Analysis of the capillary-force-based μDMFC (micro direct methanol fuel cell) supplied with pure methanol

Analysis of the capillary-force-based μDMFC (micro direct methanol fuel cell) supplied with pure methanol

Energy xxx (2015) 1e6 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Analysis of the capillary-f...

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Energy xxx (2015) 1e6

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Analysis of the capillary-force-based mDMFC (micro direct methanol fuel cell) supplied with pure methanol Zhenyu Yuan a, Jie Yang a, *, Ning Ye a, Zipeng Li b, Yuge Sun a, Hongyuan Shen a a b

College of Information Science and Engineering, Northeastern University, Shenyang 110819, China Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 January 2015 Received in revised form 21 May 2015 Accepted 9 June 2015 Available online xxx

In this paper, a capillary-force-based mDMFC(micro direct methanol fuel cell) supplied with pure methanol is presented. A 2D (two-dimensional) steady state model is established to investigate the methanol distribution inside the low concentration chamber with the barrier layer patterned on different diffusion materials. Simulation results illustrate that both methanol diffusion coefficient of the barrier layer and the effective mass transfer area have significant effects on inner methanol distribution. In addition, the effect of capillary force at both inlet and outlet ends of the capillary channel between the pure methanol and the low concentration methanol are simulated. To further prove the feasibility of this supply method, a 3D (three-dimensional) transient model is finally established to monitor the variation of methanol concentration with the change of the operating duration. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Passive direct methanol fuel cell Supply method Pure methanol Capillary force

1. Introduction Passive mDMFC (micro direct methanol fuel cell) has been considered as one of the most attractive energy sources for portable electronics with the advantages of simple-structure, easy-to-store fuels, and exemption of auxiliary devices. Current studies show that the optimal concentration of the passive fuel cell is in the range of 4.0e6.0 mol L1 [1e4]. However, the conventional low concentration methanol supply in mDMFC will result in a limited lifetime of the fuel cell and frequent needs for fuel supply. Thus, significant attentions have been devoted to the mDMFC with highconcentration methanol recently. The key factor of improving the performance and the stability of mDMFC is to optimize the corresponding supply structure for high-concentration methanol [5e10]. Chan et al. [11] designed and fabricated the a mDMFC featured with a self-adjusted passive fuel supply method. The cell system includes a fuel reaction container, a storage container with spring, a valve to control fuel supply, and a pressure control valve. Under normal operating condition, the high-concentration methanol solution in the fuel storage container will be driven to the reaction container with reduced concentration. The major obstacle of this approach, however, is how to maintain the methanol concentration level in

* Corresponding author. Tel./fax: þ86 24 83683832. E-mail addresses: [email protected], [email protected] (Z. Yuan), [email protected] (J. Yang).

the reaction container in order to sustain the fuel supply and minimize the methanol permeation. Abdelkareem et al. [12] designed a novel porous graphite plate between the storage container and the anode plate, and concluded that this method was able to control the methanol transporting velocity. As such, the maximum power density of the cell can be raised up to 24 mW cm2 with the supply of 16.0 mol L1 methanol solution at room temperature. Even though the high-concentration methanol solution can result in a better cell performance, it cannot be directly supplied to the anode reaction region because high-concentration methanol solution may cause not only the water loss phenomenon in the PEM (proton exchange membrane) but also severe methanol permeation. Thus, in the design of mDMFC equipped with highconcentration methanol solution, it is critical to optimize the anode structure design so that the methanol solution with a proper concentration can be applied for reaction. In this study, the proposed structural design for pure methanol-supplied mDMFC is shown in the Fig. 1. The mass transfer barrier layer provides insulation between the pure methanol and the low-concentration methanol solution. During reaction, pure methanol is delivered to the low-concentration methanol container through a capillary channel when the methanol is consumed. The main advantage of this simple fuel supply mechanism is that it can prolong the stable discharge time and improve the specific energy density of the mDMFC. In our research, by systematically studying the diffusion coefficients of the material and carefully designing the capillary

http://dx.doi.org/10.1016/j.energy.2015.06.031 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Yuan Z, et al., Analysis of the capillary-force-based mDMFC (micro direct methanol fuel cell) supplied with pure methanol, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.06.031

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Fig. 1. Schematic of simulation domains.

channel, PTFE Polytetrafluoroethylene-based barrier layer is able to control the velocity of methanol solution and protect water from backward transferring. 2. Mass transfer model supplied with pure methanol 2.1. 2D steady-state model The 2D calculation region of double-containers in a passive

mDMFC is shown in Fig. 1(a), the active area is 1.0 cm2, and both of

the volume are 1.0 cm3. The established structure includes two storage containers, a barrier layer, an anode current collector, and an anode diffusion layer. This 2D model is able to describe the internal anode methanol transportation and the electroechemical reaction process. Several assumptions are made to simplify this model: (1) the mDMFC is always operating in a stable condition; (2) the anode catalyst layer is idealized as a linear boundary; (3) this model only considers the methanol consumption during reaction and diffusion processes. The mass transport can be described using the ConvectionDiffusion equation as follows:

