Droplet and Percolation Network Interactions in a Fuel Cell Gas Diffusion Layer

Product water accumulations in polymer electrolyte fuel cells can cause performance losses and reactant starvation leading to cell degradation. Liquid water removal in the form of droplets, fed by percolation networks in the gas diffusion layer (GDL), is one of the main transport mechanisms by which the water is evacuated from the GDL. In this study, the effect of droplet detachment in the gas channel on the water cluster inside the GDL has been investigated using X-ray tomographic microscopy and X-ray radiography. The droplet growth is captured in varying stages over a sequence of consecutive droplet releases, during which an in ﬂ ation and de ﬂ ation of the gas-liquid interface menisci of the percolating water structure in the GDL has been observed and correlated to changes in pressure ﬂ uctuations in the water phase via gas-liquid curvature analysis. © 2020 The Author(s). Published on behalf of The Electrochemical Society by IOP Publishing Limited. This is an open access

2][3] One specific application used in energy conversion is the polymer electrolyte fuel cell (PEFC) in which this transport process plays an essential role.During the electrochemical reaction of hydrogen and oxygen, water is generated in the cathode catalyst layer.The water needs to be removed continuously to allow access of the reactant gas to the catalytically active sites and sustain the electrochemical reaction.A porous material, termed a gas diffusion layer (GDL), is used to transport the product water from the catalyst layer to the gas channels in the flow field plate (FFP), where the water is carried with the reactant gas stream towards the cell outlet.][6] There are two main mechanisms of water transport through the GDL from the catalyst layer towards the flow field plates; (i) vapor phase transport 7 via diffusion and convection towards the flow field plates, where the water vapor is removed by the gas stream, and (ii) liquid phase transport 8,9 driven by the formation of a percolation network within the GDL.If the percolation networks grow too large, resulting in a high liquid water saturation of the GDL, gas transport in the remaining free pore space is not sufficient to sustain high rates of the electrochemical reaction.This phenomenon is commonly referred to as flooding.The main factors determining the interaction of the GDL with the water cluster are the pore morphology and the contact angle between the water and fibers forming the pore surface.While the pore morphology is a direct result of the fiber arrangement, hydrophobic coatings are applied to increase the water contact angle, thereby confining the water clusters to keep the GDL liquid saturation low and maintain continuity of the gas phase, especially at high current density operation.Understanding and managing the liquid water clusters inside the GDL is required to improve PEFC technology.
However, studying the water percolation networks is not trivial, as many methods of investigation are inapplicable in the confines of a fuel cell.][15][16] During formation of the percolation network, the pressure of the water phase (p w ) increases while the water spreads until it emerges on the GDL surface (breakthrough).After emerging, a decline in water pressure is observed as the droplet forms on the surface and increases in size up to the point when the droplet is detached by the gas flow in the channel.Following the detachment, the water pressure increases again as a new droplet has to form resulting in a periodic pressure fluctuation.While the effect of this pressure evolution on the droplet can be studied with visual instrumentation, the response and behavior of the percolation network is largely obstructed by the GDL and as such little is known regarding the behavior of the percolation network within the GDL during droplet release.
7][18][19][20][21][22][23] With these methods, 2D and 3D information about the internal structure of the GDL and the water distribution in its pores can be obtained.While many projections have to be recorded during XTM, inherently lowering the temporal resolution compared to radiography, developments in fast XTM of PEFCs with scan times of about 1 s 24,25 make it possible for dynamic effects to be investigated in 3D with tomography.
Using a combination of XTM and X-ray radiography, we aim to obtain a more complete picture of the droplet formation and detachment cycle and its impact on the percolation network inside the GDL.The 3D information of the water cluster that can be deduced from XTM in the range of seconds linked to information about the dynamics of droplet detachment in the gas channel recorded at a higher temporal resolution via X-ray radiography, providing an unprecedented level of insight.As pressure equalization in the water phase is the main way of interaction between the percolation network and the droplet, the pressure inside the water phase is determined through interfacial curvature analysis of the segmented XTM data.detachment in the gas channel and their interaction (Fig. 1a).It consisted of a GDL sandwiched between a flow field plate, emulating a channel section of a fuel cell cathode bipolar plate, and a water injector.The injector (PEEK) featured a pathway, through which demineralized water was supplied to the bottom of the GDL while it simultaneously served as a stable mount for the other components.To prevent the injected water from spreading uncontrolled between the injector field and the GDL, a 50 μm thick hydrophobic gasket with a circular, laser cut hole (Ø 500 μm) was placed between them.The hole in the gasket was centered under the gas channel to increase the likelihood for the generated percolation network to evolve droplets in the gas channel without them getting in contact with the channel walls.A single rectangular gas channel with a depth of 300 μm and a width of 800 μm (Fig. 1b) was supplied with dry nitrogen at 25 °C to establish a constant flow in the gas channel with an average velocity of 15 m s −1 .A GDL sample from Sigracet (SGL 24 BA) with 5 wt% PTFE was used in this study.It was determined to have an average porosity of 0.75 (based on XTM segmenation) which can not consider binder porosity compared to 0.74. 26Advancing and receding contact angle values of 159°and 119°respectively, were measured using the sessile droplet method on a GDL sample of the same type.It was positioned between the injector and flow channel and compressed from its original thickness of 190 μm to 180 μm in the gas channel and 150 μm under the ribs.For the water injection a 5 ml Hamilton syringe in a syringe pump (KD Scientific 110) was used, feeding water at a constant injection rate of 350 nl min −1 to the injector.Using Faraday's law, this can be determined to be equivalent to a current density of 32 A cm −2 relative to the injection area (0.196 mm 2 ).This high rate of injection was necessary to ensure the formation of droplets in the presence of evaporation into the dry nitrogen gas stream in the channel.
