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Wetting characteristic of bubble on micro-pillar structured surface under a water pool
Experimental Thermal and Fluid Science 100 (2019) 135–143
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Wetting characteristic of bubble on micro-pillar structured surface under a water pool
T
⁎
Seol Ha Kima, Hyun Sun Parka, , Donggun Kob, Moo Hwan Kima a b
Division of Advanced Nuclear Engineering, POSTECH, Pohang 790-784, Republic of Korea Department of Mechanical Engineering, POSTECH, Pohang 790-784, Republic of Korea
A R T I C LE I N FO
A B S T R A C T
Keywords: Contact angle Bubble Droplet Work of adhesion
In this study, the contact angle of air bubbles on a micro-structured surface under a water pool is experimentally investigated. A previous study “Kang and Jacobi, Equilibrium Contact Angles of Liquids on Ideal Rough Surfaces, Langmuir (2011)” adopted the work of adhesion as the additional work of the process of droplet contact on a textured surface, and it explained the reason for failure of the classical theoretical model (Wenzel equation) in real wetting tests. We extended the above concept to bubble interaction with the textured surface. First, the bubble contact angles on the textured surface were modeled based on the concept of the work of adhesion in the free energy calculation. Second, the contact angle of air bubbles was measured on the bottom of test surfaces under a water pool. The test-section surfaces have micro-pillars with a size of 5–40 μm prepared by the microelectromechanical systems (MEMS) technique. The bubble contact angles were compared with both the modeled bubble shape and classical prediction (Wenzel & Cassie–Baxter equations). In addition, detail wetting features which shows wetting transition and critical wetting behavior of bubble were discussed.
1. Introduction Since the wetting of droplets and bubbles on a solid surface plays dominant role in various liquid-vapor-solid physical systems, the wetting characteristics have attracted tremendous interest in not only fundamental research but also many industrial applications such as oil recovery, lubrication, liquid coating, printing, and spray quenching. The understanding of droplet wetting also provides insight into the heat transfer of the liquid-vapor phase change in cases of a droplet on a heating/cooling surface, and the cooling performance of condensation and spray cooling have been directly attributed to the wetting features [1–6]. In other hand, the wetting feature with bubble also plays an important role in bubble-wall interaction processes (e.g., material flotation, fluidized bed, and particle sedimentation). For instance, nucleate boiling, which is applied in various energy conversion process (e.g., nuclear power plants, electronic cooling devices, and air-conditioning), strongly depends on the bubble behavior [7–15]. In general, the wetting of droplets and bubbles on a solid surface can be characterized by the contact angle (θ), which indicates the surfaceenergy state of the rigid solid. The contact angle at the triple line, where the three phase (liquid, gas and solid) coexist, results from the balance of the surface tension between the two phases (Young’s relation) on an ideal smooth surface as follows [16].: ⁎
σsg−σsl = σlg cosθ .
(1)
Recently, numerous textured surfaces have been introduced to modify the wetting physics (contact angle). For textured surfaces with nano- and micro-scale morphologies, droplets meet two types of wetting states: the Wenzel state and Cassie–Baxter state, which correspond to a fully wetted state and partially wetted state, respectively [17,18]. Such textured surfaces can yield extreme wetting conditions such as superhydrophilic (θ < 10°) and superhydrophobic (θ > 160°). For a long time, these contact angles on various textured surfaces have been evaluated based on the Wenzel and Cassie–Baxter model. However, numerous inconsistencies with this classical model have been reported [19–22]. For example, the Wenzel model frequently failed to explain the droplet contact angle on textured surfaces when the intrinsic contact angle, which is the contact angle without roughened condition, is less than 90°. Recently, Kang and Jacobi [23] proposed a modification to the classical model that introduces the work of adhesion between the liquid droplet and surface, and it explains successfully the droplet contact angles on textured surfaces. Compared with the droplet wetting analysis, wetting feature with bubble has been studied less extensively. Because it was considered that the basic principle of determining the wetting shape and dynamics in terms of surface energy analysis are not different regardless of the
Corresponding author. E-mail addresses: fi[email protected] (S.H. Kim), [email protected] (H.S. Park), [email protected] (D. Ko), [email protected] (M.H. Kim).
https://doi.org/10.1016/j.expthermflusci.2018.09.001 Received 3 May 2018; Received in revised form 30 July 2018; Accepted 2 September 2018 Available online 04 September 2018 0894-1777/ © 2018 Elsevier Inc. All rights reserved.
Experimental Thermal and Fluid Science 100 (2019) 135–143
S.H. Kim et al.
σ θ ϕ
Nomenclature V A w r F d g h
volume [m3] area [m2] work of adhesion [N/m] roughness [–] Helmholtz Free Energy [J] diameter [m] gap [m] height [m]
Subscripts l g s Y D B
Greek symbols ρ
surface tension [N/m] contact angle [°] solid fraction [–]
liquid gas solid Young’s relation droplet bubble
density [kg/m3]
phases (droplet and bubble), relatively less test and discussion of the bubble-wall interaction have been performed. However, it can be applicable only if the wetting process follows the quasi-equilibrium process, which is a relatively slow interaction. In the bubble-wall contacting condition, the surrounding fluid which has relatively much high density and viscosity than drop-air condition can have an influence on the adhesion process or dynamic wetting process of bubble-wall interaction. According to the author’s literature survey and understand, only a couple of studies about the bubble contact angle varying the bubble size and related properties has been reported. [24,25]. In general, bubble contact angle (θB ) on a flat surface can be estimated by Young’s equations, and it can be measured by the captive bubble method (sessile bubble method) [26], that a bubble of air is injected on downwardfacing solid surface, instead of placing a drop on the solid as in the case of the sessile drop method [27–29]. It was reported that there are different fluctuation in contact angle between droplet bubble on rough surfaces, depending on the captive bubble method and sessile drop method. [30]. Additionally, bubble size and contact angle also have an influence on the air bubble/aqueous phase/paraffin system, and it was proposed to modify the Young’s equations with the line-tension to predict the dynamic contact angle (See Eq. (2)) [31]. This modified equation is applicable to homogeneous, rigid, flat, horizontal, and smooth solid surfaces, and it is expressed as follows:
σsg−σsl = σlg cosθ +
σslg r
.
(2)
where σslg is the line tension: the excess free energy in the region of the triple interface. Drelich et al. also showed that the surface roughness and heterogeneity strongly influence the dynamic contact angle and bubble size, particularly the receding contact angle [32]. As mentioned above, several researchers have studied the fundamentals of wetting features (static/dynamic) for various surface conditions and fluidic environmental conditions. In this study, in order to evaluate the bubble contact angle on designed micro-pillar structured surface in terms of wetting transition and prediction model applicability, simple bubble captive method of experimental work has been performed. For the experiments, textured surfaces were prepared by the microelectromechanical system (MEMS) technique and a coating method. The air bubble contact angles were measured by the captive bubble method and the results were compared with the modified Kang & Jacobi work for bubble-wall interaction. This study on bubble interfacial phenomena may give a fundamental picture of the bubble–wall interaction and the relevant applications. 2. Modeling of bubble contact angle We are going to derive the bubble contact angle on textured surface based on the Kang and Jacobi’s work [23], which is briefly reviewed in
(a) Droplet wetting State 2
State 1 Air
Liquid
(b) Bubble de-wetting
Air
Liquid
Fig. 1. Modeling of wetting by (a) a droplet and (b) a bubble. 136
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Appendix A. According to the Kang and Jacobi model, the apparent contact angle of a droplet on a textured surface could be predicted depending on its wetting state (Wenzel or Cassie-Baxter), adopting the work of adhesion concept. The work of adhesion is the additional energy consumed during the wetting or dewetting process. Here, the previous work was modified to predict the bubble contact angle depending on the wetting state of bubble. We would like to adopt the classical wetting states (Wenzel state and Cassie-Baxter states) to bubble-oriented points. In other words, Wenzel state of bubble is fully dried and Cassie-Baxter state of bubble is partially dried on tip of micropillars. As shown in Fig. 1, the bubble-wall interaction process has a directional movement opposite to that in the above theory for droplets. Because of the buoyancy of an air bubble in a liquid pool, the de-wetting process with the bubble on the surface involves the upward motion of the bubble. In addition, since the spherical object and spherical cap are changed from liquid, for droplet wetting, to air (gas), for bubble dewetting, the geometric relation (volume and area) of the contact angle should be modified. The geometric information of a bubble system is summarized in the Table 1. On solving the mass and energy conservation equations, the specific work of adhesion during the bubble dewetting process can be derived, as in the droplet wetting analysis (see Appendix A).
ρV1, g = ρV2, g ,
(Mass)
4 =
(
(2 − cosθY )(1 + cosθY )2 4
)
(Energy)
−cosθY .
= ϕ·
(2 − cosθY )(1 + cosθY )2/3) 4
sin2θY
) − 1 (1−ϕ).