  V$  Deff VC þ C:u ¼ R

(1)

where C denotes the concentration and Deff is the effective diffusion coefficient given by:

Deff ¼ Dε1:5 s1:5

(2)

where s is the liquid saturation and ε is the porosity. The momentum transport in diffusion layer is defined by Darcy law:



Kkr Vp ml

(3)

where K and kr represent the absolute permeability and the relative permeability, respectively, and m is the viscosity. kr in Equation (3) can be further modified as:

kr ¼ s

3

The continuity equation can be described as:

(4)

v ðrεÞ þ V$ðp:uÞ ¼ F vt

(5)

where r represents the density, and F is the source term. In this model, the external environmental conditions were set to the room temperature (293 K) and standard atmosphere pressure (1.013  105 Pa). According to [13] and [14], methanol diffusion coefficient in the barrier layer was selected within five groups from 2.0  1010 m2 s1 to 1.5  109 m2 s1. In addition, the open-ratio was set to be 0.4. The low-concentration methanol solution has direct contact with the MEA membrane. The variation of the low-concentration methanol solution is the main study focus in this paper because: (1) extremely high methanol concentration may cause the severe methanol permeation; (2) extremely low methanol concentration may cause the concentration polarization and significant cell performance degradation. According to the previous assumptions, the boundary conditionl for the interface between the pure methanol container and the barrier layer can be set as liquid inlet with the concentration of 24.5 mol L1 (pure methanol), and the corresponding internal boundary condition was set as continuous; II is the boundary of the anode catalyst layer, which can be set as liquid outlet with the corresponding flux quantity NMeOH described as:

NMeOH ¼

CMeOH;acl i i þ Deff þ nMeOH d MeOH;mem d 6F F mem

(6)

where i denotes the anode current density (A m2), Deff MeOH;mem represents the methanol diffusion coefficient in mass transfer membrane (m2 s1), CMeOH,acl is the methanol concentration in anode catalyst layer (mol L1), dmem is the thickness of electron exchange membrane (m), and nMeOH is the drag coefficient of the d methanol solution. The momentum transport was described by Darcy law in the calculation domain. The boundary between the current collector and the diffusion layer was set to be “pressure”. The momentum transport boundary on the anode catalyst layer was set as “inflow/ outflow”, and the concrete liquid velocity can be described as:

u_l ¼ ðNMeOH  MMeOH þ NH2O  MH2O Þ=rho_l

(7)

where MMeOH represents the molar mass of methanol (kg mol1), NH2O is the water permeation amount (mol (m2 s)1), MH2O is the

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molar mass of water (kg mol1), and rho_l is the density of methanol solution (kg m3). Coupling with momentum/mass transfer equations and electroechemical reaction equation, the established 2D model can be solved using FEA (finite element analysis) method. The steady-state concentration distribution in low-concentration container with different barrier layer diffusion coefficients is shown in Fig. 2 when the operating current is set as 30 mA. Five different methanol diffusion coefficients of 2  1010 m2 s1, 5.25  1010 m2 s1, 8.5  1010 m2 s1, 1.175  109 m2 s1 and 1.5  109 m2 s1 were selected during the simulation, and the corresponding average methanol concentration are 8.091 mol L1, 8.685 mol L1, 9.212 mol L1, 9.725 mol L1 and 10.232 mol L1, respectively. The data indicates that larger methanol diffusion coefficient yield higher methanol concentration in the low-concentration container. Therefore, the barrier layer with the lowest methanol diffusion coefficient is the optimal candidate for the methanol permeation inhibition. This 2D steady-state model validated our prediction that the anode double-container structure could replenish pure methanol solution from the high-concentration container to the lowconcentration container through the barrier layer. Simulation results proved that an appropriate mass transfer barrier layer could be greatly helpful to achieve the equilibrium between the methanol supplement and consumption. It is also demonstrated that transfer barrier layer with lower diffusion coefficient is more effective. Therefore, this novel anode structure is capable of improving the energy density of the mDMFC.