An analysis of the capillary number with the liquid velocity v, the viscosity of the non-wetting phase m n and the gas-water interfacial tension g yielded a capillary number of = -Ca log 4.85 10 or lower which is still well within the regime of capillary fingering 27 and does not result in a loss of generality in the results.
To verify that the vertical orientation of the gas channel does not influence the behavior of the water structures, the Bond number (Bo) was calculated for the GDL and the gas channel domain: where g represents the gravitational constant, R the radius of the water cluster, r D the density difference between nitrogen and water and g the gas-water interfacial tension.The Bond numbers for the largest possible spherical water cluster in the GDL and the gas channel domain are given in Table I.
Even when assuming water droplets large enough to fill the respective domains (R Max ), the values for the Bond number are far below 1, indicating that the effect of interfacial tension largely outweighs the impact of gravity on the droplet shape and behavior.This confirms the viability of this experiment in a vertical arrangement without any loss of generality.For completeness, the droplet radius required to have a balance of the effects of interfacial tension and gravity is 2750 μm.
Image acquisition and processing.-X-rayimaging was performed at the TOMCAT beamline of the Swiss Light Source (SLS) with a GigaFRoST high speed camera 28 in combination with a microscope from Elya Solutions.Before the tomographic microscopy, radiograms were recorded for 20 s with a frame time of 10 ms to gather detailed dynamics of the droplet formation and detachment.During the acquisition of these radiograms, the GDL was oriented  Journal of The Electrochemical Society, 2020 167 084506 perpendicular to the beam, resulting in an image showing a top down view of the droplet in the channel.The radiograms were segmented using a combination of median filtering for denoising and and a manually selected global threshold.An automatic fitting was used to extract the projected 2D area of the droplet, A D 2 from every frame.The circularity w of the segmented droplet shape was computed as a measure of droplet deformation for each frame using the 2D perimeter P .It was assumed that for small droplets that don't reach far into the channel domain, the shape is not dominated by the gas flowing in the channel and is thus close to spherical (w ∼ 1).Under this assumption, the volume of water contained in the droplet V D 3 was calculated by using the radius R D 2 of a circle with equivalent area to A : The XTM imaging of the water containing GDL was performed with an exposure time of 3 ms for each of the 251 projections resulting in a scan time of 0.75 s for a full tomogram similar to Eller et al. 24 This comparably fast scan procedure was used to image the water during the continuous injection to obtain a set of 10 XTM images.After each XTM, a 1.8 s period was needed for back rotation of the rotation stage of the beamline to be ready to acquire the next scan resulting in a scanning period of 2.55 s.A slower, higher quality scan was employed to obtain the dry structure.The dry structure tomogram was obtained after the injection experiment was performed to reduce the impact of radiation dose.A summary of all relevant parameters for both radiography and tomography can be found in Table II below.
The image processing and segmentation (Fig. 2) was performed using an in house methodology implemented in ImageJ consisting of image subtraction, thresholding and morphological operations (see flow chart representation in Fig. 2).As a first step, the high quality, dry, data (Fig. 2b) was aligned to Cartesian coordinates and the water containing data (Fig. 2a) registered to it.Next, the dry data was subtracted from the water containing data after median filtering to obtain a difference image, enhancing the water signal (Fig. 2c).The difference image was then segmented using median filtering for denoising and thresholding steps combined with binary morphological operations, resulting in a binary mask for the water inside the cell (Fig. 2d).For the dry structure segmentation (Fig. 2e), a combination of median filtering for denoising, thresholding and binary morphological operations was used.This was necessary because the SGL GDL features a microporous binder material that exhibits strong grayscale variations in the tomographic image, resulting in unsatisfactory results when using a simple global thresholding.The porosity of the binder could not be resolved with the present voxel size and as a result, binder and fibers were labeled as solid.In a final step (Fig. 2f) the two segmented structures were combined into a single image for each of the 10 scans.Note that the surfaces of the large droplet downstream of the gas flow showed motion artefacts because expansion during the scan lead to a smeared gray scale (Figs.2a and 2c).This made it difficult to reliably segment the droplet water surface at all locations and therefore channel droplets were excluded from the curvature analysis.
The segmented data of the droplet in the channel was used in collaboration with Martin Andersson et al., 29 comparing droplet growth on the GDL surface modeled with a volume of fluid simulation to the droplet growth obtained from XTM imaging, ignoring any processes in the GDL.
Liquid pressure in porous media.-Thepressure difference Dp across the gas-water interface of a water cluster in a porous media can be described using the Young-Laplace equation: where R 1 and R 2 are the principal radii of curvature.The gas-water interfacial curvature of the percolation water cluster was analyzed to estimate the pressure drop across the interface.This was done using a method of 3D surface identification, smoothing and characterization previously applied to multiphase flow problems in rocks by Lin et al. 30,31 which determines the principal radii (R 1 and R 2 ) describing the surface curvature.Thereby, the voxelated liquid-void interface area is represented by a surface mesh that interpolates between the voxels to achieve a volume preserving surface smoothing.
Under the simplifying assumption of cylindrical pores, an alternative expression of the Young-Laplace equation can be used, linking the diameter of an idealized pore and the surface wettability to the pressure drop across the gas-water interface.
Here, q denotes the observed water-solid contact angle measured through the liquid phase, and R pt is the radius of the cylindrical pore surrounding the meniscus.From this equation it can be seen that interfaces in larger pores result in a lower pressure drop while more hydrophobic surfaces cause a higher pressure drop across the interface.

