Colloids and Surfaces A: Physicochem. Eng. Aspects 384 (2011) 653–660
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Colloids and Surfaces A: Physicochemical and
Engineering Aspects
journal homepage: www.elsevier.com/locate/colsurfa
Liquid filling in a corner with a fibrous wall—An application to two-phase flow in
PEM fuel cell gas channels
Cody D. Rath, Satish G. Kandlikar ∗
Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY, USA
a r t i c l e
i n f o
Article history:
Received 3 January 2011
Received in revised form 13 May 2011
Accepted 19 May 2011
Available online 27 May 2011
Keywords:
PEMFC
Concus–Finn condition
Contact angle hysteresis
Contact line
a b s t r a c t
The Concus–Finn condition has been established as a useful criterion to determine the rise height of a
body of liquid bounded by a container in which two sides create a vertex. In the work presented here,
the same principles are applied in the microscopic region of the contact line at the vertex created by the
intersection of the gas channel (GC) wall and the fibrous gas diffusion layer (GDL) in a polymer electrolyte
membrane (PEM) fuel cell. Recent efforts on water management issues in fuel cells have provided valuable
insight into the water emergence and two-phase flow in gas channels. One of the main areas of focus
is the accumulation of water in the reactant gas channels. Several works have focused on transport
through the GDL or the growth of a droplet in an open area without taking into account the channel wall
interactions. This issue is addressed in this work at a fundamental level by investigating droplet formation
and accumulation in a corner. This work utilizes an experimental approach that visualizes the dynamics
of water at the intersection of two interfaces of varying surface energies and surface topographies. It has
been determined that the local microscopic contact angle is a critical parameter when determining the
behavior of a growing droplet as it interacts with the channel wall and the values were found to exceed
the measured contact angles for the surfaces due to the severely strained interface of the droplet over
the fibrous matrix. Also, the Concus–Finn condition can be successfully used to determine the conditions
of the droplet in the corner, based on the local microscopic contact angle, which can then be used to
determine optimal angle to promote water management. For typical fuel cell materials, this angle has
been determined to be less than about 52◦ to avoid filling of the corner with water.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
1.1. PEMFC
Over the past two decades, there have been several techniques
employed to investigate water management issues associated with
PEMFCs. Recently, focus has been on the influence of the gas diffusion layer (GDL) and the gas channel (GC) using transparent
materials [1–6]. Tuber et al. [6] was the first group to use a transparent fuel cell to study the effects of the GDL materials on water
management. They found that GDLs with a hydrophobic PTFE coating tend to distribute water more randomly within the channels
because of the fact that the hydrophobic polymer acts like a barrier to liquid water within the GDL pores. Ous and Arcoumanis [2]
also visualized water accumulation characteristics using a transparent fuel cell to study the effects of air flow, external loading, and
droplet location within the channel. It was found that droplet size
is inversely proportional to the air velocity and that increasing the
∗ Corresponding author. Tel.: +1 585 475 6728.
E-mail address: [email protected] (S.G. Kandlikar).
0927-7757/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.colsurfa.2011.05.039
external load delayed the amount of time it took for the first droplet
to grow. Also, for droplets in contact with the side wall, growth was
a gradual process, in comparison to the rapid growth that occurs in
the center of the channel. Simulations were also completed which
indicate capillary force to be the dominant driving force behind
droplet growth. This agrees with the more fundamental work of
Wang et al. [7] in which a model was developed to predict single
and two phase flow within a channel. This model determined that
water accumulation is controlled by capillary action and molecular
diffusion.
More recently there have been extensive studies involving visually accessible fuel cells. Transparent components were used to
visually study the effects of GDL, channel geometry and maldistribution in a 50 cm2 fuel cell [3,4,8]. Neutron radiography was also
used to identify water accumulation within an operating fuel cell
for various channel geometries and material sets [5,9]. It was found
that flow patterns, i.e. slug, film and mist flow, emerged based on
the operating conditions of the fuel cells and that more water accumulates in the channels at lower air flow rates causing a decrease
in operational efficiency.
