Dynamic Percolation and Droplet Growth Behavior in Porous

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Dynamic Percolation and Droplet Growth Behavior in Porous Electrodes for Polymer Electrolyte Fuel Cells Charles Quesnel, Ren Cao, Jorge Lehr, Anne-Marie Kietzig, Adam Z Weber, and Jeff T Gostick J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b06197 • Publication Date (Web): 09 Sep 2015 Downloaded from http://pubs.acs.org on September 23, 2015

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The Journal of Physical Chemistry

Dynamic Percolation and Droplet Growth Behavior in Porous Electrodes of Polymer Electrolyte Fuel Cells Charles Quesnel1, Ren Cao1, Jorge Lehr2, Anne-Marie Kietzig2, Adam Z. Weber3 and Jeff T. Gostick1,a

1

Porous Materials Engineering and Analysis Lab Department of Chemical Engineering McGill University Montreal, QC H3A 2B2

2

Surface Engineering Lab Department of Chemical Engineering McGill University Montreal, QC H3A 2B2

3

Lawrence Berkeley National Lab Energy Storage and Distributed Resources Division Berkeley, CA 94720

a

corresponding author: [email protected]

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Abstract The percolating flow of liquid water in the gas-diffusion layer (GDL) of polymer-electrolyte fuel cells (PEFCs) was studied ex situ using a simple water-injection experiment. Water was injected into the top of the sample so the droplet was free to detach from the bottom, allowing for uninterrupted study of the dynamic cycle of droplet appearance, growth, and detachment. Although droplets emerged from a single point on the GDL, the measured pressure response in the water phase was clearly not equivalent to a single needle. The behavior of the system was explained by the simultaneous filling and inflating of many menisci, resulting in extended periods with no droplet activity at the GDL surface, followed by the sudden eruption of a droplet at the breakthrough site as all interfaces deflated and their stored water was directed towards the droplet. A simple numerical model was presented that could qualitatively explain the observed behavior. Tests were performed on GDLs, with and without microporous layers (MPLs) and all observed behavior could be interpreted in terms of the proposed model. MPLs shifted the behavior to a more needle-like behavior which was consistent with the MPL reducing the number of invading liquid clusters in the system.

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1. Introduction Understanding the impact of water inside polymer-electrolyte fuel cells (PEFCs) on their performance is a long-standing challenge. One of the main difficulties with this research has been the poorly understood behavior of water in the porous fuel-cell electrodes, which differ in important ways from conventional porous materials such as rock and sand. PEFC electrodes are a multilayered sandwich of a fibrous medium or gas-diffusion layer (GDL) and a porous coating called the microporous layer (MPL) with pore sizes differing by several orders of magnitude from the GDL; they are very thin (80%); have a neutral wettability with non-wetting additives such as polytetrafluoroethylene (PTFE).

Many of these

characteristics have been designed or engineered into the electrode in an attempt to avoid or at least manage the presence of liquid water and multiphase flow in the pore space1–3. In most cases it is not clear how and why these features work, or how to develop improved designs. For instance, the presence of the highly hydrophobic MPL has long been known to aid operation at high-current-density conditions4,5, however, several reports have now appeared on the benefits of incorporating hydrophilic particles into the MPL matrix which presumably provide some water storage or route of low resistance for water escape6–8. This apparently contradicts the belief that the MPL should be hydrophobic9,10, and certainly highlights the empirical trial-anderror approach to electrode design insofar as water management is concerned. The complex nature of these layers and the lack of insight into the physical processes occurring within them clearly hinder the design of improved electrode assemblies. Moreover, it is difficult to develop a valid multiphase fuel-cell model to predict performance since the role and impact of liquid water is challenging to include. It is known from visualization studies on cells with transparent flow fields11,12, and x-ray13–16 radiography or tomography studies that liquid water does indeed flow from the catalyst layer (CL) to the channel through the MPL and GDL in some form of capillary invasion. One common observation in these works is the so-called ‘eruptive’ nature of water transport, meaning that water emerges from the GDL in discrete droplets. Moreover, these droplets tend to appear at the same location and at a relatively constant frequency.

This general behavior can be

qualitatively understood in terms of invasion percolation, since water will exit the GDL by a

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pathway of the largest accessible pores, which naturally terminates on the GDL outlet at a single location.

Furthermore, because the liquid is constantly generated at the CL by the

electrochemical reaction, the droplet continuously grows until it reaches some ‘critical’ size and detaches11,12,17, whence droplet growth starts anew.

