Microfluid Nanofluid
DOI 10.1007/s10404-014-1375-1
RESEARCH PAPER
Contact line characteristics of liquid–gas interfaces
over grooved surfaces
Preethi Gopalan • Satish G. Kandlikar
Received: 11 April 2013 / Accepted: 13 October 2013
Ó Springer-Verlag Berlin Heidelberg 2014
Abstract Surface wetting is an important phenomenon in
many industrial processes including micro- and nanofluidics. The wetting characteristics depend on the surface
tension forces at the three-phase contact line and can be
altered by introducing patterned groove structures. This
study investigates the effect of the grooves on the transition
in the wetting behavior between the Cassie to Wenzel
regimes. The experiments demonstrate that the wettability
on a patterned surface depends on the spacing factor
(S = channel depth/channel width). The spacing factor
influences the contact angle, contact angle hysteresis, and
the transition characteristics between the Cassie and
Wenzel states. It was noted that under certain conditions
(S [ 1) the droplet behaved as a Cassie droplet, while
exhibiting Wenzel wetting the rest of the time on the silicon microchannels tested. This criterion was used to design
the groove structures on the sidewall of the proton
exchange membrane fuel cell gas channel to remove the
water effectively. The water coming from the land region
into the gas channel is pulled by the grooves to the top wall
where the airflow aided in its removal. Also, the contact
angles measured on the surfaces were compared with the
classical models that use wetted area, and the contact line
model that uses the three-phase contact line length. It was
found in our experiments that the contact line model predicts the contact angle on the patterned groove surfaces
more accurately than the classical models.
Keywords Scaling factor Droplet Patterned groove
surfaces Roughness Surface tension Wettability
1 Introduction
P. Gopalan S. G. Kandlikar (&)
Microsystem Engineering, Rochester Institute of Technology,
Rochester, NY 14623, USA
e-mail: [email protected]
Wetting and non-wetting of a surface have been widely
studied in the literature. Surface wetting in general is an
important phenomenon that occurs in many industrial
processes such as lithography, chemical coating, painting,
drying, heat transfer, and surface engineering (Peters et al.
2000; Podgorski et al. 2000; Kandlikar 2001). It is also
found to be of importance in micro- and nanofluidics
applications such as lab-on-a-chip, MEMS, and miniaturized sensors (Teh and Lu 2008; Tafti et al. 2011; Duparré
et al. 2002). The two important limits of wettability are:
(a) complete wetting or superhydrophilic behavior—a
droplet spreads completely on the surface and forms a thin
layer; and (b) completely non-wetting or superhydrophobic
behavior—the droplet remains spherical without spreading
on the surface. To understand the conditions leading to
these two states, the wettability of a flat surface is determined by measuring the equilibrium contact angle. In
1805, Young developed a model (Eq. (1)) which is commonly used to characterize the wettability criterion of a
smooth surface (Young 1805).
P. Gopalan
e-mail: [email protected]
ðcos hc ¼ ðcSV cSL Þ=cLV Þ
S. G. Kandlikar
Mechanical Engineering, Rochester Institute of Technology,
Rochester, NY 14623, USA
where hc is the equilibrium contact angle on a smooth
surface, and cSV, cSL, and cLV are the interfacial tensions
ð1Þ
123
Microfluid Nanofluid
between the solid–vapor, solid–liquid, and liquid–vapor
states, respectively.
A surface is said to be hydrophilic if the contact angle is
less than 90°, whereas it is hydrophobic if the contact angle
is greater than 90°. Surfaces between contact angles 0°–20°
are classified as superhydrophilic, whereas surfaces with
contact angles between 150° and 180° are known as superhydrophobic. Typically, as a droplet advances on a
surface, the leading edge of the droplet makes an advancing contact angle and the trailing edge end forms a
receding contact angle. The difference between the
advancing and receding contact angles is defined as contact
angle hysteresis. Superhydrophobic surfaces are characterized by low contact angle hysteresis as a droplet can roll
off a surface very easily, and vice versa for superhydrophilic surfaces. Roughness on a surface affects the contact
angle hysteresis as well as the apparent contact angle of the
surface. To understand the wetting characteristics on a
rough or chemically heterogeneous surface, the Wenzel
model introduces an average contact angle h* on a rough
surface in terms of a roughness factor r (the ratio between
the actual surface area and the apparent surface area on a
rough surface) as given by Eq. (2) which can be used to
predict the apparent contact angle on a rough surface
(Wenzel 1936).
cos h ¼ r cos hc
ð2Þ
According to this model, a droplet placed on a rough
surface would spread until it finds the equilibrium position
given by the contact angle h*. It also predicts that the
roughness on a surface enhances its wettability if a surface
is hydrophilic, and then the roughness causes it to become
more hydrophilic (or more hydrophobic if the surface is
initially hydrophobic) (Quéré 2008; Bhushan et al. 2007).