(7)
2
3.1. Sample preparation A set of textured surfaces were prepared by etching polished silicon wafers by the MEMS technique. Two types of surface energy, which determines wettability, were obtained by the chemical coating of a selfassembled monolayer (SAM), and six types of surface morphologies were achieved by deep reactive ion etching (DRIE). In order to etch with local selectivity, a photoresist (PR, AZ-1512) was coated with its own specific patterns. The coated PR was chemically stabilized (PR developing: 300 MIF Developer). The uncovered area was etched to 20μm depth by the DRIE process, and the covered silicon area was protected from the etching. After the etching process, all chemicals on the surface were removed through air Plasma process (see Fig. 3a). Six types of surface morphologies including a smooth surface were designed, and 2 sets of test sample (12 samples) were prepared. After the etching process, one set of samples (6 samples) was coated with octadecyltrichlorosilane (ODTS) by the SAM method. [33] Since the SAM method coats the surface uniformly with a monolayer of organics, which is only a few nanometers in thickness, this coating does not allow any additional roughness of the test surface. Finally, two types of chemistry groups (bare Si and ODTS-coated) were prepared. Therefore, in total, 12 test samples were used in this experiment. Table 1 summarizes the design configuration of the test samples, as well as their roughness and solid fraction. Fig. 3 shows scanning electron microscopy (SEM) images of the test samples. In general, the test samples have micro-scale (5–40 μm) cylindrical structures, and the height of the structures are designed to be 20 µm. In this study, the geometric morphologies of the test samples are measured by a 3D profiler. The experimental results are described based on the measured value. The prepared textured surface has a range of roughness which is πdh a ratio between actual area and projected area (r = 1 + 2 , 1−3.7 )
(4)
−2(1 + cosθY )
(5)
The specific work of adhesion of bubble de-wetting shows trends opposite to those for liquid droplet wetting along the surface contact angle, as shown in Fig. 2. As mentioned above, in bubble de-wetting on a surface, three types of wetting can be considered: de-wetting on an ideal smooth surface, a fully dry bubble (here, called Wenzel bubble) on a textured surface, and a partially dry (Cassie-Baxter bubble) bubble on a textured surface. In the case of the fully dry state, the dry area between air and the solid increases with the roughness, which is area fraction between actual area and projected area. Thus, by solving the modified energy conservation equation for the bubble, the apparent contact angle on a rough surface can be predicted as follows:
1−cosθB, W −2 ⎛ ⎝
(
3. Experiments
2/3
(Work of adhesion for bubbles)
⎠
1 + cosθY −2
sin2 θY
Bubble
(2 − cosθB, C )(1 + cosθB, C )2/3) ⎞ 4
sin2θB, C
(3)
σlg Alg,1 + σsl Asl,1 = (σlg Alg,2 + σsl Asl,2 ) + w·Asg,2 ,
w σlg
1 + cosθB, C −2 ⎛ ⎝
(d + g )
and (ϕ =
solid πd2 4(d + g )
fraction
that
is
area portion of micropillar top 2 , 0.08−0.51), where d , g and h are the diameter and gap and
height of the micro pillar structure.
(2 − cosθB, W )(1 + cosθB, W )2/3) ⎞ 4
3.2. Contact angle measurement
⎠
sin2θB, W 1−cosθY −2 = r·
(
(2 − cosθY )(1 + cosθY )2/3) 4
sin2θY
).
First, we measured the droplet contact angle with a controlled volume of D.I. water (3 µL, Room temperature) on the prepared test samples. On the each samples, three or four times of measurements have been carried out and averaged. Second, in order to measure the
(6)
According to above equation, the critical contact angle under the fully dry condition is 136°, which is the peak of the work of adhesion for bubble de-wetting. This result indicates that only a highly hydrophobic surface (θ > 136°) can cause the bubble contact angle to increase with the roughness. In other words, under the fully dry condition, for most textured surfaces, the bubble contact angle decreases with the increase of roughness. While the contact angle of a liquid droplet usually increases with the roughness, the bubble contact angle decreases. In the case of the partially dried state, the dry area between air and the solid decreases with the decrease of the solid fraction. In the same manner as for the fully dry state, by solving the modified energy conservation equation for a bubble, the apparent contact angle on a rough surface can be predicted with respect to the solid fraction, which is area fraction between bubble (or droplet) contacted area and projected area, as follows:
Table 1 Geometric information on a spherical droplet and bubble on a surface. Parameter Droplet
Bubble
Spherical
Spherical cap
Volume (V)
4 3 πr 3
Liquid-gas surface area (Alg)
4πr 2
2 3 1 + cosθ− cos3θ 3 4 12 2 2πr ·(1 + cosθ)
(
Solid-liquid surface area (Asl)
0
Solid-gas surface area (Asg)
π(r sinθ)2
Volume (V)
4 3 πr 3
Liquid-gas surface area (Alg)
4πr 2
2 3 1 − cosθ + cos3θ 3 4 12 2 2πr ·(1−cosθ)
Solid-liquid surface area (Asl)
π(r sinθ)2 0
π(r sinθ)2
Solid-gas surface area (Asg)
137
πr 3
)
π(r sinθ)2 0 πr 3
(
0
)
Experimental Thermal and Fluid Science 100 (2019) 135–143
S.H. Kim et al.
) [-]
1.0 lg
Specific work of adhesion (w/
Droplet Wetting
Droplet (Eq. A5) [23] Bubble (Eq. 5)
0.8
Silicon
63
bare
0.6
Bubble de-Wetting
, ,
54
0.4
ODTS 0.2
coated
,
,
105
109 0.0
0
30
60
90
Contact angle (
120 o
150
Fig. 4. Contact angle of droplet and bubble on plain smooth surfaces (Silicon bare and ODTS coated).
180
[]
Fig. 2. Work of adhesion (droplet and bubble).
bubble contact angle, simple water pool (13 × 13 × 25 cm3 ) were prepared. The test section faced downward while an air bubble was injected upward to the test sample surface by a syringe. When an air bubble contacted the test surface, images were captured by an optical camera (Nikon 700D), from which the bubble shape and contact angle were measured. The volume (3.5 mm3) of the injected air bubble was controlled, and the rising distance was kept short to minimize the rising inertia of the air bubble. Fig. 4 shows the contact angle shape of droplet and bubble on plain surface of two kinds of wettability condition. 4. Results 4.1. Droplet contact angle on textured surfaces First, we measured the droplet contact angle on smooth surface on silicon and ODTS coated, and each samples show contact angles of 63° and 109°, respectively. (See Fig. 4) And, for the textured condition, the droplet contact angle increases with structures on the surface regardless of wettability condition. Fig. 5 summarized the droplet contact angle trend which increases on the textured surface. According to the classical Wenzel equation (Eq. (A6)), however, the contact angle of the droplet should decrease with the increase of roughness if the contact angle on a plain surface is less than 90°. This trend of increase of the contact angle
(a)
Silicon wafer
(b)
Fig. 5. Droplet contact angle on prepared samples.
PR pattern
PR coating
Etching (DRIE)
(c)
50 μm
Cleaning (Air Plasma)
(d)
50 μm
60 μm
Fig. 3. Sample preparation and micropillar structure shape: (a) Fabrication process and geometric parameter: d (diameter), g (gap) and h (height), (b) structure 1, (c) structure 2, and (d) structure 3. 138
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on the structured silicon surface has been explained by the concept of the work of adhesion, and the experimental observations of this study agree well with the prediction for Wenzel state by Kang and Jacobi. Similarly, for the ODTS-coated surface, the contact angle increased sharply on introducing the structures. This increase can be explained by the Cassie–Baxter model because the droplets partially wet the tip of the textures because of the ODTS coating. The silicon structured surface shows droplets in only the Wenzel state, and the ODTS-coated structured surface shows droplets in the Cassie–Baxter state.
• •
measured, and the general trends show good agreement with the modified bubble contact angle prediction. The ODTS-coated structured surface shows two possible states of bubble-wall interaction with a transition between them. The ODTS-coated structured surface with a roughness higher than the Wenzel limit shows a contact angle that does not agree with the prediction for any state of bubbles.
5. Discussion
4.2. Bubble contact angle on textured surfaces
In general, the bubble contact angles on the prepared textured surfaces show good agreement with the modified Kang and Jacobi prediction for bubble contact angle on textured surfaces, nonetheless, a couple of wetting behaviors mentioned above are worthy of further discussion.