Several groups have highlighted the importance of geometry
while designing efficient gas channels. Akhtar et al. [10] measured
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C.D. Rath, S.G. Kandlikar / Colloids and Surfaces A: Physicochem. Eng. Aspects 384 (2011) 653–660
the pressure drop within five different gas channels with varying
aspect ratios. It was determined that the aspect ratio played an
important role on the water transport characteristics. Metz et al.
[1] investigated the effect of the channel geometry on the water
removal characteristics of the reactant gas channels. A novel trapezoidal channel design was used to remove water based on capillary
action and the principles of the Concus–Finn condition. The work by
Metz et al. primarily used the simulation of droplet growth near a
channel wall with varying contact angles and open angles to determine the force drawing a droplet away from the GDL surface. The
results show that the surface properties and channel geometries
have a profound effect on the water accumulation. This is in agreement with Zhang et al. [11] who found that hydrophilic channels
are preferable for water removal. Zhu et al. [12] analyzed the effect
of channel geometry on pressure drop, water saturation, and coverage ratio using numerical simulations. The various geometries
used were rectangular, curved bottom rectangular, trapezoidal,
up-side down trapezoidal, and semicircular. Rectangular channels
were found to have smaller/quicker droplets whereas the upside
down trapezoidal had the worst saturation and coverage ratio.
Hao and Chen [13] developed a simple analytical model to predict the droplet moving velocity in a channel. A force balance was
used to find velocity, however, several assumptions were made
which include neglecting the existence of a side wall. De Luca et al.
[14] investigated droplet detachment when exposed to a shear
stress and compared two methods for modeling droplet growth:
the torque balance equation (TBE) and the force balance equation
(FBE). The FBE was shown to be a more accurate method for high
shear stress and small pore diameter, however, this work also did
not incorporate any side wall effects. The local behavior of a growing droplet in a GDL and its interaction with the channel walls has
received little attention in the literature. This paper addresses this
gap by applying the theory established by Concus and Finn regarding rise height of a liquid in a container as a function of surface
properties [15]. A brief overview of this work is first presented
below for completeness.
1.2. Concus–Finn condition
The Concus–Finn condition was first published by Concus and
Finn in 1969 [15]. The rise height of a fluid in an open wedge shaped
container was derived based on the theory developed by Young
[16]. Young’s equation is used to predict the rise height, u, of a
liquid in a small capillary tube of radius, r, and is given as:
uO ≈
2 cos gr
(1)
where is the surface tension, is the contact angle, is the density,
and g is the gravitational constant. Concus and Finn then applied
this to a container of liquid to determine the amount of rise height
at the vertex of the wedge, with both surfaces having the same
contact angle, at an open angle of 2˛ [15]. The equations derived
are as follows:
∇
∇u
1 + uzx + uzy
cos =
= ku + 2H
∇u
1 + uzx + uzy
·n
(2)
(3)
where H is a constant governing the mean curvature and k = g/.
The Concus–Finn condition states that the surface is unbounded
for:
˛+<
2
(4)
Fig. 1. (a) Image of Concus–Finn wedge container modeled and (b) plot of
Concus–Finn condition for wedge container reproduced from [17] where the condition for existence for the given setup falls within the shaded region, R, which is
inclined across the square × area representing the values of the contact angle
and
for each surface, 2 and 1 , respectively. For the points lying in the region of D+
1
, no solution can exist. For the points lying in the region of D+
and D−
, a solution
D−
1
2
2
may exist but cannot have continuous normal unit vectors up to the vertex.
In other words, the surface height is unpredictable for this condition
given by Eq. (4). For the case where ˛ + ≥ /2, the surface rise
height is predictable.
Several years later, Concus and Finn applied their earlier derivations to a wedge domain in which the surface energy, i.e. the contact
angle, of the two angled surfaces have different values [17]. New
boundary conditions were developed that incorporate the difference in contact angle between the two surfaces. These conditions
were represented graphically as seen in Fig. 1. In this figure, Concus
and Finn describe the condition for existence for the given setup
shown in Fig. 1(a) to fall within the shaded region, R, which is
inclined across the square × area as shown in Fig. 1(b). The
x and y axes represent the values of the contact angle for each surface, 2 and 1 , respectively. For the points lying in the region of D+
1
and D−
, no solution can exist. For the points lying in the region of
1
D+
and D−
, a solution may exist but cannot have continuous normal
2
2
unit vectors up to the vertex [17].
