0
Research Papers

# Study of Water Droplet Removal on Etched-Metal Surfaces for Proton Exchange Membrane Fuel Cell Flow ChannelOPEN ACCESS

[+] Author and Article Information
S. Shimpalee

Department of Chemical Engineering,
University of South Carolina,
Columbia, SC 29208
e-mail: shimpale@cec.sc.edu

V. Lilavivat

National Metal and Materials Technology Center,
National Science and Technology Development Agency,
114 Thailand Science Park,
Pathum Thani 12120, Thailand

1Corresponding author.

Manuscript received November 4, 2015; final manuscript received March 7, 2016; published online April 5, 2016. Assoc. Editor: Matthew Mench.

J. Electrochem. En. Conv. Stor. 13(1), 011003 (Apr 05, 2016) (7 pages) Paper No: JEECS-15-1004; doi: 10.1115/1.4033098 History: Received November 04, 2015; Revised March 07, 2016

## Abstract

Within a proton exchange membrane fuel cell (PEMFC), the transport route of liquid water begins at the cathode catalyst layer, and then progresses into the gas diffusion layer (GDL) where it then goes into the flow channel. At times, significant accumulation of liquid droplets can be seen on either side of the membrane on the surface of the flow channel. In this work, liquid water and the flow dynamics within the transport channel were examined experimentally, with the channel acting as an optical window. Ex situ interpretations of the liquid water and flow patterns inside the channel were established. Liquid water droplet movements were analyzed by considering the change of the contact angle with different flow rates. Also, various surface roughness of stainless steel was used to determine the relationships between flow rate and the contact angles. When liquid water is found within the gas channels of PEMFCs, the channels' characteristic changes become more dominant and it becomes more of a necessity to monitor the effects. Physical motion of water droplets in the flow channels of PEMFCs is important. The surface roughness properties were used to describe the contact angle and the droplet removal force on the stainless steel flow channel.

<>

## Introduction

PEMFCs are energy generators, suitable for many applications with differing requirements. Liquid water accumulation and removal are the major problems in maintaining high performance in PEMFCs operation [1,2]. Generally, the water production from electrochemical reactions is transported to the gas channel through the GDL by a pressure gradient [3]. Excess liquid water from condensation can form droplets or slug and prevent the transport of oxygen at the cathode and/or the transport of hydrogen at the anode to the catalyst. This phenomenon is commonly known as “flooding.” The liquid water inside the fuel cell can appear in the GDL [4], as water drops appear from pores of the GDL and flow into the cathode gas flow channel. The drops can then grow into slugs that span the cross section of the flow channels [5,6]. Turhan et al. [7] addressed significant liquid droplet accumulation in the fuel cell on the surface of the flow channel with in situ neutron imaging. The presence of liquid droplets has a strong effect on the pressure drop within the flow channel [8,9]. For these reasons, water management is one of the important issues in PEMFC development, which is vital to achieve maximum performance and durability of PEMFCs.

Among all of the fuel cell components, the bipolar plate has been shown to have the highest accumulation of liquid droplets [10]. Also, the bipolar plate is one of the major components that contribute significantly toward the PEMFCs manufacturing cost [1113]. The current research focuses on metal bipolar plates manufactured by electro-etching technology, which is a low-cost, high-volume manufacturing process capable of producing metallic bipolar plates [14,15]. The experimental setup in this research calls for varying surface roughness of the electro-etching steel plate [16].

The contact angle of the droplet is a key factor used to analyze the movement characteristics of water droplets on solid planes [17]. This method was introduced by Young [18]. Knowing that the contact angle is related to the surface tension of a solid, liquid, and vapor, Young suggested an equation that described the contact angle on a smooth surface by considering the interfacial energies at the triple line where the vapor, liquid, and solid phases come into contact with one another as shown in Fig. 1. In the equation

Display Formula

(1)$cos θ=γSV−γSLγLV$

where γSL, γSV, and γLV indicate the interfacial free energies per unit area of solid–liquid (SL), solid–gas (SV), and liquid–gas (LV) interfaces, and θ is the contact angle of droplet. If the liquid wets the surface (hydrophilic surface), the value of the static contact angle is 0 deg ≤ θ ≤ 90 deg; however, if the liquid does not wet the surface (hydrophobic surface), the value of the contact angle is 90 deg ≤ θ ≤ 180 deg.

Wenzel [19] proposed an equation demonstrating the contact angle on a rough surface by modifying Young's equation to the following: Display Formula

(2)$cos θ′=r(γSV−γSL)γLV=r cos θ$

where r is the roughness factor and θ′ is the apparent contact angle. In this equation, the value of r is always bigger than unity. Therefore, surface roughness improves the hydrophilicity of the hydrophilic surface. Thus, under these parameters in the equation, the apparent contact angle will be changed with the roughness factor.

