 l a u 2.0 d i s e 1.0 R
MPL GDBL-1 GDBL-2 Total
0.0 0
50
100 150 200 250 300 350
x (μm) (c)
0
50
100
150
200
250
300
dGDBL-1 (μm) (d)
Fig. 4. The effect of porosity arrangement in positive direction (0.8/0.9 for GDBL-1 and GDBL-2, respectively) on (a) liquid water saturation distribution and (b) The amount of liquid water remaining in the GDL, and in negative direction (0.9/0.8 for GDBL-1 and GDBL-2, respectively) on (c) liquid water saturation distribution and (d) The amount of liquid water remaining in the GDL (according to the thickness of GDBL-1 changed from 0 mm (0%) to 300 mm (100%) with the same contact angle of 140 for GDBL-1 and GDBL-2).
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6
I.M. Kong et al. / Energy xxx (2016) 1e10
0.2
0.1
(δGDBL-1, δGDBL-2), μm (0, 300) (120, 180) (240, 60)
0.0 0
Liquid water saturation, S
0.3
5.0
θGDBL-1=120°, θGDBL-2 =140°
50
(60, 240) (180, 120) (300, 0)
θGDBL-1=120°, θGDBL-2 =140°
4.0 3.0
MPL GDBL-1 GDBL-2 Total
2.0 1.0 0.0 0
100 150 200 250 300 350
50
100
150
200
x (μm)
δGDBL-1 (μm)
(a)
(b)
θGDBL-1=140°, θGDBL-2 =120° (δGDBL-1, δGDBL-2), μm
0.2
Residual water, Q (mg)
Liquid water saturation, S
0.3
(0, 300)
(60, 240)
(120, 180) (240, 60)
(180, 120) (300, 0)
0.1
0.0
5.0
250
300
? GDBL-1=140°, ? GDBL-2 =120°
) g 4.0 m ( Q3.0 ,r e t a w2.0 l a u d i 1.0 s e R
MPL GDBL-1 GDBL-2 Total
0.0
0
50
100 150 200 250 300 350
0
50
x (μm)
100
150
200
250
300
dGDBL-1 (μm)
(c)
(d)
Fig. 5. The effect of contact angle arrangement in positive direction (120 /140 for GDBL-1 and GDBL-2, respectively) on (a) liquid water saturation distribution and (b) The amount of liquid water remaining in the GDL, and in negative direction (140 /120 for GDBL-1 and GDBL-2, respectively) on (c) liquid water saturation distribution and (d) The amount of liquid water remaining in the GDL (according to the thickness of GDBL-1 changed from 0 mm (0%) to 300 mm (100%) with the same porosity of 0.8 for GDBL-1 and GDBL-2).
0 to 300 mm, the amount of liquid water remaining in GDBL-1 was increased and that in GDBL-2 was decreased. However, as shown in Fig. 4(c), the liquid water saturation in GDBL-1 was extremely increased so that the total amount of liquid water in GDL became larger than single GDBL. Therefore, double GDBL with porosity arrangement in negative direction with proper thickness ratio of GDBL-1 and GDBL-2 helps water retention. In fact, the effect of double GDBL with porosity arrangement in negative direction was verified experimentally in the previous researches [32,33]. In the researches, the cell showed a better performance with a modified GDL containing double GDBL with porosity arrangement in negative direction under low humidity conditions. However, the cell performance was worse under sufficiently humidified conditions, where water removal is more important than water retention. The result of this study is coincided with the result of Zhan et al. [20,21]. In their research, for the GDLs with the same equivalent porosity, they compared the effects of linear gradient and parabolic gradient. Then, they concluded that linear gradient is more effective than parabolic gradient. Based on the result of present study, the result is reasonable because linear gradient has parabolic gradient has combination effect of positive direction and negative direction of porosity. 3.2.2. Double GDBL with different hydrophobicity Since the degree of hydrophobicity can be represented by the contact angle (one of the measurable parameter) [24e32], in this study, contact angle was used to evaluate the effect of
hydrophobicity. Fig. 5 shows the effect of double GDBL with different contact angles on liquid water saturation distribution and the amount of water remaining each layer. In order to explore the directional effect of contact angle arrangement, for convenience, two different contact angle arrangements of 120 /140 and 140 / 120 were introduced to GDBL-1/GDBL-2. The thickness of GDBL-1 was also adjusted from 0 mm to 300 mm. As shown in Fig. 2, with single GDBL, water removal ability of GDL was improved with increased porosity and/or contact angle (hydrophobicity). In Fig. 4, water removal ability of GDL was improved with porosity arrangement of double GDBL in positive direction. Then, Fig. 5 shows similar trends but different tendency in property direction compared with the result shown in Fig. 4. In the case of contact angle, water removal ability of GDL was enhanced with the contact angle arrangement in negative direction. These results are reasonable in terms of capillary pressure. The liquid water in a porous media flows to the region where lower capillary pressure formed. In a porous media, capillary pressure is a function of porosity, contact angle, and liquid water saturation and can be expressed as