Few works have investigated the effects of a corner interface
on a growing droplet. Chang et al. [18] investigated a droplet resting on an exterior corner. It was found that as the droplet contacts
the edge of the corner, the contact line gets pinned and the contact angle exceeds the equilibrium contact angle. The critical angle
reached before the contact line moves over the edge of the corner is
dependent on the properties of the surface the droplet is on, not the
new surface the contact line invades. The scale used for this work
was relatively large. Hwang et al. [19] conducted simulations of a
droplet near an interior corner at a given angle. This study purely
focuses on molecular dynamics and does not take into consideration the physical properties of the surfaces; however, it was found
that as the angle decreased between the base and side wall, the
effect of the wall increased. This trend was found to be similar for
different droplets of varying sizes.
The work presented here will investigate the behavior of a
droplet as it grows out of the GDL and interacts with the side wall by
applying the Concus–Finn condition. This work will represent the
conditions that occur in the gas channel of PEMFC and will help in
developing a fundamental understanding of the process that leads
to channel blockage (slug) and/or film flow within an operating fuel
cell. The Concus–Finn condition will be used to predict the resulting water build up given certain conditions regarding the surface
properties of the base and side wall materials as well as the angle
created at the interface of the two surfaces.
2. Experimental
As mentioned earlier, there is little work in literature that
addresses the local behavior of the droplet interfaces as it interacts
C.D. Rath, S.G. Kandlikar / Colloids and Surfaces A: Physicochem. Eng. Aspects 384 (2011) 653–660
655
2.1. Experimental setup
Fig. 2. Image of droplet–channel wall interaction for corner illustrating filling and
non-filling of the corner.
with the GDL and the channel side wall. The objective of the experimental setup is to visualize these interfaces during the dynamic
transition from a growing droplet on the GDL alone to contact
between the GDL and wall. Fig. 2 highlights two possible scenarios that are expected to occur during this growth process. As the
droplet grows and contacts the side wall, it can potentially become
either (a) pinned at the interface, “non-filling”, or (b) the liquid
can be drawn into the corner intersection, “filling”. This behavior
is determined by the contact angles of each surface and the open
angle of the intersection.
A test section was designed to investigate the droplet–channel
wall interactions as shown by the schematic in Fig. 3. The main test
section is comprised of a polycarbonate, namely LexanTM , base that
holds the GDL sample. A side wall is mounted on top of the GDL to
create the corner and can be clamped at various angles. A droplet
is pushed through a preferential pore in the base material using a
Model 11 Plus syringe pump from Harvard Apparatus, and as the
droplet grows out of the GDL, it comes in contact with the side wall
similar to the way it would in a PEMFC gas channel. This process
is captured using a Keyence VW-6000 high speed digital camera
capable of up to 24,000 fps. For the purposes of this investigation
the high speed videos were captured at frame rates ranging from
250 to 1000 fps to achieve the best clarity and resolution. Keyence
Motion Analyzer software was used to analyze the videos in order
to characterize the dynamics of the droplet. The contact angle and
contact line velocity were extracted from the videos using this software. Fig. 3 also illustrates a simplified view of the interfaces that
form between the droplet and the base/side walls. The four interfaces are the upper and lower contact lines on the side wall, UCL
and LCL, respectively, and the inner and outer contact lines on the
base, ICL and OCL, respectively.
2.2. Contact angle measurement
It is important to establish the contact angle hysteresis for all
surfaces being tested before the corner effects were investigated.
Fig. 3. (a) Schematic of test setup used to characterize emerging droplet consisting of a PC. High speed camera with 50× optics, syringe pump and main test section (base
with water inlet, GDL, and side wall) mounted on a vibration isolation table. (b) Graphic representation of droplet interfaces including the outer and inner contact lines on
the base and the upper and lower contact lines on the side wall.
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C.D. Rath, S.G. Kandlikar / Colloids and Surfaces A: Physicochem. Eng. Aspects 384 (2011) 653–660
Table 1
Static advancing and receding contact angle measurements.
