Proceedings of the 3rd European Conference on Microfluidics - Microfluidics 2012 - Heidelberg, December 3-5, 2012
µFLU12-255
CONTACT LINE CHARACTERISTICS OF LIQUID-GAS INTERFACES
OVER CONFINED/STRUCTURED SURFACES
Preethi Gopalan1 and Satish G. Kandlikar*1,2
1
Microsystem Engineering, Rochester Institute of Technology, Rochester, NY, 14623, USA
[email protected]
2
Mechanical Engineering, Rochester Institute of Technology, Rochester, NY, 14623, USA
[email protected]
KEY WORDS
Bond Number, Scaling Factor, Droplet, Patterned Surfaces, Roughness, Surface Tension, Wettability
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 roughness structures. This study investigates the effect of these surfaces on the transition in
wetting behavior from the Cassie to Wenzel regime. The experiments demonstrate that this transition is influenced by
the size and shape of the roughness patterns. It was also found that the wettability on a patterned surface depends on
the non-dimensional Bond Number (Bo) and the spacing factor (S = channel depth/channel width). The Bo and S both
influence the contact angle and contact angle hysteresis as well as the transition of droplet behavior between Cassie
and Wenzel states. It was noted that under certain conditions (Bo < 3.5*10-3 and S > 1) the droplet behaved as a Cassie
droplet, while exhibiting Wenzel wetting the rest of the time for the silicon microchannels tested. 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, for the roughness structures used, that the
contact line model predicts the contact angle on the patterned surfaces more accurately than the classical models and
can be used to predict surface-wettability.
1.
INTRODUCTION
Wetting and non-wetting of a surface has been widely studied in 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 (1-3). It is also found to be of importance in micro
and nanofluidics applications such as lab on a chip, MEMS, and miniaturized sensors (4-6). 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 (7, 8). In 1805, Young developed a model (Eq. (1)) which is commonly used to characterize the
wettability criterion of a smooth surface (9).
cos θc = (γSV - γSL)/γLV
(1)
where θc is the equilibrium contact angle on a smooth surface, and γSV, γSL, γLV are the interfacial tensions
between the solid-vapor, solid-liquid, and liquid-vapor states respectively.
*
Corresponding author
1
© SHF 2012
Proceedings of the 3rd European Conference on Microfluidics - Microfluidics 2012 - Heidelberg, December 3-5, 2012
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 - 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 θ 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 (10).
cos θ = r cos θc
(2)
According to this model, a droplet placed on a rough surface would spread until it finds the equilibrium
position given by the contact angle θ. It also predicts that the roughness on a surface enhances its wettability
if a surface is hydrophilic, then the roughness causes it to become more hydrophilic (or more hydrophobic if
the surface is initially hydrophobic) (11, 12).
For porous surfaces, Cassie-Baxter (CB) developed a model in 1944 (13) which includes the material
heterogeneity, fi for calculating the apparent contact angle which is given by Eq. (3).
cos θCB =  fi cos θi
(3)
where θi 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 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 (14-18). Some recent experiments have also shown that surfaces with texture sizes in the
range 1-20 nm can exhibit superhydrophobicity (16, 17, 19). 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 (14, 20-23). Consequently, modification to the
classical model based on the contact line length has been proposed (14, 20, 23-25). It was also shown that
both the Wenzel and CB models are not valid when the droplet size is comparable to the roughness height
(26-30). In 2007, Nosonovsky derived the following equation, Eq. (4) to determine the contact angle on a
rough surface at the triple line.
cos θrough = r(x,y) cos θsmooth
(4)
and for a composite surface, the CB equation was modified to use the contact line of the droplet as shown in
Eq. (5).
cos θcomposite = f1(x,y) cos θ1 + f2(x,y) cos θ2
(5)
There have also been further studies to understand the effect of apparent contact angle for a given surface on
the wetting characteristics (20, 31-51) as well as analyzing the Cassie - Wenzel (CW) wetting regimes
transition (36, 37, 46, 48, 49, 51-53) which is critical. Understanding the mechanism of wetting transitions is
very essential for designing highly stable superhydrophobic surfaces. Different microstructure surfaces have
been developed to achieve the superhydrophobic state. It has been observed that the droplets on these
surfaces are in Cassie state rather than in Wenzel state (54). 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. Accordingly, various mechanisms used previously to promote the wetting
transitions such as depositing the droplet from a higher position (55, 56), applying external pressure (57),
electrowetting – application of voltage (58), and vibrating the substrate in horizontal and vertical directions
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© SHF 2012
Proceedings of the 3rd European Conference on Microfluidics - Microfluidics 2012 - Heidelberg, December 3-5, 2012
(59-62), corroborate with this fact. But on the basis of a very few attempts that were made to understand the
wetting transition on a pillar structure (12, 54), 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 (57). Furthermore, there is a lack of relevant work
examining the transition of wettability on a groove structure and analyzing the effects of geometricstructural parameters of the wetting transition on a 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 specifically 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.