Results and Discussion
The X-ray radiography observation of droplet formation and detachment revealed three repeating states: (I) no droplet visible on the GDL surface, (II) growth of the droplet, and (III) droplet detachment.On average, the time between two consecutive droplet detachments was determined to be 4.3 s for the chosen combination of liquid injection rate and channel gas flow speed (350 nl min −1 and 15 m s −1 respectively), with no droplet visible on average for 0.7 s and droplet growth for 3.6 s.For different gas velocities in the gas channels it can be expected, that the droplet detachment diameter would decrease with increasing gas velocity [32][33][34]

and increasing
Table II.Imaging parameters used for the fast XTM scans during water injection and the slow scan used to obtain a high quality reference image of the dry structure as well as radiographic imaging.injection rate 35 and so the droplet detachment period would as well.However, if the droplet would touch the channel walls before detaching from the GDL surface at different conditions, then a different liquid flow pattern would establish in the gas channel. 36he volumetric evolution of the droplet growth with time observed via X-ray radiography and assessed via circularity analysis (Eq. 3) and spherical droplet volume estimation (Eq.4) is shown in Fig. 3.The moment when a droplet is first visible in the radiographic images, it has a volume of 2 nl.It grows at a constant rate fulfilling the circularity criterion (ω ∼ 1) until it reaches a size of around 6 nl (labelled in blue in Fig. 3).After this point of growth, the droplet shape changes to tear shaped (see radiography image inserts in Fig. 3) and the circularity criterion is violated (ω < 0.88).Therefore, the spherical droplet volume estimation becomes invalid as it overestimates the droplet volumes suggesting an unrealistic increased grow rate until detachment (labeled in gray).The droplet volume at the moment of detachment was estimated to be average 14 nl by linearly extrapolating the growth rate between droplet formation and droplet volumes of 6 nl with a circularity above 0.88 until the time of droplet detachment.
By comparing the slope of the initial droplet growth rate to the rate of water injection, the evaporation caused by the dry nitrogen gas stream was identified with an average evaporation rate of 70 nl min −1 (±20 nl min −1 ), which is one fifths of the liquid water injection rate.
As the droplet, release rate was not synchronized, but slower than the scan rate of the XTM imaging during the continuous injection, XTM images captured the water structure in different stages of the droplet formation cycle identified by radiography.Figure 4 shows different stages of droplet formation rearranged in order of increasing droplet size.For visibility, the GDL was cropped to a square region of 750 by 750 μm 2 containing the percolation water cluster.This illustrates not only the state of the water free GDL surface of period (I) (Fig. 4a) but also the transition from a small, rather spherical droplet (Fig. 4b) to a large tear shaped one (Fig. 4c), extending over the surface of the GDL before detachment (Fig. 4d).In total, four scans were obtained in a state without a droplet present on the GDL surface (scans 1, 3, 5 and 8) and four cases with a large tear-shaped droplet (scan 2, 4, 7 and 9).The remaining two (scans 6 and 10) show a small droplet (intermediate) starting to form on the GDL surface.
To identify changes in GDL saturation during the droplet formation cycle, the water volume distribution over the height of the GDL was analyzed by summing up the volume of water per slice (each 3 μm thick) parallel to the GDL surface.The resulting curves are plotted in Fig. 5a for a representative dataset for each of the three stages before (red), after (blue) and at the very onset of droplet formation (green).Overall, the water volume decreases for all cases with increasing height from the injection point (height 0 μm) until a height of ∼120 μm, where the volumes at different times start to diverge.In the case where no droplet is present (red) the water volume goes to zero at the GDL surface while for the intermediate states (green) the volume increases slightly and for the large droplet states (blue) it shows a significant increase above this height.The cause of this is the droplet rolling over in the gas channel and partially reentering the GDL domain in a pore next to the breakthrough location (see cross-section in Fig. 5b).
For a better comparison of the percolation water clusters, Fig. 5c shows averaged volumes of water in the GDL before (red) and after droplet formation (blue).Below the height where the droplet roll over affects the volume analysis (∼120 μm) the volume of water after droplet formation is consistently lower than before droplet formation, highlighted in the zoom-in of Fig. 5c  amounts to a total of 0.3 nl (11000 voxels) between the two states corresponding to a 2% change relative to the total volume of the percolation network in the GDL before droplet formation (15 nl).The water distribution is in terms of GDL saturation is shown in Fig. 5d for two different analyzed GDL volumes.A strong dependency of the saturation values on the analyzed GDL volume can be found, since the percolation clusters stems from a very localized liquid injection into the GDL.The saturation stays constant for the lower 40 μm for the cylindrical as well as the rectangular GDL domain, which is due to GDL porosity fluctuations throughout the thickness of the GDL.
For a qualitative visual comparison between the two states of the percolation network before and after droplet formation, the data sets closest to the respective average water distributions are shown superimposed in Fig. 6.As before, red indicates the water cluster before droplet formation and blue after droplet formation.If voxels were water filled in both states, priority was given to the state after droplet formation (blue).With this labeling method, red features indicate an inflation of the percolation network before breakthrough and droplet formation.