Fig. 4. Image of contact angle measurements for static advancing and receding
contact angles on a SGL-25BC GDL sample.
Therefore the static advancing, adv , and static receding, rec , contact angles were measured for the side wall surfaces as well as the
GDL, namely SGL-25BC, which is a bi-layer carbon paper produced
by Sigracet® , and is 235 ␮m thick with a PTFE coating of 5 wt.%
as reported by the manufacturer. The measurements were taken
using a VCA Optima Surface Analysis System from ADT Products,
Inc. An example of an image can be seen in Fig. 4, which shows the
static advancing and receding contact angles for a droplet on an
SGL-25BC GDL sample. To determine the advancing and receding
contact angles, a droplet is deposited on substrate from a syringe
while video captures growth. The frame at which the static maximum angle is observed is captured for measurement. The droplet
is then removed by withdrawing the syringe and the minimum
static angle is captured to determine the receding angle. These values are used to determine the hysteresis, = adv − rec . The lines
represent the measured contact angle being formed by the droplet.
In addition to the GDL sample, smooth vapor polished LexanTM ,
which was produced by chemical vapor etching to remove small
scratches for improving optical clarity of machined surfaces, was
also tested. After polishing is complete, the vapor evaporates off of
the part, leaving it free from chemical contamination. The contact
Surface
Material
Base
Side wall
Side wall
Side wall
Side wall
SGL-25BC
Untreated LexanTM
Hydrophobic LexanTM
Graphite
Gold plated copper
adv (◦ )
147
85
116
89
88
rec (◦ )
138
61
83
34
32
(◦ )
9
24
33
55
56
angles were also measured for the vapor polished LexanTM with a
hydrophobic coating from 3M. The coating is applied to the surface,
and then it dries to a thin transparent film which promotes antiwetting (hydrophobic) properties. LexanTM was chosen due to the
fact that it is easier to work with for this type of experiment. The
measured values for the contact angles of these surfaces are listed in
Table 1. The values of advancing contact angle for graphite and gold
plating (which are typical production fuel cell materials) are also
listed in this table for reference showing that these values are very
similar to that of untreated LexanTM . These values are an average
of 5 measurements which are within 2% of the average value for a
given material.
3. Results and discussion
3.1. Droplet dynamics
Using the Motion Analysis software from Keyence, several key
values can be measured from the high speed videos that characterize the dynamics of the droplet–channel interactions. The position
and movement of the contact line as well as the contact angle can
be measured on a frame by frame basis. An example of this can be
seen in Fig. 5 which shows images taken from a droplet growing on
the GDL perpendicular to untreated Lexan at 1000 fps and 50×. In
these images, the wall is highlighted by the dark line in the center,
with the original droplet on the left, and a reflection in the wall
surface appearing on the right. When contact is first made at time
t = 1 ms, the droplet begins to be drawn into the corner. At t = 2 ms,
Fig. 5. Sequence of images showing a droplet in contact with a GDL base perpendicular to an untreated Lexan side wall where 2˛ = 90◦ , ICL = 147◦ and LCL,Unt = 85◦ .
C.D. Rath, S.G. Kandlikar / Colloids and Surfaces A: Physicochem. Eng. Aspects 384 (2011) 653–660
657
values are initially relatively high as the droplet transitions from
equilibrium on the GDL surface alone, to interacting with the two
surfaces. Both velocities then decrease as the equilibrium height is
reached. After a given amount of time the lower contact line reaches
the corner where VLCL = 0. Considering the size of the droplets, the
contacts lines are moving quite quickly which allows the corner to
be filled within 3 or 4 ms. This behavior can be explained by applying the Concus–Finn condition to the corner geometry as discussed
in the following section.
3.2. Concus–Finn condition
Fig. 6. Plot of lower contact line height on an untreated side wall for different
droplets where: 2˛ = 90◦ , ICL = 147◦ and LCL,Unt = 85◦ .
the upper contact line between the droplet and the wall then begins
to climb up the wall. This overall change in droplet shape is caused
by the disruption of the static equilibrium state prior to contact.