For porous surfaces, Cassie–Baxter (CB) developed a
model in 1944 (Cassie and Baxter 1944) which includes the
material heterogeneity, fi for calculating the apparent
contact angle which is given by Eq. (3).
cos hCB ¼
X
fi cos hi
ð3Þ
where hi is the contact angle belonging to the area fraction
i. The CB model also suggests that a textured surface
enhances the hydrophobicity of a given surface. In the
literature, it has been shown that textured surfaces of different sizes (10–100 nm) act as superhydrophobic surfaces
that are very useful in manufacturing and chemical industries (Gao and McCarthy 2007a; Gao et al. 2007; ChangHwan and Chang-Jin 2006; Dorrer and Rühe 2008;
Autumn and Hansen 2006). Some recent experiments have
also shown that surfaces with texture sizes in the range
1–20 nm can exhibit superhydrophobicity (Dorrer and
123
Rühe 2008; Gao and McCarthy 2006; Chang-Hwan and
Chang-Jin 2006). Both the Wenzel and CB models are
extensively used to predict the apparent contact angle on
rough and porous surfaces, respectively. However, the fact
that these models take into account the total contact area of
the droplet on the surface is still a controversial and much
debated topic by various groups (Extrand 2003; Gao and
McCarthy 2007a; b). Consequently, modification to the
classical model based on the contact line length has been
proposed (Gao and McCarthy 2007b; Extrand 2003;
Nosonovsky 2007b). It was also shown that both the
Wenzel and CB models are not valid when the droplet size
is comparable to the roughness height (Drelich and Miller
1993; Bhushan and Chae 2007; Choi et al. 2009). In 2007,
Nosonovsky derived the Eq. (4) to determine the contact
angle on a rough surface at the triple line.
cos hrough ¼ r ðx; yÞ cos hsmooth
ð4Þ
and for a composite surface, the CB equation was modified
to use the contact line of the droplet as shown in Eq. (5).
cos hcomposite ¼ f1 ðx; yÞ cos h1 þ f2 ðx; yÞ cos h2
ð5Þ
There have been a number of further studies to understand the effect of apparent contact angle on the wetting
characteristics (Bico et al. 2002; Nosonovsky 2007a, c,
Yoshimitsu et al. 2002; Thiele et al. 2003; Gao and
McCarthy 2007a, b; Extrand 2003; Herminghaus 2000;
Shibuichi et al. 1996; Barthlott and Neinhuis 1997; Bormashenko et al. 2007b; Ishino and Okumura 2008), as well
as on analyzing the Cassie–Wenzel (CW) wetting regimes
transition (Lafuma and Quere 2003; Yoshimitsu et al.
2002; McHale et al. 2005; Liu and Lange 2006; Ishino and
Okumura 2008; Bormashenko et al. 2006, 2007a, b). Both
Cassie and Wenzel states are equilibrium states obtained
from thermodynamic arguments. In dynamic settings, they
might not be approached as the system might get trapped in
other equilibrium states far from Cassie and Wenzel. A
series of study was performed to understand this dynamic
behavior of the droplet over heterogeneous surfaces as well
(Savva et al. 2011a, b; Vellingiri et al. 2011).
Understanding the mechanism of wetting transitions is
very essential for designing highly stable superhydrophobic
surfaces. It has been observed that the droplets on these
surfaces are in Cassie state rather than in Wenzel state
(Koishi et al. 2009). This is mainly because the droplets in
the Wenzel state are pinned more strongly on the textured
surface than in the Cassie state and lead to a larger contact
angle hysteresis. Therefore, the Cassie state is preferred
over the Wenzel state to obtain superhydrophobicity. It has
also been established that for highly rough surfaces, the
Cassie state is more prevalent over the Wenzel state.
Microfluid Nanofluid
Accordingly, various mechanisms used previously to promote the wetting transitions such as depositing the droplet
from a higher position (He et al. 2003; Jung and Bhushan
2008), applying external pressure (Forsberg et al. 2011),
electrowetting—application of voltage (Bahadur and Garimella 2009) and vibrating the substrate in horizontal and
vertical directions (Daniel et al. 2005; Celestini and Kofman 2006; Noblin et al. 2004; Meiron et al. 2004) corroborate with this fact. But on the basis of a few studies
that were made to understand the wetting transition on a
pillar structure (Koishi et al. 2009; Bhushan et al. 2007), it
was confirmed that the smaller and more densely packed
structures lead to better stability of the droplet which acts
as a Cassie droplet. However, to achieve maximum roll-off
over the superhydrophobic surfaces, a large separation
between the structures is required, which may lead to
droplet instability and result in CW transition (Forsberg
et al. 2011). Furthermore, there is a lack of relevant work
examining the transition of wettability on a groove structure and analyzing the effects of geometric structural
parameters of the wetting transition on a grooved surface.
It is therefore essential to gain an in-depth understanding of
the droplet behavior under different scenarios in order to
optimize the surface characteristics for a specific application. In this manuscript, we focus on understanding the
wetting transitions of a groove structure as a function of
height of the grooves, spacing between the grooves and
presence of small capillary structures (secondary roughness) on the surface and apply this for proton exchange
membrane fuel cell (PEMFC) application.
Table 1 Dimensions of the
groove patterned silicon chip
Chip
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Land Width
(µm)
38
38
97
99
37
40
39
101
39
98
39
99
37
39
99
199
199
2 Experiments
Experiments were performed to understand how the groove
patterned roughness affects the CW transition and to
evaluate which methodology (contact line or contact area)
predicts the contact angle on a rough surface more accurately. For these experiments, \1 0 0[ p-type silicon chips
of 20 mm 9 20 mm size with etched microchannels and
chips with different roughness patterns were used. Table 1
shows the roughness patterns that are formed by the
channel grooves on the silicon chip.
