Pore network modelling for fuel cell diffusion media

Transcription

1 Pore network modelling for fuel cell diffusion media A. Bazylak, V. Berejnov, D. Sinton and N. Djilali Department Dept. of Mechanical Engineering and Institute for Integrated Energy Systems, University of Victoria, Victoria, British Columbia, Canada (Bazylak), (Berejnov), (Sinton), (Djilali) ABSTRACT Over the past ten years, pore network modelling has mainly been used to study displacement processes in idealized porous media related to geological flows, with petroleum and environmental applications. In this work, the application of pore network modelling to elucidate transport phenomena in the fuel cell gas diffusion layer (GDL) is discussed. Studying the GDL with pore network modelling requires the appropriate definition of network parameters to describe the media as well as the conditions of fluid invasion that represent realistic transport processes. We begin with a two-dimensional pore network model with a single mobile phase invading a hydrophobic media, whereby the slow capillary dominated flow process follows invasion percolation. Pore network geometries are designed for directed water transport, and transparent hydrophobic microfluidic networks are fabricated. Comparisons between the numerical and experimental flow patterns show reasonable agreement. 1 INTRODUCTION In the polymer electrolyte membrane fuel cell (PEMFC), hydrogen is introduced at the anode, and oxygen is introduced at the cathode, as shown in Fig. 1. These gases travel through the gas distribution channels of the bipolar plates and diffuse through the gas diffusion layer (GDL) to reach their respective catalyst layers, where electrochemical reactions of hydrogen oxidation and oxygen reduction occur. Inlet gases, hydrogen and oxygen, are typically humidified so that when they reach the catalyst layer, they help hydrate the membrane to ensure ionic conductivity. At the anode, hydrogen splits into protons and electrons, and while protons travel through the membrane, electrons travel through an external load to reach the cathode. At the cathode, oxygen combines with these electrons and protons to produce water and heat. bipolar plate catalyst (anode) GDL load membrane GDL H e - 2 H + O 2 e - catalyst (cathode) bipolar plate Figure 1: Schematic of a PEMFC. H O 2 The successful operation of the PEMFC relies on water management. An inadequate amount of water in the fuel cell can lead to membrane dehydration, which can accelerate membrane degradation, such as holes, that could potentially lead to fuel cross-over [2]. However, excess liquid water in the GDL can lead to flooding, a situation in which reactant gases are restricted from reaching the catalyst sites [1, 6]. Flooding in the gas channels also inhibits gaseous transport, in addition to causing non-uniform reactant distributions and parasitic pressure losses. Further losses could be introduced by the hindrance of waste heat in a flooded GDL [3]. Fuel starvation can also lead to severe electrocatalyst degradation through cell reversal [7]. The presence of liquid water also leaves the fuel cell vulnerable to further mechanical degradation resulting from ice formation and operation at sub-freezing temperatures [3, 9]. The GDL is typically 200 µm thick and composed of carbon fibers either oriented randomly and pressed