Fig. 6 shows the bubble contact angle trend along the surface conditions. First, on the smooth silicon surface, the bubble contact angle (54°) was slightly less than the droplet contact angle (62°) (See Fig. 4). It is considered that the difference of the wetting environment which is humidity and size of droplet/bubble affect the slight difference. The bubble on the silicon structured surface shows decreased contact angles compared to that on the smooth silicon surface, keeping the spherical shape of the bubble. As the bubble contacts only the top of each micro structure, its wetting state is the Cassie–Baxter state. In contrast with the droplet case, the bubble Cassie-Baxter state has a liquid layer between structures, which is same as a partially dry state. The trends of contact angles on the structured surface are also consistent with the prediction for the partially dry condition (Cassie-Baxter bubble equation) (Eq. (7)). As the solid fraction decreases (here, a solid fraction of 1 indicates a smooth plain surface), the bubble contact angle decreases. This implies that the air bubble could not percolate between micropillars, as expected for the Cassie–Baxter state of bubble. In the case of the ODTS-coated surface, as shown in Fig. 6, the plain surface shows a contact angle of 105°, which is similar to the droplet contact angle on the ODTS-coated smooth surface (109°). Interestingly, the S1-3 surface allows the bubble to have two ranges of contact angles during the test. Because of the unstable wetting features, two possible wetting states of the bubble could be observed. The detailed physical reason for the two possible contact angles on each structured surface (S1-3) is discussed in the Discussion section. In short, the lower contact angles result from the metastable step of the bubble de-wetting process. First, bubbles approach and contact the tip of a cylindrical structure, maintaining the spherical shape (partially dry state). Then, the bubbles underwent a transition from the spherical shape to a hemispherical shape, and the air bubble percolated into the structures (fully dry state). Through the wetting transition, the bubble contact angle increases. The bubble contact angle before the transition were compared with the Cassie–Baxter bubble contact angle (Eq. (7)), and the contact angle after transition were compared with that for the fully dried state (Wenzel bubble contact angle; Eq. (6)), as shown in Fig. 6. These results indicate that the transition observed in this experiment can be interpreted as a transition between the Cassie–Baxter bubble state and Wenzel bubble state. In addition, structures 4 and 5, which have a high roughness ratio (or a small gap between micro pillars), show trends inconsistent with the predictions of both the Cassie–Baxter bubble state and Wenzel bubble state. According to the Wenzel bubble state prediction (Eq. (6)) for the ODTS-coated surface, the bubble contact angle decreases with the increase of roughness, and the angle becomes 0° at a roughness ratio of 2.7. The small contact angle of the Wenzel bubble state indicates that the bubble keeps the spherical shape on the structured surface. The reason for this behavior remains unclear, and the author’s interpretation is discussed in the subsequent section. The important experimental observations from this study are summarized as follows
5.1. Bubble-wall interaction transition on ODTS-coated structured surface The dual state of the Cassie–Baxter state bubble and the Wenzel state bubble has been observed on the ODTS-coated structured surface for S1-S3 (See Fig. 6), and it implies that the state transition between two states takes place in this experiment. As shown in the illustration that depicts the bubble-solid contacts of Fig. 7, the Cassie-Baxter state of bubble transits to Wenzel state of bubble with the bubble percolation between the micropillars. In addition, while the ODTS-coated structured surface triggers the wetting transition, the Si structured surface does not. Here, the evaluation of the free energy of bubbles in both states (Wenzel and Cassie–Baxter) and the possibility of transition on the prepared surfaces are discussed. Wetting transition of droplet on micropillar surface has been discussed in several literatures. [34–37] In general, the previous studies focused on the transition event of hydrophobic condition of micropillars, and it was reported that the transition was triggered by high spacing ratio ( g / d ) which increases gravitational effect against to the capillary effect which maintain the Cassie-Baxter state of droplet. According to the J. Bico [37], the wetting transition of the droplet on structured surface can be analyzed by considering the change of free energy. During the dynamic wetting/de-wetting of triple line, the minimal free energy path would determine the wetting state and contact angle of droplet. In the same context, we also applied the concept of minimal free energy to the bubble-wall interaction process to explain the transition mentioned above. The free energy (F) of a wetting bubble consists of three types of surficial energy under a constant
• The
droplet contact angles on the prepared test samples were measured, and the trends of contact angles agree well with the prediction of Kang and Jacobi. The bubble contact angles were also
Fig. 6. Bubble contact angle trend on the prepared samples. The three red hollowed rectangular □ (S1, S2, S3) are dual wetting state of the bubble. 139
Experimental Thermal and Fluid Science 100 (2019) 135–143
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C.B. state
Free energy, (F)
Initial state
=
.
5.2. Bubble contact angle prediction on surfaces with high roughness
Wenzel state of bubble
-
As the roughness of the ODTS-coated surface increases, the bubble contact angle in the Wenzel state is predicted to decrease (Eq. (6)). As shown in Fig. 6, S1-S3 produce decreasing trends of the bubble contact angle. However, in S4 and S5, which have higher roughness, the bubble contact angle is predicted to have low value (< 5°), but the measurements are inconsistent with the prediction (Eq. (6)). The zero contact angle in the Wenzel state indicates a spherical shape of the bubble, but the bubble observed here is inconsistent with both the Wenzel state contact angle and Cassie–Baxter state contact angle. First, we evaluated the limiting roughness condition for Wenzel state by the spherical shape of bubble (or droplet) based on the Wenzel state equations (Eqs. (6) and (A8)). Fig. 8 shows the Wenzel state limits depending on the contact angle of a droplet and bubble on plain smooth surface condition. In case of droplet wetting, as the contact angle approach to the 90°, the limiting roughness decrease to around 2. Since over 90° of droplet contact angle, the wetting state is expected to be Cassie-Baxter behavior, the limiting condition of droplet was evaluated below 90°. For the bubble case, as it has opposite behavior, the Wenzel limiting condition of bubble has been evaluated between 90° and 135°. All the experimental cases were compared under the limiting trend. The only S4 and S5 of bubble are over the limiting condition of Wenzel state. And, the two cases couldn’t produce proper matches with any modeled values in this study. It is unclear yet that the unpredictable wetting state over Wenzel wetting limit. In order to figure out how the bubble on the high roughness condition can’t be modeled based on the Kang and Jacobi principle, we considered the pressure at the triple line as the roughness increases. Fig. 9 shows the bubble de-wetting feature (on ODTS condition) as the roughness condition increases to the limiting condition (r ∼ 2.75) in terms of contact angle and curvature near the triple line and corresponding capillary pressure. As the roughness increases, the radius of interface curvature near the triple line decrease and the liquidgas interface approaching to tip of the micropillars. First, the decreased radius of interface curvature affects the capillary pressure at the tripe line, and it triggers high interfacial stress on high roughness condition. In addition, the liquid-gas interface which becomes closed to the tip of the micro pillars may have intermittent contacting opportunity and trigger wetting state change. Here, it is conjectured that the highly stressed liquid-gas interface and the close condition between the interface and structures cause the failure of the contact angle prediction based on the Kang and Jacobi analysis. In addition, the upward buoyancy force of the bubble supports the unstable interfacial behavior, which may result in the collapse of the liquid-gas interface on the high-roughness surfaces (S4 and S5). Moreover, we consider that the bubble may have a mixed wetting state (Wenzel and Cassie–Baxter), with both liquid and air between structures. The exact limiting condition and physical mechanism remain unclear, and further discussion is required with sensitive imaging technique.
< >
ODTS coated on S2
Liquid trapped on struc structures tures
Transition Tran Tr n
Bubble wetting process & state Fig. 7. Wetting (De-wetting) state transition of bubble on the ODTS-coated surface (S1-3).
temperature and pressure:
F = σlg Alg + σsl Asl + σsg Asg .
(8)
By calculating the energy change (ΔF = FC . B−FWenzel ) through the transition, the possibility of transition is discussed here. Positive quantities of energy change (ΔF ) indicate a lower energy condition in the Wenzel state, and transition is possible. The Young’s relation can express the free energy as follows:
F = σlg Alg + σsl Asl + (σlg cosθY −σsl ) Asg .
(9)
The three types of interfacial area can be obtained from Tables 1 and 2. Here, the roughness and solid fraction of the structured surface are required to reflect the bubble state condition. The liquid-gas interfacial tension (σlg ) is a known property value, and only the solidliquid interfacial tension (σsg ) is unknown in the above relation. The free energy can be expressed in terms of the two properties as follows:
F = σlg (Alg + Asg cosθY ) + σsl (Asl −Asg ).
(10)
Since both the known (σlg ) and unknown (σsg ) properties are constant in any wetting state, the change of the two parentheses can give us the sign determinant of the free energy. If the values in the two parentheses show a positive change from the Cassie–Baxter to Wenzel condition, the free energy would increase. If both values are negative, the free energy should decrease. Table 3 summarizes the change of the two values in the parentheses (Eq. (10)) by assuming the initial bubble size a 1 (no units). In the ODTS-coated structured surface, both values show a positive change, indicating a lower free energy in the Wenzel state of the bubble. However, the silicon structured surface shows a negative value of the free-energy change, implying that there is no physical possibility for the wetting-state transition. According to the above wetting analysis, the lowest energy state in the ODTS-coated cases is the fully dry condition. However, this result does not explain whether the wetting process must have a metastable state. The physical reason for the metastable state’s occurrence in ODTS-coated condition remains unclear. The author conjectures that the rising bubble has a very small upward inertia in the experiments; consequently, the liquid-gas interface cannot percolate the structures. To cause a receding wetting condition on the structures with the rising air bubble, a sufficient kinetic energy is required at the triple line. In addition, Fig. 6 shows that the contact angles of the metastable state (Cassie–Baxter) are somewhat lower than the prediction and show a significant fluctuation. This implies that the wetting state of the bubble is in a locally mixed condition. In general, the metastable states show a fluctuating behavior, and it would transition to a lower-energy state through environmental perturbation.