2.1 Comparison of contact line model with contact
area-based model
The drying technique of dyed liquid was used to measure
the contact line length and contact area with the silicon
patterned surface. It was then used to determine which
model predicts the contact angle on the patterned rough
surface accurately.
2.2 Drying technique to measure contact line length
and contact area
A 5-lL droplet was placed on the patterned surface, and
the contact angle was measured using a VCA Optima
Surface Analysis System. The droplet behavior pattern on
each chip was observed using a confocal laser scanning
microscope (CLSM) and a Keyence high-speed camera.
The contact angle on the rough surface was calculated
Channel
Width (µm)
41
71
103
71
201
40
171
39
200
250
161
201
250
140
200
200
250
Depth (µm)
193
204
200
200
198
111
114
114
112
102
121
151
200
112
107
109
114
Land Width
Channel Width
123
Microfluid Nanofluid
Fig. 1 CLSM image of a red-dyed droplet on a silicon chip after the
liquid was allowed to evaporate
using the classical Wenzel and Cassie models (Eqs. 2 and
3, respectively), and compared with the calculated contact
angle using the contact line model given by Eqs. 4 and 5.
For calculating the contact line length and the contact area
of the droplet, a red-dyed water droplet was placed on the
chip’s surface and allowed to evaporate. When the droplet
evaporated, an impression of the contact boundaries on the
surface was found. The chip was then imaged using the
CLSM to estimate the actual and apparent contact areas
and the contact line lengths. Figure 1 shows the contact
area of the droplet after the evaporation of the dyed liquid.
the chip were in the range of 141°–156° (chips with
roughness patterns are hydrophobic), whereas the contact
angle on a bare silicon without any roughness pattern was
around 85° (hydrophilic), thereby confirming that patterns
etched on the surface (in this case, with roughness of order
100 lm) can drastically change the surface wettability.
Secondly, when the contact angles estimated from the
wetted area and contact line models were compared, it was
observed that the contact area-based model under-predicted
the contact angle. However, the predictions based on the
contact line-based model on the patterned surface were
accurate within ±1.5 %. The Wenzel model-based predictions were very inaccurate (error margin of 45–50 %)
compared with the measurements, whereas CB model
predictions were within ±15 %. Hence, according to these
results, contact line model can be considered to be more
appropriate for estimating contact angles on patterned
roughness surfaces as suggested by the previous studies
(Nosonovsky 2007a, c; Bico et al. 2002).
2.3 Influence of Scaling Factor on Wettability
Transition
2.2.1 Contact angle measurement
The contact angles measured using the VCA optima contact angle measurement tool are given in Table 2. The
contact line and contact area measured using the CLSM to
calculate the contact angles using Wenzel, Cassie, and
contact line models are given in Table 2 as well. It was
observed from the data that the contact angles measured on
For different values of channel depth and width, the
droplets exhibited Wenzel or Cassie type behavior as
shown in Fig. 2, and at times, even a metastable state
behavior in our experiments. The complete set of observed
behavior for different channel configurations is shown in
Table 3. Channels with widths greater than 161 lm
behaved like Wenzel droplets. It was also observed that for
Table 2 Comparison on contact angle prediction on a patterned rough using contact area-based model and the contact line model
Chip
Land
area
(mm2)
Channel
area
(mm2)
Land
contact
line (mm)
1
0.9
2.8
3.0
2
0.9
2.6
3
1.0
2.6
4
1.9
5
Surface
wettability
Measured
contact
angle (°)
Contact angle
(Wenzel Eq.)
(°)
Contact angle
(Cassie–Baxter
Eq.) (°)
Contact angle
(contact line
using Eq. 5) (°)
1.2
Cassie
141.1
–
138.2
141.2
2.1
1.2
Cassie
143.7
–
135.9
147
2.0
1.1
Cassie
149.7
–
134.6
146.2
3.5
2.4
1.2
Cassie
145.5
–
127.9
144.9
2.7
5.6
3.7
8.8
Cassie
156.5
–
130.2
132.8
6
1.4
2.7
2.2
20.4
Cassie
151.1
–
141.5
151.9
7
0.9
2.7
3.1
1.1
Wenzel
141.5
85.1
139.1
141.1
8
9
1.4
1.7
2.8
2.1
1.9
2.4
4.4
3.1
Cassie
Wenzel
155.5
120.4
–
76.2
135.2
115.8
150.1
126.5
10
2.0
2.1
6.4
9.0
Wenzel
125.5
79.5
119.8
131.7
11
1.9
6.1
7.7
35.6
Metastable
160.4
83.4
137.2
158.5
12
2.0
7.6
6.8
45.9
Metastable
164.1
82.9
139.3
162.3
13
0.9
2.9
3.5
15.6
Metastable
165.8
85.4
136.5
160.1
14
0.8
2.8
4.1
29.1
Metastable
162.8
81.9
137.3
158.5
15
1.9
2.4
3.2
4.6
Wenzel
138.9
76.5
117.8
136.5
16
0.9
0.98
1.2
1.7
Wenzel
143.1
80.1
120.3
140.5
17
2.0
2.2
3.3
4.4
Wenzel
145.7
81.6