Pc ff ð3 ÞgðqÞJðSÞ
f ð3 Þ ¼
ð1 3 Þ 3
(18)
(19)
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I.M. Kong et al. / Energy xxx (2016) 1e10
gðqÞ ¼ cosðqÞ
(20)
JðSÞ ¼ 1:417S 2:120S2 þ 1:263S3
(21)
7
Then, as shown in Fig. 6, the capillary pressure decreases with increase of porosity and decrease of contact angle. Since relatively higher capillary pressure in GDBL-1 and lower capillary pressure in GDBL-2 helps water removal, double GDBLs with a porosity arrangement in positive direction and/or contact angle arrangement in negative direction were effective on improving water removal ability of GDL. 3.3. Optimization As mentioned, the amount of liquid water remaining in GDL should be as small as possible for effective water removal. Fig. 7 shows the minimum amount of water remaining in the GDL, Qmin, with optimized thickness ratio of GDBLs at each porosity and/ or contact angle arrangements. It was found that when the porosity of GDBL-2 was 0.9, Qmin appears regardless of contact angle arrangements. It means that, in order to maximize the water removal ability of GDL, the porosity of GDBL near the gas flow channel should be maximized. Also, when the porosity of GDBL-1 was smaller than that of GDBL-2 (porosity arrangement in positive direction), Qmin was minimized when the contact angles of GDBL1and GDBL-2 are maximized. Next, when the porosity of GDBL-1 was similar to that of GDBL-2 (single GDBL), Qmin was minimized when the difference of contact angles were maximized. Lastly, when the porosity of GDBL-1 was larger than that of GDBL-2 (porosity arrangement in negative direction), Qmin with the contact arrangement of 140 /130 and 140 /120 is the same as the result of 140 /140 except near the range where the porosity of GDBLs are the same. It was because porosity arrangement in negative direction significantly reduces water removal ability of GDL so that the Qmin appears when the thickness of GDBL-1 is 300 mm (single GDBL with GDBL-1). Based on the results shown in Fig. 7, the optimization can be classified into two cases; when the porosity of GDBL-2 is fixed to 0.9, and when the porosity of GDBL-1 and GDBL-2 are the same. Fig. 8(a) shows the minimum amount of liquid water remaining in GDL according to the varied porosity of GDBL-1, with a fixed porosity of 0.9 for GDBL-2. The corresponding thickness of GDBL-1 is shown in Fig. 8(b). The result shows that Qmin was remarkably changed between the porosity range of 0.8 and 0.9 for GDBL-1.
Fig. 7. The effect of porosity arrangements on the amount of liquid water remaining in the GDL with (a) the same contact angle and (b) the contact angle arrangement in negative direction for GDBL-1 and GDBL-2.
10
1.0 Pc ,high
Pc ,high
0.8
6
g(θ)
f(ε)
8
4 2
0.6 0.4 0.2
Pc ,low
Pc ,low
0.0
0 0.1
0.4
0.7
1.0
90
120
150
ε
θ
(a)
(b)
180
Fig. 6. The effect of (a) porosity and (b) contact angle on the capillary pressure in a porous media.
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8
I.M. Kong et al. / Energy xxx (2016) 1e10
3.4
εGDBL-2=0.9
2.7
(θGDBL-1, θGDBL-2) (120°, 120°)
(130°, 130°)
2.6
(140°, 140°)
(140°, 130°)
(140°, 120°)
(130°, 120°)
2.5 2.4
3.0 2.8 2.6
2.3
2.4
2.2
2.2 0.5
0.6
0.7
0.8
εGDBL-1=εGDBL-2
3.2
Qmin (mg)
Qmin (mg)
2.8
(θGDBL-1, θGDBL-2)
0.5
0.9
(120°, 120°)
(130°, 130°)
(140°, 140°)
(140°, 130°)
(140°, 120°)
(130°, 120°)
0.6
0.7
(a)
150
0.9
εGDBL-1=εGDBL-2
250
(120°, 120°)
(130°, 130°)
(140°, 140°)
(140°, 130°)
(140°, 120°)
(130°, 120°)
δGDBL-1 (μm)
δGDBL-1 (μm)
300
(θGDBL-1, θGDBL-2)
200
0.8
(a)
εGDBL-2=0.9
250
0.9
εGDBL
εGDBL-1
300
0.8
100 50
200 150 (θGDBL-1, θGDBL-2)
100
(140°, 130°) (140°, 120°)
50
(130°, 120°) 0
0 0.5
0.6
0.7
0.8
0.9
εGDBL-1
0.5
0.6
0.7
εGDBL
(b)
(b)
Fig. 8. Properties of double GDBL for (a) Minimum amount of liquid water remaining in GDL and (b) corresponding thickness of GDBL-1 for this, with a fixed porosity of 0.9 for GDBL-1.