The droplet experiences a transient phase as the surface tension
balances the forces imposed on the droplet by the side wall surface energy. It can be seen that within the first 5 ms of contact the
droplet has filled the corner and the final shape has been achieved.
The same behavior occurred for the hydrophobic Lexan at an
open angle of 2˛ = 90◦ with the droplet spreading on contact at
t = 1 ms and by t = 5 ms the corner has been completely filled. The
height of the lower contact line, HLCL , was measured from the still
images. For each data point, the variability envelope is ±15% for
height, which is shown by error bars in Fig. 6, and 0.1% for the
time measurement. The values for untreated and treated hydrophobic Lexan perpendicular to the GDL are shown in Fig. 7. It can be
seen that the height of the contact line decreases exponentially as
the lower contact line spreads to the corner. This trend is shown
to be the same for both surfaces and after a certain amount of
time the contact line reaches the corner where HLCL = 0. The velocity of the lower contact line, VLCL , at the perpendicular angle was
also measured from the video and is shown for the untreated and
hydrophobic Lexan in Fig. 7. The velocities are calculated by evaluating the change in position from the previous time step to the
current time step relative to the change in time (1 ms). Due to the
fact that the interface was always moving in the same direction, the
values are plotted as absolute values. Fig. 7 shows that the velocity
As mentioned in Section 1.2, the Concus–Finn condition was
intended to predict the rise height of a liquid partially filling a
wedge shaped container, however, it can also be used to describe
the liquid behavior at the intersection of two surfaces with an open
angle of 2˛. More specifically, when applied to the corner setup
being tested here, the Concus–Finn condition can predict whether
or not water will be drawn into the corner or if it will remain pinned
at or close to the point of contact. Fig. 8 illustrates an example
of the plot developed by Concus–Finn, shown in Section 1.2. The
entire rectangle shown in this plot represents the area where the
Concus–Finn condition is satisfied; however, the only line of interest for this application is top solid line which represents the limiting
Fig. 8. Plot of theoretical Concus–Finn condition for untreated and hydrophobic
Lexan at 2˛ = 60◦ and 45◦ , respectively, where ICL = 147◦ and LCL,Unt = 85◦ and
LCL,Hy = 116◦ .
Fig. 7. Plot of lower contact line (a) height and (b) velocity on the side wall at 2˛ = 90◦ where ICL = 147◦ , LCL,Unt = 85◦ and LCL,Hy = 116.
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C.D. Rath, S.G. Kandlikar / Colloids and Surfaces A: Physicochem. Eng. Aspects 384 (2011) 653–660
side wall contact angle and decreases linearly with increasing base
contact angle for a constant open angle, 2˛. The equation for this
line is given as:
W,Limit = (2˛ + ) − B
(5)
where W,Limit is the limiting wall contact angle and B is base contact angle. The symbols plotted on the graph represent the location
of the two interior contact angle values of ICL and LCL with the
coordinates of each point given as (x,y) equal to ( ICL , LCL ) at values
±2%. The location of each point on the plot can be used to graphically predict whether or not the corner will fill. A point located
within the rectangle below the limiting line indicates the corner
will be filled when the droplet contacts the side wall. If the point
falls in the D−
region, the corner will not fill. For the geometry and
1
orientation being tested, sections D+
, D+
, and D−
are absorbed into
1
2
2
the R region to form two main regions, filling and non-filling. Using
the measured values listed above in Table 1, it can be seen in Fig. 7
that both the untreated and hydrophobic Lexan fall below the line
for a perpendicular wall. This indicates that the corner should be
filled when a droplet is in contact with the GDL base and the side
wall as shown in the images in Fig. 5 as well as the plots in Fig. 7.
Due to the manufacturing processes employed in making
the gas channels, as well as GDL intrusion into the GDL, the
interface between the side wall and GDL might not make a perfect
90◦ angle. Also, in some cases, trapezoidal or triangular channels
may be employed with different corner angles. Therefore, the effect
of varying side wall angles on the contact line height and velocity
is also investigated and the Concus–Finn condition is used to predict the behavior of the droplet. Referring to Fig. 8 it can be seen
that the point for the untreated wall on GDL falls below the 60◦ line
(—) indicating that the corner should fill. For the 45◦ angle (- - -),
the point falls above the line indicating non-filling of the corner.