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2.2. Improved 2D steady-state model The model in the previous subsection utilized the barrier layer with different diffusion coefficients to optimize the supply of the pure methanol for the mDMFC. However, the methanol concentration in the low-concentration container was still slightly higher than the desired level. Methanol diffusion coefficient and open porosity are difficult to change because of the characteristics of the material. Meanwhile, it is simpler and more efficient to optimize the mass transfer quantity by controlling the size of the effective diffusion area. In this subsection, the barrier layer boundary is reduced to the 10% and 5% of the original length while the other conditions remain the same. The PTPF-based hydrophobic barrier layer was selected as the insulation between the high-concentration and low-concentration containers. Capillary-force-based transport process in the barrier layer was also simulated to demonstrate the proposed supply method. In the simulation, the diameter of capillary channel was set to be 0.5 mm, 5% of the original length. The calculation domain is shown in Fig. 1(b) (see the magnified area). Because the simulation region is symmetric, the calculation was performed only on the right half of the capillary area in order to reduce the computational load. Based on the principle of the surface tension, methanol transporting process in the capillary channel was analyzed. The whole process from methanol entering the capillary channel to reaching the final steady state is shown in Fig. 3, which reveals that the methanol molecules started to permeate along the capillary

Fig. 2. Methanol concentration with different diffusion coefficients.

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Fig. 3. The process of methanol entering the capillary channel.

channel to the low-concentration container immediately after the pure methanol contacted capillary channel (T ¼ 0). As shown in the figure, wall-attachment effect appeared when the methanol solution entered capillary channel. At T ¼ 7.5  105 s, liquid surface inclination reached its maximum value, and the wall-attachment effect was reduced with the increase of the methanol solution entering the capillary channel; At T ¼ 1.75  104 s, methanol solution completely entered the capillary channel and a “concave curve” was formed by the liquid surface. Meanwhile, methanol in the capillary channel continued permeating to low-concentration container owing to the capillary effect. Fig. 4 indicates that: (1) At T ¼ 4.75  104 s, pure methanol occupied half of the capillary channel length; (2) At T ¼ 9.75  104 s, pure methanol entirely passed the capillary channel and reached low-concentration container. The corresponding methanol concentration distribution is shown in Fig. 5, given the effective transferring boundary of the barrier layer is 10% of the full-length. The diffusion coefficients of the three planes from the bottom to the top of the figure are 2  1010 m2 s1, 8.5  1010 m2 s1 and 1.5  109 m2 s1, respectively. When the diffusion coefficient of barrier layer are 1.5  109 m2 s1 and 8.5  1010 m2 s1, the average methanol concentration are 9.046 mol L1 and 8.538 mol L1, which slightly decreased when compared with the previous results. The average methanol concentration in the anode diffusion layer is 7.168 mol L1 when the diffusion coefficient is 2  1010 m2 s1. The simulation of the methanol concentration distribution was also carried out when the effective transferring boundary of barrier layer is 5% of the full-length, as shown in Fig. 6. As can be observed from the figure, when the diffusion coefficient of barrier layer are 1.5  109 m2 s1 and 8.5  1010 m2 s1, the average methanol concentration are 8.296 mol L1 and 6.724 mol L1. The bottom plot is the methanol concentration distribution with the diffusion coefficient of 2  1010 m2 s1. In this case, the average methanol concentration in low concentration container is 5.025 mol L1, which is within the best concentration range for passive mDMFC.

Based on above studies, it is efficient to control anode methanol distribution via decreasing the effective transferring region. Furthermore, with the precise control of the methanol distribution, pure methanol can be slowly transported from the highconcentration container to the low-concentration container while maintaining the optimal methanol concentration and inhibiting the methanol permeation effectively.

3. 3D transient model The simulation results of previous 2D stable model indicate that the anode double-container structure could facilitate the supply of the pure methanol. In addition, the methanol solution that directly contacts the MEA can also be maintained in a proper concentration range via improving the effective diffusion area of the barrier layer. To further demonstrate the applicability of the proposed structure, a 3D transient model was also established to analyze the methanol variation in the low-concentration container. The established 3D model is similar to the 2D model, but the assumption of operating condition is changed from the steady state to the transient state. The calculation domain is shown in Fig. 1(c). Based on the simulation results of 2D steady model, the methanol diffusion coefficient in the barrier layer was selected to be 2  1010 m2 s1, and the effective area was set to be 0.25% of the whole area since the area ratio was equal to the square of the boundary ratio. Because there was a concentration gradient for the methanol solution in the container, the central point in the lowconcentration container was selected as the reference point for recording the change of the methanol concentration. Fig. 7 depicts the variation of the methanol concentration in the low-concentration container at different discharging time. It can be observed that methanol concentration in the low-concentration container illustrates an extreme slow declining trend, and the novel supply method shows a relatively stable performance. After the fuel cell had been discharged for 30 h with a constant

Please cite this article in press as: Yuan Z, et al., Analysis of the capillary-force-based mDMFC (micro direct methanol fuel cell) supplied with pure methanol, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.06.031

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Fig. 4. The process of methanol passing the capillary channel.

discharging current of 30 mA, methanol concentration in the lowconcentration container decreased from 5 mol L1 to 3.8 mol L1. To demonstrate the advantage of the proposed method, a comparison was conducted to the conventional structure in which the cell patterned with only low-concentration container of 5 mol L1. As shown in Fig. 7(b), there are obvious variations in the

output of the conventional structure, followed by a gradual decrease. After 8 h of discharging, methanol concentration in the low-concentration container decreased dramatically to 1.5 mol L1. The simulation results of 3D transient model shows that the barrier layer not only stabilizes the supply of the pure methanol, but also effectively prolongs the operating time.