This description, however, does not

consider the behavior of water inside the porous layers and out of sight. Furthermore, very few studies have looked closely at percolation in dual-layer materials such as GDLs with MPLs. The MPL is particularly enigmatic. Many attributes have been ascribed to this layer in attempts to explain its beneficial effects, including forcing water to the anode9,18, forcing single point injection into the GDL10,19,20, and increasing the thermal resistance to vaporize water21–23. Most likely, the MPL plays any or all of these roles at least part of the time, and additional insights are needed. Numerous experimental investigations have considered the behavior of liquid water percolating through GDLs with and without MPLs in controlled ex-situ tests. Litster et al24 conducted some early work on injection of water into the GDL, while visualizing the top outlet surface with a microscope.

As they were only interested in the evolution of the liquid

configuration inside the GDL, the experiment was terminated upon breakthrough. Their main finding was that multiple fingers of water invaded into the GDL simultaneously, and that some fingers appeared to retract as others advanced. There are two problems with this explanation, however. Firstly, the finger in question only retracted 10 µm, whereas pore sizes were on the order of 20 to 40 µm.

Secondly, it has since become clear that liquid water does not

spontaneously retract from GDL materials25 due to their modest hydrophobicity, more aptly called “neutral wettability”. Gao et al26 extended the work of Litster et al. by measuring the liquid-phase pressure during injection, as well as injecting past the point of breakthrough to observe multiple droplet formation cycles. They saw that the liquid pressure followed a sawtooth pattern as each droplet grew, but because they injected in the upward direction the accumulation of water on top of the sample quickly interfered with the experiment. They did not report observing any spontaneous retraction of water fingers. Similar experiments were conducted by Bazylak et al27 with the outlet face arranged as a gas flow channel so droplets were swept away to some extent. They reported saw-tooth pressure spikes due to droplet 4 ACS Paragon Plus Environment

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eruption, but they too had eventual water accumulation (‘slug flow’) in the outlet channel that terminated the experiment. They observed that water breakthrough occurring at one point could cease in preference to another point elsewhere. The meaning of this result is difficult to interpret due to the impact of flowing gas, potential evaporation, and droplets moving about on the outlet face. There are a number of other experimental studies in the literature that have investigated water breakthrough behavior28,29,29–31, but these generally all include a flow fieldtype sample holder and/or flowing gas so the pure behavior of the droplet growth-anddetachment cycle is disrupted or obscured.

Numerous other reports of liquid water

breakthrough and flow through GDLs are available, but these don’t focus on the droplet behavior, and focus on threshold pressures32 or permeability of the layer33,34 as functions of hydrophobic treatment or compression. Gostick et al35 presented a related experiment with the sample holder inverted such that the outlet face was oriented down. This was a crucial difference since liquid-water droplets could easily detach by gravity and fall away to make room for subsequent drops, enabling the growth-detachment cycle to repeat uninterrupted, yielding a very repetitive saw-tooth pressure profile. It was noted that there was a fairly long time gap (i.e. 10 to 20 s) between the detachment and reappearance of the next drop. It was speculated that some of the water from within the GDL was entrained with the falling droplet, and the time lag was due to refilling the water pathway to the outlet. As will be shown below, however, this explanation is probably not correct.

Liu and Pan36 investigated the droplet growth-and-

detachment cycle, but they did not provide a complete theoretical explanation for their results. In the present work, the ‘eruptive’ water-droplet behavior is considered in more detail, with particular focus on the liquid-pressure response of the system rather than visualizing the liquid water behavior. The droplet growth/detachment cycle and resultant pressure profile contains valuable information about the water behavior inside the GDL and MPL. This potential is explored more closely in the present work by studying GDLs with and without MPLs. Attempts are also made to mimic the behavior of the MPL using hydrophobic membranes as MPL analogues to delineate the impact of the cracks and blemishes typically found in real MPLs. To help interpret the observed experimental behavior, a model was developed that explains the unusual saw-tooth pressure profiles, the disparity between initial breakthrough pressure and 5 ACS Paragon Plus Environment


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subsequent droplet emergence pressures in GDLs with MPLs, the apparent retraction of water interfaces, the appearance of multiple droplets sites, and the shedding of multiple droplets in quick succession from a given site.

2. Model Development The following model was developed to help in interpreting the transient pressure data and droplet behavior observed experimentally. The model is similar to the common ‘bundle-oftubes’ model, but the volume of fluid in the tubes themselves and only considers the inflating and deflating of menisci with time, and is referred to below as the ‘bulging menisci model’. The aim of this model is to demonstrate that water storage in the bulging menisci is sufficient to explain many of the observed phenomena in transient percolation. Consider first the situation of a droplet emerging from a single tube as shown in Figure 1(a). At time t0 the liquid water does not protrude from the tip and the meniscus is flat with zero curvature. According to the Young-Laplace equation this corresponds to a capillary pressure (PC = PL – PG = 0) of PC = 2σH

(1)

where σ is the surface tension, and H is the curvature of the meniscus. For a fully non-wetting system with spherical menisci, the curvature is related to the meniscus curvature by H =

1 r

(2)

