# Interaction of Vibration and Air Flow-Accelerating Droplet Emission from the Gas Diffusion Layer of Proton Exchange Membrane Fuel Cell

Authors: Sitong Chen; Xueke Wang; Tong Zhu; Xiaofeng Xie
Journal: International Journal of Photoenergy
 (2019)

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## Abstract

In order to explore the influence of vibration that the vehicles are often subjected on water management of PEMFC, the dynamic characteristics of vibrating droplet on gas diffusion layer (GDL) surface were investigated through a high-speed image technology. The operating condition of vertical and horizontal excitations separately or coupled with air flow under different frequencies and amplitudes are applied on the substrate, so that the laws for the transition from Wenzel-Cassie regime to Cassie regime and the contact angle, the deformation rate for the width and height are obtained. It is observed that the wetting diameter of the droplet is smaller than the initial value under vertical vibration, making it easier for the gas to discharge the water droplets from the PEMFC. For the horizontal excitation, the droplet is pulled apart when the applied energy exceeded the cohesive energy at elevated frequency and amplitude. Moreover, as to the interaction of vibration and air flow, the droplet was more likely to move forward under the gas-driven force.


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## Body

## 1. Introduction

With the steady promotion of public awareness on environmental protection and sustainable development, fuel cells will become the major power options to replace the traditional fossil energy in the future. Among all kinds of fuel cells, the proton exchange membrane fuel cell (PEMFC) has a very wide range of application in military and civil fields, such as aerospace industry, deep-sea submarines, stationary and portable power sources, or transportation sector, because it offers low operating temperatures, high energy conversion efficiency, rapid cold start-up, no pollution, long service life, and compact structure [1, 2]. As an alternative vehicular power train, the PEMFC has extensive market prospect in automotive application, the world’s major car manufacturers in recent years have launched their new PEMFC models. From 2013 to the end of 2017, the PEMFC passenger cars’ global sales totaled 6,475 vehicles, 3,382 of which were sold in 2017, accounting for 52.23% of the total sales [3].In the actual road conditions, the PEMFCs in vehicles are often subjected to the harsh dynamic situations accompanied with mechanical vibration and shock. Passenger vehicles generally experience vibrations in the range of 8-16 Hz due to the unevenness of the road and the oscillation of the axel and wheel with the suspension system [4]. The long-term vibration behaviors may cause and exacerbate the defects of PEMFC components, such as pinholes, cracks, and delamination, having influence on the performance, durability, and reliability of the PEMFC stack [5, 6]. Therefore, the effect and function mechanism of vibrations on PEMFCs have gained more and more attention from researchers, mainly by means of experiments and numerical simulations for further insight.Rajalakshmi et al. [7] subjected a 500 W PEMFC stack to shocks, random and swept-sine excitations by using a vibrating platform at various frequencies and different acceleration in three axe directions. The electrochemical performance of the stack is in good agreement before and after the vibration and shock tests, showing the mechanical integrity of the system, and a posttesting stack inspection shows a minor compression force release at the bolts. Diloyan et al. [8] experimentally investigated the effect of different constant mechanical vibration conditions on platinum particle agglomeration and growth in the catalyst layer of a Membrane Electrode Assembly (MEA) for a PEMFC with a 25 cm2 active surface area. By using 300 h accelerated tests and transmission electron microscopy (TEM), they came to the conclusion that the average diameter of Pt particles under vibration is 10% smaller than the ones without vibration conditions. Hou et al. [9–13] conducted a series of long-term strengthened road vibration studies on PEM fuel cell stack with a road simulation test bench and a six-channel multiaxial simulation table. They analyzed and determined the negative changes in gas tightness, electrical insulation, characteristic parameters (open circuit voltage V0, Tafel slope b, and ohmic resistance R), steady-state efficiency, and hydrogen utilization, as well as performance degradation of the fuel cell stack in detail.Another part of related studies in the published works is mainly focused on numerical simulations. Ahmed et al. [14] developed a three-dimensional finite element model of a PEMFC for the free vibration analysis. They modelled the PEMFC as a laminated composite plate composed of a membrane, gas diffusion electrodes, and bipolar plates and then investigated the relationship between natural frequency and material thickness, Young’s modulus, and density for each component layer. Banan et al. [15] established a two-dimensional model based on the cohesive element approach to predict the delamination and crack evolution at the membrane/catalyst layer interface in PEMFCs. After a parametric study, they found the effects of amplitude and frequency of applied vibrations as well as initial delamination length on damage propagation. Al-Baghdadi [16] created a model about the natural frequencies and mode shapes of the PEM fuel cell stack to discuss how the natural frequency varies as a function of material properties and thickness of the stack components, number of cells, and misalignment during assembly process under a vibration environment.However, the transport of liquid water under vibration conditions in PEMFCs remains an area of research in progress. Breziner et al. [17] failed to run a custom-made fuel cell stack with a clear window in the cathode side and replaced it with a commercial, 36 cm2 single cell to investigate the influence exerted by frequency and acceleration of vibration on the overall fuel cell performance. They conjectured that the decay could be due to an alteration of water transport in the MEA. Santamaria et al. [18] experimentally characterized water droplet motion and adhesion on GDL materials in the presence of vibration. They designed a simplified experimental setup to consider only GDL and liquid interface effects. Moreover, they concluded that vibration leads to liquid redistribution that causes an increased wetting diameter and reduced height, resulting in up to a 15% higher net force required for removing water from PEFC GDL materials. Sellman and Santamaria [19] on this basis added a single Lexan channel mounted on the vibration stage to simulate two-phase flow. The results show that flow-channel detachment velocity is increased for higher vibration scenarios potentially due to altered droplet aerodynamics and net adhesion force. This work uses ex situ experimental techniques to progressively investigate the dynamic characteristics of vibrating droplet on GDL surface under vertical and horizontal excitations separately or coupled with air flow through high-speed image technology, which is motivated by the performance fluctuation of the PEMFC from the in situ experiment.