Cassie–Baxter [20] reported an equation describing the contact angle at a heterogeneous surface combined of a solid and air. When a surface area has a wetted surface area fraction f with a water contact angle θ, the contact angle on the surface can be expressed by using the following equation, assuming that the water–air contact angle is 180 deg, Display Formula

(3)$cos θ′=f cos θ+(1−f)cos 180deg=f cos θ+f−1$

There were many works on the origin and validation of the Wenzel and Cassie–Baxter equations [2125]. When the surface roughness is high, the Cassie–Baxter's model is a more favorable candidate than Wenzel's [26]. In the case of Cassie–Baxter's model, the liquid droplet on the rough surface can cause air to become stuck between the solid and liquid interface, causing an addition of air–liquid interfaces. Bikerman [27] studied water droplets on different surface roughness of stainless steels with the contact angle of 90 deg and suggested that the surface roughness offers resistance for sliding droplet movement.

The behavior of the liquid droplet was predicted on the foundation of dynamic contact angle measurements, which can be estimated by the adhesion force on the surface. During the experiment, the dynamic behavior of the droplet was analyzed through the contact angle measurements as reported by Theodorakakos et al. [28]. In this work, various surfaces roughness of stainless steel was chosen to examine the impacts of surface properties on the droplet behavior.

## Experimental Procedure

To determine the amount of distortion and movement of a droplet in a small flow channel, an experimental channel was set up as shown in Fig. 2. This figure shows the channel assembly used in this experiment, first reported by Venkatraman et al. [29]. It contains of three objects: a top, a bottom, and an inserted floor. The top and bottom are made from transparent polycarbonate. This allows easy spotting of the water drops inside the channel. The top piece was polished with a solvent to produce an optical finish. The bottom part has a slot for insertion of the sample. The inserted floor, located at the center of the channel, is for installing the sample. The sample can be replaced for evaluating different materials. To determine the distortion and the movement of the liquid droplet under different surface properties, samples of electrochemically etched stainless steel plates with various average roughness (Ra) values were placed into the inserted channel floor space. The average roughness (Ra) and roughness factor (r) were measured by AFM (Veeco Dimension 3100, Veeco Metrology Group, Santa Barbara, CA). Figure 3 shows the typical morphology and cross section profile of stainless steel sample surface which consists of assemblies of needlelike structures. It is noted that for each sample, the AFM measurement was performed at three different positions on the sample in order to confirm the uniform roughness. For visualization, this experiment must be performed in a channel larger than a typical fuel cell flow channel while maintaining the same ratio of channel width (w) and channel depth (d) of 2.0. In this work, w is 4 mm and d is 2 mm, while for the typical fuel cell's flow channel, w is 1.0 mm and d is 0.5 mm. The length of the channel is 120 mm, which is long enough for flow rates up to 2500 cm3/min to be fully developed as laminar flow. One side of the channel is joined to compressed air via a pressure regulator and a nozzle valve is operated by a flow meter in order to control flow rates. The other side of the channel is attached to the outside environment.

Venkatraman et al. [29] studied how the droplet height per the depth of flow channel (h/d) affects the pressure drop in the channel. They found that if the droplet height per the depth of flow channel (h/d) is greater than 80%, there is a large pressure drop within the flow channel. A liquid water droplet on the size of 10 μl, which is equivalent to h/d of 84%, was chosen to perform the experiments.

A 10 μl droplet was positioned on top of the sample, and then, the channel was closed. The air was delivered to the channel for this experiment corresponding to that typical flow rate found on the cathode side of PEMFC. The air was released into the channel at a certain flow rate, which was controlled by a mass flow controller. Then, the profile of the water drop was observed using a microscope. Due to water evaporation especially at higher air flow rates, a new droplet was used after exposing the channel to air at a particular flow rate, and the experiment was replicated at gradually higher flow rates. The flow rate was gradually risen from 0 to 2500 cm3/min (Re = 0–925). The experiment was stopped if the droplet began to move. All experiments were done at 25 °C.

Reynolds numbers (Re) were calculated using the density (ρ) and viscosity (μ) of dry air at 1 atm and 25 °C, ρ = 1.205 kg/m3 and μ = 1.81 × 105 Pa·s, Display Formula

(4)$Re=ρQDhAμ$

where Q is the volumetric flow rate, A is the cross-section area, and Dh is the hydraulic diameter of the rectangular channel [30]. The hydraulic diameter was calculated using the wetted perimeter (Pr) and the cross-section area Display Formula

(5)$Dh=4APr=4wd2d+2w=23w$

The contact angles of liquid droplet were measured to confirm the hypothesis of the drops have spherical segments. The advancing and the receding angles, θa and θr, of droplet distortion were measured from images taken by microscope. For every flow rate, three images were taken to measure the contact angle. Each image has the color and contrast adjusted to make the droplet standout before measuring the advancing and the receding angles using protractor software (i.e., dinocapture). Figure 4 illustrates the water droplet deformation and the changing of advancing and receding contact.