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 × 20 mm size with
etched microchannels and chips with different roughness patterns were used. Tab. 1 shows the roughness
patterns that are formed by the channel grooves on the silicon chip.
Chip
1
2
3
4
5
6
7
8
9
10
11
12
Land
Width (µm)
38
38
97
99
37
40
39
101
39
98
39
99
Channel
Width (µm)
41
71
103
71
201
40
171
39
200
250
161
201
Depth
(µm)
193
204
200
200
198
111
114
114
112
102
121
151
Land Width
Channel Width
Table 1. Dimensions of the silicon chip type 1
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 patterned
rough surface accurately.
2.1 Drying Technique to Measure Contact Line Length and Contact Area
A 5 µL 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 using the classical Wenzel and Cassie models (Eq. 2 and Eq. 3 respectively), and compared
with the calculated contact angle using the contact line model given by Eq. 4 and Eq. 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. Fig. 1 shows the contact area of the droplet after the evaporation of
the dyed liquid.
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© SHF 2012
Proceedings of the 3rd European Conference on Microfluidics - Microfluidics 2012 - Heidelberg, December 3-5, 2012
Figure 1. CLSM image of a red dyed droplet on a silicon chip after the liquid was allowed to evaporate.
2.1.1 Contact Angle Measurement
The contact angles measured using the VCA optima contact angle measurement tool are given in Tab. 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 Tab. 2 as well. It was observed from the data that the contact angles
measured on the chip were in the range of 141° - 156° (therefore, chips with roughness patterns are
hydrophobic) whereas the contact angle on 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 µm) can drastically change the surface-wettability. Secondly, when the contact angle data based on
wetted area and contact line were compared, it was observed that the contact area based model underpredicted the contact angle. However, the predictions based on the contact line based model on the patterned
surface was accurate within ±1.5%. The Wenzel model based predictions were very inaccurate (error margin
of 45-50%) compared to 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.
Contact
Land Channel
Land
Channel
Measured
Contact Angle Contact Angle
Surface
Angle
Chip Area
Area
Contact
Contact
Contact
(Cassie-Baxter (Contact Line
Wettability
(Wenzel
(mm2) (mm2) Line (mm) Line (mm)
Angle (°)
Eq.) (°)
Using Eq. 5) (°)
Eq.) (°)
1
0.9
2.8
3.0
1.2
Cassie
141.1
138.2
141.2
2
0.9
2.6
2.1
1.2
Cassie
143.7
135.9
147
3
1.0
2.6
2.0
1.1
Cassie
149.7
134.6
146.2
4
1.9
3.5
2.4
1.2
Cassie
145.5
127.9
144.9
5
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
9
1.7
2.1
2.4
3.1
Wenzel
120.4
76.2
115.8
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
Table 2. Comparison on contact angle prediction on a patterned rough using contact area based model and the contact
line model
2.2 Influence of Bond Number and Scaling Factor on Wettability Transition
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 tabulated in Tab. 3. Channels with widths greater
than 161 µm behaved like Wenzel droplets. It was also observed that for a channel width above 161 µm the
droplet sometimes enters into a metastable state and transitions into Wenzel type. This illustrates that the
droplet wetting characteristics is affected by the channel width. This width is non-dimensionalized using the
Bond Number,
Bo = gW2(ρL - ρG)/γLV
(6)
where g is the acceleration due of gravity, W is the channel width, γLV is the surface tension of the droplet, ρL
and ρV are the density of a droplet and the medium surrounding it respectively. Bond Number is a ratio of
gravitational to surface tension forces. Tab. 3 includes the Bo for all channel configurations tested.
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Proceedings of the 3rd European Conference on Microfluidics - Microfluidics 2012 - Heidelberg, December 3-5, 2012
(b)
(a)
Figure 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)
Chip
1
2
3
4
5
6
7
8
9
10
11
12
Channel
Width (W)
(µm)
41
71
103
71
201
40
171
39
200
250
161
201
Depth
(H) (µm)
193
204
200
200
198
111
114
114
112
102
121
151
Bond
Number (Bo)
(Bo*10-3)
0.23
0.69
1.43
0.68
5.51
0.22
3.96
0.21
5.42
8.51
3.51
5.47
Scaling
Factor
(S)
4.71
2.87
1.94
2.82
0.99
2.78
0.67
2.92
0.56
0.41
0.75
0.75
Wetting
Type
Cassie
Cassie
Cassie
Cassie
Cassie
Cassie
Wenzel
Cassie
Wenzel
Wenzel
Metastable
Metastable
Contact
Angle
Measured
141.1
143.7
149.7
145.5
156.5
148.6
141.5
155.5
120.4
125.5
160.4
164.1
Table 3. Effect of Bond Number (Bo) and Scaling Factor (S) on Wettability Transition
In general, it was seen from the table that for 100 µm deep roughness, increasing the channel width or Bo
causes the wetting characteristics to transition from the Cassie to Wenzel regime. For Bo < 3.5*10-3, the
droplet remains in the Cassie regime, and for 3.5*10-3 < Bo < 5.4*10-3 the droplet is in the transition region
between Cassie to Wenzel. Around Bo = 5.4*10-3, the droplet completely transitions to Wenzel regime.