## 2. Experimental Methods and Apparatus

At first, an in situ experiment was performed to investigate the effect of PEMFC performance under mechanical vibration. As to the PEMFC, a commercially available Nafion® 211 membrane with an active area of 25 cm2 and SGL-25BC carbon papers of which the porosity was 80% and the air permeability was 1.0 cm3/(cm2·s) were chosen. The Pt catalyst loading of both cathode and anode sides was 0.5 mg cm−2. For under the vibrational frequency of 25 Hz, the amplitude of 2.5 mm and the PEMFC operating conditions are summarized in Table 1; after repetitive tests, a sudden rise in cell voltage while loading vibration was obtained. According to this law, the influence of vibration on the performance of the vehicle stack will be more obvious under the condition of a large area and multiple cells. Therefore, we designed an ex situ test platform with an image acquisition system to explore the critical condition of the vibrating droplet on GDL surface.Table 1
The experimental operating conditions.
Current density (mA/cm2)
Temperature (°C)
Stoichiometry (air/H2)
Relative humidity (air/H2)
300
65
2/1.2
0/0


### 2.1. Experimental Setup

The image acquisition system consists of a high-speed camera (OLYMPUS i-SPEED TR), a macro lens (OLYMPUS SZ61), an auxiliary light, and a computer. The high-speed camera is equipped with a macro lens so as to collect clearer real-time images, as is displayed in Figure1(a). There are two kinds of light sources employed in this test shown in Figures 1(b) and 1(c): one is the halogen light source, as the backlight for observing the dynamic behavior of vibrating droplet on GDL surface, can avoid the uneven color distribution caused by photochromatic migration. The other is the LED light (LG-150E), serving as a reflection light source. The vibration generator can provide horizontal excitations and vertical excitations in the frequency range from 1 Hz to 600 Hz with the maximum displacement of 5 mm, capable of acceleration amplitude up to 20 g. It can be used to simulate the real vehicle vibration frequencies ranging from 17 Hz to 40 Hz with the maximum amplitude of 0.95 g during its operation [20, 21]. In this paper, each experiment was repeated three times under stable test condition control to avoid accidental phenomena.Figure 1
The photographs of the high-speed camera and light source.
(a)
(b)
(c)


### 2.2. Description of the Experimental Test Platform

Figure2 exhibits the schematic diagram of the droplet vibration tests which were realized by using the vibration generator, the image acquisition system, and the mass flow controller. The GDL substrate was tightly seated to the vibration generator and illuminated by a cold light source with a high-speed camera mounted opposite to record the movement of water droplet under vibration conditions. In view of the diameter of water droplets in the gas flow channels of PEMFC which was usually between 0.6 mm and 1 mm, we used a pipettor to put the deionized water droplet on the surface of GDL and fixed a nozzle 2 mm away from the droplet with a diameter of 0.8 mm, which was connected to the mass flow meter in order to control the gas flow rate.Figure 2
The schematic diagram of droplet vibration experiment.


## 2.1. Experimental Setup

The image acquisition system consists of a high-speed camera (OLYMPUS i-SPEED TR), a macro lens (OLYMPUS SZ61), an auxiliary light, and a computer. The high-speed camera is equipped with a macro lens so as to collect clearer real-time images, as is displayed in Figure1(a). There are two kinds of light sources employed in this test shown in Figures 1(b) and 1(c): one is the halogen light source, as the backlight for observing the dynamic behavior of vibrating droplet on GDL surface, can avoid the uneven color distribution caused by photochromatic migration. The other is the LED light (LG-150E), serving as a reflection light source. The vibration generator can provide horizontal excitations and vertical excitations in the frequency range from 1 Hz to 600 Hz with the maximum displacement of 5 mm, capable of acceleration amplitude up to 20 g. It can be used to simulate the real vehicle vibration frequencies ranging from 17 Hz to 40 Hz with the maximum amplitude of 0.95 g during its operation [20, 21]. In this paper, each experiment was repeated three times under stable test condition control to avoid accidental phenomena.Figure 1
The photographs of the high-speed camera and light source.
(a)
(b)
(c)


## 2.2. Description of the Experimental Test Platform

Figure2 exhibits the schematic diagram of the droplet vibration tests which were realized by using the vibration generator, the image acquisition system, and the mass flow controller. The GDL substrate was tightly seated to the vibration generator and illuminated by a cold light source with a high-speed camera mounted opposite to record the movement of water droplet under vibration conditions. In view of the diameter of water droplets in the gas flow channels of PEMFC which was usually between 0.6 mm and 1 mm, we used a pipettor to put the deionized water droplet on the surface of GDL and fixed a nozzle 2 mm away from the droplet with a diameter of 0.8 mm, which was connected to the mass flow meter in order to control the gas flow rate.Figure 2
The schematic diagram of droplet vibration experiment.