118.9
141.5
123
Channel
contact line
(mm)
Microfluid Nanofluid
Wettability Transition
Cassie
Metastable
Wenzel
Fig. 2 Contact angle measurements, a Chip 5-droplet sitting on the
air in the channel area (Cassie type wetting), b Chip 7-droplet fills the
channel area (Wenzel type wetting)
0
0.4 0.8 1.2 1.6
2
2.4 2.8 3.2 3.6
4
4.4 4.8 5.2
Scaling Factor
Table 3 Effect of scaling factor (S) on wettability transition
Chip
Channel
width
(W) (lm)
Depth
(H) (lm)
Scaling
factor
(S = H/W)
Wetting
type
Contact
angle
measured
141.1
1
41
193
4.71
Cassie
2
71
204
2.87
Cassie
143.7
3
4
103
71
200
200
1.94
2.82
Cassie
Cassie
149.7
145.5
5
201
198
0.99
Cassie
156.5
6
40
111
2.78
Cassie
148.6
7
171
114
0.67
Wenzel
141.5
8
39
114
2.92
Cassie
155.5
9
200
112
0.56
Wenzel
120.4
10
250
102
0.41
Wenzel
125.5
11
161
121
0.75
Metastable
160.4
12
201
151
0.75
Metastable
164.1
13
250
200
0.8
Metastable
165.8
14
140
112
0.82
Metastable
162.8
15
200
107
0.54
Wenzel
138.9
16
200
109
0.55
Wenzel
143.1
17
250
114
0.46
Wenzel
145.7
Fig. 3 Wettability transition from Wenzel to Cassie regime on a
groove patterned roughness as a function of scaling factor (S)
(a)
(b)
170
Metastable
Contact Angle (°)
160
a channel width above 161 lm the droplet sometimes
enters into a metastable state and transitions into Wenzel
type. This illustrates that the droplet wetting characteristics
are affected by the channel width.
In addition to the channel width effect, an additional
effect of roughness height was observed. While a droplet is
in the Cassie state, reducing the roughness height beyond a
certain limit transforms it into Wenzel state. This is caused
when the roughness height is smaller than the depth to
which liquid projects into the channel.
The effect of channel depth can be seen by comparing
chips 5 and 9. Both have similar widths of around 200 lm,
but chip 5 is 198 lm deep while chip 9 is 112 lm deep.
The deeper chip 5 exhibits the Cassie state, while the
shallower chip 9 exhibits Wenzel behavior. Thus, it is seen
that the channel width and the roughness height both
150
Cassie
140
130
Wenzel
120
110
100
0
1
2
3
4
5
Scaling Factor
Fig. 4 a Contact angle measurements on chip 11 showing metastable
state of the droplet. The droplet sits on the air gap and acts as Cassie
type wetting on one roughness and also fills the channel on other side
of the roughness showing Wenzel type wetting. b Contact angle
measured on the chip surface as a function of scaling factor
123
Microfluid Nanofluid
Table 4 Dimensions of the
silicon chip with secondary
roughness features
Land Channel
Notch Notch
Depth
Chip Width Width
Length Width
(µm)
(µm)
(µm)
(µm)
(µm)
18
199
100
194
19
12
Notch Scaling
Gap Factor
(µm)
90
1.94
Surface
Wettability
Observed
Wenzel
19
199
200
158
20
11
100
0.79
Wenzel
20
198
201
207
19
12
99
1.03
Wenzel
21
198
201
208
30
32
89
1.04
Wenzel
22
199
200
199
31
12
88
0.99
Wenzel
23
199
71
208
30
32
89
2.93
Wenzel
24
199
40
199
31
32
88
4.92
Wenzel
25
197
140
194
30
12
87
1.39
Wenzel
Secondary Roughness
Pattern
Notch Length
Notch Width
Notch Gap
Notch Length
Notch Width
26
198
161
193
31
32
86
1.20
Wenzel
27
100
99
186
19
12
80
1.87
Wenzel
affected the wetting characteristics. There was no effect
observed due to the land width variation on the wetting
characteristics of any surfaces used.
To better understand the relationship of the droplet
behavior and the geometric parameters of grooves (or
roughness features) at shallow roughness features, a scaling
factor S was used and it is given by Eq. (6).
S ¼ H=W
ð6Þ
where H is the channel depth or roughness height, and W is
the channel width. This factor was introduced earlier by
Bhushan et al. (12) for pillared roughness features where
the scaling factor was used as a ratio of pillar diameter to
the pitch of the pillars. The scaling factors for different
chips used in our experiments varied between 0.4 and 4.8
and are shown in Table 3. The scaling factor is plotted in
Fig. 3 to determine the transition point between Wenzel
and Cassie regimes. It was observed that the droplets
remain distinctly in the Cassie regime for S [ 1, in the
Wenzel regime for S \ 0.7, and in a metastable state or
transition state for 0.7 \ S \ 1. In the metastable regime,
the droplet showed both Wenzel and Cassie type wetting
behaviors as shown in Fig. 4a. The contact angle measured
on different chips was also plotted against the scaling
factor and is shown in Fig. 4b where it is seen that Wenzel
type droplets have comparatively lower contact angles
compared with the Cassie droplets. Therefore, for patterned
surfaces, the transition point from Wenzel to Cassie can be
considered to occur around the scaling factors of 0.7–1.