The stainless steel plate from electro-etching process made by Faraday Technology, Inc. (Englewood, OH) was used in this study. The surface roughness of the sample plate was changed by changing the etching parameters, specifically increasing or decreasing the forward (anodic) peak voltage of the etching waveform or removing the reverse (cathodic) peak voltage from the waveform. The surface roughness selected for the samples should cover the range of the roughness found in other manufacturing processes. Note that Faraday Technology, Inc. has never analyzed the surface chemistry after electro-etching. It is possible that there could be small chemical changes in the concentration of the alloying elements on the stainless steel. The chromium concentration increases at the surface of 316 l stainless steel subsequent to electro-etching versus mechanical polishing when the oxide thickness was the same in both processes.

## Theoretical Analysis of Macroscopic Force Balance

A macroscopic force balance has been established in the flow channel in order to predict the behavior of the water droplet [31]. In general, the shape of the liquid droplet on the surface is controlled by the normal stress on the free surface as a result of gravity, fluid flow within the drops, and surface tension. Gravity has negligible effects on the small droplets, and the shape of a simple drop is spherical. Figure 5 illustrates a macroscopic force balance model of the droplet in the presence of air flow. Figure 5(a) shows image of the droplet in the presence of air flow from experiment. Figure 5(b) gives a schematic view of control volume chosen for analysis taken from Ref. [7]. The control volume is defined with planes A and B, and the depth is equal to the diameter of the droplet. The pressure difference between A and B is the total pressure force. Pressure force (Fp) is created by the difference of pressure between the front and back of droplet in the flow field and can be written as

Display Formula

(6)$FP=(PA−PB)×Area=(PA−PB)2B×2R$

where PA and PB represent the pressure at A and B planes, and $2B×2R$ denotes the cross-section area of the control volume [31]. The drag force (Fdrag) is produced by the shear of fluid alongside the surface of the droplet, and the difference of pressure is the total exerted force on the droplet. Therefore, the macroscopic force balance is given by Display Formula

(7)$Fdrag=FP+Fshear$

where Fshear is the shear force exerting on the top of droplet due to the no-slip condition. In static condition, the drag force is balanced by the surface tension force, which is the force that relates to the attractive force by molecules of a liquid and the surface contact angles of the droplet emerging on the plate as represented in Eq. (8) for stable condition. If the surface tension force is equal or more than the drag force, the droplet will not move from the channel. The crucial condition is the point when the droplet starts to move. In the force balance model, the critical state is the situation when the surface tension is counterbalanced by drag force. If the drag force is increased above the critical point, the droplet will become unstable and start to move from the channel. Display Formula

(8)$FST≥Fdrag$

The force caused by surface tension is a key factor in the balance equation because it is connected to traction and contact angle of water droplets evolving in the channel surface. By considering the flow of gas to be Newtonian, fully developed, and laminar, the pressure drop is related to pressure, average velocity, and the height of the channels. The pressure drop throughout the control volume can be expressed as [31,32] Display Formula

(9)$PA−PB=3μu′b22R$

where u′ is the average velocity above the droplet. Based on incompressible fluid, u′ can be approximately $u′=(B/b)U$, where U is the average velocity. Therefore, from Eqs. (6) and (9), the pressure force becomes Display Formula

(10)$FP=24μB2UH2(B−H2)3(1−cos θa)2$

where Display Formula

(11)$R=H1−cos θa$

The shear stress at the top surface of Newtonian fluid is Display Formula

(12)$τxy=3μu′b$

Substituting u′ and b, the shear force of the control volume becomes Display Formula

(13)

From the above equation, the drag force was calculated by droplet geometry and the Reynolds number.

## Results and Discussion

This experiment was set up to study the behavior of water droplet inside the flow channel at different Re number and surface roughness. The results show the impacts on droplet distortion and onset motion inside the flow channel.

###### Effect of Surface Roughness on Water Droplet Behavior.

The static contact angle of a 10 μl liquid water droplet on stainless steel samples with different surface roughness was measured as shown in Fig. 6. The results show that the static contact angle of the droplet increases with increasing the surface roughness (Ra). In this case, the static contact angle of the droplet on a stainless steel plate is 82 deg for Ra = 0.02 μm, 85 deg for Ra = 0.30, 86 deg for Ra = 0.27, and 94 deg for Ra = 0.73 μm. Therefore, the contact angle is dependent on surface roughness. Moreover, with the same volume of droplet, the height of the droplet also depends on the contact angle. The height of droplet goes up with the increasing of contact angle as shown in Fig. 6.