Hence, increasing the channel width or Bo makes the droplet unstable and leads to Wenzel wetting.
Transition of wetting behavior on the chip as a function of Bo is shown in Fig. 3(a).
In addition to the Bo 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
µm, but chip 5 is 198 µm deep while chip 9 is 112 µm 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 affected the wetting characteristics. There was no effect observed due to land width 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 = H/W
5
(6)
© SHF 2012
Proceedings of the 3rd European Conference on Microfluidics - Microfluidics 2012 - Heidelberg, December 3-5, 2012
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 – 4.8 and are shown in Tab. 3. The scaling factor was plotted in Fig. 3(b) to determine the
transition point between Wenzel and Cassie regimes. It was observed that the droplets remain distinctively in
the Cassie regime for S > 1, in the Wenzel regime when 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. 4(a). The contact angle measured on different chips was also plotted against the
scaling factor and is shown in Fig. 4(b) where it is seen that Wenzel type droplets have comparatively lower
contact angles compared to 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.
Wettability Transition
Wettability Transition
2.5
Cassie
2.5
Cassie
2
Metastable1.5
Wenzel
2
Metastable1.5
Wenzel
1
0.5
1
0.5
0
0
0
1
2
3
4
5
6
7
8
9
0
0.4
0.8
1.2
Bond Number
1.6
2
2.4
2.8
3.2
3.6
4
4.4
4.8
5.2
Scaling Factor
(a)
(b)
Figure 3. Wettability transition from Wenzel to Cassie regime on a groove patterned roughness as a function of (a)
Bond Number (b) Scaling Factor
170
Metastable
160
Contact Angle(°)
150
Cassie
140
130
Wenzel
120
110
100
0
1
2
3
4
5
Scaling Factor
(a)
(b)
Figure 4. (a) Contact angle measurements on chip 11 showing metastable state of the droplet. The droplet sits on the air
gap and act 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
It is experimentally seen that the channel width or the Bo is one of the main parameters that determines the
wettability of a surface. At shallow roughness, the channel width alone cannot determine the wetting
characteristics. Hence, the scaling parameter S also needs to be considered. For the conditions tested in our
experiments, the droplet would be in the Cassie state for S > 1 and Bo < 3.5*10-3. If both of these conditions
are not met, the droplet would transform into the Wenzel state.
2.3 Effect of Secondary Roughness Features
Contact angle measurements were also performed on the chips with small notches on the grooved surfaces.
These additional features can be considered secondary roughness features and were used to study the
wettability of such surfaces. The dimensions of the chips and the secondary roughness patterns used in the
experiment are given in Tab. 4. The contact angle measurement on chips 13 - 22 showed that the droplets
filled the channel area and acted as Wenzel droplets. Based on the dependency of Bond Number and scaling
factor, Cassie type behavior should have been observed for Bo < 3.5*10-3 and S > 1. However, when the Bo
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Proceedings of the 3rd European Conference on Microfluidics - Microfluidics 2012 - Heidelberg, December 3-5, 2012
and S for the chips were calculated, it was observed that they exhibited Wenzel type wetting behavior and
necessitated further analysis.
The wetted contact area and the contact line lengths were obtained using the dyed water drying technique as
mentioned previously. Fig. 5(a) shows the contact line of the droplet after the evaporation of the liquid on a
secondary rough surface. The contact angles using Wenzel model were not found to match with the contact
angle measurements as shown in Tab. 5. 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. 5(b). 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 affects the overall droplet profile and results 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. It was found that the contact angle values were reasonable compared to 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 contact angle values
measured using the VCA Optima contact angle measurement tool.