2.4 Effect of secondary roughness features
Contact angle measurements were also performed on chips
with small notches on the grooved surfaces. These additional features can be considered as secondary roughness
123
Notch Gap
features. The dimensions of the chips and the secondary
roughness patterns used in the experiments are given in
Table 4. The contact angle measurement on chips 18–27
showed that the droplets filled the channel area and acted as
Wenzel droplets for all the chips tested. S value was calculated for all the chips and is shown in Table 4. Based on
the dependency of the scaling factor, Cassie type behavior
should have been observed for chips having S [ 1. However, all the chips exhibited Wenzel type wetting behavior
and this necessitated further analysis.
To analyze the droplet behavior on a secondary roughness chip, the dyed liquid droplet was placed on the chip
and allowed to dry similar to the dyed water drying technique mentioned earlier. The contact line of the droplet
after the evaporation of the liquid on a secondary rough
surface was imaged using CLSM and is shown in Fig. 5a.
The contact line image was further examined near the
secondary roughness regions which indicated that the notch
area near the three-phase contact line remained unstained,
and hence, the droplets acted as the Cassie type droplets
shown in Fig. 5b. However, underneath the droplet, the
liquid filled the entire channel area, including the notches.
One possible reason for this behavior is that the sharp
corners of the secondary roughness structures affect the
overall droplet profile and result in the droplet filling into
the channel region. On the other hand, near the three-phase
contact line, the droplet curves around without filling the
secondary roughness gaps and acts as a Cassie droplet. To
further validate the droplet regime results and its wettability, the contact angle was calculated using CB model on
the patterned surfaces and is shown in Table 5. It was
found that the contact angle values were reasonable compared with the Wenzel model prediction with an error
margin of ±15 % from the measured values. When the
contact line-based model for porous media was used, the
values were closer with an error margin of ±4 % from the
Microfluid Nanofluid
(a)
100 µm
100 µm
(b)
Fig. 5 a The droplet contact line on the chip surface after the liquid
has evaporated and left behind the contact line mark. b The zoomed
image of the contact line to show that near the three-phase contact
line droplet did not fill the notches and hanged on the air gap;
however, inside the droplet area the liquid filled the notches
contact angle values measured using the VCA Optima
contact angle measurement tool.
2.5 Application to 3D roughness features—gas
diffusion layer
To further evaluate the applicability of the contact line
model, the contact angle measurements were performed on
Fig. 6 CLSM image of a red-dyed droplet on the MRC-105 GDL
after the liquid was allowed to evaporate
commercially available gas diffusion layer (GDL) surfaces
(textured carbon fibers such as SGL-25BC, TGP-H-060 and
MRC-105 used in proton exchange membrane fuel cell
applications) which have a uniform roughness (with
roughness values ranging from 150 to 200 lm). The contact
line of the droplet and the wetted area were measured using
the CLSM as shown in Fig. 6, and these data were used for
predicting the contact angle on the rough GDL surfaces.
The contact angles measured were in the range of 145°–
148°, while the angles predicted using the CB model were
found to be around 132°–142° as shown in Table 6. However, the contact line model-based predictions of contact
angles showed it to be within the range of 146°–150°. It is
therefore evident from these model-based comparisons that
Table 5 Wettability and contact angles calculated using contact line and contact area-based model on secondary roughness features
Chip
Land
area
(mm2)
Channel
area
(mm2)
Land
contact
line (mm)
Channel
contact line
(mm)
Surface
wettability
(actual)
Measured
contact
angle (°)
Contact angle
(Wenzel Eq.)
(°)
Contact angle
(Cassie–Baxter
Eq.) (°)
Contact angle
(contact line
using Eq. 5) (°)
18
1.1
1.6
2.2
9.1
Cassie
145.3
73.7
114.9
140.1
19
1.1
1.8
1.6
13.5
Cassie
152.4
80.2
125.6
152.5
20
21
1.0
0.8
2.0
1.9
3.4
7.7
26.8
12.0
Cassie
Cassie
151.5
122.3
80.2
81.8
130.7
133.1
151.4
125.1
22
0.6
1.6
1.9
14.7
Cassie
151.1
79.3
135.3
151.4
23
2.2
2.6
1.4
5.5
Cassie
122.3
83.5
120.5
121.5
24
1.6
1.8
2.4
13.5
Cassie
154.4
82.23
145.3
152.4
25
0.9
1.2
2.4
13.7
Cassie
152.9
82.78
150.3
153.7
26
0.8
1.0
0.7
4.0
Cassie
156.8
83.98
150.6
159.3
27
0.6
0.8
0.9
2.2
Cassie
146.3
84.4
142.2
147.2
123
Microfluid Nanofluid
Table 6 Comparison of contact angle prediction on carbon fiber papers using Cassie–Baxter and contact line models
Type of GDL
Land
area
(mm2)
Channel
area
(mm2)
Land
contact line
(mm)
Channel
contact line
(mm)
Surface
wettability
Measured
contact angle
(°)
Contact angle
(Cassie–Baxter
Eq.) (°)
Contact angle
(contact line using
Eq. 5) (°)
SGL-25BC
0.2
0.5
0.4
3.2
Cassie
148
132.4
150.4
MRC-105
(6 % PTFE)
0.3
0.7
0.6
4.0
Cassie
148
132.4
150.4
TGP-H-060
(6 % PTFE)
0.3
1.0
0.8
4.4
Cassie
145
141.5
146.8
the contact line-based model is more appropriate than the
classical model in determining the contact angle on a rough
or heterogeneous surface.