Fig. 5. Distributing of methanol concentration with 10% of the full-length.

Fig. 6. Distributing of methanol concentration with 5% of the full-length.

Please cite this article in press as: Yuan Z, et al., Analysis of the capillary-force-based mDMFC (micro direct methanol fuel cell) supplied with pure methanol, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.06.031

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Fig. 7. Variation curve of the methanol concentration in the low-concentration container.

4. Conclusion In this paper, the supplying method of pure methanol for passive mDMFC was implemented based on the capillary force, and the capillary channel between the high-concentration container and the low-concentration container was applied to ensure the stable fuel supplying. A multi-physics model coupled with mass and momentum transport was established to investigate the steadystate methanol distribution under different diffusion coefficients. Furthermore, the optimal design of anode structure was conducted using the barrier layer patterned with capillary channels for different open-ratios, and the complete process of the methanol transportation in the capillary channel was also analyzed. Finally, a 3D transient model was established to observe the methanol variation in the low-concentration container at different operating duration. The results revealed that the average methanol concentration was 5.025 mol L1 when diffusion coefficient in the barrier layer was 2  1010 m2 s1, which is in the best range for passive mDMFC. The transient model also revealed that methanol concentration in the low-concentration container decreased from 5 mol L1 to 3.8 mol L1 when the cell was discharged for 30 h at the constant current of 30 mA. Simulation results proved that the proposed supply method could effectively prolong the operation time of the fuel cell. The analysis provides a theoretical foundation for the portable application of mDMFC. Acknowledgments The work described in this paper was supported by the National Natural Science Foundation of China (No. 61372015), Research Fund for the Doctoral Program of Higher Education (No.

20130042120023) and Fundamental Research Funds for the Central Universities in China (No. N140403001 and No. N120204001). References [1] Carton JG, Lawlor V, Olabi AG, Hochenauer C, Zauner G. Water droplet accumulation and motion in PEM (proton exchange membrane) fuel cell minichannels. Energy 2012;39:63e73. [2] Carton JG, Olabi AG. Design of experiment study of the parameters that affect performance of three flow plate configurations of a proton exchange membrane fuel cell. Energy 2010;35:2796e806. [3] Na YS, Kwon JM, Kim H, Cho HJ, Song Inseob. Characteristics of a direct methanol fuel cell system with the time shared fuel supplying approach. Energy 2013;50:406e11. [4] Tafaoli-Masoule M, Bahrami A, Elsayed EM. Optimum design parameters and operating condition for maximum power of a direct methanol fuel cell using analytical model and genetic algorithm. Energy 2014;70:643e52. [5] Ye Q, Zhao TS. A natural-circulation fuel delivery system for direct methanol fuel cells. J Power Sources 2005;147:196e202. [6] Xu C, Faghri Amir, Li XL. Methanol and water crossover in a passive liquid-feed direct methanol fuel cell. Int J Hydrogen Energy 2010;35:1769e77. [7] Guo Z, Cao Y. A passive fuel delivery system for portable direct methanol fuel cells. J Power Sources 2004;132:86e91. [8] Yang YM, Liang YC. A direct methanol fuel cell system with passive fuel delivery based on liquid surface tension. J Power Sources 2007;165:185e95. [9] Eccarius Steffen, Tian XH, Krause Falko. Completely passive operation of vapor-fed direct methanol fuel cells for portable applications. J Micromechanics Microengineering 2008;18:1e9. [10] Kim HK. Passive direct methanol fuel cells fed with methanol vapor. J Power Sources 2006;162:1232e5. [11] Chan YH, Zhao TS, Chen R. A small mono-polar direct methanol fuel cell stack with passive operation. J Power Sources 2008;178:118e24. [12] Abdelkareem Mohammad Ali, Yoshitoshi Tsukasa, Tsujiguchi Takuya. Vertical operation of passive direct methanol fuel cell employing a porous carbon plate. J Power Sources 2010;195:1821e8. [13] Wang ZH, Wang CY. Mathematical modeling of liquid-feed direct methanol fuel cells. J Electrochem Soc 2003;150:508e19. [14] Chen R, Zhao TS, Yang WW. Two-dimension two-phase thermal model for passive direct methanol fuel cells. J Power Sources 2008;175:276e87.

Please cite this article in press as: Yuan Z, et al., Analysis of the capillary-force-based mDMFC (micro direct methanol fuel cell) supplied with pure methanol, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.06.031