From the results, we have proposed a model explaining contact angles on rough surfaces by using a combination of Wenzel's and Cassie–Baxter's models [33]. The surface roughness was assumed to be a sequence of uniform needles, as presented in Fig. 7. The contact angle on this surface is expressed by the following equation:

Display Formula

(14)$cos θ′=rf cos θ+f−1$

where θ′ is the apparent contact angle on a rough surface, θ is the equilibrium contact angle on a flat surface, r is a roughness factor, and f is the solid surface area fraction. The roughness factor is the quotient of the actual area of a rough surface to the geometrically projected area. The solid surface area fraction is the area fraction of the surface in contact with the water. The solid surface area fraction f can be calculated from Eq. (14). The surface properties obtained in this equation are given in Table 1. From this table, the behavior of water shows that the contact angle increases with increasing of the average surface roughness while the solid surface area fraction of the surface is decreasing. The larger area of solid surface indicates that more air can be trapped in the rougher surface, which increases the droplet contact angle. The solid surface area fraction trends to increase with surface roughness. However, the contact angle of surface with Ra = 0.3 μm is lower than the surface with Ra = 0.27 μm, which implies that the solid surface area fraction depends on surface pattern rather than surface roughness.

###### The Effect of Surface Roughness on Pressure Drop Inside the Flow Channel.

Figure 8 illustrates the sequence photography of the dynamic behavior of water droplets on the stainless steel plate with roughness Ra = 0.73 μm under different flow rates. The flow rate of the air inlet was initiated at 0 cm3/min (Re = 0), and then, it was gradually increased. The results show that the contact angle's hysteresis increased with higher flow rates (Reynolds number increases). These results are similar to the sliding angle of a droplet [22,34]. The shape of the droplet at different flow rates was observed. From these sequence photographs, the shapes of the droplet on surfaces with different Ra values at each Re were combined together as shown in Fig. 9. The shape of the droplet such as height, radius, and width of water droplet was measured at each Reynolds number. This measurement was repeated three times using the different droplets for reproducibility. This measurement was used to calculate the pressure drop across droplet as shown in Eq. (9).

The intention of the flow inside the gas channel is to have low resistance, and the pressure drop represents flow resistance in the gas channel. Therefore, the pressure drop in the flow channel is one of the important parameters to evaluate the performance of the gas flow channel. Figure 10 shows the results of the calculated pressure drop at the critical point when the droplet starts to move versus the roughness of the flow channel. The result indicates that the pressure drop increases with increasing the surface roughness of the flow channel. From Eq. (9), the height of the droplet critically impacts the pressure drop in the flow channel, which significantly increases with the height of the droplet. Note that the larger contact angle on the surface results in the higher height of the droplet. Sakai et al. [22] stated that the resistance force is related to the pressure force on the droplet against the solid surface.

Bikerman [27] and Wolfram and Faust [35] studied the relating forces that involve the movement of the droplets from different roughness of the surface. They proposed that the force to move the droplet from the surface is proportional to the surface roughness. For the droplet in the flow channel, Fig. 11 shows the calculation of drag force on droplet against Reynolds number under different surface roughness. The drag force is varied with Reynolds number or flow rate. The higher Reynolds number gives the higher drag force. In this figure, the drag force trends to follow the surface roughness. However, the surface with Ra = 0.27 μm exhibits higher drag force compared to the surface with Ra = 0.3 μm. This implies that the surface roughness is not enough to be the key factor of the drag force. It is noted that the roughness value includes a few unknown parameters such as surface pattern.

Miwa et al. [33] pointed out that the interaction energy between water and a solid surface is relative to the contact area, which is the roughness factor times the solid area fraction (true contact area factor). Figure 12 presents a linear relationship between the total drag force from the calculation against the roughness factor times solid area fraction, rf. This figure shows that the drag force is the function of roughness factor and solid area fraction. A straight line was fitted to the points inferring that the surface tension force of solid surface is controlled by the roughness factor r and solid area fraction f. The roughness factor times solid area fraction indicates the area of droplet that attaches on the surface. Detailed analyses on the impact of chemical composition at the wider range of materials will be addressed in future work.

## Conclusions

In this study, the droplet distortion and elimination from the surface of a fuel cell channel was revealed by using visualization of a water droplet within a predetermined air flow. The measured contact angles for stainless steel samples with different surface roughness values at temperature of 25 °C were reported. The results show that the contact angle rises slightly with the increasing values of surface roughness. The least amount of air flow and pressure drop required to transport the water droplets were described. The surface roughness which has the best water removal properties at the lowest pressure drop was found to be the smoothest surface. The surface roughness equation given in this work can describe the relationship between contact angle, roughness factor, and solid area fraction. However, the temperature correction for surface tension might need to be taken into consideration if the operating temperature is significantly different. The resistant force, which is acting against the pressure force, is a linear correlation to the product of the solid area fraction and the roughness factor. A smoother surface of the flow channel may help to reduce the pressure drop affected by the liquid droplet and also improve the water removal away from the flow channel.

## Acknowledgements

The authors would like to thank the NSF I/U CRC for Fuel Cells (Grant No. EEC-0324260) and the Department of Energy (Grant No. DE-EE0000471) for their financial support. They gratefully acknowledge the support of Faraday Technology, Inc. and Entegris, Inc. for assisting this work. Also, the authors would like to thank Professor John W. Van Zee and Professor X. Li for their suggestions on the surface roughness model.