By rearranging Eq. (5), it is also possible to determine the critical
open angle for two given sidewall surfaces. For untreated Lexan,
the critical open angle is 52◦ .
The image sequences corresponding to these two angles can be
seen in Fig. 9. The 60◦ angle behaves similar to the perpendicular
wall. The droplet spreads as soon as it makes contact with the side
wall and after the first 5 ms the entire corner has filled. For the 45◦
angle, the droplet gets pinned as soon as it contacts the side wall at
t = 1 ms. The contact line moves slightly as the droplet continues to
grow, however, it reaches an equilibrium height and it can be clearly
seen that the corner is not being filled by the droplet after the same
amount of time. This initial movement is caused by the transient
behavior of the droplet as it moves towards an equilibrium state,
however, once the contact angles are established the Concus–Finn
condition becomes the dominating factor.
To characterize the effect of the open angle, 2˛, Fig. 10 shows
the lower contact line height and velocity on an untreated Lexan
side wall at three different open angles of 2˛ = 90◦ , 60◦ , and 45◦ ,
respectively. At 2˛ = 90◦ and 60◦ the LCL reaches the corner so that
HLCL = 0. However, for the 2˛ = 45◦ angle, HLCL does not go to zero
within the same time frame. Instead, it gets pinned at a given height
above the corner. It can also be seen that the velocity oscillates for
Fig. 9. Sequence of images of a droplet contacting hydrophilic Lexan at 2˛ = 60◦ (a) and 45◦ (b).
Fig. 10. Plot lower contact line (a) height and (b) velocity for untreated Lexan at different open angles where ICL = 147◦ and LCL,Unt = 85◦ .
C.D. Rath, S.G. Kandlikar / Colloids and Surfaces A: Physicochem. Eng. Aspects 384 (2011) 653–660
Fig. 11. Plot of measured Concus–Finn condition for hydrophobic Lexan at 2˛ = 90◦
and 85◦ , respectively, where ICL = 147◦ and LCL,Hy = 116◦ .
the 2˛ = 60◦ and 45◦ angles. These oscillations illustrate the fact
that there is a stick-shift movement of the contact line as it moves
towards the corner. This is an important process that highlights
the significance of the contact angle and open angle affecting the
droplet dynamics.
3.3. Local microscopic contact angle
Through the video analysis of the hydrophobic sidewall it was
found that as the droplet is trying to reach equilibrium, the contact
angles being formed on the contact lines are constantly changing
and the end result did not agree with the predicted Concus–Finn.
Using the measured values for the hydrophobic Lexan and GDL
found in Table 1, it can be determined that the critical open angle
for the hydrophobic wall is 83◦ . However, it was observed that the
corner was only filled for an open angle of 2˛ = 90◦ . This indicates
that the contact angles measured using the stand alone measurement system may not represent the local interface condition of the
droplet with the severely strained interface in the corner. Instead
of just employing the measured values of static surface contact
angles, the instantaneous local contact angles were measured from
the videos for each time step. Fig. 11 shows the Concus–Finn plot
for the first 10 ms of an open angle of 2˛ = 90◦ and 85◦ . Each point
represents (x,y) equal to ( ICL , LCL ), the light dotted lines represent
the measured hysteresis for the hydrophobic wall as well as the
GDL base, the solid symbols indicate filling, and the open symbols
indicate non-filling. It can be seen that the majority of the points fall
above the rectangle indicating that it does not fill for the 85◦ angle
659
Fig. 12. Plot of measured Concus–Finn condition for hydrophobic Lexan at 2˛ = 60◦
and 45◦ , respectively, where ICL = 147◦ and LCL,Unt = 85◦ .
whereas the measured value for the static contact angle indicates
that it should fill.