While Fig. 6a shows the full GDL domain in the rendered subvolume, in Fig. 6b only the fibers touching and thus shaping the percolation network are visible.This highlights the difference between the two states in the pore throats of the GDL structure and it can be seen that most menisci in these throats show an inflation before droplet formation.Apart from the large deformation in the feed path at the breakthrough location, it is visible that especially the large throats show a significant volumetric change between the two states.This is to be expected as from equation 6 it can be seen that the pressure drop across a meniscus in a throat is inversely proportional to the throat radius.This means that the airwater interfaces spanning large pore throats experience a higher degree of deformation compared to the ones in small throats when exposed to the same pressure fluctuation.For completion, Fig. 6c shows just the superposition of the two states without any fibers.
The image series Figs.6d-6h shows single in-plane slices, extracted at different heights from the injection location in 30 μm intervals starting near the injection location (d) and ending close to the gas channel (h).These images provide additional insights into the interaction between the water phase and the fiber structure in the GDL and verify the dominant deformation of the water cluster in the pore connecting the main body of the percolating network with the breakthrough location (center of (e) and (f)).
The observed deformations of the water percolation cluster are in good accordance with the characteristic pressure fluctuations reported for repeated breakthrough events such as droplet formation and detachment. 13,14Right before the breakthrough event, the pressure in the water structure is reported to peak, this is equivalent to the state before droplet formation, at which point we see an inflated percolation network.While after the breakthrough event, the pressure was found to drop, in the present study this correlates to the state after droplet formation where the percolation network contracts.
To determine the extent of this pressure fluctuation in the present case, two segmented data sets, one before and one after droplet formation, were analyzed for their principal radii on a discretized meshing of the gas-water interface.The analysis was limited to the interfaces in the GDL domain, excluding the droplet in the channel domain.
Figure 7 shows the extracted interface curvature before and after droplet formation.The peak positions of the almost overlapping curvature distributions have been determined using curve fitting and correspond to a pressure drop Dp (using Eq. 5) across the interface of 24 mbar (2400 Pa) before and 22 mbar (2200 Pa) after droplet formation.This is in agreement with the observed behavior of the percolation network described above and also fits well to the range of reported breakthrough pressures for SGL 24 BA (∼22 mbar). 18he interfacial curvature distribution showed a wide spread, which may be associated to the presence of small interfacial sections of the single water cluster being analyzed and the voxel size of 3 μm limiting the accuracy to which the interface curvature and the precise shape of the gas-solid-liquid interface can be determined.Furthermore, the segmentation of the noisy XTM data may have resulted in assignment errors of the phases at the gas-solid-liquid interface.The influence of such assignment errors on the curvature distribution is evaluated by imposing a distance requirement D and only including data points above this distance from the three-phase contact line.This excludes regions near the three-phase contact where segmentation errors are largest 37 and the interactions of the fibers and the menisci cannot be resolved with the given resolution.water cluster during consecutive droplet formation cycles on the GDL surface in the course of liquid water injection into the GDL.
X-ray radiography allowed precise insight in the timing of the droplet release formation and detachment cycle with a period of about 4.3 s from which droplet grow rates were estimated.The X-ray tomographic microscopy scans captured different stages of the droplet growth and the corresponding percolating water cluster states within the GDL with a scan time of 0.75 s and a repetition rate of 2.55 s.
Periodic drainage of the percolation cluster in the top third of the GDL thickness after droplet detachment was observed, while the break-through location remained stable for the observation time.In the bottom 2/3 of the GDL thickness the percolation cluster showed much lower fluctuations of only 0.3 nl (2% of the total water volume contained in the GDL).The minor water volume change in the bulk GDL was clearly identified for the first time as gas-liquid menisci movement in the pore throats as predicted by theory.
It was further demonstrated how the determination of the gaswater interfacial curvature can be used to estimate the pressure drop across the gas-liquid interface of the percolation network from XTM images capturing the trend of pressure fluctuation that matches well with previously published values.This method holds great potential for future 4D imaging studies, especially thanks to recent beamline instrumentation upgrades, 38 as it allows for the determination of water pressures during operando PEFC XTM imaging.
We are confident that future 4D XTM studies with such advanced analysis approaches will improve the understanding of transient twophase water transport processes in PEFCs, provide crucial validation data for 3D PEFC microstructure models and ultimately enable improved GDL material design for increased PEFC efficiency.