## 3. Results and Discussion

Due to the strong hydrophobicity of the diffusion layer surface in PEMFC, the water generated by the reaction exists in the form of droplets on the GDL. From Figure3(a), the droplets will present different contact forms for the low surface flatness and the uneven distribution of PTFE as well as different pore structures of GDL. Figure 3(b) shows the infiltrating state of the droplets on the rough surface, which are the Wenzel regime, the Cassie regime, and the Wenzel-Cassie regime, respectively [22, 23]. The water produced by PEMFC breaks through the GDL and reaches the surface, which exists briefly in the regime of Wenzel, and then, the droplets will be in the form of Wenzel-Cassie [19]. As to a droplet in the Wenzel-Cassie regime, it receives the vibration energy Ek, the adhesion power between the droplet and GDL surface Ea, and the cohesion force Er generated when the droplet is stretched.Figure 3
(a) The carbon paper and droplet and (b) different contact patterns of droplet on the GDL.
(a)
(b)For a vibration device with vibrational frequencyf and amplitude A, the energy transmitted to the droplet through the vibration is given as follows [24]:
(1)Eko∝12ρV2πfA2.The kinetic energy transferred to the droplet by vibration is as follows:(2)Ek=k⋅12ρV2πfA2,where k is the energy transfer efficiency, ρ is the density of the droplet, V is the volume of the droplet, f is the vibrational frequency, and A is the amplitude. It is necessary to overcome the adhesion power between the droplet and solid surface to realize the transition of the droplet state on GDL surface:
(3)Ea=γ1ν1+cosθΔA.WhenEk<Ea, the droplet cannot change from the Wenzel-Cassie regime to the Cassie regime, while Er>Ek>Ea, the droplet starts the transition from the Wenzel-Cassie regime to the Cassie regime.


### 3.1. Dynamic Performance of the Droplet under Vertical Vibration

It was found in the experiment that as the vibration amplitude increased, there were three different situations when the vertical vibration at a certain value of frequency was applied to the surface of GDL. In Figure4(a), the vibration deformation of the droplet on GDL was too small to start the transition from the Wenzel-Cassie regime to the Cassie regime while the input frequency was 20 Hz and the amplitude was 1 mm. Keeping the same frequency and gradually increasing the amplitude to 2 mm, the droplet would be snapped during oscillation, leaving a trail behind. As shown in Figure 4(b), after falling back to the GDL surface, the droplet could not break away again for cyclic motion. It can be observed from Figure 4(c) that when the amplitude was increased to 2.5 mm, the vibrational energy of the droplet could overcome the adhesion power between droplet and GDL surface so that the droplet was completely separated from the gas diffusion layer to achieve the transition from the Wenzel-Cassie regime to the Cassie regime.Figure 4
Under the vertical vibration frequency of 20 Hz, different amplitude conditions, the movement of droplets on the surface of GDL.
(a)
(b)
(c)If the vibration amplitude remained unchanged and the frequency was variate, the vibrating mode of the droplet had the similar variation trend as that under the same frequency. From Figure5, it can be found that after vibrating at an amplitude of 2 mm and the frequencies added from 15 Hz to 30 Hz, the vibration of the droplet became apparent and the droplet accomplished the transition from the Wenzel-Cassie regime to the Cassie regime at a larger frequency. For the water management of the PEMFC, Figures 4(c) and 5(c) are ideal state as the droplets completely bounced off the GDL surface and were easily blown away under a small gas flow rate.Figure 5
Under the vertical vibration amplitude of 2 mm, different frequency conditions, the movement of droplets on the surface of GDL.
(a)
(b)
(c)The deformation rate is a parameter to quantitatively measure the deformation extent of the droplet with time. In this work, the gradient of the wetting diameterD/D0 and the height H/H0 during the droplet vibration were analyzed in real time, where D0, D, H0, and H represent the wetting diameter and height of the droplet at rest or under vibration, respectively. Figure 6(a) shows the maximum height of the droplet increasing with the augmentation of amplitudes, and the droplet height presents a periodical change with the cycle of vibrating motion at a constant frequency of 20 Hz. When the amplitude was 1 mm, the height of the droplet deformed little, while the droplet being vibrated at an amplitude of 2 mm, its height reached two different maximum values, which were 1.8 h0 and 1.6 h0 within 60 ms. The peak value came up to 3.0 h0 with the amplitude added to 2.5 mm. Furthermore, there was a correspondence between the gradient of the wetting diameter and the height of the droplet. When the wetting diameter reached the maximum value, the corresponding height of the droplet was the minimum as shown in Figure 6(b).Figure 6
The change rate of the droplet with time under different amplitudes: (a) height of droplet and (b) wetting diameter of droplet.
(a)
(b)To observe how the frequencies influence the wetting diameter and the height of the droplet at a constant amplitude of 2 mm, the results of the experiments are exhibited in Figure7. The maximum of the droplet height gradually rises along with the increase of frequency; also, the vibrational frequencies of the droplet were different under various driving frequencies. When the driving frequency was 15 Hz, which was basically consistent with the vibrational frequency, the droplet always contacted with the GDL surface. With the rise of driving frequency to 20 Hz and 30 Hz, the wetting diameter was decreased to 0 during 11-27 ms and 12-20, 43-58 ms so that the vibrational frequencies were corresponding to 22 Hz (T=45ms) and 32 Hz (T=31ms), different from the driving frequencies.Figure 7
The change rate of the droplet with time under different frequencies: (a) height of droplet and (b) wetting diameter of droplet.
(a)
(b)The gradient of the maximum height of droplet under different frequencies was obtained by calculating the average value of the maximum height of droplet in three cycles under various frequencies and amplitudes. As shown in Figure8, the gradient of the droplet height increased with the augmentation of frequency at the same amplitude, especially under large amplitude (2.5 mm), and the gradient of the maximum height of droplet enhanced rapidly. When the vibrational frequency was greater than 15 Hz and the amplitude was 2.5 mm, the droplet was separated from the surface of GDL. When the frequency was greater than 20 Hz and the amplitude was 2 mm, the droplet broke away from the GDL surface.Figure 8
The maximum gradient of droplet height at different frequencies.