2.6 Application to the proton exchange membrane fuel
cell (PEMFC) gas channel
It was observed in the PEMFC gas channel that the byproduct water emerging due to the electrochemical reactions occurring in the membrane mostly comes through the
land region (Mench 2008). Once the liquid water comes to
the gas channel through the land region, the water gets
pinned at the corners of the gas channel and eventually
leads to slug flow in the gas channel (Gopalan and Kandlikar 2012a). To avoid water stagnation near the channel
corners, groove patterned surfaces were designed on the
channel sidewall to suck the water through the grooves to
the top of the channel. Once the water reaches the top of
the channel, the airflow inside the gas channel would
remove the liquid water. To design the groove pattern on
the sidewall, the scaling factor S was used as a predictive
tool to understand the change in wettability of the channel
sidewall due to rough pattern introduced in the channel
walls. According to the scaling factor, if S B 1 then the
liquid would behave as a Wenzel wetting. For the fuel cell
application, the groove pattern needs to act as Wenzel
wetting to draw the liquid inside the grooves. Once the
liquid is drawn in the groove the capillary forces will pull
the liquid to the top of the grooves. Therefore, the grooves
were designed such that the S was less than 1. The image of
the grooves on the sidewall of the gas channel is shown in
Fig. 7.
The grooves made on the channel wall had a depth of
150 lm and a width of 200 lm. The S was calculated to be
0.75 which means that the liquid water would fill the
grooves and they would act as a capillary to suck the water
to the top of the capillary or the channel.
For this experiment, a base plate with polycarbonate was
used with the MRC-105 GDL placed on it with a preferential pore drilled in the GDL for the liquid water to
123
emerge on the GDL. A syringe pump was used to pump the
water through the GDL under the land region. The sidewall
with the grooved pattern was placed on top of the GDL.
The top wall made up of polycarbonate was placed on the
groove patterned sidewall to form a 100-lm-long channel.
More detailed explanation of the experimental set up is
provided in the earlier paper by the authors (Gopalan and
Kandlikar 2012a, b). High-speed videos were captured to
visualize the liquid water behavior near the channel corners
using Keyence VW-6000 high-speed camera. The videos
showed that the water coming from the land area was
sucked by the capillary grooves and the water rose to the
top wall faster than its growth on the GDL inside the
channel area. Figure 8 shows the image sequence of the
liquid water growth from the land area on the groove
pattern into the PEMFC gas channel. This shows that using
the scaling factor one can predict the wetting behavior on a
groove surface accurately.
However, the suction by the capillary grooves used for
this experiment was not strong enough to pull the liquid
quickly to the top due to the large size of the capillary
grooves. Therefore, grooves with smaller channel depth
and width are needed to achieve good capillary rise inside
the grooves before the liquid grows inside the channel area.
This is being incorporated in the future design of the
sidewalls for the PEMFC gas channel.
3 Conclusions
Experimental studies were performed to understand the
transition of the wetting regime and the transition behavior
on patterned microchannel surfaces having roughness features greater than 100 lm. Among several parameters
considered, it was observed that the change in the land
width has no effect on the droplet wettability, while the
channel width and the channel depth have considerable
effects on the wetting transition behavior. A non-dimensional number, scaling factor S (ratio of channel height to
channel width) was used to predict the transition regime for
Microfluid Nanofluid
400 µm
(a)
(b)
Fig. 7 a Grooves pattern design on the sidewalls of the gas channel, b experimental image of the grooves on the channel wall
400 µm
Liquid emerging in the grooves
400 µm
Liquid sucked by the grooves
400 µm
Liquid moving due to capillary forces
400 µm
Liquid growing in the channel
Fig. 8 Sequence image of the liquid water growth on the groove pattern in the PEMFC gas channel
the silicon surfaces with microchannels. For S [ 1, the
droplet was found to be in the Cassie regime, and for all
other conditions it was in the Wenzel regime. The droplet
on the chips with secondary roughness behaved as Wenzel
droplet, but they acted as Cassie droplet near the threephase contact line regime. Classical models using the
wetted area and the contact line length were used to calculate the contact angle on patterned rough surfaces, and it
was observed that the contact line model predicted the
contact angle on the rough surfaces more accurately compared with the wetted area-based models. Scaling factor
method was used to predict the wetting phenomenon on a
grooved surface for a PEMFC application. Using this criterion, the groove structures were designed on the sidewall
of the PEMFC gas channel to remove the water effectively.
The water coming from the land region into the gas channel
was pulled by the grooves to the top wall where the airflow
aided in its removal.
Acknowledgments This work was conducted 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-EE0000470.