6. Conclusion In this study, the wetting features of bubbles on micro-structured Table 2 Test sample set (surface morphology).
140
Parameter
Diameter (d )
Pitch (d + g )
Height (h )
Roughness (r )
Solid Fraction (ϕ )
Structure Structure Structure Structure Structure
20 20 40 20 10
40 60 60 25 15
20 20 20 20 20
1.7854 1.3491 1.6981 3.0106 3.7925
0.1963 0.0873 0.3491 0.5027 0.3491
1 2 3 4 5
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Table 3 Free-energy change between the Cassie-Baxter and Wenzel state. Structure 1
Si ODTS
Structure 2
Structure 3
Alv + cosθAsv
Asl −Asv
Alv + cosθAsv
Asl −Asv
Alv + cosθAsv
Asl −Asv
−0.021 4.787
−0.939 15.666
−0.003 5.75
−0.375 4.25
−0.066 4.553
−1.607 5.272
through bubble captive tests. The previous model of droplet contact angle was modified for application to bubble-wall interaction event. The modified prediction of the bubble contact angle on smooth and textured surfaces has been validated through experimental observation using test surfaces prepared with a micro-fabrication technique and coating. Generally, the test results show good agreement with the modified bubble contact angle prediction based on the Kang and Jacobi analysis. On the Si structured surfaces, the bubble is in a Cassie–Baxter state, in which liquid exists between structures. On hydrophobic structured surfaces, however, the bubble is in both the Cassie–Baxter state and Wenzel state, producing two ranges of contact angles. This dual state of bubble-wall interaction has been discussed through the wetting transition process in terms of the free energy analysis. In addition, the wetting characteristics of bubbles on high roughed structured surface have been discussed. When the roughness is greater than the critical condition for the modified contact angle prediction, the contact angle of bubble couldn’t be predicted based on either state of wetting. Here, it was conjectured that the failure of contact angle prediction over the Wenzel wetting state limit attributes to the increased capillary pressure and liquid-gas interface shape near the triple line. It is expected that this study may contribute to the basic understanding of bubble-wall interaction events in various thermal-fluidic engineering field.
Fig. 8. The limiting condition of roughness for Wenzel state (droplet and bubble). The squares are the experimental condition of this study and the hollowed rectangular □ (Bubble contact angle of S4 and S5 on ODTS coated surface) are over the limiting condition.
Conflict of interest The authors declare no competing financial interest.
Acknowledgment This research was supported by National Research Foundation of Korea (NRF), South Korea grants funded by Korean government (MSIP) (NRF-2015M2A8A2074795, 2016R1A6A3A03008942). The major author is working at Chinese Academy of Science, Institute of Engineering Thermophysics (Beijing) from 2016 Oct. now, and this experiments and discussion were carried out in POSTECH.
Fig. 9. Bubble shape and wetting characteristics under a high roughness.
surfaces have been analytically predicted and experimentally observed Appendix A A.1. Droplet contact angle (review of the analysis of Kang and Jacobi [23]) Kang and Jacobi [23] explained how the surface morphology affects the wettability of liquid droplets on solids by introducing the work of adhesion. First, they considered the process of dosing a droplet slowly on an ideal surface, as shown in Fig. 1(a). By adopting the additional work of adhesion during the wetting process (state 1 → state 2) and several basic assumptions, they could predict the contact angle of a water droplet on a textured surface. As a key concept of their study, the work of adhesion is an additional surface energy change during the wetting process. The
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assumptions in the wetting of ideal surfaces are as follows: the surface energy dominates the process, the surface is homogeneous, there is no contactangle hysteresis, the line tension is negligible, all body forces are negligible, electromagnetic forces are negligible, the liquid does not diffuse into the solid, and all properties are constant. Under the above assumptions, they calculated the following three conservation equations and one interface area constraint:
ρV1 = ρV2,
(Mass conservation)
σsg−σsl = σlg cosθY ,
(A1)
(Force relation: Young's equation [16])
(A2)
σlg Alg,1 + σsg Asg,1 = (σlg Alg,2 + σsg Asg,2 ) + w·Asl,2 . (Energy conservation)
(A3)
The parameter w is the work of adhesion per unit solid-liquid contact area, and it has the same units as surface tension. The work of adhesion changes with respect to an intrinsic feature of the solid-liquid pair and the geometric conditions of the solid surface. The solid-gas interfacial area (Asg,1 ) in the initial state of surface energy between the solid and gas is the same as the solid-liquid interfacial area (Asl,1 ) on the bottom of the liquid droplet in the final state:
Asg,1 = Asl,2 .
(A4)
The parameter w/ σlg is the work of adhesion for the liquid-gas surface tension, termed the “specific work of adhesion” in the previous study. By solving the energy conservation (Eq. (A3)) with the geometric relation between a liquid droplet and spherical cap in Table 1, the specific work of adhesion along the contact angle can be evaluated as follows [23]:
4
w = cosθY + σlg
(
(2 + cosθY )(1 − cosθY )2 4
)
2/3
−2(1−cosθY )
sin2θ
(A5)
On adopting the specific work of adhesion (A5) in the energy conservation equation (A3), the contact angle of a droplet on various textured surfaces can be calculated by a simple iterative method. They analyzed two types of wetting states on a textured surface: the fully wetted state (Wenzel model) and partially wetted state (Cassie–Baxter model). In the case of a fully wetted droplet on a rough surface, the contact area of the droplet increases with the area ratio (roughness, r), which is the ratio of the solid-liquid contact area to the solid-liquid interfacial area projected on the solid plane:
As' = r·As .
(A6)
The wetted solid surface area is increased by roughness. Thus, energy conservation for the textured surface in the process of full wetting should consider the enlarged area as follows:
σlg Alg,1 + σsg A' sg,1 = (σlg A'lg,2 + r·σsg A' sg,2 ) + r·w·A' sl,2 .
(A7)
By solving the above energy relation with the work of adhesion (Eq. (A5)) and Table 1, the apparent contact angle on the textured surface under the full wetting condition can be expressed as follows:
1−cosθD, W −2 ⎛ ⎝
(2 + cosθD, W )(1 − cosθD, W )2/3) ⎞ 4
⎠ = r·
sin2θD, W
1−cosθ−2
(
(2 + cosθY )(1 − cosθY )2/3) 4
sin2θY
).
(A8)
Here, θD, W is the apparent droplet contact angle of the rough surface under Wenzel state, and the solution shows trends different from those of the classical apparent contact angle prediction, which is based on the Wenzel equation [17]:
cosθD, W = r·cosθY .
(A9)
According to the Wenzel equation, the apparent contact angle on a rough surface increases with the roughness ratio if the contact angle on a smooth surface is greater than the 90°. While the Wenzel equation indicates that the critical contact angle is 90°, the Kang and Jacobi approach (Eq. (A8)) indicates that the critical contact angle is approximately 48°, which is the peak point for the work of adhesion, and You et al. modified the critical condition (∼43°) through analytical and experimental test [38]. In the case of a partially wetted droplet on a textured surface, the liquid-solid contact area decreases with the decrease of the solid fraction (ϕ ), which is the ratio between the top-facing area of structures and the projected area. As the solid fraction of the surface is changed from 1 to 0, the wetted solid surface area is decreased. Thus, the energy conservation for a textured surface in the partial wetting process is as follows:
σlg Alg,1 + ϕ·σsv A' sv,1 = (σlg A'lg,2 + (1−ϕ)·σlg A' sl,2 + ϕ·σsl A' sl,2 ) + ϕ·w·A' sl,2 .
(A10)
By solving the above energy relation with the work of adhesion (Eq. (A5)) and Table 1, the apparent contact angle on a textured surface under the partial wetting condition can be expressed as follows:
1−cosθD, C −2 ⎛ ⎝
(2 + cosθD, C )(1 − cosθD, C )2/3) ⎞ 4
sin2θD, C
⎠ = ϕ·
1−cosθ−2
(
(2 + cosθY )(1 − cosθY )2/3) 4
sin2θ
) − 1 (1−ϕ). 2
(A11)
The above equation (Eq. (A11)) agrees well with the prediction of the Cassie–Baxter model.