### 3.2. Dynamic Performance of the Droplet under Horizontal Vibration

Under a constant horizontal frequency of 20 Hz from Figure9, it can be seen that while the amplitude was increased to 2 mm, the droplet showed a tendency of fracture at 10 ms and left a water film on the surface of GDL, stretching the wetting diameter between the droplet and GDL surface longer. With the rise of amplitude to 2.5 mm in Figure 9(c), the droplet would be snapped during the expansion, leaving a trail, because the bottom of the droplet was still attached to the micropores of the GDL due to its viscosity and the applied energy exceeded the cohesive energy of the droplet so that the droplet was pulled off to form a new small droplet. For an 8 μL droplet, keeping the same amplitude at 2 mm and inputting a changing vibrational frequency (less than 7 Hz), the variation trend was similar as the case above, as shown in Figure 10.Figure 9
Under the horizontal vibration frequency of 20 Hz, different amplitude conditions, the movement of droplets on the surface of GDL.
(a)
(b)
(c)Figure 10
Under the horizontal vibration amplitude of 2 mm, different frequency conditions, the movement of droplets on the surface of GDL.
(a)
(b)
(c)
(d)The static contact angle of the droplet changes under the condition of horizontal vibration. The contact angle corresponding to the front contact point is known as the advancing contact angleθA, and that corresponding to the rear contact point is called the receding contact angle θB. The difference between the advancing contact angle and the receding contact angle (θA‐θB) is contact angle hysteresis.Figure11 exhibits the periodic changes of the advancing contact angle (θA) and the receding contact angle (θB). As the vibration moved to the right from the equilibrium position, the advancing contact angle of the droplet increased gradually and reached the maximum value of 172° when the vibration arrived at the far-right end. Accordingly, the receding contact angle decreased gradually to the minimum value of 80° and the contact angle hysteresis (θA‐θB) gradually enhanced in the process just as 0-17 ms in Figure 11(b). As mentioned above, the wetting diameter of the droplet became larger so that the adhesion force between the droplet and GDL rose up. Therefore, even if the contact angle of the droplet increased to the maximum, the droplet did not scroll on the GDL. When the vibration moved from the far-right end to the far-left end, the advancing contact angle of the droplet gradually decreased to the minimum value of 76°, but the receding contact angle gradually enhanced to the maximum value of 165°. While the advancing contact angle reduced to equal to the receding contact angle, the droplet was in the equilibrium position. At this point, the wetting diameter of the droplet was smallest and the height was largest.Figure 11
The variation of the droplet with time at the frequency of 20 Hz and the amplitude of 1 mm: (a) contact angle and (b) contact angle hysteresis.
(a)
(b)Under a larger amplitude, the shape of the droplet changed significantly so that the advancing contact angle and the receding contact angle of the droplet could not be measured accurately. Therefore, the shape of the droplet was represented by its wetting diameter. Figure12 shows the variation of the droplet wetting diameter with time under the frequency of 20 Hz and the amplitude of 2 mm as well as 2.5 mm. The wetting diameter of the droplet changed irregularly with the vibration. When the amplitude was 2 mm, the wetting diameter of the droplet was larger than the initial diameter. There were more water molecules entering the micropores of the GDL, adding the adhesion force between the droplet and GDL. With the augmentation of the amplitude to 2.5 mm, the wetting diameter of the droplet gradually decreased in the initial stage. At 21 ms, the droplet was pulled apart to form a small droplet which vibrated in the new position and after that, the wetting diameter first decreased and then increased.Figure 12
The variation of the droplet wetting diameter with time under different amplitudes.Figure13 clearly indicates the displacement of the droplet central point varying with time under different amplitudes. With the rise of amplitude, the maximum displacement of the droplet gradually increased and the displacement of the droplet increased and decreased correspondingly with the recirculation of the vibration in the horizontal direction. At the amplitude of 1 mm, the maximum displacement in the positive direction was close to that in the negative direction, both of which were 0.5 mm. It indicated that the droplet did not slip on the GDL surface. When the amplitude increased to 2 mm, the positive displacement (1.4 mm) of the droplet central point was greater than the negative displacement (0.6 mm) so that the droplet slid. As the amplitude added up to 2.5 mm, the droplet fractured at 21 ms and then the formed droplet would reciprocate in the new equilibrium position.Figure 13
The variation of the droplet displacement with time.