2 together (carbon paper) or woven together (carbon cloth). The GDL is sandwiched on both sides of the membrane electrode assembly, as shown in Fig. 1, and provides several key functions. It provides mechanical support for the membrane electrode assembly. The highly conductive carbon fibers provide pathways for electronic transport between the catalyst layer and the current collecting plates. The void spaces that result from the fiber orientation provide pathways for gaseous fuel transport and excess heat removal. The GDL is also treated with a hydrophobic coating to enhance excess liquid water removal. Excess liquid water is a major limiting factor to increased performance, durability and lifetime, which is why there is great interest to investigate liquid water transport in this complex hydrophobic media. However, the opaque nature of the GDL, as shown in Fig. 2, currently used in the PEM fuel cell greatly limits the direct observation of through-plane water transport. This limitation provides challenges to identifying and understanding the transport processes that govern two phase flow in this complex media, and in turn this inhibits the advancement of water management techniques needed to improve fuel cell performance. Pore network models provide an alternative to continuum phase models to elucidate transport phenomena and determine transport parameters in porous media. Continuum modelling of porous media becomes unattractive when the porous media has a complex three-dimensional heterogeneous and disordered geometry, such as the gas diffusion layer. Numerically tracking phase interfaces and calculating surface tension forces becomes computationally expensive. In contrast, pore network modelling is an intermediate approach where the disordered porous media is represented by an equivalent network of pores and throats, and the throats are assigned varying hydraulic conductivities. In this work, we will discuss the employment of a GDL-representative pore network model to design porous media with directed water transport. An inhouse software package [4] featuring invasion percolation with trapping is employed to numerically model the drainage process [8]. Transparent experimental microfluidic chips containing these pore networks are employed to compliment the development of a GDLrepresentative pore network model. Invasion flow patterns are visualized in the transparent microfluidic networks using fluorescence microscopy, and the time series evolution of liquid water transport through the networks are measured. Figure 2: SEM image of Toray gas diffusion paper TGP-H-060. Length bar represents 200 µm. 2 PORE NETWORK MODEL In pore network modeling, a porous media, such as the GDL, is mapped into a set of interconnected pores and throats (Fig. 3), where the throats are assigned varying hydraulic conductivities. In capillary dominated flows (such as slow drainage), a simplified displacement criterion can be implemented. In the invasion percolation with trapping model, the throat with the largest conductivity at the interface is invaded by the invading fluid at each discrete step, and the formation of phase clusters is tracked. The conservation of mass is calculated for each pore in the network, producing a set of linear equations that are used to solve for pore pressures. A network realization produces a static configuration of the invading phase pattern. Each network realization is deterministic, which means the static invading phase pattern is determined by the throat size distribution of the network. Pore Throat Figure 3: Schematic of a pore network illustrating location of pores and throats. In this work, square pore networks of dimension n L x n L were employed. The invading phase entered the network along the top side (inlet), and the invad-

3 ing fluid propagated through toward the opposite side (outlet). The invasion was stopped once breakthrough was reached, where breakthrough is defined as when the first throat at the outlet is filled with the invading fluid. Previously, this model was applied to perform a stochastic analysis of relative permeability, capillary pressure and their dependence on invading phase saturation [4]. Since each simulation is deterministic, several random realizations were performed to investigate variations in the multiphase parameters. In this work, the deterministic nature of the pore network invasion provided a useful tool to compare with experimental results. Fig. 4 shows a sample numerical breakthrough pattern in relation to a fuel cell schematic. Membrane electrode assembly Figure 5: Schematic illustrating the photomask generation process: (a) regular square lattice, (b) translation of regular lattice in both the horizontal and vertical directions, (c) resulting arrangement of random pore network. directions. To implement a diagonal bias of Θ bias = 45, for each square obstacle, Y = X. The ratio of vertical to horizontal obstacle translations can be adjusted to implement the desired diagonal bias for 0 < Θ bias < 90, as shown in Eqn. 1. GDLs Bipolar plate tanθ bias = Y X (1) Gas channel Figure 4: Schematic showing the pore network model results of an example simulation with respect to PEMFC geometry. 2.1 Pore Network Design The pore network generation procedure begins with a regular lattice of square obstacles. Fig. 5 (a) shows a schematic of the regular lattice, where w is the throat width, and L is the obstacle square side length. A random translational perturbation is then applied to each obstacle, as shown in Fig. 5 (b), where X refers to the horizontal translation, and Y refers to the vertical translation of the original obstacle. Fig. 5 (c) is the resulting schematic of a portion of the random pore network. All hydraulic throat radii employed in this work are characteristic of Toray TGP-H-060 gas diffusion layers [5] Radial Gradients The procedure to generate a pore network with a radial gradient is illustrated in Fig. 6. The first step is to begin with a regular lattice of square obstacles, as shown in Fig. 6 (a). (a) (c) w L Y r X (b) (d) L w Y R X Diagonal Bias To generate an isotropic random pore network, the translation of the regular lattice in the horizontal direction X and the vertical direction Y must be independent. It is also possible to generate a random pore network with a diagonal bias by coupling the translation of the regular lattice in the horizontal and vertical Figure 6: Procedure for generating photomask for a pore network with a prescribed radial gradient: (a) regular square lattice, (b) radial translation of individual square obstacles, (c) network with radial gradient, (d) random perturbations applied to the network with a radial gradient.