Figure 1 .
Figure 1.(a) Imaging cell comprised of injector and flow field plate (FFP) with a single gas channel (GC).(b) Cuts along and through the channel, indicating the positioning of the hydrophobic gasket and the GDL as well as the channel geometry.(c) Schematic depictions of the changing state of the waterfront with changing water pressure before and after droplet formation in a cross-section of the cell (top) and between two fibers (bottom).

Figure 2 .
Figure 2. Schematic representation of the imaging pipeline with the water containing data (a), dry data (b), difference image of water and dry data (c), segmented water mask (d), the segmented dry mask of fiber and binder (e) and the combined segmented image (f).

Figure 3 .
Figure 3. Droplet volume evolution over time (dashed line) relative to the start of growth of a selected droplet.(I) water free GDL surface, (II) droplet growth and (III) detachment.(blue) linear growth region used to fit the growth rate.The solid line exemplary indicates the water injection rate into the setup.Two frames show radiographic images of the droplet 1 s and 2.5 s after breakthrough.
. The horizontal error bars indicate the standard deviation of the water volume and show the significance of the volumetric change observed.The difference in water volume in the GDL domain below 120 μm

Figure 5 .
Figure 5. (a) The water volume, determined in 3 μm thick slices at different heights of the GDL and channel for three representative states of droplet formation.(b) Renderings of two representative states before and after droplet formation with a cutout revealing the internal water distribution.(c) Water volume distribution in the GDL domain averaged for the four cases before droplet formation and the four cases after droplet formation with a large droplet.(d) Saturation at different heights in the GDL for a cylindrical region of interest of diameter 500 μm centered above the injection port and for the full 750 by 750 μm 2 GDL area shown in (b) and Fig. 4.

Figure 6 .
Figure 6.Visualizations of a superposition of the two states, before and after droplet formation (red and blue).When both states were occupying the same voxel, priority was given to the state after droplet formation (blue).(a) The full GDL structure in the region of interest.(b) Here, only fiber voxels near the water cluster are shown.(c) The superposition of the water clusters.(d)-(h) In-plane slices extracted at 30 μm intervals with (d) located close to the injection point and (h) near the gas channel as indicated by the outlines in (a)-(c).

Table I .
Evaluation of the Bond number for largest possible, spherical water clusters in the GDL and channel domains.