References
Autumn K, Hansen W (2006) Ultrahydrophobicity indicates a nonadhesive default state in gecko setae. J Comp Physiol 192(11):
1205–1212. doi:10.1007/S00359-006-0149-Y
Bahadur V, Garimella SV (2009) Preventing the Cassie–Wenzel
transition using surfaces with noncommunicating roughness
elements. Langmuir 25(8):4815–4820. doi:10.1021/LA803691M
Barthlott W, Neinhuis C (1997) Purity of the sacred lotus, or escape
from contamination in biological surfaces. Planta 202(1):1–8.
doi:10.1007/S004250050096
Bhushan B, Chae J (2007) Wetting study of patterned surfaces for
superhydrophobicity. Ultramicroscopy 107(10–11):1033–1041.
doi:10.1016/J.ULTRAMIC.2007.05.002
Bhushan B, Nosonovsky M, Chae J (2007) Towards optimization of
patterned superhydrophobic surfaces. J R Soc Interface
4(15):643–648. doi:10.1098/RSIF.2006.0211
Bico J, Thiele U, Quéré D (2002) Wetting of textured surfaces.
Colloids Surf A 206(1–3):41–46. doi:10.1016/S0927-7757
(02)00061-4
Bormashenko E, Stein T, Whyman G, Bormashenko Y, Pogreb R
(2006) Wetting properties of the multiscaled nanostructured
polymer and metallic superhydrophobic surfaces. Langmuir
22(24):9982–9985. doi:10.1021/LA061622M
Bormashenko E, Bormashenko Y, Stein T, Whyman G, Pogreb R,
Barkay Z (2007a) Environmental scanning electron microscopy
study of the fine structure of the triple line and Cassie–Wenzel
wetting transition for sessile drops deposited on rough polymer
substrates. Langmuir 23(8):4378–4382. doi:10.1021/LA0634802
Bormashenko E, Pogreb R, Whyman G, Bormashenko Y, Erlich M
(2007b) Vibration-induced Cassie–Wenzel wetting transition on
rough surfaces. Appl Phys Lett 90(20):201912–201917
Cassie ABD, Baxter S (1944) Wettability of porous surfaces. Trans
Faraday Soc 40:546–551
Celestini F, Kofman R (2006) Vibration of submillimeter-size
supported droplets. Phys Rev E 73(4):041602
Chang-Hwan C, Chang-Jin K (2006) Fabrication of a dense array of
tall nanostructures over a large sample area with sidewall profile
and tip sharpness control. Nanotechnology 17(21):5326
Choi W, Tuteja A, Mabry JM, Cohen RE, McKinley GH (2009) A
modified Cassie–Baxter relationship to explain contact angle
123
Microfluid Nanofluid
hysteresis and anisotropy on non-wetting textured surfaces.
J Colloid Interface Sci 339(1):208–216. doi:10.1016/J.JCIS.
2009.07.027
Daniel S, Chaudhury MK, de Gennes PG (2005) Vibration-actuated
drop motion on surfaces for batch microfluidic processes.
Langmuir 21(9):4240–4248. doi:10.1021/LA046886S
Dorrer C, Rühe J (2008) Wetting of silicon nanograss: from
superhydrophilic to superhydrophobic surfaces. Adv Mater
20(1):159–163. doi:10.1002/ADMA.200701140
Drelich J, Miller JD (1993) Modification of the Cassie equation.
Langmuir 9(2):619–621. doi:10.1021/LA00026A043
Duparré A, Flemming M, Steinert J, Reihs K (2002) Optical coatings
with enhanced roughness for ultrahydrophobic, low-scatter
applications. Appl Opt 41(16):3294–3298
Extrand CW (2003) Contact angles and hysteresis on surfaces with
chemically heterogeneous islands. Langmuir 19(9):3793–3796.
doi:10.1021/LA0268350
Forsberg P, Nikolajeff F, Karlsson M (2011) Cassie-Wenzel and
Wenzel-Cassie transitions on immersed superhydrophobic surfaces under hydrostatic pressure. Soft Matter 7(1):104–109
Gao L, McCarthy TJ (2006) A perfectly hydrophobic surface (HA/
HR = 180°/180°). J Am Chem Soc 128(28):9052–9053. doi:10.
1021/JA062943N
Gao L, McCarthy TJ (2007a) Reply to ‘‘comment on how Wenzel and
Cassie were wrong by Gao and Mccarthy’’. Langmuir
23(26):13243–13243. doi:10.1021/LA703004V
Gao L, McCarthy TJ (2007b) How Wenzel and Cassie were wrong.
Langmuir 23(7):3762–3765. doi:10.1021/LA062634A
Gao X, Yan X, Yao X, Xu L, Zhang K, Zhang J, Yang B, Jiang L
(2007) The dry-style antifogging properties of mosquito compound eyes and artificial analogues prepared by soft lithography.
Adv Mater 19(17):2213–2217. doi:10.1002/ADMA.200601946
Gopalan P, Kandlikar SG (2012a) Droplet-sidewall dynamic interactions in PEMFC gas channels. J Electrochem Soc 159(8):F468–
F475. doi:10.1149/2.066208JES
Gopalan P, Kandlikar SG (2012b) Effect of channel materials on the
behavior of water droplet emerging from GDL into PEMFC gas
channels. ECS Trans 50(2):503–512
He B, Patankar NA, Lee J (2003) Multiple equilibrium droplet shapes
and design criterion for rough hydrophobic surfaces. Langmuir
19(12):4999–5003. doi:10.1021/LA0268348
Herminghaus S (2000) Roughness-induced non-wetting. Europhys
Lett 52(2):165–170
Ishino C, Okumura K (2008) Wetting transitions on textured
hydrophilic surfaces. Eur Phys J e: Soft Matter Biol Phys
25(4):415–424. doi:10.1140/EPJE/I2007-10308-Y
Jung YC, Bhushan B (2008) Dynamic effects of bouncing water droplets
on superhydrophobic surfaces. Langmuir 24(12):6262–6269.