[2] Z. Lan, X.H. Ma, X.D. Zhou, M.Z. Wang, Theoretical study of dropwise condensation heat transfer: effect of the liquid-solid surface free energy difference, J. Enhanc. Heat Transf. 16 (1) (2009) 61–71. [3] S.S. Beaini, V.P. Carey, Strategies for developing surfaces to enhance dropwise condensation: exploring contact angles, droplet sizes, and pattern surfaces, J.
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Wetting characteristic of bubble on micro-pillar structured surface under a water pool
T
⁎
Seol Ha Kima, Hyun Sun Parka, , Donggun Kob, Moo Hwan Kima a b
Division of Advanced Nuclear Engineering, POSTECH, Pohang 790-784, Republic of Korea Department of Mechanical Engineering, POSTECH, Pohang 790-784, Republic of Korea
A R T I C LE I N FO
A B S T R A C T
Keywords: Contact angle Bubble Droplet Work of adhesion
In this study, the contact angle of air bubbles on a micro-structured surface under a water pool is experimentally investigated. A previous study “Kang and Jacobi, Equilibrium Contact Angles of Liquids on Ideal Rough Surfaces, Langmuir (2011)” adopted the work of adhesion as the additional work of the process of droplet contact on a textured surface, and it explained the reason for failure of the classical theoretical model (Wenzel equation) in real wetting tests. We extended the above concept to bubble interaction with the textured surface. First, the bubble contact angles on the textured surface were modeled based on the concept of the work of adhesion in the free energy calculation. Second, the contact angle of air bubbles was measured on the bottom of test surfaces under a water pool. The test-section surfaces have micro-pillars with a size of 5–40 μm prepared by the microelectromechanical systems (MEMS) technique. The bubble contact angles were compared with both the modeled bubble shape and classical prediction (Wenzel & Cassie–Baxter equations). In addition, detail wetting features which shows wetting transition and critical wetting behavior of bubble were discussed.
1. Introduction Since the wetting of droplets and bubbles on a solid surface plays dominant role in various liquid-vapor-solid physical systems, the wetting characteristics have attracted tremendous interest in not only fundamental research but also many industrial applications such as oil recovery, lubrication, liquid coating, printing, and spray quenching. The understanding of droplet wetting also provides insight into the heat transfer of the liquid-vapor phase change in cases of a droplet on a heating/cooling surface, and the cooling performance of condensation and spray cooling have been directly attributed to the wetting features [1–6]. In other hand, the wetting feature with bubble also plays an important role in bubble-wall interaction processes (e.g., material flotation, fluidized bed, and particle sedimentation). For instance, nucleate boiling, which is applied in various energy conversion process (e.g., nuclear power plants, electronic cooling devices, and air-conditioning), strongly depends on the bubble behavior [7–15]. In general, the wetting of droplets and bubbles on a solid surface can be characterized by the contact angle (θ), which indicates the surfaceenergy state of the rigid solid. The contact angle at the triple line, where the three phase (liquid, gas and solid) coexist, results from the balance of the surface tension between the two phases (Young’s relation) on an ideal smooth surface as follows [16].: ⁎
σsg−σsl = σlg cosθ .
(1)
Recently, numerous textured surfaces have been introduced to modify the wetting physics (contact angle). For textured surfaces with nano- and micro-scale morphologies, droplets meet two types of wetting states: the Wenzel state and Cassie–Baxter state, which correspond to a fully wetted state and partially wetted state, respectively [17,18]. Such textured surfaces can yield extreme wetting conditions such as superhydrophilic (θ < 10°) and superhydrophobic (θ > 160°). For a long time, these contact angles on various textured surfaces have been evaluated based on the Wenzel and Cassie–Baxter model. However, numerous inconsistencies with this classical model have been reported [19–22]. For example, the Wenzel model frequently failed to explain the droplet contact angle on textured surfaces when the intrinsic contact angle, which is the contact angle without roughened condition, is less than 90°. Recently, Kang and Jacobi [23] proposed a modification to the classical model that introduces the work of adhesion between the liquid droplet and surface, and it explains successfully the droplet contact angles on textured surfaces. Compared with the droplet wetting analysis, wetting feature with bubble has been studied less extensively. Because it was considered that the basic principle of determining the wetting shape and dynamics in terms of surface energy analysis are not different regardless of the
Corresponding author. E-mail addresses: fi[email protected] (S.H. Kim), [email protected] (H.S. Park), [email protected] (D. Ko), [email protected] (M.H. Kim).
https://doi.org/10.1016/j.expthermflusci.2018.09.001 Received 3 May 2018; Received in revised form 30 July 2018; Accepted 2 September 2018 Available online 04 September 2018 0894-1777/ © 2018 Elsevier Inc. All rights reserved.
Experimental Thermal and Fluid Science 100 (2019) 135–143
S.H. Kim et al.
σ θ ϕ
Nomenclature V A w r F d g h
volume [m3] area [m2] work of adhesion [N/m] roughness [–] Helmholtz Free Energy [J] diameter [m] gap [m] height [m]
Subscripts l g s Y D B
Greek symbols ρ
surface tension [N/m] contact angle [°] solid fraction [–]
liquid gas solid Young’s relation droplet bubble
density [kg/m3]
phases (droplet and bubble), relatively less test and discussion of the bubble-wall interaction have been performed. However, it can be applicable only if the wetting process follows the quasi-equilibrium process, which is a relatively slow interaction. In the bubble-wall contacting condition, the surrounding fluid which has relatively much high density and viscosity than drop-air condition can have an influence on the adhesion process or dynamic wetting process of bubble-wall interaction. According to the author’s literature survey and understand, only a couple of studies about the bubble contact angle varying the bubble size and related properties has been reported. [24,25]. In general, bubble contact angle (θB ) on a flat surface can be estimated by Young’s equations, and it can be measured by the captive bubble method (sessile bubble method) [26], that a bubble of air is injected on downwardfacing solid surface, instead of placing a drop on the solid as in the case of the sessile drop method [27–29]. It was reported that there are different fluctuation in contact angle between droplet bubble on rough surfaces, depending on the captive bubble method and sessile drop method. [30]. Additionally, bubble size and contact angle also have an influence on the air bubble/aqueous phase/paraffin system, and it was proposed to modify the Young’s equations with the line-tension to predict the dynamic contact angle (See Eq. (2)) [31]. This modified equation is applicable to homogeneous, rigid, flat, horizontal, and smooth solid surfaces, and it is expressed as follows:
σsg−σsl = σlg cosθ +
σslg r
.
(2)
where σslg is the line tension: the excess free energy in the region of the triple interface. Drelich et al. also showed that the surface roughness and heterogeneity strongly influence the dynamic contact angle and bubble size, particularly the receding contact angle [32]. As mentioned above, several researchers have studied the fundamentals of wetting features (static/dynamic) for various surface conditions and fluidic environmental conditions. In this study, in order to evaluate the bubble contact angle on designed micro-pillar structured surface in terms of wetting transition and prediction model applicability, simple bubble captive method of experimental work has been performed. For the experiments, textured surfaces were prepared by the microelectromechanical system (MEMS) technique and a coating method. The air bubble contact angles were measured by the captive bubble method and the results were compared with the modified Kang & Jacobi work for bubble-wall interaction. This study on bubble interfacial phenomena may give a fundamental picture of the bubble–wall interaction and the relevant applications. 2. Modeling of bubble contact angle We are going to derive the bubble contact angle on textured surface based on the Kang and Jacobi’s work [23], which is briefly reviewed in
(a) Droplet wetting State 2
State 1 Air
Liquid
(b) Bubble de-wetting
Air
Liquid
Fig. 1. Modeling of wetting by (a) a droplet and (b) a bubble. 136
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S.H. Kim et al.
Appendix A. According to the Kang and Jacobi model, the apparent contact angle of a droplet on a textured surface could be predicted depending on its wetting state (Wenzel or Cassie-Baxter), adopting the work of adhesion concept. The work of adhesion is the additional energy consumed during the wetting or dewetting process. Here, the previous work was modified to predict the bubble contact angle depending on the wetting state of bubble. We would like to adopt the classical wetting states (Wenzel state and Cassie-Baxter states) to bubble-oriented points. In other words, Wenzel state of bubble is fully dried and Cassie-Baxter state of bubble is partially dried on tip of micropillars. As shown in Fig. 1, the bubble-wall interaction process has a directional movement opposite to that in the above theory for droplets. Because of the buoyancy of an air bubble in a liquid pool, the de-wetting process with the bubble on the surface involves the upward motion of the bubble. In addition, since the spherical object and spherical cap are changed from liquid, for droplet wetting, to air (gas), for bubble dewetting, the geometric relation (volume and area) of the contact angle should be modified. The geometric information of a bubble system is summarized in the Table 1. On solving the mass and energy conservation equations, the specific work of adhesion during the bubble dewetting process can be derived, as in the droplet wetting analysis (see Appendix A).
ρV1, g = ρV2, g ,
(Mass)
4 =
(
(2 − cosθY )(1 + cosθY )2 4
)
(Energy)
−cosθY .