### 3.3. Dynamic Performance of the Air Flow-Induced Droplet under Vibration

Above all, several experiments about the dynamic performance of the air flow-induced droplet without vibration were performed. The movement of the 8μL water droplet on GDL surface at different air velocities of 2.76 m/s, 3.39 m/s, 3.9 m/s, and 4.52 m/s is shown in Figure 14. From Figures 14(a) and 14(b), it can be observed that at a low gas flow rate, the receding contact angle of the droplet gradually decreased and the advancing contact angle gradually increased over time, because the force that the gas put on the droplet was less than the adhesion force between the droplet and GDL, which prevented the droplet from leaving the GDL surface and formed a small water film. As the flow rate increased to 3.9 m/s, the tail of the droplet was stretched as shown in Figure 14(c). When the flow rate reached 4.52 m/s, the drag force of the gas made the droplet forming a slender column, the front of the droplet contacted with the GDL, and the tail was suspended in the air. At this moment, although the drag force was not enough to overcome the adhesion force between the droplet and GDL, it exceeded the cohesion force of the droplet so that the droplet suspended in the air was pulled apart.Figure 14
The movement of 8μL droplet on GDL surface under different air velocities.
(a)
(b)
(c)
(d)To discuss the motion characteristics of the droplets with different volumes on GDL surface, the droplets of 6μL, 8 μL, and 10 μL at the air velocity of 5 m/s were investigated in Figure 15. The 6 μL droplet completely broke away from the GDL, and the bottom of the 8 μL and 10 μL droplets fractured and migrated on the surface of GDL. In addition, the wetting diameter of the 10 μL droplet was larger compared with the 8 μL droplet. This was because the gravity and adhesion force of the droplet tiny in size were small, and the force of the gas could overcome the adhesion force and gravity of the droplet under a larger gas flow rate, making the droplet float above the GDL.Figure 15
The movement of different volume droplets on GDL surface at air velocity of 5 m/s.
(a)
(b)
(c)Furthermore, the surface properties of the GDL also affect the movement of the droplet. Figure16 shows the movement of the 6 μL droplet on the surface of dry or wet GDL at the gas flow rate of 5 m/s. On the dry GDL surface, the bottom of the droplet separated from the GDL under the gas-driven force and moved forward. While on the wet GDL surface, the contact angle of the droplet became smaller and the wetting diameter as well as the adhesion force of the droplet increased, making it difficult for the droplet to break away from the GDL surface. The droplet was elongated and fractured under the gas-driven force, forming several small droplets on the GDL surface.Figure 16
The movement of droplets on the surface of dry or wet GDL at air velocity of 5 m/s.
(a)
(b)Taking the vibration into account, the direction of the vibration is also an important factor to the movement of the droplet. Figure17 shows the movement of the 6 μL droplet on GDL surface under the interaction of vertical vibration and air flow at a frequency of 20 Hz and an amplitude of 1.5 mm. According to the above analysis, the droplet could not start the transition from the Wenzel-Cassie regime to the Cassie regime under this condition, but the height of the droplet changed. The gas flow rate was 2 m/s, less than the critical velocity of the water droplet. It can be seen from the picture that the droplet could not break away from GDL under the gas-driven force in the first 20 ms. After 34 ms, the vibration provided an upward force for the droplet to be stretched, the wetting diameter between the droplet and GDL became shorter, and the height of the droplet increased. At the same time, the gas-driven force on the droplet enhanced so that the droplet bounced off the GDL surface at 74 ms. It should be pointed out that when the vibration provided a downward force to the droplet, the height of the droplet decreased while the contact line and the adhesion force became larger; meanwhile, the gas-driven force reduced, making it difficult for the droplet to break away from the GDL. The same thing happened when the droplet stopped vibrating.Figure 17
The movement of 6μL droplet on GDL surface under the interaction of vertical vibration and air flow.The movement of an 8μL droplet on GDL surface under the interaction of horizontal vibration and air flow at a frequency of 20 Hz and an amplitude of 1 mm was shown in Figure 18. The gas flow rate was 2 m/s, less than the critical velocity of the water droplet. Under the effect of the gas, the contact angle of the droplet changed (t=11ms); when the vibration was opposite to the direction of the gas-driven force on the droplet, the droplet moved from right to left in the horizontal direction (t=43ms) and could not overcome the adhesion force to break away from the GDL. When the vibration was in the same direction as the gas-driven force on the droplet, the droplet was elongated (t=58ms); at 68 ms, the droplet was pulled off and moved forward under the effect of the gas on the surface of GDL.Figure 18
The movement of 8μL droplet on GDL surface under the interaction of horizontal vibration and air flow.