4 The distance of each square obstacle from the central coordinate axis is labeled r. The square obstacle is then translated in the radial direction to a new radial distance, R, from the origin, as shown in Fig. 6 (b). The new radial distance, R, is transformed by the following expression: R r + αr2 r max (2) Where, α is the coefficient that is employed to vary the radial gradient of the network. The radial gradient, G, is the increase in throat width per obstacle, beginning from the central coordinate axis. After a regular network (with radial distance, r) is transformed into a new network (with radial distance, R), the radial gradient, G, was numerically measured. Numerical tests yield the following expression between G, α, r max, and N: G = 4r max N 2 α (3) Fig. 6 (c) shows the resulting pore network design when a radial gradient has been applied to the regular lattice of square obstacles. The final step is to apply a random translation with independent horizontal ( X) and vertical ( Y) perturbations to each obstacle. An example of the resulting pore network pattern is shown in Fig. 6 (d). Figure 7: Microfluidic fabrication procedure for network chips: (a) a high resolution network photomask is produced with AutoCAD; (b) a substrate is coated with a 25 µm thick photoresist layer and polymerized with UV exposure; (c) non-polymerized photoresist is chemically etched leaving a planar 3D network structure (master); (d) a PDMS cast produces the elastomeric replica of the network, which can be assembled irreversibly within the PDMS base (e1), and the flow pattern can be measured (e2). 3 MICROFLUIDIC FABRICATION Fabricating the microfluidic network consisted of four stages: designing and printing a network photomask (Fig. 7 (a)), fabricating a master (Fig. 7 (b, c)), fabricating an elastomer replica (Fig. 7 (d)), and assembling the microfluidic chip (Fig. 7 (e1)). The result was a transparent elastomeric microfluidic chip, which consisted of a system of rectangular (25 x L x W µm) microscale channels embossed in a PDMS polymer (Fig. 7 (e)). The length, L, and width, W, of the channels were distributed in the following ranges: L ( µm), W ( µm), respectively. The dimensions of the square networks were approximately 15 mm x 15 mm, with approximately 5000 throats. As shown in Fig. 7 (a), the mask manifiold consisted of: delivery channels (1, 2), pressure-drop channels (3), inlet/outlet manifolds (4), and the pore network pattern. Once the network patterns were designed and generated, they were inserted into the AutoCAD template. AutoCAD drawings were printed on transparencies with a high resolution (5K, 10K, and 20K dpi) commercial printer (Outputcity, California). These transparencies were employed as photomasks for fabricating the negative masters. A microscope glass slide (75 mm x 51 mm, Esco, NH) was spin-coated with SU8-25 epoxy negative tone photoresist (MicroChem, USA) and subjected to a prebaking period 20 min. A photomask was placed over the solid photoresist film and exposed to UV light as indicated in Fig. 7 (b). After 4 min of exposure, the slide was post baked for approximately min at 95 C to enable polymer cross linkage. The slide was submerged in SU8 developer (MicroChem, USA) for approximately 2 min to remove the non-polymerized SU8-25 photoresist. The developed slide was dried with a high pressure air jet and heated at 95 C for 30 min to produce the channel network. A polymethylsiloxane (PDMS) polymer (Sylgard 184, Dow Corning, NY) was cast against the master and cured, as shown in Fig. 7 (d). This yielded an elastomeric replica containing a positive structure of the network channels. The PDMS replica was combined with a PDMS covered glass slide, as shown in Fig. 7 (e1).