Starting at time t0, water is injected into the system at a rate Q, causing the meniscus to inflate into a lens with a positive curvature and a corresponding increase in the capillary pressure. For a spherical meniscus, its volume can be found from the geometry of spherical sections (i.e. lenses) using V =

πh 6

(3R

2

+h

)

(3)

where R is the tube radius, and h is the height of the lens, given as

h = r − r 2 − R2

(4)

where r is the radii of the sphere to which the lens belongs. At time t1 the lens becomes a semispherical cap of curvature H = 1/R, where R is the radius of the tube. As shown in Figure 6 ACS Paragon Plus Environment

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1(c), t1 corresponds to a peak in the capillary pressure, because as the droplet continues to grow between times t1 and t2 the curvature actually decreases. The volume of the droplet after the peak pressure is achieved is calculated using Eq.(3) with the following expression for h since the meniscus is now the hemispherical section of the sphere, rather than the lens

h = r + r 2 − R2

(5)

Finally, at time t2, the mass of the droplet exceeds the ability of the surface-tension forces to hold the droplet in place and it falls away. The pressure profile in Figure 1(c) shows a rapid increase in capillary pressure from t0 and t1, followed by a very gradual drop between t1 and t2. This is because water is injected at a constant rate Q, so the time required to fill the volume of the semispherical cap is small, while a substantial amount of time is required to create the large droplet that finally detaches and falls away. In the reported studies of pressure profiles during water injection into GDLs, however, the opposite has been the case, with long waits for the droplet to appear followed by rapid growth and detachment of the droplet. This seemingly contradictory behavior is actually fully explained by the model outlined above when applied to many pores in parallel rather than a single tube. Consider the two-tube system shown in Figure 1(b). Between t0 and t1, liquid is continually pumped into the system at a constant rate Q, though no droplet appears. This was previously attributed to replenishment of the drained pore space, but in light of the present model, this period corresponds to the inflating of the multiple air-water interfaces that exist in the system. A longer time lag means that there are many interfaces that must be inflated simultaneously. The volume of water added to the system can be found by summing the growth of each lens. At time t1 the interfaces have all been inflated to the same curvature, H, which corresponds to the breakthrough pressure of the outlet pore, PC,b = 2σ/R1. As shown in Figure 1(d), this results in a peak capillary pressure that is followed by a rapid, nearly instantaneous drop in capillary pressure between t1 and t2. During this period a droplet is visible on the surface, but the growth rate of the droplet is much more rapid than can be explained by the injection rate Q. This can be understood by reference to Eq.(1), since the decrease in measured PC means that all the interfaces in the system (with the exception of the breakthrough site) are deflating and adding their stored water to the injected water Q. All this water is directed into the single 7 ACS Paragon Plus Environment


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droplet at the breakthrough site, hence its rapid growth.

Note that the growth of the

breakthrough droplet into a larger spherical droplet, and the recession of the internal interfaces back to flatter lenses, both correspond to a decrease in curvature H and capillary pressure. According to this model, the entire process of droplet appearance, growth, and detachment can occur without any rearrangement of the water configuration(i.e. invasion of any new pores) in the GDL, only inflating and deflating of otherwise stationary, pinned interfaces. In fact, the retraction observed by Litster et al24 may well have been a deflating interface, for which their reported 10 µm displacement is within reason. The present model also does not require any ‘entrainment’ of internal water with falling droplet, which is one of the prevailing explanations for the long time gaps between water drops14,28,30,35.

3. Experimental Liquid water was injected through different GDL samples using a holder similar to that described previously35. In the present work, several practical improvements were made to the holder to prevent damaging the sample during mounting, to avoid bowing of the sample under applied liquid pressure, and to eliminate gaps between the layers. The modified sample holder is shown in Figure 2. In the present study, Toray 090 with 20% PTFE with and without a MPL were tested. The materials were supplied by the Automotive Fuel Cell Cooperation who applied the PTFE and MPL in-house. Toray 090 samples were chosen since they are the most mechanically rigid GDLs available, as this helps minimize bowing of the sample under pressure. SEM images of the samples used here are shown in Figure 3 at two different magnifications. The MPL images in Figure 3(b) indicate that the MPL penetrated well into the fiber structure, as fibers are actually still visible on the surface. Also shown in Figure 3(c) are images of a 20 µm PTFE filtration membrane (Sterlitech) that was used as an analogue for an MPL in some experiments. The visual similarity between these and the MPL is striking, with both showing similar sized poretype defects and inclusions; the PTFE membrane even has a fibrous substructure running through it, although this is likely immaterial to the present studies.