## 3.1. Dynamic Performance of the Droplet under Vertical Vibration

It was found in the experiment that as the vibration amplitude increased, there were three different situations when the vertical vibration at a certain value of frequency was applied to the surface of GDL. In Figure4(a), the vibration deformation of the droplet on GDL was too small to start the transition from the Wenzel-Cassie regime to the Cassie regime while the input frequency was 20 Hz and the amplitude was 1 mm. Keeping the same frequency and gradually increasing the amplitude to 2 mm, the droplet would be snapped during oscillation, leaving a trail behind. As shown in Figure 4(b), after falling back to the GDL surface, the droplet could not break away again for cyclic motion. It can be observed from Figure 4(c) that when the amplitude was increased to 2.5 mm, the vibrational energy of the droplet could overcome the adhesion power between droplet and GDL surface so that the droplet was completely separated from the gas diffusion layer to achieve the transition from the Wenzel-Cassie regime to the Cassie regime.Figure 4
Under the vertical vibration frequency of 20 Hz, different amplitude conditions, the movement of droplets on the surface of GDL.
(a)
(b)
(c)If the vibration amplitude remained unchanged and the frequency was variate, the vibrating mode of the droplet had the similar variation trend as that under the same frequency. From Figure5, it can be found that after vibrating at an amplitude of 2 mm and the frequencies added from 15 Hz to 30 Hz, the vibration of the droplet became apparent and the droplet accomplished the transition from the Wenzel-Cassie regime to the Cassie regime at a larger frequency. For the water management of the PEMFC, Figures 4(c) and 5(c) are ideal state as the droplets completely bounced off the GDL surface and were easily blown away under a small gas flow rate.Figure 5
Under the vertical vibration amplitude of 2 mm, different frequency conditions, the movement of droplets on the surface of GDL.
(a)
(b)
(c)The deformation rate is a parameter to quantitatively measure the deformation extent of the droplet with time. In this work, the gradient of the wetting diameterD/D0 and the height H/H0 during the droplet vibration were analyzed in real time, where D0, D, H0, and H represent the wetting diameter and height of the droplet at rest or under vibration, respectively. Figure 6(a) shows the maximum height of the droplet increasing with the augmentation of amplitudes, and the droplet height presents a periodical change with the cycle of vibrating motion at a constant frequency of 20 Hz. When the amplitude was 1 mm, the height of the droplet deformed little, while the droplet being vibrated at an amplitude of 2 mm, its height reached two different maximum values, which were 1.8 h0 and 1.6 h0 within 60 ms. The peak value came up to 3.0 h0 with the amplitude added to 2.5 mm. Furthermore, there was a correspondence between the gradient of the wetting diameter and the height of the droplet. When the wetting diameter reached the maximum value, the corresponding height of the droplet was the minimum as shown in Figure 6(b).Figure 6
The change rate of the droplet with time under different amplitudes: (a) height of droplet and (b) wetting diameter of droplet.
(a)
(b)To observe how the frequencies influence the wetting diameter and the height of the droplet at a constant amplitude of 2 mm, the results of the experiments are exhibited in Figure7. The maximum of the droplet height gradually rises along with the increase of frequency; also, the vibrational frequencies of the droplet were different under various driving frequencies. When the driving frequency was 15 Hz, which was basically consistent with the vibrational frequency, the droplet always contacted with the GDL surface. With the rise of driving frequency to 20 Hz and 30 Hz, the wetting diameter was decreased to 0 during 11-27 ms and 12-20, 43-58 ms so that the vibrational frequencies were corresponding to 22 Hz (T=45ms) and 32 Hz (T=31ms), different from the driving frequencies.Figure 7
The change rate of the droplet with time under different frequencies: (a) height of droplet and (b) wetting diameter of droplet.
(a)
(b)The gradient of the maximum height of droplet under different frequencies was obtained by calculating the average value of the maximum height of droplet in three cycles under various frequencies and amplitudes. As shown in Figure8, the gradient of the droplet height increased with the augmentation of frequency at the same amplitude, especially under large amplitude (2.5 mm), and the gradient of the maximum height of droplet enhanced rapidly. When the vibrational frequency was greater than 15 Hz and the amplitude was 2.5 mm, the droplet was separated from the surface of GDL. When the frequency was greater than 20 Hz and the amplitude was 2 mm, the droplet broke away from the GDL surface.Figure 8
The maximum gradient of droplet height at different frequencies.