## Nomenclature

• A =

cross-sectional areas

• b =

half of distance between droplet to channel

• B =

half of channel depth

• d =

channel depth

• Dh =

hydraulic diameter of the rectangular channel

• f =

solid surface area fraction

• F =

force

• Pr =

perimeter

• Q =

volumetric flow rates

• r =

roughness factor

• R =

• Re =

Reynolds numbers

• U =

average velocity of air in channel

• u′ =

average velocity above the droplet

• w =

channel width

• W =

width of droplet

• α =

sliding angle

• γ =

interfacial free energies per unit area

• θ =

contact angle

• θ′ =

apparent contact angle

• μ =

viscosity of air

• ρ =

density of air

• τ =

shear stress

Subscripts
• a =

• LV =

liquid–gas

• P =

pressure

• r =

receding

• SL =

solid–liquid

• ST =

surface tension

• SV =

solid–gas

## References

Devrim, Y. , Erkan, S. , Bac, N. , and Eroglu, I. , 2009, “ Preparation and Characterization of Sulfonated Polysulfone/Titanium Dioxide Composite Membranes for Proton Exchange Membrane Fuel Cells,” Int. J. Hydrogen Energy, 34(8), pp. 3467–3475.
Gallagher, K. G. , Pivovar, B. S. , and Fuller, T. F. , 2009, “ Electro-Osmosis and Water Uptake in Polymer Electrolytes in Equilibrium With Water Vapor at Low Temperatures,” J. Electrochem. Soc., 156(3), pp. B330–B338.
Tuber, K. , Pocza, D. , and Hebling, C. , 2003, “ Visualization of Water Buildup in the Cathode of a Transparent PEM Fuel Cell,” J. Power Sources, 124(2), pp. 403–414.
Yamada, H. , Hatanaka, T. , Murata, H. , and Morimoto, Y. , 2006, “ Measurement of Flooding in Gas Diffusion Layers of Polymer Electrolyte Fuel Cells With Conventional Flow Fields,” J. Electrochem. Soc., 153(9), pp. A1748–A1754.
Colosqui, C. E. , Cheah, M. J. , Kevrekidis, I. G. , and Benziger, J. B. , 2011, “ Droplet and Slug Formation in Polymer Electrolyte Membrane Fuel Cell Flow Channels: The Role of Interfacial Forces,” J. Power Sources, 196(23), pp. 10057–10068.
Hellstern, T. , Gauthier, E. , Cheah, M. J. , and Benziger, J. B. , 2013, “ The Role of the Gas Diffusion Layer on Slug Formation in Gas Flow Channels of Fuel Cells,” Int. J. Hydrogen Energy, 38(35), pp. 15414–15427.
Turhan, A. , Kim, S. , Hatzell, M. , and Mench, M. M. , 2010, “ Impact of Channel Wall Hydrophobicity on Through-Plane Water Distribution and Flooding Behavior in a Polymer Electrolyte Fuel Cell,” Electrochim. Acta, 55(8), pp. 2734–2745.
Cheah, M. J. , Kevrekidis, I. G. , and Benziger, J. B. , 2013, “ Water Slug Formation and Motion in Gas Flow Channels: The Effects of Geometry, Surface Wettability, and Gravity,” Langmuir, 29(31), pp. 9918–9934. [PubMed]
Cheah, M. J. , Kevrekidis, I. G. , and Benziger, J. B. , 2013, “ Water Slug to Drop and Film Transitions in Gas-Flow Channels,” Langmuir, 29(48), pp. 15122–15136. [PubMed]
Akhtar, N. , Qureshi, A. , Scholta, J. , Hartnig, C. , Messerschmidt, M. , and Lehnert, W. , 2009, “ Investigation of Water Droplet Kinetics and Optimization of Channel Geometry for PEM Fuel Cell Cathodes,” Int. J. Hydrogen Energy, 34(7), pp. 3104–3111.
Middelman, E. , Kout, W. , Vogelaar, B. , Lenssen, J. , and de Waal, E. , 2003, “ Bipolar Plates for PEM Fuel Cells,” J. Power Sources, 118(1–2), pp. 44–46.
Cunningham, B. , and Baird, D. G. , 2006, “ The Development of Economical Bipolar Plates for Fuel Cells,” J. Mater. Chem., 16(45), pp. 4385–4388.
Bar-On, I. , Kirchain, R. , and Roth, R. , 2002, “ Technical Cost Analysis for PEM Fuel Cells,” J. Power Sources, 109(1), pp. 71–75.
McCrabb, H. , Lozano-Morales, A. , Snyder, S. , Gebhart, L. , and Taylor, E. , 2009, “ Through Mask Electrochemical Machining,” ECS Trans., 19(26), pp. 19–33.