5 4 RESULTS Flow visualizations were achieved using a Leica DMI 6000B fluorescence inverted microscope: HCX PL Fluotar 1.25 x 0.04 objective (Leica, Germany) with Leica LAS AF fluorescence-image-operation software. The microscope stage scans were synchronized with image acquisition using a high resolution, highly sensitive CCD camera (Hamamatsu Orca AG). Each network image was assembled from individual images from each of the four quadrants (Fig. 7 (e2)) within a time period of 2 s. An aqueous solution of fluorescein was utilized. Fluid flow was controlled with a syringe pump employing flow rates ranging from Q = L/min. These flow rates correspond to capillary numbers, Ca, in the range of , which are representative of the GDL in PEM fuel cell operating conditions. Numerical and experimental pore networks with identical network templates were invaded with liquid water. Fig. 8 shows the numerically and experimentally determined breakthrough patterns for 48 x 48 pore networks with (a) isotropic perturbations, (b) diagonally biased perturbations, and (c) a radial gradient. For each network design in Fig. 8 shown from left to right are: a scaled down schematic version of the photomask, the numerical breakthrough and the experimental breakthrough patterns. Fig. 8 shows that the influence of relatively minor long range perturbations can significantly alter liquid water transport in the porous medium. By comparing the percolation patterns shown in Fig. 8 (a) and (b), the effect of a diagonal bias on the pore network compared to the isotropically random pore network is evident. This influence on transport is particularly significant considering that the visual difference in network geometry is relatively minor (compare the Photomask column), and cannot be detected when comparing their respective photomasks alone. Fig. 8 (c) illustrates the effect of a radial gradient on the liquid water transport. With a positive radial gradient, larger throat sizes are located around the outer edges of the pore network. As expected in a hydrophobic medium, the liquid penetrates the throats with the lowest threshold capillary pressure, which are the largest throats. With an applied radial gradient, the liquid saturation is zero at the center of the network and increases with radial distance from the center. With this radial gradient design, liquid water percolates along the outer left and right sides of the network, until breakthrough is achieved. The radial gradient effectively provides directed water transport along the sides of the media. (a) (b) (c) Photomask Numerical Experimental Figure 8: Comparison of numerical and experimental random pore network breakthrough patterns for (shown left to right): (a) isotropic perturbations, (b) diagonally biased perturbations, and (c) radial gradient. Each numerical and experimental result comparison is accompanied by a portion of the actual photomask schematic with a reduced number of obstacles for clarity (along left column).

6 5 CONCLUSIONS In this work, we discussed the application of a quasistatic pore network model for directed water transport in porous media. This two-dimensional pore network model consisted of a single mobile phase invading a hydrophobic media, whereby the slow capillary dominated flow process followed invasion percolation. The procedure to design isotropically and diagonally biased networks was described. Microfluidic network fabrication using soft lithography was described, and the experimental and numerical flow patterns showed reasonable agreement. The implementation of directed water transport in GDLs has the potential to improve liquid water management and improve the lifetime and durability of the PEM fuel cell. ACKNOWLEDGEMENTS The authors are grateful for the financial support of the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Canada Research Chair Program, and the National Research Council (NRC). The authors would also like to acknowledge the support of the Canadian Foundation for Innovation (CFI). [6] U. Pasaogullari and C.-Y. Wang. Liquid water transport in gas diffusion layer of polymer electrolyte fuel cells. Journal of the Electrochemical Society, 151 (3):A399 A406, [7] A. Taniguchi, T. Akita, K. Yasuda, and Y. Miyazaki. Analysis of electrocatalyst degradation in PEMFC caused by cell reversal during fuel starvation. Journal of Power Sources, 130:42 49, [8] D. Wilkinson and J. Willemsen. Invasion percolation: a new form of percolation theory. Journal of Physics A: Mathematical and General, 16: , [9] Q. Yan, H. Toghiani, Y. Lee, K. Liang, and H. Causey. Effect of sub-freezing temperatures on a PEM fuel cell performance, startup and fuel cell components. Journal of Power Sources, 160(2): , Oct REFERENCES [1] T. Berning and N. Djilali. A three-dimensional, multi-phase, multicomponent model of the cathode and anode of a PEM fuel cell. Journal of the Electrochemical Society, 150(12):A1589 A1598, [2] S. Knights, K. Colbow, J. St-Pierre, and D. Wilkinson. Aging mechanisms and lifetime of PEFC and DMFC. Journal of Power Sources, 127(1-2): , Mar [3] J. Kowal, A. Turhan, K. Heller, J. Brenizer, and M. Mench. Liquid water storage, distribution, and removal from diffusion media in PEFCS. Journal of the Electrochemical Society, 153(10):A1971 A1978, [4] B. Markicevic, A. Bazylak, and N. Djilali. Determination of transport parameters for multiphase flow in porous gas diffusion electrodes using a capillary network model. Journal of Power Sources, 171(2): , [5] M. Mathias, J. Roth, J. Fleming, and W. Lehnert. Handbook of Fuel Cells, chapter Diffusion media materials and characterization, pages John Wiley & Sons, Ltd., New York, 2003.