= ϕ·
(2 − cosθY )(1 + cosθY )2/3) 4
sin2θY
) − 1 (1−ϕ).
(7)
2
3.1. Sample preparation A set of textured surfaces were prepared by etching polished silicon wafers by the MEMS technique. Two types of surface energy, which determines wettability, were obtained by the chemical coating of a selfassembled monolayer (SAM), and six types of surface morphologies were achieved by deep reactive ion etching (DRIE). In order to etch with local selectivity, a photoresist (PR, AZ-1512) was coated with its own specific patterns. The coated PR was chemically stabilized (PR developing: 300 MIF Developer). The uncovered area was etched to 20μm depth by the DRIE process, and the covered silicon area was protected from the etching. After the etching process, all chemicals on the surface were removed through air Plasma process (see Fig. 3a). Six types of surface morphologies including a smooth surface were designed, and 2 sets of test sample (12 samples) were prepared. After the etching process, one set of samples (6 samples) was coated with octadecyltrichlorosilane (ODTS) by the SAM method. [33] Since the SAM method coats the surface uniformly with a monolayer of organics, which is only a few nanometers in thickness, this coating does not allow any additional roughness of the test surface. Finally, two types of chemistry groups (bare Si and ODTS-coated) were prepared. Therefore, in total, 12 test samples were used in this experiment. Table 1 summarizes the design configuration of the test samples, as well as their roughness and solid fraction. Fig. 3 shows scanning electron microscopy (SEM) images of the test samples. In general, the test samples have micro-scale (5–40 μm) cylindrical structures, and the height of the structures are designed to be 20 µm. In this study, the geometric morphologies of the test samples are measured by a 3D profiler. The experimental results are described based on the measured value. The prepared textured surface has a range of roughness which is πdh a ratio between actual area and projected area (r = 1 + 2 , 1−3.7 )
(4)
−2(1 + cosθY )
(5)
The specific work of adhesion of bubble de-wetting shows trends opposite to those for liquid droplet wetting along the surface contact angle, as shown in Fig. 2. As mentioned above, in bubble de-wetting on a surface, three types of wetting can be considered: de-wetting on an ideal smooth surface, a fully dry bubble (here, called Wenzel bubble) on a textured surface, and a partially dry (Cassie-Baxter bubble) bubble on a textured surface. In the case of the fully dry state, the dry area between air and the solid increases with the roughness, which is area fraction between actual area and projected area. Thus, by solving the modified energy conservation equation for the bubble, the apparent contact angle on a rough surface can be predicted as follows:
1−cosθB, W −2 ⎛ ⎝
(
3. Experiments
2/3
(Work of adhesion for bubbles)
⎠
1 + cosθY −2
sin2 θY
Bubble
(2 − cosθB, C )(1 + cosθB, C )2/3) ⎞ 4
sin2θB, C
(3)
σlg Alg,1 + σsl Asl,1 = (σlg Alg,2 + σsl Asl,2 ) + w·Asg,2 ,
w σlg
1 + cosθB, C −2 ⎛ ⎝
(d + g )
and (ϕ =
solid πd2 4(d + g )
fraction
that
is
area portion of micropillar top 2 , 0.08−0.51), where d , g and h are the diameter and gap and
height of the micro pillar structure.
(2 − cosθB, W )(1 + cosθB, W )2/3) ⎞ 4
3.2. Contact angle measurement
⎠
sin2θB, W 1−cosθY −2 = r·
(
(2 − cosθY )(1 + cosθY )2/3) 4
sin2θY
).
First, we measured the droplet contact angle with a controlled volume of D.I. water (3 µL, Room temperature) on the prepared test samples. On the each samples, three or four times of measurements have been carried out and averaged. Second, in order to measure the
(6)
According to above equation, the critical contact angle under the fully dry condition is 136°, which is the peak of the work of adhesion for bubble de-wetting. This result indicates that only a highly hydrophobic surface (θ > 136°) can cause the bubble contact angle to increase with the roughness. In other words, under the fully dry condition, for most textured surfaces, the bubble contact angle decreases with the increase of roughness. While the contact angle of a liquid droplet usually increases with the roughness, the bubble contact angle decreases. In the case of the partially dried state, the dry area between air and the solid decreases with the decrease of the solid fraction. In the same manner as for the fully dry state, by solving the modified energy conservation equation for a bubble, the apparent contact angle on a rough surface can be predicted with respect to the solid fraction, which is area fraction between bubble (or droplet) contacted area and projected area, as follows:
Table 1 Geometric information on a spherical droplet and bubble on a surface. Parameter Droplet
Bubble
Spherical
Spherical cap
Volume (V)
4 3 πr 3
Liquid-gas surface area (Alg)
4πr 2
2 3 1 + cosθ− cos3θ 3 4 12 2 2πr ·(1 + cosθ)
(
Solid-liquid surface area (Asl)
0
Solid-gas surface area (Asg)
π(r sinθ)2
Volume (V)
4 3 πr 3
Liquid-gas surface area (Alg)
4πr 2
2 3 1 − cosθ + cos3θ 3 4 12 2 2πr ·(1−cosθ)
Solid-liquid surface area (Asl)
π(r sinθ)2 0
π(r sinθ)2
Solid-gas surface area (Asg)
137
πr 3
)
π(r sinθ)2 0 πr 3
(
0
)
Experimental Thermal and Fluid Science 100 (2019) 135–143
S.H. Kim et al.
) [-]
1.0 lg
Specific work of adhesion (w/
Droplet Wetting
Droplet (Eq. A5) [23] Bubble (Eq. 5)
0.8
Silicon
63
bare
0.6
Bubble de-Wetting
, ,
54
0.4
ODTS 0.2
coated
,
,
105
109 0.0
0
30
60
90
Contact angle (
120 o
150
Fig. 4. Contact angle of droplet and bubble on plain smooth surfaces (Silicon bare and ODTS coated).
180
[]
Fig. 2. Work of adhesion (droplet and bubble).
bubble contact angle, simple water pool (13 × 13 × 25 cm3 ) were prepared. The test section faced downward while an air bubble was injected upward to the test sample surface by a syringe. When an air bubble contacted the test surface, images were captured by an optical camera (Nikon 700D), from which the bubble shape and contact angle were measured. The volume (3.5 mm3) of the injected air bubble was controlled, and the rising distance was kept short to minimize the rising inertia of the air bubble. Fig. 4 shows the contact angle shape of droplet and bubble on plain surface of two kinds of wettability condition. 4. Results 4.1. Droplet contact angle on textured surfaces First, we measured the droplet contact angle on smooth surface on silicon and ODTS coated, and each samples show contact angles of 63° and 109°, respectively. (See Fig. 4) And, for the textured condition, the droplet contact angle increases with structures on the surface regardless of wettability condition. Fig. 5 summarized the droplet contact angle trend which increases on the textured surface. According to the classical Wenzel equation (Eq. (A6)), however, the contact angle of the droplet should decrease with the increase of roughness if the contact angle on a plain surface is less than 90°. This trend of increase of the contact angle
(a)
Silicon wafer
(b)
Fig. 5. Droplet contact angle on prepared samples.
PR pattern
PR coating
Etching (DRIE)
(c)
50 μm
Cleaning (Air Plasma)
(d)
50 μm
60 μm
Fig. 3. Sample preparation and micropillar structure shape: (a) Fabrication process and geometric parameter: d (diameter), g (gap) and h (height), (b) structure 1, (c) structure 2, and (d) structure 3. 138
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on the structured silicon surface has been explained by the concept of the work of adhesion, and the experimental observations of this study agree well with the prediction for Wenzel state by Kang and Jacobi. Similarly, for the ODTS-coated surface, the contact angle increased sharply on introducing the structures. This increase can be explained by the Cassie–Baxter model because the droplets partially wet the tip of the textures because of the ODTS coating. The silicon structured surface shows droplets in only the Wenzel state, and the ODTS-coated structured surface shows droplets in the Cassie–Baxter state.
• •
measured, and the general trends show good agreement with the modified bubble contact angle prediction. The ODTS-coated structured surface shows two possible states of bubble-wall interaction with a transition between them. The ODTS-coated structured surface with a roughness higher than the Wenzel limit shows a contact angle that does not agree with the prediction for any state of bubbles.
5. Discussion
4.2. Bubble contact angle on textured surfaces
In general, the bubble contact angles on the prepared textured surfaces show good agreement with the modified Kang and Jacobi prediction for bubble contact angle on textured surfaces, nonetheless, a couple of wetting behaviors mentioned above are worthy of further discussion.