McCrabb, H. , Taylor, E. , Lozano-Morales, A. , Shimpalee, S. , Inman, M. , and Van Zee, J. W. , 2010, “ Through-Mask Electroetching for Fabrication of Metal Bipolar Plate Gas Flow Field Channels,” ECS Trans., 33(1), pp. 991–1006.
Shimpalee, S. , Lilavivat, V. , Van Zee, J. W. , McCrabb, H. , and Lozano-Morales, A. , 2011, “ Understanding the Effect of Channel Tolerances on Performance of PEMFCs,” Int. J. Hydrogen Energy, 36(19), pp. 12512–12523.
Extrand, C. W. , 1998, “ A Thermodynamic Model for Contact Angle Hysteresis,” J. Colloid Interface Sci., 207(1), pp. 11–19. [PubMed]
Young, T. , 1805, “ An Essay on the Cohesion of Fluids,” Philos. Trans. R. Soc. London, 95, pp. 65–87.
Wenzel, R. N. , 1936, “ Resistance of Solid Surfaces to Wetting by Water,” Ind. Eng. Chem., 28(8), pp. 988–994.
Cassie, A. B. D. , and Baxter, S. , 1944, “ Wettability of Porous Surfaces,” Trans. Faraday Soc., 40, pp. 546–551.
Hejazi, V. , and Nosonovsky, M. , 2013, “ Contact Angle Hysteresis in Multiphase Systems,” Colloid Polym. Sci., 291(2), pp. 329–338.
Sakai, M. , Kono, H. , Nakajima, A. , Zhang, X. , Sakai, H. , Abe, M. , and Fujishima, A. , 2009, “ Sliding of Water Droplets on the Superhydrophobic Surface With ZnO Nanorods,” Langmuir, 25(24), pp. 14182–14186. [PubMed]
Gao, L. , and McCarthy, T. J. , 2007, “ How Wenzel and Cassie Were Wrong,” Langmuir, 23(7), pp. 3762–3765. [PubMed]
Patankar, N. A. , 2003, “ On the Modeling of Hydrophobic Contact Angles on Rough Surfaces,” Langmuir, 19(4), pp. 1249–1253.
Chen, X. F. , Wang, X. P. , and Xu, X. M. , 2013, “ Effective Contact Angle for Rough Boundary,” Physica D, 242(1), pp. 54–64.
Li, X. M. , Reinhoudt, D. , and Crego-Calama, M. , 2007, “ What Do We Need for a Superhydrophobic Surface? A Review on the Recent Progress in the Preparation of Superhydrophobic Surfaces,” Chem. Soc. Rev., 36(8), pp. 1350–1368. [PubMed]
Bikerman, J. J. , 1950, “ Sliding of Drops From Surfaces of Different Roughnesses,” J. Colloid Sci., 5(4), pp. 349–359.
Theodorakakos, A. , Ous, T. , Gavaises, A. , Nouri, J. M. , Nikolopoulos, N. , and Yanagihara, H. , 2006, “ Dynamics of Water Droplets Detached From Porous Surfaces of Relevance to PEM Fuel Cells,” J. Colloid Interface Sci., 300(2), pp. 673–687. [PubMed]
Venkatraman, M. , Shimpalee, S. , Van Zee, J. W. , Moon, S. I. , and Extrand, C. W. , 2009, “ Estimates of Pressure Gradients in PEMFC Gas Channels Due to Blockage by Static Liquid Drops,” Int. J. Hydrogen Energy, 34(13), pp. 5522–5528.
Bird, R. , Stewart, W. , and Lightfoot, E. , 1966, Transport Phenomena, 7th ed., Wiley, New York.
Kumbur, E. C. , Sharp, K. V. , and Mench, M. M. , 2006, “ Liquid Droplet Behavior and Instability in a Polymer Electrolyte Fuel Cell Flow Channel,” J. Power Sources, 161(1), pp. 333–345.
Chen, K. S. , Hickner, M. A. , and Noble, D. R. , 2005, “ Simplified Models for Predicting the Onset of Liquid Water Droplet Instability at the Gas Diffusion Layer/Gas Flow Channel Interface,” Int. J. Energy Res., 29(12), pp. 1113–1132.
Miwa, M. , Nakajima, A. , Fujishima, A. , Hashimoto, K. , and Watanabe, T. , 2000, “ Effects of the Surface Roughness on Sliding Angles of Water Droplets on Superhydrophobic Surfaces,” Langmuir, 16(13), pp. 5754–5760.
Mortazavi, V. , D'Souza, R. M. , and Nosonovsky, M. , 2013, “ Study of Contact Angle Hysteresis Using the Cellular Potts Model,” Phys. Chem. Chem. Phys., 15(8) pp. 2749–2756. [PubMed]
Wolfram, E. , and Faust, R. , 1978, Wetting, Spreading, and Adhesion, Academic Press, New York.
View article in PDF format.