doi:10.1021/LA8003504
Kandlikar SG (2001) A theoretical model to predict pool boiling CHF
incorporating effects of contact angle and orientation. J Heat
Transfer 123(6):1071–1079
Koishi T, Yasuoka K, Fujikawa S, Ebisuzaki T, Zeng XC (2009)
Coexistence and transition between Cassie and Wenzel state on
pillared hydrophobic surface. Proc Natl Acad Sci 106(21):
8435–8440. doi:10.1073/PNAS.0902027106
Lafuma A, Quere D (2003) Superhydrophobic states. Nat Mater
2(7):457–460
Liu B, Lange FF (2006) Pressure induced transition between
superhydrophobic states: configuration diagrams and effect of
surface feature size. J Colloid Interface Sci 298(2):899–909.
doi:10.1016/J.JCIS.2006.01.025
McHale G, Aqil S, Shirtcliffe NJ, Newton MI, Erbil HY (2005)
Analysis of droplet evaporation on a superhydrophobic surface.
Langmuir 21(24):11053–11060. doi:10.1021/LA0518795
123
Meiron TS, Marmur A, Saguy IS (2004) Contact angle measurement
on rough surfaces. J Colloid Interface Sci 274(2):637–644.
doi:10.1016/J.JCIS.2004.02.036
Mench MM (2008) Basic electrochemical principles. In: Fuel cell
engines. Wiley, pp 29–61. doi:10.1002/9780470209769.CH2
Noblin X, Buguin A, Brochard-Wyart F (2004) Vibrated sessile
drops: transition between pinned and mobile contact line
oscillations. Eur Phys J e: Soft Matter Biol Phys 14(4):
395–404. doi:10.1140/EPJE/I2004-10021-5
Nosonovsky M (2007a) Model for solid-liquid and solid–solid friction
of rough surfaces with adhesion hysteresis. J Chem Phys
126(22):224701–224706
Nosonovsky M (2007b) Multiscale roughness and stability of superhydrophobic biomimetic interfaces. Langmuir 23(6):3157–3161.
doi:10.1021/LA062301D
Nosonovsky M (2007c) On the range of applicability of the Wenzel
and Cassie equations. Langmuir 23(19):9919–9920. doi:10.1021/
LA701324M
Peters RD, Yang XM, Kim TK, Sohn BH, Nealey PF (2000) Using
self-assembled monolayers exposed to X-rays to control the
wetting behavior of thin films of diblock copolymers. Langmuir
16(10):4625–4631. doi:10.1021/LA991500C
Podgorski L, Chevet B, Onic L, Merlin A (2000) Modification of
wood wettability by plasma and corona treatments. Int J Adhes
Adhes 20(2):103–111. doi:10.1016/S0143-7496(99)00043-3
Quéré D (2008) Wetting and roughness. Annu Rev Mater Res 38(1):71–99.
doi:10.1146/ANNUREV.MATSCI.38.060407.132434
Savva N, Pavliotis GA, Kalliadasis S (2011a) Contact lines over
random topographical substrates. Part 1 statics. J Fluid Mech
672:358–383. doi:10.1017/S0022112010005975
Savva N, Pavliotis GA, Kalliadasis S (2011b) Contact lines over
random topographical substrates. Part 2 dynamics. J Fluid Mech
672:384–410. doi:10.1017/S0022112010005987
Shibuichi S, Onda T, Satoh N, Tsujii K (1996) Super water-repellent
surfaces resulting from fractal structure. J Phys Chem
100(50):19512–19517. doi:10.1021/JP9616728
Tafti EY, Londe G, Chunder A, Zhai L, Kumar R, Cho HJ (2011)
Wettability control and flow regulation using a nanostructureembedded surface. J Nanosci Nanotechnol 11(2):1417–1420.
doi:10.1166/JNN.2011.3400
Teh KS, Lu YW (2008) Surface nanostructuring of biocompatible
polymer for wettability control in MEMS. In: IEEE 21st international conference on micro electro mechanical systems 2008
(MEMS 2008), 13–17, pp 363–366. doi:10.1109/MEMSYS.2008.
4443668
Thiele U, Brusch L, Bestehorn M, Bär M (2003) Modelling thin-film
dewetting on structured substrates and templates: bifurcation
analysis and numerical simulations. Eur Phys J E: Soft Matter
Biol Phys 11(3):255–271. doi:10.1140/EPJE/I2003-10019-5
Vellingiri R, Savva N, Kalliadasis S (2011) Droplet spreading on
chemically heterogeneous substrates. Phys Rev E 84(3):036305
Wenzel RN (1936) Resistance of solid surfaces to wetting by water.
Ind Eng Chem 28(8):988–994. doi:10.1021/IE50320A024
Yoshimitsu Z, Nakajima A, Watanabe T, Hashimoto K (2002) Effects
of surface structure on the hydrophobicity and sliding behavior
of water droplets. Langmuir 18(15):5818–5822. doi:10.1021/
LA020088P
Young T (1805) An essay on the cohesion of fluids. Philos Trans R
Soc Lond 95:65–87. doi:10.1098/RSTL.1805.0005