Fig. 9. Properties of double GDBL for (a) Minimum amount of liquid water remaining in GDL and (b) corresponding thickness of GDBL-1 for this, with the same porosities of GDBL-1 and GDBL-2.
When the porosity of GDBL-1 was below 0.8, the change in Qmin is negligible. Since low porous layer increases the risk of flooding, the higher porosity of GDBL-1 is better for gas diffusion. As shown In Fig. 8(a), the lowest Qmin appeared when the porosity of GDBL-1 is 0.82 and contact angles are 140 /140 for GDBL-1/GDBL-2. In this case, the optimized thicknesses are 120 mm (40% of total thickness of GDBLs) for GDBL-1 and 180 mm for GDBL-2, respectively. With this optimized arrangement, Qmin was lowered by 9.2% compared with the lowest value of Qmin in MPL coated single GDBL (with 3GDBL ¼ 0.9, qGDBL ¼ 140 ). Next, Fig. 9(a) shows the minimum amount of liquid water remaining in GDL according to the varied porosity of GDBLs, when the porosity of GDBL-1 and GDBL-2 are the same. The
corresponding thickness of GDBL-1 is shown in Fig. 9(b). Although the contact angle arrangement was less effective on water removal compared with porosity arrangement, contact angle arrangement is still important and necessary. When the porosities of GDBL-1 and GDBL-2 are the same (3GDBL-1 ¼ 3GDBL-2), the lowest Qmin appeared when the contact angle arrangement is 140 for GDBL-1 and 120 for GDBL-2, respectively. Therefore, in order to find out GDBL properties for Qmin, the difference of contact angles should be maximized. In addition, the optimized Qmin appeared where 3GDBL1 ¼ 3GDBL-2 ¼ 0.9 with thicknesses of 203 mm (67.67% of total thickness of GDBLs) for GDBL-1 and 100 mm for GDBL-2, respectively. With this optimized arrangement of contact angle, Qmin was lowered by 5.6% compared with the lowest value of Qmin in MPL
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I.M. Kong et al. / Energy xxx (2016) 1e10
coated single GDBL (with
3GDBL
¼ 0.9, qGDBL ¼ 140 ).
4. Conclusions In this study, in order to improve the water removal ability of GDL, double GDBL structure was introduced. With one-dimensional steady-state model based on the capillary pressureesaturation relationship, the effect of porosity and contact angle arrangements of double GDBL was investigated under varied thickness ratio of GDBL-1 (0e100%). Since relatively higher capillary pressure in GDBL-1 and lower capillary pressure in GDBL-2 helps water removal, double GDBLs with a porosity arrangement in positive direction and/or a contact angle arrangement in negative direction were effective on improving water removal ability of GDL. In terms of water removal, the optimized porosity, contact angle and thickness of GDBLs are 0.82, 140 , 120 mm for GDBL-1 and 0.9, 140 , 180 mm for GDBL-2, respectively. If the porosity of GDBL-1 and GDBL-2 are the same, the optimized arrangement becomes 0.9, 140 , 203 mm for GDBL-1 and 0.9, 120 , 97 mm for GDBL-2, respectively. The result of this study provides an inspiration on how to design the property of double GDBL functionalized on water removal. Acknowledgements This work was supported by the Brain Korea 21 Plus Project (F14SN02D1310)of Seoul National University. This research was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2013R1A2A1A01014589). Nomenclature
Q C
Faraday constant (C mol1) molecular weight (g mol1) current density (A cm2) active area (cm2) Leverett J-function saturation capillary pressure (Pa) permeability (m2) relative permeability Kozeny constant porosity fiber diameter (m) volume (m3) flux (kg s1 m1) GDL thickness directional distance (mm) thickness(mm) surface tension (N m1) density (kg m3) dynamic viscosity (Pa s) kinematic viscosity (m2 s1) contact angle ( ) effective diffusion coefficient of water through membrane liquid water remaining in GDL (mg) integral constant
Subscript nw w l g P
non-wetting phase wetting phase liquid gas pore
F M i A J S Pc K kr kK 3
df V q x
d s r m n q a
H2O GDBL MPL
9
water gas diffusion backing layer micro porous layer
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