## References

Devrim, Y. , Erkan, S. , Bac, N. , and Eroglu, I. , 2009, “ Preparation and Characterization of Sulfonated Polysulfone/Titanium Dioxide Composite Membranes for Proton Exchange Membrane Fuel Cells,” Int. J. Hydrogen Energy, 34(8), pp. 3467–3475.
Gallagher, K. G. , Pivovar, B. S. , and Fuller, T. F. , 2009, “ Electro-Osmosis and Water Uptake in Polymer Electrolytes in Equilibrium With Water Vapor at Low Temperatures,” J. Electrochem. Soc., 156(3), pp. B330–B338.
Tuber, K. , Pocza, D. , and Hebling, C. , 2003, “ Visualization of Water Buildup in the Cathode of a Transparent PEM Fuel Cell,” J. Power Sources, 124(2), pp. 403–414.
Yamada, H. , Hatanaka, T. , Murata, H. , and Morimoto, Y. , 2006, “ Measurement of Flooding in Gas Diffusion Layers of Polymer Electrolyte Fuel Cells With Conventional Flow Fields,” J. Electrochem. Soc., 153(9), pp. A1748–A1754.
Colosqui, C. E. , Cheah, M. J. , Kevrekidis, I. G. , and Benziger, J. B. , 2011, “ Droplet and Slug Formation in Polymer Electrolyte Membrane Fuel Cell Flow Channels: The Role of Interfacial Forces,” J. Power Sources, 196(23), pp. 10057–10068.
Hellstern, T. , Gauthier, E. , Cheah, M. J. , and Benziger, J. B. , 2013, “ The Role of the Gas Diffusion Layer on Slug Formation in Gas Flow Channels of Fuel Cells,” Int. J. Hydrogen Energy, 38(35), pp. 15414–15427.
Turhan, A. , Kim, S. , Hatzell, M. , and Mench, M. M. , 2010, “ Impact of Channel Wall Hydrophobicity on Through-Plane Water Distribution and Flooding Behavior in a Polymer Electrolyte Fuel Cell,” Electrochim. Acta, 55(8), pp. 2734–2745.
Cheah, M. J. , Kevrekidis, I. G. , and Benziger, J. B. , 2013, “ Water Slug Formation and Motion in Gas Flow Channels: The Effects of Geometry, Surface Wettability, and Gravity,” Langmuir, 29(31), pp. 9918–9934. [PubMed]
Cheah, M. J. , Kevrekidis, I. G. , and Benziger, J. B. , 2013, “ Water Slug to Drop and Film Transitions in Gas-Flow Channels,” Langmuir, 29(48), pp. 15122–15136. [PubMed]
Akhtar, N. , Qureshi, A. , Scholta, J. , Hartnig, C. , Messerschmidt, M. , and Lehnert, W. , 2009, “ Investigation of Water Droplet Kinetics and Optimization of Channel Geometry for PEM Fuel Cell Cathodes,” Int. J. Hydrogen Energy, 34(7), pp. 3104–3111.
Middelman, E. , Kout, W. , Vogelaar, B. , Lenssen, J. , and de Waal, E. , 2003, “ Bipolar Plates for PEM Fuel Cells,” J. Power Sources, 118(1–2), pp. 44–46.
Cunningham, B. , and Baird, D. G. , 2006, “ The Development of Economical Bipolar Plates for Fuel Cells,” J. Mater. Chem., 16(45), pp. 4385–4388.
Bar-On, I. , Kirchain, R. , and Roth, R. , 2002, “ Technical Cost Analysis for PEM Fuel Cells,” J. Power Sources, 109(1), pp. 71–75.
McCrabb, H. , Lozano-Morales, A. , Snyder, S. , Gebhart, L. , and Taylor, E. , 2009, “ Through Mask Electrochemical Machining,” ECS Trans., 19(26), pp. 19–33.
McCrabb, H. , Taylor, E. , Lozano-Morales, A. , Shimpalee, S. , Inman, M. , and Van Zee, J. W. , 2010, “ Through-Mask Electroetching for Fabrication of Metal Bipolar Plate Gas Flow Field Channels,” ECS Trans., 33(1), pp. 991–1006.
Shimpalee, S. , Lilavivat, V. , Van Zee, J. W. , McCrabb, H. , and Lozano-Morales, A. , 2011, “ Understanding the Effect of Channel Tolerances on Performance of PEMFCs,” Int. J. Hydrogen Energy, 36(19), pp. 12512–12523.
Extrand, C. W. , 1998, “ A Thermodynamic Model for Contact Angle Hysteresis,” J. Colloid Interface Sci., 207(1), pp. 11–19. [PubMed]
Young, T. , 1805, “ An Essay on the Cohesion of Fluids,” Philos. Trans. R. Soc. London, 95, pp. 65–87.
Wenzel, R. N. , 1936, “ Resistance of Solid Surfaces to Wetting by Water,” Ind. Eng. Chem., 28(8), pp. 988–994.
Cassie, A. B. D. , and Baxter, S. , 1944, “ Wettability of Porous Surfaces,” Trans. Faraday Soc., 40, pp. 546–551.
Hejazi, V. , and Nosonovsky, M. , 2013, “ Contact Angle Hysteresis in Multiphase Systems,” Colloid Polym. Sci., 291(2), pp. 329–338.
Sakai, M. , Kono, H. , Nakajima, A. , Zhang, X. , Sakai, H. , Abe, M. , and Fujishima, A. , 2009, “ Sliding of Water Droplets on the Superhydrophobic Surface With ZnO Nanorods,” Langmuir, 25(24), pp. 14182–14186. [PubMed]
Gao, L. , and McCarthy, T. J. , 2007, “ How Wenzel and Cassie Were Wrong,” Langmuir, 23(7), pp. 3762–3765. [PubMed]
Patankar, N. A. , 2003, “ On the Modeling of Hydrophobic Contact Angles on Rough Surfaces,” Langmuir, 19(4), pp. 1249–1253.
Chen, X. F. , Wang, X. P. , and Xu, X. M. , 2013, “ Effective Contact Angle for Rough Boundary,” Physica D, 242(1), pp. 54–64.
Li, X. M. , Reinhoudt, D. , and Crego-Calama, M. , 2007, “ What Do We Need for a Superhydrophobic Surface? A Review on the Recent Progress in the Preparation of Superhydrophobic Surfaces,” Chem. Soc. Rev., 36(8), pp. 1350–1368. [PubMed]
Bikerman, J. J. , 1950, “ Sliding of Drops From Surfaces of Different Roughnesses,” J. Colloid Sci., 5(4), pp. 349–359.
Theodorakakos, A. , Ous, T. , Gavaises, A. , Nouri, J. M. , Nikolopoulos, N. , and Yanagihara, H. , 2006, “ Dynamics of Water Droplets Detached From Porous Surfaces of Relevance to PEM Fuel Cells,” J. Colloid Interface Sci., 300(2), pp. 673–687. [PubMed]
Venkatraman, M. , Shimpalee, S. , Van Zee, J. W. , Moon, S. I. , and Extrand, C. W. , 2009, “ Estimates of Pressure Gradients in PEMFC Gas Channels Due to Blockage by Static Liquid Drops,” Int. J. Hydrogen Energy, 34(13), pp. 5522–5528.
Bird, R. , Stewart, W. , and Lightfoot, E. , 1966, Transport Phenomena, 7th ed., Wiley, New York.
Kumbur, E. C. , Sharp, K. V. , and Mench, M. M. , 2006, “ Liquid Droplet Behavior and Instability in a Polymer Electrolyte Fuel Cell Flow Channel,” J. Power Sources, 161(1), pp. 333–345.
Chen, K. S. , Hickner, M. A. , and Noble, D. R. , 2005, “ Simplified Models for Predicting the Onset of Liquid Water Droplet Instability at the Gas Diffusion Layer/Gas Flow Channel Interface,” Int. J. Energy Res., 29(12), pp. 1113–1132.
Miwa, M. , Nakajima, A. , Fujishima, A. , Hashimoto, K. , and Watanabe, T. , 2000, “ Effects of the Surface Roughness on Sliding Angles of Water Droplets on Superhydrophobic Surfaces,” Langmuir, 16(13), pp. 5754–5760.
Mortazavi, V. , D'Souza, R. M. , and Nosonovsky, M. , 2013, “ Study of Contact Angle Hysteresis Using the Cellular Potts Model,” Phys. Chem. Chem. Phys., 15(8) pp. 2749–2756. [PubMed]
Wolfram, E. , and Faust, R. , 1978, Wetting, Spreading, and Adhesion, Academic Press, New York.