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3.1. Sample Mounting In previous work35 it was a challenge to mount samples tight enough to prevent leaks without damaging them. Over-tightening created cracks in the sample through which water would preferentially flow, invalidating the experiment. A new holder was designed to avoid this problem by clamping the sample periphery but directing water through the center region of the sample by placing a water impermeable PTFE membrane with a ¼” hole above the sample. The sample stack is shown in Figure 2(left). Above the PTFE membrane was placed a hydrophilic PVDF membrane with 220 nm pores. This membrane acted as a filter to remove particulates from the water, which were found to block the pores of the sample and cause anomalous results as discussed further in Section 4.3. The water was 18 MΩ deionized water, pre-filtered with a 30 nm filter to remove particulates. A stainless steel mesh was placed below the sample to support the GDLs and prevent bowing and bending. This mesh had a ½” hole in the center to provide a sufficiently large outlet region for the droplets to emerge without interference. This was found to be insufficient at the high pressures required to invade the samples with an MPL, so a support rod was extended upward to just touch the bottom of the sample and hold it in place. Droplets would occasionally emerge under or near to this rod, which invalidated the experiment.

Another mesh (without a ½” hole) was placed above the

sample to apply uniform force over the sample stack to keep the layers in close contact and prevent water from flowing into any gaps. 3.2. System Setup The system is depicted in Figure 2(right). A syringe pump was connected to the top of the sample holder using all stainless steel tubing. The syringe was glass with a PTFE plunger. All components in the piping system were therefore rigid with the exception of the pressure sensor diaphragm, which must displace in order to detect pressure changes. This rigidity was essential to ensure that all water injected by the pump was in fact entering the sample, or else massbalance calculations become inaccurate37. For the same reason, it was essential to avoid trapping air bubbles when priming the system with water, as they would compress and decompress with the rising and falling system pressure. This not only interferes with massbalance calculations, but obscures the dynamic effects of the liquid-water interfaces inflating 9 ACS Paragon Plus Environment


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and deflating. The sample holder was clear acrylic plastic which allowed visual confirmation that no bubbles were present. The stopcock on the top of the sample holder remained open during assembly to allow fluid to escape as parts were tightened. The pressure head due to the height of this water column was about 500 Pa, which was not enough to invade the samples during assembly, but means that all tests started at non-zero capillary pressure. 3.3. Testing Protocol To begin the test, the syringe pump was engaged at a rate of 4 uL/min, equivalent to PEFC operating at 1 A/cm2 for the ¼” injection region. The experiment started when the stopcock was closed to force all injected water into the sample.

Liquid pressure was measured at 0.1 s

intervals with a 0 to 200 kPa pressure gauge (Omega PX-409). No filtering or signal conditioning was applied to the pressure signal, as it was vital to get maximum temporal resolution in order to observe the transient pressure changes. This resulted in a somewhat noisy signal at lower pressures, but the results were still acceptable. Finally, images of the outlet face were recorded using a USB microscope oriented at an angle to avoid falling droplets. 3.4. Numerical Solution of Bulging Menisci Model Capillary pressure versus time profiles were simulated using Eqs.(1) to (5). A flow diagram of the solution procedure is shown in Figure 4. Even though time is the independent variable, it is numerically simpler to treat capillary pressure as the independent variable, by inserting a value of PC into Eq. (1), solving for r using Eq.(2), inserting r into Eq.(4) to find hi, determining Vi from Eq.(3), then solving for the elapsed time using t=

1 N ∑ Vi Q i =1

(6)

This procedure is repeated by incrementing PC to higher values until the breakthrough pressure PC,b of pore 1 is reached, where PC,b is found using Eq.(1) with r = R1. Note this model assumes a contact angle of 180°, rather than the more neutral values of 110-120° that are observed on these materials. This assumption allows the use of the established geometrical relationships used in Eqs. (3) to (5), although it means the model offers only qualitative insights. Extending this system of equations to include intermediate contact angles and more realistic 10 ACS Paragon Plus Environment

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pore shapes (non-cylindrical, non-parallel pore walls, surface roughness, etc) is a sizable task, and is left for future work. After breakthrough of pore 1, the system capillary pressure is decremented. The volume of each menisci in the non-breakthrough pores is found from the same equations, but because the PC has decreased, their volume also decreases resulting in stored water being injected back into the system. All of this liberated water, as well as the injected water Q is gained by the droplet in the breakthrough pore which consequently grows very rapidly. The volume of the growing droplet can be found from Eq.(3), using h from Eq.(5), but the numerical procedure applied during this period differs from that for the inflation period. The difficulty lies in finding a value of PC that when applied to all pores ensures the amount of water lost by the deflating menisci equals that gained by the growing droplet. The approach taken here is to decrement PC in fixed steps, calculating the decrease in lens volume ∆VLENS, followed by finding the volume increase of the droplet ∆VDROPLET.

When decrementing PC, there are three cases. (1) If Σ|∆VLENS|

Dynamic Percolation and Droplet Growth Behavior in Porous

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