Land Channel
Notch Notch Notch Bond Scaling Surface
Depth
Chip Width Width
Length Width Gap Number Factor Wettability
(µm)
(µm)
(µm)
(µm) (µm) (µm) Bo*10-3
Observed
13
199
100
194
19
12
90
1.36
1.94
Wenzel
14
199
200
158
20
11
100
5.44
0.79
Wenzel
15
198
201
207
19
12
99
5.49
1.03
Wenzel
16
198
201
208
30
32
89
5.49
1.04
Wenzel
17
199
200
199
31
12
88
5.44
0.99
Wenzel
18
199
71
208
30
32
89
0.69
2.93
Wenzel
19
199
40
199
31
32
88
0.22
4.92
Wenzel
20
197
140
194
30
12
87
2.66
1.39
Wenzel
21
198
161
193
31
32
86
3.52
1.20
Wenzel
22
100
99
186
19
12
80
1.33
1.87
Wenzel
Secondary Roughness
Pattern
Notch Length
Notch Width
Notch Gap
Notch Length
Notch Width
Notch Gap
Table 4. Dimensions of the silicon chip with secondary roughness features
(a)
100 µm
(b)
Figure 5. (a) Shows the droplet contact line on the chip surface after the liquid has evaporated and left behind the
contact line mark. (b) Shows 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.
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Proceedings of the 3rd European Conference on Microfluidics - Microfluidics 2012 - Heidelberg, December 3-5, 2012
Chip
Land Channel
Land
Area
Area
Contact
Line
(mm2) (mm2)
(mm)
Channel
Contact
Line
(mm)
Contact
Contact
Contact Angle
Surface Measured
Angle
Angle
(Contact Line
Wettability Contact
(Cassie(Wenzel
Using Eq. 5)
(Actual) Angle (°)
Baxter Eq.)
Eq.) (°)
(°)
(°)
Cassie
145.3
73.7
114.9
140.1
Cassie
152.4
80.2
125.6
152.5
Cassie
151.5
80.2
130.7
151.4
13
1.1
1.6
2.2
9.1
14
1.1
1.8
1.6
13.5
15
1.0
2.0
3.4
26.8
16
0.8
1.9
7.7
12.0
Cassie
122.3
81.8
133.1
125.1
14.7
Cassie
151.1
79.3
135.3
151.4
17
0.6
1.6
1.9
18
2.2
2.6
1.4
5.5
Cassie
122.3
83.5
120.5
121.5
19
1.6
1.8
2.4
13.5
Cassie
154.4
82.23
145.3
152.4
20
0.9
1.2
2.4
13.7
Cassie
152.9
82.78
150.3
153.7
21
0.8
1.0
0.7
4.0
Cassie
156.8
83.98
150.6
159.3
22
0.6
0.8
0.9
2.2
Cassie
146.3
84.4
142.2
147.2
Table 5. Wettability and contact angle calculated using contact line and contact area based model on a secondary
roughness features.
2.4 Application to 3D Roughness Features – Gas Diffusion Layer
To further evaluate applicability of the contact line model, the contact angle measurements were performed
on 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 - 200 µm). The contact line of the droplet and the wetted
area were measured using the CLSM as shown in Fig. 6 and this data was 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 Tab. 6. However, the
contact line model-based predictions of contact angles showed it to be in the range of 146° - 150°. It is
therefore evident from these model based comparisons that the contact line based model is more appropriate
than the classical model in determining the contact angle on a rough or heterogeneous surface.
100 µm
Figure 6. CLSM image of a red dyed droplet on the MRC-105 GDL after the liquid was allowed to evaporate.
Type of GDL
SGL- 25BC
MRC-105
(6% PTFE)
TGP-H-060
(6% PTFE)
Land
Area
(mm2)
0.2
Channel
Land
Channel
Measured Contact Angle Contact Angle
Surface
Area
Contact
Contact
Contact (Cassie-Baxter (Contact Line
Wettability
(mm2) Line (mm) Line (mm)
Angle (°)
Eq.) (°)
Using Eq. 5) (°)
0.5
0.4
3.2
Cassie
148
132.4
150.4
0.3
0.7
0.6
4.0
Cassie
148
132.4
150.4
0.3
1.0
0.8
4.4
Cassie
145
141.5
146.8
Table 6. Comparison of contact angle prediction on carbon fiber papers using Cassie-Baxter and contact line models
8
© SHF 2012
Proceedings of the 3rd European Conference on Microfluidics - Microfluidics 2012 - Heidelberg, December 3-5, 2012
3. CONCLUSIONS
Experimental studies were performed to understand the transition of the wetting regime on patterned
microchannel surfaces having roughness features greater than 100 µm. 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.
Wetting transition from Cassie to Wenzel wetting on a surface was observed with increasing channel width
or Bond Number (Bo). Two non-dimensional numbers, Bo and scaling factor S were used to predict the
transition regime for the silicon surfaces with microchannels. For Bo < 3.5*10-3 and S > 1 the droplet would
be in the Cassie regime, and for all other conditions it would show Wenzel wetting. The droplets on the chips
with secondary roughness behaved as Wenzel droplets, but near the three phase contact line regime they
acted as Cassie droplets. Classical models using wetted area and contact line 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 to the wetted area based models.
ACKNOWLEDGEMENTS
This work was carried out in the Thermal Analysis and Microfluidics and Fuel Cell Laboratory (TAµFL),
Rochester Institute of Technology, Rochester, NY.
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