## 3.2. Dynamic Performance of the Droplet under Horizontal Vibration

Under a constant horizontal frequency of 20 Hz from Figure9, it can be seen that while the amplitude was increased to 2 mm, the droplet showed a tendency of fracture at 10 ms and left a water film on the surface of GDL, stretching the wetting diameter between the droplet and GDL surface longer. With the rise of amplitude to 2.5 mm in Figure 9(c), the droplet would be snapped during the expansion, leaving a trail, because the bottom of the droplet was still attached to the micropores of the GDL due to its viscosity and the applied energy exceeded the cohesive energy of the droplet so that the droplet was pulled off to form a new small droplet. For an 8 μL droplet, keeping the same amplitude at 2 mm and inputting a changing vibrational frequency (less than 7 Hz), the variation trend was similar as the case above, as shown in Figure 10.Figure 9
Under the horizontal vibration frequency of 20 Hz, different amplitude conditions, the movement of droplets on the surface of GDL.
(a)
(b)
(c)Figure 10
Under the horizontal vibration amplitude of 2 mm, different frequency conditions, the movement of droplets on the surface of GDL.
(a)
(b)
(c)
(d)The static contact angle of the droplet changes under the condition of horizontal vibration. The contact angle corresponding to the front contact point is known as the advancing contact angleθA, and that corresponding to the rear contact point is called the receding contact angle θB. The difference between the advancing contact angle and the receding contact angle (θA‐θB) is contact angle hysteresis.Figure11 exhibits the periodic changes of the advancing contact angle (θA) and the receding contact angle (θB). As the vibration moved to the right from the equilibrium position, the advancing contact angle of the droplet increased gradually and reached the maximum value of 172° when the vibration arrived at the far-right end. Accordingly, the receding contact angle decreased gradually to the minimum value of 80° and the contact angle hysteresis (θA‐θB) gradually enhanced in the process just as 0-17 ms in Figure 11(b). As mentioned above, the wetting diameter of the droplet became larger so that the adhesion force between the droplet and GDL rose up. Therefore, even if the contact angle of the droplet increased to the maximum, the droplet did not scroll on the GDL. When the vibration moved from the far-right end to the far-left end, the advancing contact angle of the droplet gradually decreased to the minimum value of 76°, but the receding contact angle gradually enhanced to the maximum value of 165°. While the advancing contact angle reduced to equal to the receding contact angle, the droplet was in the equilibrium position. At this point, the wetting diameter of the droplet was smallest and the height was largest.Figure 11
The variation of the droplet with time at the frequency of 20 Hz and the amplitude of 1 mm: (a) contact angle and (b) contact angle hysteresis.
(a)
(b)Under a larger amplitude, the shape of the droplet changed significantly so that the advancing contact angle and the receding contact angle of the droplet could not be measured accurately. Therefore, the shape of the droplet was represented by its wetting diameter. Figure12 shows the variation of the droplet wetting diameter with time under the frequency of 20 Hz and the amplitude of 2 mm as well as 2.5 mm. The wetting diameter of the droplet changed irregularly with the vibration. When the amplitude was 2 mm, the wetting diameter of the droplet was larger than the initial diameter. There were more water molecules entering the micropores of the GDL, adding the adhesion force between the droplet and GDL. With the augmentation of the amplitude to 2.5 mm, the wetting diameter of the droplet gradually decreased in the initial stage. At 21 ms, the droplet was pulled apart to form a small droplet which vibrated in the new position and after that, the wetting diameter first decreased and then increased.Figure 12
The variation of the droplet wetting diameter with time under different amplitudes.Figure13 clearly indicates the displacement of the droplet central point varying with time under different amplitudes. With the rise of amplitude, the maximum displacement of the droplet gradually increased and the displacement of the droplet increased and decreased correspondingly with the recirculation of the vibration in the horizontal direction. At the amplitude of 1 mm, the maximum displacement in the positive direction was close to that in the negative direction, both of which were 0.5 mm. It indicated that the droplet did not slip on the GDL surface. When the amplitude increased to 2 mm, the positive displacement (1.4 mm) of the droplet central point was greater than the negative displacement (0.6 mm) so that the droplet slid. As the amplitude added up to 2.5 mm, the droplet fractured at 21 ms and then the formed droplet would reciprocate in the new equilibrium position.Figure 13
The variation of the droplet displacement with time.