Fig. 6 shows the bubble contact angle trend along the surface conditions. First, on the smooth silicon surface, the bubble contact angle (54°) was slightly less than the droplet contact angle (62°) (See Fig. 4). It is considered that the difference of the wetting environment which is humidity and size of droplet/bubble affect the slight difference. The bubble on the silicon structured surface shows decreased contact angles compared to that on the smooth silicon surface, keeping the spherical shape of the bubble. As the bubble contacts only the top of each micro structure, its wetting state is the Cassie–Baxter state. In contrast with the droplet case, the bubble Cassie-Baxter state has a liquid layer between structures, which is same as a partially dry state. The trends of contact angles on the structured surface are also consistent with the prediction for the partially dry condition (Cassie-Baxter bubble equation) (Eq. (7)). As the solid fraction decreases (here, a solid fraction of 1 indicates a smooth plain surface), the bubble contact angle decreases. This implies that the air bubble could not percolate between micropillars, as expected for the Cassie–Baxter state of bubble. In the case of the ODTS-coated surface, as shown in Fig. 6, the plain surface shows a contact angle of 105°, which is similar to the droplet contact angle on the ODTS-coated smooth surface (109°). Interestingly, the S1-3 surface allows the bubble to have two ranges of contact angles during the test. Because of the unstable wetting features, two possible wetting states of the bubble could be observed. The detailed physical reason for the two possible contact angles on each structured surface (S1-3) is discussed in the Discussion section. In short, the lower contact angles result from the metastable step of the bubble de-wetting process. First, bubbles approach and contact the tip of a cylindrical structure, maintaining the spherical shape (partially dry state). Then, the bubbles underwent a transition from the spherical shape to a hemispherical shape, and the air bubble percolated into the structures (fully dry state). Through the wetting transition, the bubble contact angle increases. The bubble contact angle before the transition were compared with the Cassie–Baxter bubble contact angle (Eq. (7)), and the contact angle after transition were compared with that for the fully dried state (Wenzel bubble contact angle; Eq. (6)), as shown in Fig. 6. These results indicate that the transition observed in this experiment can be interpreted as a transition between the Cassie–Baxter bubble state and Wenzel bubble state. In addition, structures 4 and 5, which have a high roughness ratio (or a small gap between micro pillars), show trends inconsistent with the predictions of both the Cassie–Baxter bubble state and Wenzel bubble state. According to the Wenzel bubble state prediction (Eq. (6)) for the ODTS-coated surface, the bubble contact angle decreases with the increase of roughness, and the angle becomes 0° at a roughness ratio of 2.7. The small contact angle of the Wenzel bubble state indicates that the bubble keeps the spherical shape on the structured surface. The reason for this behavior remains unclear, and the author’s interpretation is discussed in the subsequent section. The important experimental observations from this study are summarized as follows
5.1. Bubble-wall interaction transition on ODTS-coated structured surface The dual state of the Cassie–Baxter state bubble and the Wenzel state bubble has been observed on the ODTS-coated structured surface for S1-S3 (See Fig. 6), and it implies that the state transition between two states takes place in this experiment. As shown in the illustration that depicts the bubble-solid contacts of Fig. 7, the Cassie-Baxter state of bubble transits to Wenzel state of bubble with the bubble percolation between the micropillars. In addition, while the ODTS-coated structured surface triggers the wetting transition, the Si structured surface does not. Here, the evaluation of the free energy of bubbles in both states (Wenzel and Cassie–Baxter) and the possibility of transition on the prepared surfaces are discussed. Wetting transition of droplet on micropillar surface has been discussed in several literatures. [34–37] In general, the previous studies focused on the transition event of hydrophobic condition of micropillars, and it was reported that the transition was triggered by high spacing ratio ( g / d ) which increases gravitational effect against to the capillary effect which maintain the Cassie-Baxter state of droplet. According to the J. Bico [37], the wetting transition of the droplet on structured surface can be analyzed by considering the change of free energy. During the dynamic wetting/de-wetting of triple line, the minimal free energy path would determine the wetting state and contact angle of droplet. In the same context, we also applied the concept of minimal free energy to the bubble-wall interaction process to explain the transition mentioned above. The free energy (F) of a wetting bubble consists of three types of surficial energy under a constant
• The
droplet contact angles on the prepared test samples were measured, and the trends of contact angles agree well with the prediction of Kang and Jacobi. The bubble contact angles were also
Fig. 6. Bubble contact angle trend on the prepared samples. The three red hollowed rectangular □ (S1, S2, S3) are dual wetting state of the bubble. 139
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C.B. state
Free energy, (F)
Initial state
=
.
5.2. Bubble contact angle prediction on surfaces with high roughness
Wenzel state of bubble
-
As the roughness of the ODTS-coated surface increases, the bubble contact angle in the Wenzel state is predicted to decrease (Eq. (6)). As shown in Fig. 6, S1-S3 produce decreasing trends of the bubble contact angle. However, in S4 and S5, which have higher roughness, the bubble contact angle is predicted to have low value (< 5°), but the measurements are inconsistent with the prediction (Eq. (6)). The zero contact angle in the Wenzel state indicates a spherical shape of the bubble, but the bubble observed here is inconsistent with both the Wenzel state contact angle and Cassie–Baxter state contact angle. First, we evaluated the limiting roughness condition for Wenzel state by the spherical shape of bubble (or droplet) based on the Wenzel state equations (Eqs. (6) and (A8)). Fig. 8 shows the Wenzel state limits depending on the contact angle of a droplet and bubble on plain smooth surface condition. In case of droplet wetting, as the contact angle approach to the 90°, the limiting roughness decrease to around 2. Since over 90° of droplet contact angle, the wetting state is expected to be Cassie-Baxter behavior, the limiting condition of droplet was evaluated below 90°. For the bubble case, as it has opposite behavior, the Wenzel limiting condition of bubble has been evaluated between 90° and 135°. All the experimental cases were compared under the limiting trend. The only S4 and S5 of bubble are over the limiting condition of Wenzel state. And, the two cases couldn’t produce proper matches with any modeled values in this study. It is unclear yet that the unpredictable wetting state over Wenzel wetting limit. In order to figure out how the bubble on the high roughness condition can’t be modeled based on the Kang and Jacobi principle, we considered the pressure at the triple line as the roughness increases. Fig. 9 shows the bubble de-wetting feature (on ODTS condition) as the roughness condition increases to the limiting condition (r ∼ 2.75) in terms of contact angle and curvature near the triple line and corresponding capillary pressure. As the roughness increases, the radius of interface curvature near the triple line decrease and the liquidgas interface approaching to tip of the micropillars. First, the decreased radius of interface curvature affects the capillary pressure at the tripe line, and it triggers high interfacial stress on high roughness condition. In addition, the liquid-gas interface which becomes closed to the tip of the micro pillars may have intermittent contacting opportunity and trigger wetting state change. Here, it is conjectured that the highly stressed liquid-gas interface and the close condition between the interface and structures cause the failure of the contact angle prediction based on the Kang and Jacobi analysis. In addition, the upward buoyancy force of the bubble supports the unstable interfacial behavior, which may result in the collapse of the liquid-gas interface on the high-roughness surfaces (S4 and S5). Moreover, we consider that the bubble may have a mixed wetting state (Wenzel and Cassie–Baxter), with both liquid and air between structures. The exact limiting condition and physical mechanism remain unclear, and further discussion is required with sensitive imaging technique.
< >
ODTS coated on S2
Liquid trapped on struc structures tures
Transition Tran Tr n
Bubble wetting process & state Fig. 7. Wetting (De-wetting) state transition of bubble on the ODTS-coated surface (S1-3).
temperature and pressure:
F = σlg Alg + σsl Asl + σsg Asg .
(8)
By calculating the energy change (ΔF = FC . B−FWenzel ) through the transition, the possibility of transition is discussed here. Positive quantities of energy change (ΔF ) indicate a lower energy condition in the Wenzel state, and transition is possible. The Young’s relation can express the free energy as follows:
F = σlg Alg + σsl Asl + (σlg cosθY −σsl ) Asg .
(9)
The three types of interfacial area can be obtained from Tables 1 and 2. Here, the roughness and solid fraction of the structured surface are required to reflect the bubble state condition. The liquid-gas interfacial tension (σlg ) is a known property value, and only the solidliquid interfacial tension (σsg ) is unknown in the above relation. The free energy can be expressed in terms of the two properties as follows:
F = σlg (Alg + Asg cosθY ) + σsl (Asl −Asg ).