This phenomenon emphasizes the importance of the local
instantaneous contact angle because of the fact that the severely
strained interface of the droplet interior at the corner causes the
contact angle to exceed the accepted measured value which may
alter the expected outcome. The fibrous nature of the GDL surface
also yields a different local microscopic contact angle as seen from
the videos. The Concus–Finn condition does not agree when considering the static measured values; however, it is satisfied when
using the instantaneous local microscopic values. Fig. 12 shows the
local contact angles for the untreated Lexan for an open angle of
2␣ = 60◦ and 45◦ , respectively, as shown previously. It can be seen
that although the droplet behaves as predicted, there is a relatively
large spread for the contact angle values. It can also be seen that
the values exceed the accepted measured values, represented by
the light dotted lines, by up to 35%.
An easier way to visualize this spread is to examine the contact
angles as a function of time. Fig. 13 shows the change in upper and
lower contact angles as a function of time during the first 10 ms for
untreated Lexan at 2˛ = 60◦ . It can be seen that during the transition
period, both the upper and lower contact lines have contact angles
above the measured hysteresis value. After the corner is filled at
t = 5 ms, the upper and lower contact angles fall within the hysteresis. During this process, the lower contact angle reaches a maximum
value of 31% higher than the hysteresis measurement. Fig. 13 also
shows the plot of wall contact angles for an open angle of 2˛ = 45◦ .
Fig. 13. Plot of contact angle for untreated Lexan at 2˛ equal to (a) 60◦ and (b) 45◦ where ICL = 147◦ and LCL,Unt = 85◦ .
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It can be seen that the lower contact angle remains higher than the
advancing angle, as much as 35%, even after it gets pinned in the
corner at t = 6 ms. The upper contact line approaches an equilibrium
height at this same time step, however, the angle falls within the
measured hysteresis. The oscillations in the contact angle can be
seen as well, illustrating the stick-shift mechanism.
4. Conclusion
The work presented here has brought attention to some of the
fundamental issues that are still affecting water management in
PEMFCs. The behavior of a droplet as it comes in contact with two
surfaces with varying surface energies is a key issue that has several applications including but not limited to hydrogen fuel cells. It
has been shown that the contact angle hysteresis is an important
parameter that must be incorporated in order to accurately study
and understand the transient behavior of water–channel interactions. High speed videos have shown that the transition from a
resting droplet on a flat surface to a droplet pinned in a corner
is a complex process. Once initial contact was made between the
droplet and the wall, the droplet was drawn into a corner and a
transition took place that resulted in either filling or non-filling
of the corner. The height of the contact line, HLCL , interior to the
corner was found to decrease exponentially until an equilibrium
height was reached.
The actual transition from the droplet being stationary on the
base only to equilibrium in the corner was shown to be an oscillatory process inducing a contact angle hysteresis on both the GDL
surface as well as the wall. The high speed video also revealed that
the contact angles created in the corner were very different from
those measured in the stand alone contact angle measuring system.
This difference suggests that the local microscopic contact angle
is a crucial parameter when considering droplet and channel wall
interactions.
Another major outcome of this work was to establish the use of
the Concus–Finn condition to determine whether or not a droplet
will fill the corner when in contact with two surfaces with varying
contact angles at a given open angle. The condition for existence can
be represented graphically on a by axis system as a function of
the wall and base contact angles. The theoretical existence shown
on this plot is validated by the high speed video. The Concus–Finn
condition can also be used to determine critical values for open
angle and/or surface energy which can be beneficial to PEMFC
design for improved water management. The results obtained here
indicate that, for the GDL and the hydrophilic surfaces similar to
those commonly employed in fuel cell applications, the corner filling will not occur when the corner angle is around 52◦ or smaller.
Future research recommended in this area includes the development of a model describing what forces are dominant in the
transient behavior of the droplet–channel interaction. More experimentation is also suggested to validate this model and study
different surfaces in addition to the LexanTM used for this study.
The effect of surface roughness of the side wall also needs to be
taken into account as well. The use of advanced imaging techniques
is recommended to visualize the local microscopic contact angles
and contact lines in relation to the fibrous topology of the surface.
Acknowledgements
This work was completed in the Thermal Analysis, Microfluidics,
and Fuel Cell Laboratory in the Department of Mechanical Engineering at the Rochester Institute of Technology and was supported
by the US Department of Energy under contract No. DE-FG3607G017018.
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