## 3.3. Dynamic Performance of the Air Flow-Induced Droplet under Vibration

Above all, several experiments about the dynamic performance of the air flow-induced droplet without vibration were performed. The movement of the 8μL water droplet on GDL surface at different air velocities of 2.76 m/s, 3.39 m/s, 3.9 m/s, and 4.52 m/s is shown in Figure 14. From Figures 14(a) and 14(b), it can be observed that at a low gas flow rate, the receding contact angle of the droplet gradually decreased and the advancing contact angle gradually increased over time, because the force that the gas put on the droplet was less than the adhesion force between the droplet and GDL, which prevented the droplet from leaving the GDL surface and formed a small water film. As the flow rate increased to 3.9 m/s, the tail of the droplet was stretched as shown in Figure 14(c). When the flow rate reached 4.52 m/s, the drag force of the gas made the droplet forming a slender column, the front of the droplet contacted with the GDL, and the tail was suspended in the air. At this moment, although the drag force was not enough to overcome the adhesion force between the droplet and GDL, it exceeded the cohesion force of the droplet so that the droplet suspended in the air was pulled apart.Figure 14
The movement of 8μL droplet on GDL surface under different air velocities.
(a)
(b)
(c)
(d)To discuss the motion characteristics of the droplets with different volumes on GDL surface, the droplets of 6μL, 8 μL, and 10 μL at the air velocity of 5 m/s were investigated in Figure 15. The 6 μL droplet completely broke away from the GDL, and the bottom of the 8 μL and 10 μL droplets fractured and migrated on the surface of GDL. In addition, the wetting diameter of the 10 μL droplet was larger compared with the 8 μL droplet. This was because the gravity and adhesion force of the droplet tiny in size were small, and the force of the gas could overcome the adhesion force and gravity of the droplet under a larger gas flow rate, making the droplet float above the GDL.Figure 15
The movement of different volume droplets on GDL surface at air velocity of 5 m/s.
(a)
(b)
(c)Furthermore, the surface properties of the GDL also affect the movement of the droplet. Figure16 shows the movement of the 6 μL droplet on the surface of dry or wet GDL at the gas flow rate of 5 m/s. On the dry GDL surface, the bottom of the droplet separated from the GDL under the gas-driven force and moved forward. While on the wet GDL surface, the contact angle of the droplet became smaller and the wetting diameter as well as the adhesion force of the droplet increased, making it difficult for the droplet to break away from the GDL surface. The droplet was elongated and fractured under the gas-driven force, forming several small droplets on the GDL surface.Figure 16
The movement of droplets on the surface of dry or wet GDL at air velocity of 5 m/s.
(a)
(b)Taking the vibration into account, the direction of the vibration is also an important factor to the movement of the droplet. Figure17 shows the movement of the 6 μL droplet on GDL surface under the interaction of vertical vibration and air flow at a frequency of 20 Hz and an amplitude of 1.5 mm. According to the above analysis, the droplet could not start the transition from the Wenzel-Cassie regime to the Cassie regime under this condition, but the height of the droplet changed. The gas flow rate was 2 m/s, less than the critical velocity of the water droplet. It can be seen from the picture that the droplet could not break away from GDL under the gas-driven force in the first 20 ms. After 34 ms, the vibration provided an upward force for the droplet to be stretched, the wetting diameter between the droplet and GDL became shorter, and the height of the droplet increased. At the same time, the gas-driven force on the droplet enhanced so that the droplet bounced off the GDL surface at 74 ms. It should be pointed out that when the vibration provided a downward force to the droplet, the height of the droplet decreased while the contact line and the adhesion force became larger; meanwhile, the gas-driven force reduced, making it difficult for the droplet to break away from the GDL. The same thing happened when the droplet stopped vibrating.Figure 17
The movement of 6μL droplet on GDL surface under the interaction of vertical vibration and air flow.The movement of an 8μL droplet on GDL surface under the interaction of horizontal vibration and air flow at a frequency of 20 Hz and an amplitude of 1 mm was shown in Figure 18. The gas flow rate was 2 m/s, less than the critical velocity of the water droplet. Under the effect of the gas, the contact angle of the droplet changed (t=11ms); when the vibration was opposite to the direction of the gas-driven force on the droplet, the droplet moved from right to left in the horizontal direction (t=43ms) and could not overcome the adhesion force to break away from the GDL. When the vibration was in the same direction as the gas-driven force on the droplet, the droplet was elongated (t=58ms); at 68 ms, the droplet was pulled off and moved forward under the effect of the gas on the surface of GDL.Figure 18
The movement of 8μL droplet on GDL surface under the interaction of horizontal vibration and air flow.


## 4. Conclusions

The PEMFCs in vehicles are often subjected to the harsh operation environment accompanied with mechanical vibration in the actual road conditions. In this paper, we designed an ex situ test platform with an image acquisition system to explore the dynamic characteristics of the vibrating droplet on GDL surface. It was found in the study that when the vertical vibration amplitude was 2.5 mm and the frequency was greater than 15 Hz or the amplitude was 2 mm and the frequency was greater than 20 Hz, the droplet was completely separated from the GDL surface to achieve the transition from the Wenzel-Cassie regime to the Cassie regime. The wetting diameter of the droplet was smaller than the initial diameter for a long time during an oscillation cycle, which made it easier for the gas to discharge the droplets from the PEMFC. While the horizontal vibration amplitude was 2.5 mm and the frequency was larger than 20 Hz or the amplitude was 2 mm and the frequency was larger than 30 Hz, the applied energy exceeded the cohesive energy of the droplet in the expansion process, resulting in the droplet being pulled apart. For the amplitude and frequency larger than 1 mm and 10 Hz, the wetting diameter of the droplet enhanced and there would be more water molecules going into the micropores of the GDL. As to the movement of the droplet on GDL surface under the interaction of vibration and air flow, the droplet was easier to move forward under the gas-driven force. At the same time, the wetting diameter of the droplet added up after vibrating, making it necessary to increase the gas flow rate to achieve the purging effect. The content investigated in this paper is a fundamental understanding of the liquid behavior on GDL under mechanical vibration. It has a certain reference value for the water management of PEMFCs in the actual road conditions.



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*Source: 1674134-2019-12-10.xml*