(10)
Since both the known (σlg ) and unknown (σsg ) properties are constant in any wetting state, the change of the two parentheses can give us the sign determinant of the free energy. If the values in the two parentheses show a positive change from the Cassie–Baxter to Wenzel condition, the free energy would increase. If both values are negative, the free energy should decrease. Table 3 summarizes the change of the two values in the parentheses (Eq. (10)) by assuming the initial bubble size a 1 (no units). In the ODTS-coated structured surface, both values show a positive change, indicating a lower free energy in the Wenzel state of the bubble. However, the silicon structured surface shows a negative value of the free-energy change, implying that there is no physical possibility for the wetting-state transition. According to the above wetting analysis, the lowest energy state in the ODTS-coated cases is the fully dry condition. However, this result does not explain whether the wetting process must have a metastable state. The physical reason for the metastable state’s occurrence in ODTS-coated condition remains unclear. The author conjectures that the rising bubble has a very small upward inertia in the experiments; consequently, the liquid-gas interface cannot percolate the structures. To cause a receding wetting condition on the structures with the rising air bubble, a sufficient kinetic energy is required at the triple line. In addition, Fig. 6 shows that the contact angles of the metastable state (Cassie–Baxter) are somewhat lower than the prediction and show a significant fluctuation. This implies that the wetting state of the bubble is in a locally mixed condition. In general, the metastable states show a fluctuating behavior, and it would transition to a lower-energy state through environmental perturbation.
6. Conclusion In this study, the wetting features of bubbles on micro-structured Table 2 Test sample set (surface morphology).
140
Parameter
Diameter (d )
Pitch (d + g )
Height (h )
Roughness (r )
Solid Fraction (ϕ )
Structure Structure Structure Structure Structure
20 20 40 20 10
40 60 60 25 15
20 20 20 20 20
1.7854 1.3491 1.6981 3.0106 3.7925
0.1963 0.0873 0.3491 0.5027 0.3491
1 2 3 4 5
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Table 3 Free-energy change between the Cassie-Baxter and Wenzel state. Structure 1
Si ODTS
Structure 2
Structure 3
Alv + cosθAsv
Asl −Asv
Alv + cosθAsv
Asl −Asv
Alv + cosθAsv
Asl −Asv
−0.021 4.787
−0.939 15.666
−0.003 5.75
−0.375 4.25
−0.066 4.553
−1.607 5.272
through bubble captive tests. The previous model of droplet contact angle was modified for application to bubble-wall interaction event. The modified prediction of the bubble contact angle on smooth and textured surfaces has been validated through experimental observation using test surfaces prepared with a micro-fabrication technique and coating. Generally, the test results show good agreement with the modified bubble contact angle prediction based on the Kang and Jacobi analysis. On the Si structured surfaces, the bubble is in a Cassie–Baxter state, in which liquid exists between structures. On hydrophobic structured surfaces, however, the bubble is in both the Cassie–Baxter state and Wenzel state, producing two ranges of contact angles. This dual state of bubble-wall interaction has been discussed through the wetting transition process in terms of the free energy analysis. In addition, the wetting characteristics of bubbles on high roughed structured surface have been discussed. When the roughness is greater than the critical condition for the modified contact angle prediction, the contact angle of bubble couldn’t be predicted based on either state of wetting. Here, it was conjectured that the failure of contact angle prediction over the Wenzel wetting state limit attributes to the increased capillary pressure and liquid-gas interface shape near the triple line. It is expected that this study may contribute to the basic understanding of bubble-wall interaction events in various thermal-fluidic engineering field.
Fig. 8. The limiting condition of roughness for Wenzel state (droplet and bubble). The squares are the experimental condition of this study and the hollowed rectangular □ (Bubble contact angle of S4 and S5 on ODTS coated surface) are over the limiting condition.
Conflict of interest The authors declare no competing financial interest.
Acknowledgment This research was supported by National Research Foundation of Korea (NRF), South Korea grants funded by Korean government (MSIP) (NRF-2015M2A8A2074795, 2016R1A6A3A03008942). The major author is working at Chinese Academy of Science, Institute of Engineering Thermophysics (Beijing) from 2016 Oct. now, and this experiments and discussion were carried out in POSTECH.
Fig. 9. Bubble shape and wetting characteristics under a high roughness.
surfaces have been analytically predicted and experimentally observed Appendix A A.1. Droplet contact angle (review of the analysis of Kang and Jacobi [23]) Kang and Jacobi [23] explained how the surface morphology affects the wettability of liquid droplets on solids by introducing the work of adhesion. First, they considered the process of dosing a droplet slowly on an ideal surface, as shown in Fig. 1(a). By adopting the additional work of adhesion during the wetting process (state 1 → state 2) and several basic assumptions, they could predict the contact angle of a water droplet on a textured surface. As a key concept of their study, the work of adhesion is an additional surface energy change during the wetting process. The
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assumptions in the wetting of ideal surfaces are as follows: the surface energy dominates the process, the surface is homogeneous, there is no contactangle hysteresis, the line tension is negligible, all body forces are negligible, electromagnetic forces are negligible, the liquid does not diffuse into the solid, and all properties are constant. Under the above assumptions, they calculated the following three conservation equations and one interface area constraint:
ρV1 = ρV2,
(Mass conservation)
σsg−σsl = σlg cosθY ,
(A1)
(Force relation: Young's equation [16])
(A2)
σlg Alg,1 + σsg Asg,1 = (σlg Alg,2 + σsg Asg,2 ) + w·Asl,2 . (Energy conservation)
(A3)
The parameter w is the work of adhesion per unit solid-liquid contact area, and it has the same units as surface tension. The work of adhesion changes with respect to an intrinsic feature of the solid-liquid pair and the geometric conditions of the solid surface. The solid-gas interfacial area (Asg,1 ) in the initial state of surface energy between the solid and gas is the same as the solid-liquid interfacial area (Asl,1 ) on the bottom of the liquid droplet in the final state:
Asg,1 = Asl,2 .
(A4)
The parameter w/ σlg is the work of adhesion for the liquid-gas surface tension, termed the “specific work of adhesion” in the previous study. By solving the energy conservation (Eq. (A3)) with the geometric relation between a liquid droplet and spherical cap in Table 1, the specific work of adhesion along the contact angle can be evaluated as follows [23]:
4
w = cosθY + σlg
(
(2 + cosθY )(1 − cosθY )2 4
)
2/3
−2(1−cosθY )
sin2θ
(A5)
On adopting the specific work of adhesion (A5) in the energy conservation equation (A3), the contact angle of a droplet on various textured surfaces can be calculated by a simple iterative method. They analyzed two types of wetting states on a textured surface: the fully wetted state (Wenzel model) and partially wetted state (Cassie–Baxter model). In the case of a fully wetted droplet on a rough surface, the contact area of the droplet increases with the area ratio (roughness, r), which is the ratio of the solid-liquid contact area to the solid-liquid interfacial area projected on the solid plane:
As' = r·As .
(A6)
The wetted solid surface area is increased by roughness. Thus, energy conservation for the textured surface in the process of full wetting should consider the enlarged area as follows:
σlg Alg,1 + σsg A' sg,1 = (σlg A'lg,2 + r·σsg A' sg,2 ) + r·w·A' sl,2 .
(A7)
By solving the above energy relation with the work of adhesion (Eq. (A5)) and Table 1, the apparent contact angle on the textured surface under the full wetting condition can be expressed as follows:
1−cosθD, W −2 ⎛ ⎝
(2 + cosθD, W )(1 − cosθD, W )2/3) ⎞ 4
⎠ = r·
sin2θD, W
1−cosθ−2
(
(2 + cosθY )(1 − cosθY )2/3) 4
sin2θY
).
(A8)
Here, θD, W is the apparent droplet contact angle of the rough surface under Wenzel state, and the solution shows trends different from those of the classical apparent contact angle prediction, which is based on the Wenzel equation [17]:
cosθD, W = r·cosθY .
(A9)
According to the Wenzel equation, the apparent contact angle on a rough surface increases with the roughness ratio if the contact angle on a smooth surface is greater than the 90°. While the Wenzel equation indicates that the critical contact angle is 90°, the Kang and Jacobi approach (Eq. (A8)) indicates that the critical contact angle is approximately 48°, which is the peak point for the work of adhesion, and You et al. modified the critical condition (∼43°) through analytical and experimental test [38]. In the case of a partially wetted droplet on a textured surface, the liquid-solid contact area decreases with the decrease of the solid fraction (ϕ ), which is the ratio between the top-facing area of structures and the projected area. As the solid fraction of the surface is changed from 1 to 0, the wetted solid surface area is decreased. Thus, the energy conservation for a textured surface in the partial wetting process is as follows:
σlg Alg,1 + ϕ·σsv A' sv,1 = (σlg A'lg,2 + (1−ϕ)·σlg A' sl,2 + ϕ·σsl A' sl,2 ) + ϕ·w·A' sl,2 .
(A10)
By solving the above energy relation with the work of adhesion (Eq. (A5)) and Table 1, the apparent contact angle on a textured surface under the partial wetting condition can be expressed as follows:
1−cosθD, C −2 ⎛ ⎝
(2 + cosθD, C )(1 − cosθD, C )2/3) ⎞ 4
sin2θD, C
⎠ = ϕ·
1−cosθ−2
(
(2 + cosθY )(1 − cosθY )2/3) 4
sin2θ
) − 1 (1−ϕ). 2
(A11)
The above equation (Eq. (A11)) agrees well with the prediction of the Cassie–Baxter model.
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