## Figures

Fig. 1

Schematic of contact angle of droplet wetted to surface

Fig. 2

Photograph of the flow channel used in this study (channel width = 4 mm, channel depth = 2 mm, and channel length = 120 mm)

Fig. 3

AFM images of cross sections and 3D of the sample's surfaces

Fig. 4

Schematic of the drop in the flow channel used in this study

Fig. 5

(a) Image of the droplet in the presence of air flow and (b) schematic view of control volume chosen for analysis

Fig. 6

Static contact angle and height of 10 μl water droplet on stainless steel plate

Fig. 7

Schematic illustration of the surface model with a series of uniform needles

Fig. 8

Dynamic images of the water droplet on electrochemically etched stainless steel plate (Ra = 0.73 μm) at different Re

Fig. 9

Water droplet profile at different Reynolds numbers: (a) Ra = 0.02 μm, (b) Ra = 0.27 μm, (c) Ra = 0.30 μm, (d) Ra = 0.41 μm, and (e) Ra = 0.73 μm. _____: RE = 0; ........: RE = 185, _ _ _ _ _ : RE = 370; _ . _.: RE = 555; __ __: RE= 740; __ . __: RE = 925.

Fig. 10

The plot of pressure drop at critical point versus surface roughness (Ra)

Fig. 11

Total drag force versus Reynolds number for different roughness surface

Fig. 12

Relationship between the roughness factor times solid area fraction rf and the total drag force

## Tables

Table 1 Effect of surface roughness on wetting properties of stainless steel in the presence of water droplet

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections