Extraordinarily Rapid Rise of Tiny Bubbles Sliding beneath

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Extraordinarily Rapid Rise of Tiny Bubbles Sliding beneath Superhydrophobic Surfaces Cyuan-Jhang Wu, Cheng-Chung Chang, Yu-Jane Sheng, and Heng-Kwong Tsao Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b04645 • Publication Date (Web): 12 Jan 2017 Downloaded from http://pubs.acs.org on January 16, 2017

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Extraordinarily Rapid Rise of Tiny Bubbles Sliding beneath Superhydrophobic Surfaces Cyuan-Jhang Wu,† Cheng-Chung Chang,‡ Yu-Jane Sheng,*,‡ and Heng-Kwong Tsao*,†,§ † ‡ §

Department of Chemical and Materials Engineering, National Central University, Jhongli 320, Taiwan Department of Chemical Engineering, National Taiwan University, Taipei 106, Taiwan Department of Physics, National Central University, Jhongli 320, Taiwan

ABSTRACT: Tiny bubbles readily stick onto substrates due to contact angle hysteresis (CAH). Nevertheless, tiny bubbles can slide slowly on a tilted surface with ultralow CAH since capillarity is overcome by buoyancy. It is surprising to observe experimentally that bubbles of 3~15 µl (diameter 1.79~3.06 mm) slide beneath a tilted superhydrophobic surface at a vertical ascent rate faster than freely rising ones of high Reynold numbers ~O(102). As the tilted angle increases, the drag coefficient remains essentially the same as that of a freely rising bubble but the frontal area of the flat bubble rises monotonically. Nonetheless, the frontal area of the sliding bubble always stays much smaller than that of a freely rising bubble. Consequently, the small drag force associated with sliding bubbles is attributed to their substantially small frontal areas on superhydrophobic surfaces.

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INTRODUCTION

Tiny bubbles with their sizes less than the capillary length are present in commonplace items, such as soft drinks, and generally stick onto the inner surfaces of their containers. These adhered bubbles cannot slide upward because of the capillary force associated with contact angle hysteresis (CAH), which is ubiquitous on almost all surfaces.1-3 For large bubbles, their buoyancy exceeds the capillary resistance, thus enabling them to ascend along the surface. However, their sliding velocities are extremely slow compared with those of freely rising bubbles. This consequence is generally attributed to a small net driving force and large hydrodynamic drag.4 The presence of tiny bubbles often causes intractable problems in many scientific and industrial applications, such as the blockage of microfluidic channels5-9 and the high energy consumption during electrolysis.10 The removal of tiny adhered bubbles is difficult due to the weak buoyancy and contact angle hysteresis. Understanding the bubble motion along a superhydrophobic surface may shed some light on resolving this problem.9,11 Because bubbles can be easily deformed, the motion of a freely rising bubble in water is a complex phenomenon. Three regimes are generally classified according to the bubble volume (V).10,12-13 When V < 0.2 µl, the bubble is spherical-like and the path of the bubble motion is rectilinear. In such a case, the Reynolds number is O(1) or less, and the terminal velocity is dominated by viscous drag. When 1 µl < V < 100 µl, the bubble shape is similar to that of an oblate spheroid and the path is zigzag or helical because of the generation of a vortex in the bubble wake (Re~O(102)).14-19 In such a case, shape oscillation is clearly observable. When V > 100 µl, the bubble shape becomes a spherical cap, and the terminal velocity is dominated by inertial forces such as form drag (Re~O(103)).20 When a bubble rises along a solid wall, its rising velocity is naturally lower than that of a freely rising bubble because of the wall drag impeding the bubble motion. Because small bubbles often stick to the wall through capillarity, large bubbles (5 × 103 µl to 6 × 104 µl) have been generally used to study bubble sliding motion beneath an inclined surface.4,10,21-23 When the tilted angle is approximately 50o, the sliding velocity reaches its maximum.4 In such a case, the shape distortion from a spherical cap and shape oscillation are evident. In addition to sliding, a rising bubble can continue bouncing along an inclined surface.24,25 When the sliding or bouncing bubble is not in contact with the wall, the triple-phase contact line is absent and capillary resistance does not exist. In such cases, it is generally known that the rising speed of a bubble moving beneath an inclined wall is less than that of a freely rising one under the condition of the same bubble volumes.26,30-31 The shape of a captive bubble depends on the wettability of the liquid on the 2


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substrate. It can vary from a perfect sphere on a total wetting surface to an extremely flat cap on a superhydrophobic surface. As inspired by the biomimetic lotus effect, a superhydrophobic surface can be fabricated by manipulating the two factors of chemical composition and surface roughness. Surface modification from using low surface energy materials and hierarchical textures impedes the imbibition of liquid into grooves. Consequently, a nonwettable solid–air heterogeneous surface is formed because of the stable air pockets. When a water droplet is deposited on such superhydrophobic surfaces, solid-liquid contacts are substantially reduced, enabling its contact angle to exceed 150o.26 Water droplets often roll away easily even on an inclined surface of a tilted angle of less than 1o, revealing that CAH is negligible on superhydrophobic surfaces.27-37 Consequently, when a tiny bubble is released onto a superhydrophobic surface, the buoyancy overwhelms the unsubstantial capillary resistance and triggers the bubble motion. The sliding motion of a bubble along an inclined surface involves overcoming CAH and the moving contact line.1 In this work, the sliding motion of tiny bubbles beneath surfaces was experimentally investigated. The rising speed of a sliding bubble was determined and compared with that of a freely rising bubble.

MATERIALS AND METHODS

Materials. Copper (I) oxide (Cu2O, 99%, metal basis, 200 mesh) was purchased from Alfa Aesar (USA). Polytetrafluoroethene (PTFE, MW=80k, 200 mesh) beads microdispers was the product from Polysciences Inc. (USA). Anhydrous ethanol (C2H5OH, 99.5%) was purchased from Echo Chemical Co. (Taiwan). Potassium hydroxide (KOH, 85%) was the product from Showa Chemical Co. (Japan). The glass slides were bought from Yancheng Guanghui Medical Products Factory (China). The double-sided tape used to stick a layer of Cu2O powders on the glass slide was purchased from Symbio Inc. (Taiwan). In the fabrication of PTFE surface by electrophoresis deposition, the electrodes made of stainless steels (grade 304) were the products of Kow-Yi Co. (Taiwan). The “Parafilm” is the product from the Bemis company Inc. (USA). Preparation of a Cu2O-coated superhydrophobic surface. The double-side tape with the area of 7.5 cm × 0.5 cm was stuck on a glass slide. Afterward, 0.35 g of Cu2O powders were placed on the tape and the excess powders were removed by the other tape for many times. Eventually, the Cu2O-coated superhydrophobic surface could be obtained. Fabrication of a superhydrophobic PTFE coating on the steel surface. 0.35 g 3


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PTFE powders were dispersed in 40 ml ethanol. Then, 0.16 wt% KOH(aq) of 10 ml was added to the PTFE/ethanol suspension in order to improve the conductivity of solution. Two stainless steel were employed as electrodes and immersed in the as-prepared PTFE suspension. The electrophoretic deposition was conducted under a constant voltage mode at 30 V. After 15 min, the PTFE particles were deposited on the surface of steel at anode. Afterward, the thin film formed by PTFE was dried in room temperature and the superhydrophobic PTFE coating could be obtained. The methods of the fabrication of both superhydrophobic Cu2O and PTFE surfaces are developed in our laboratory.

Wettability analysis and bubble motion experiments. The observation of an air bubble in water were conducted at room temperature by using a Dataphysics OCA-15EC contact angle measurement system. An air bubble with specific volume was released by an automatic micro-syringe on the surfaces. Typically, 3-µl (diameter 1.79 mm) and 15-µl (diameter 3.06 mm) bubbles are generated. The bubble diameter is defined as that of a spherical bubble having the same volume as the sliding bubble. The shape of bubble were recorded by charge coupled device (CCD) camera and transformed into an enlarged image. Afterward, the wettability including contact angle and contact angle hysteresis were analyzed by the soft program (SCA20, Dataphysics). The side-view photos of a sliding bubble beneath the surfaces was recorded by high speed CCD-camera (Cam Record 450×2, Optronis) and the moving distance was measured by the built-in scale of soft program (MultiCam Easy 2007, Shengtek). The projected frontal area (Af) was difficult to observe directly by high-speed camera due to fast changes in focal planes and meniscus reflection. In this work, a feasible method was used to estimate Af based on the assumption of the circular segment. The base (d) and height (h) of the circular segment were determined from the side-view and top-view images, as shown in Fig. 1. The validity of this approach was examined by acquire the frontal view directly for some cases and compare the observed Af to the value estimated from our method.

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Figure 1. The snapshots of (a) top-view and (b) side view of sliding bubbles beneath a superhydrophobic PTFE surface. For example, consider a 15-µl bubble sliding along a PTFE surface with the tilted angle about 23o. The front-view image was the clearest image (focal plane) acquired from the movie recorded by high-speed camera and demonstrated in Fig. 2. It can be well represented by a circular segment and the frontal area determined directly by the ImageJ software is Af=4.25 mm2. The base and height obtained from the front-view image agreed with those from the side-view and top-view images. Based on the circular segment assumption, the frontal area can be estimated as Af = [πR2(2β)/360]-[d(R-h)/2], where R = (d 2/8h)+(h/2) and β = cos-1[(R-h)/R]. The estimated value was Af = 4.34 mm2, very close to the observed Af.

Figure 2. (a) The front-view image of a 15-µl bubble sliding beneath the PTFE surface with the tilted angle about 23o. (b) It can be well described by a circular 5


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segment.

RESULTS AND DISCUSSION

Tiny bubbles easily adhere to substrates because of CAH. The extent of CAH (∆θ) is defined as the difference between the advancing and receding contact angles measured in the liquid phase.1-3 Only when the buoyant force overcomes the resistant capillary force can the bubbles slide under an inclined plane. Consequently, small bubbles can move

along a tilted substrate with small CAH such as

polytetrafluoroethene (PTFE) and Parafilm. Based on the sessile drop method, the extents of CAH are ∆θ≈25ο for PTFE and 10o for Parafilm (see Figure 1S). For a vertical surface, a 10-µl bubble can move upward along the two aforementioned surfaces with a velocity of 0.026 mm/s (Reynold number Re≈0.069) (Movie 1S; the movie is sped up 64×), but a tiny 3-µl bubble remains adhered to the wall because of its weak buoyancy, as shown in Fig. 3(a). For the 3-µl bubble to rise beneath the tilted plane, ∆θ must be substantially smaller than that of Parafilm. Recently, a surface with extremely small CAH (∆θ≈2ο) was fabricated by infusing fluorinated lubricant into the porous structure of PTFE film.38 The water contact angle on this surface was approximately 110o. As illustrated in Fig. 3(b), under this surface, a 3-µl bubble could slide slowly with a tilt angle of 20o (Movie 2S; the movie is sped up 64×). Its sliding velocity along the surface was 0.027 mm/s (Re≈0.048), slower than the terminal velocity of a freely rising bubble of 3-µl (18 cm/s). This result shows that a reduction of CAH can result in the movement of tiny bubbles on a substrate.

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Figure 3. (a) An attached tiny bubble of 3-µl on a vertical PTFE or Parafilm surface. (b) Bubble motion beneath a CAH-free surface. Superhydrophobic surfaces possess both an ultrahigh water contact angle (>150o) and nearly eliminated CAH because of trapped air pockets. Consequently, a small droplet is sphere-like and moves easily on a tilted superhydrophobic surface. By contrast, a gas bubble on a superhydrophobic surface immersed in liquid is a very flat, spherical cap. Because of extremely small CAH, even tiny bubbles can move readily on such a surface. However, the bubble velocity is expected to be substantially less than that of a freely rising bubble because of the wall friction on the fluid. A difficulty encountered in studying the effect of superhydrophobicity in water is that typical superhydrophobic surfaces fail to function if they are immersed in water for too long (e.g., 5 min) because the air pockets become unstable. In this work, two types of superhydrophobic surfaces that are stable in water were fabricated to observe the motion of a bubble sliding along such an inclined surface. Superhydrophobicity was endowed by applying Cu2O powders to a glass slide and PTFE powders to a steel plate. They exhibited ultrahigh water contact angles (static contact angles) of 160o and 175o, respectively. Since the hydrophobic surfaces of both Cu2O and PTFE 7


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micron-sized powders are rough, our superhydrophobic surfaces possessing the hierarchical structure can be considered in the “Lotus” state.37 Since the contact angle hysteresis is very weak on our superhydrophobic surfaces (including PTFE and Cu2O surfaces), the advancing and receding contact angles are very close. In fact, ∆θ (< 2o) is difficult to be measured accurately. Note that if superhydrophobic surfaces exhibit large CAH (such as the transitional superhydrophobic state between Wenzel’s and Cassie’s states),37 tiny bubbles tend to stick on the surface and the sliding motion is absent. The steady rising velocity of an air bubble beneath the superhydrophobic surface can be determined by monitoring the variation of the front position of the bubble with time. Figure 4 shows the plot of the sliding displacement against time at different tilted angles (α) of superhydrophobic Cu2O-coated glass surfaces. Similar linear plots were acquired for superhydrophobic PTFE-coated steel surfaces. The reference point is 4 cm away from the point where the releasing bubble makes the first contact with the surface. All the trajectories can be depicted by straight lines, indicating that the bubble has already reached its terminal velocity in our measuring region. Note that the bubble shape oscillates continuously during its rising process. This phenomenon is typical for a freely rising bubble at high Re because the inertial force dominates over the surface tension.

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α=13o o α=25 α=53o α=64o α=72o

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Time (sec) Figure 4. Variation of the position of a bubble with time beneath the superhydrophobic Cu2O-coated glass surface at different tilted angles (α). The vertical velocity ( ‫ݒ‬௭ ) of a 3-µl bubble sliding along these tilted superhydrophobic surfaces is illustrated in Fig. 5(a). As the tilted angle (α) was increased, the parallel component of the buoyant force grew, leading to an increase of

‫ݒ‬௭ . However, ‫ݒ‬௭ reached its maximum at α = 64o and started to decline for larger values of α. The rising velocity is of O(10) cm/s. For comparison, ‫ݒ‬௭ of a similarly sized bubble sliding along a non-superhydrophobic surface with ultralow CAH (lubricant-infused surface)38 was also measured in this work. Its value is of O(0.1) mm/s which is substantially lower than that of a freely rising bubble. Moreover, it is very surprising to find that the rising velocity of a bubble beneath the superhydrophobic surface exceeded that of a freely rising bubble when the tilted angle exceeded a certain value. The presence of the solid boundary typically impedes the 9


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fluid motion around the bubble, thus hindering bubble motion. However, the ‫ݒ‬௭ of the 3-µl bubble exceeded its freely rising terminal velocity of 18 cm/s when α > 33o and reached a maximum of 32 cm/s at α = 64o. That is, this tiny bubble could slide under a superhydrophobic surface at a vertical ascent rate approximately 1.8 times faster than its freely rising terminal velocity. The sliding velocity of the bubble along the superhydrophobic surface (‫ ) ∥ݒ‬must be higher than its ‫ݒ‬௭ . The ‫ ∥ݒ‬values for different tilted angles are presented in Fig. 5(b). Evidently, the steady sliding velocity was always faster than that of a freely rising bubble in a vertical liquid column (18 cm/s for 3-µl bubbles and 24 cm/s for 15-µl bubbles). The driving buoyant force is proportional to the bubble volume and sin(α). Consequently, the ‫ ∥ݒ‬of the 15-µl bubble was higher than that of the 3-µl bubble. Also, ‫ ∥ݒ‬typically increases with the tilted angle. However, the ‫ ∥ݒ‬of the bubble reached its maximum at a certain tilted angle and then started to decline. To eliminate the influence of buoyancy (∆ρgVsinα) on velocity, the mobility of the bubble, defined as ‫ ∥ݒ‬/(∆ρgVsinα), was analyzed. A constant mobility is typically anticipated for a given bubble size. Figure 6(a) illustrates that mobility, in fact, decreased monotonically with the tilted angle and that the mobility of the 3-µl bubble was higher than that of the 15-µl bubble. This consequence indicates that the increase of α increased the hydrodynamic resistance and also highlights the influence of the bubble shape on its motion. As shown in Fig. 6(b), the shape distortion from the flat pancake (streamlined) shape generally became evident with an increase of α. Moreover, the shape of the bubble was found to be oscillatory (Movie 3S; the movie is slowed down 0.1×).

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Figure 5. (a) Variation of the vertical velocity of a bubble with the tilted angle beneath superhydrophobic Cu2O-coated glass surfaces for two bubble volumes. The inset are the photos and contact angles for Cu2O-coated and PTFE-coated surfaces, respectively. (b) Variation of the sliding velocity of a bubble with tilted angle beneath superhydrophobic Cu2O-coated and PTFE-coated surfaces for two bubble volumes. 11


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Figure 6. (a) Variation of mobility of a bubble with tilted angle beneath the superhydrophobic Cu2O-coated surface for two bubble volumes. (b) The snap-shots of bubbles sliding along the superhydrophobic Cu2O-coated surface under different tilted angles. The motion of a bubble in a fluid environment is substantially influenced by its shape and Reynolds number (Re). The shape is related to Weber number (We) and Re is based on the effective bubble diameter.12 The hydrodynamic resistance, involving form drag and skin friction, can be quantified on the basis of the drag coefficient (CD). A value of CD ≈0.47 for a sphere is substantially higher than CD ≈0.04 for a streamlined body at Re≈104.39-41 In our experiments, Re was O(102) and We~O(1), indicating that the inertial force is dominant over the viscous force and surface tension. For a freely rising bubble with a shape that deviated from sphere to oblate spheroid because of fluid inertia, the drag coefficient was CD≈0.19. By contrast, the shape of the sliding bubble beneath the superhydrophobic surfaces was a streamlined half-body. Its drag coefficient ranged from 0.16 to 0.19, which is comparable to that of a freely rising bubble (Fig. 7). This result is somewhat counterintuitive because the sliding bubble below the superhydrophobic surfaces was found in this work to be faster than the freely rising one. The drag force acting on the bubble involved the form drag and skin friction. Because of the ultralow viscosity and density of air, the skin resistance was negligible and the form drag was responsible for the resistance against the motion 12


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of freely rising and sliding bubbles. Because the drag force was FD = ρv2AfCD/2, the frontal projected area (Af) must play a paramount role. For a freely rising 15-µl bubble, Af≈26.4 mm2; however, the Af of the sliding bubble is typically five times smaller, as illustrated in Fig. 7. Therefore, the velocity of the sliding bubbles being faster than that of freely rising bubbles is attributed to the minimal frontal area of the former. The decline of ‫ ∥ݒ‬after a certain tilted angle in Fig. 5(b) may be explained by the much substantial distortion of the bubble shape leading to a significant increase in Af. All the measurements of the base and height of the sliding bubbles are repeated at least 5 times and the standard deviation of the estimated Af is less than 0.7 mm2.

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Tilted Angle (Degree) Figure 7. Variation of the frontal projected area (Af) and drag coefficient (CD) with tilted angles for a sliding bubble of 15-µl beneath the PTFE surface.

CONCLUSIONS Tiny bubbles readily stick onto substrates such as PTFE and Parafilm because of

the presence of CAH which resists the bubble motion. For a lubricant-infused PTFE film with ultralow CAH (∆θ≈2ο), the sliding motion of 3-µl bubbles on such an inclined (non-superhydrophobic) surface can be observed. However, its sliding 13


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velocity is small compared with the rising velocity of a freely rising bubble. Superhydrophobic surfaces possess nearly vanishing CAH and the shape of the bubble on them is very flat. Two kinds of superhydrophobic surfaces, with stability in water, involving coatings of Cu2O or PTFE powders on a glass slide or a steel plate, were fabricated to observe the sliding motion of tiny bubbles. The sliding velocity along those superhydrophobic surfaces, O(10) cm/s, was faster than that on a lubricant-infused PTFE surface (non-superhydrophobic but with negligible CAH), O(0.1) mm/s. The presence of the solid boundary was supposed to hinder the fluid flow and impede bubble motion. Surprisingly, a tiny bubble could slide beneath the superhydrophobic surfaces at a vertical ascent rate faster than its freely rising terminal velocity. The bubble motion on superhydrophobic surfaces was at Re~O(102). The sliding velocity generally increased along with the tilted angle but there exists a maximum. The mobility was analyzed to eliminate the influence of the driving buoyancy. It decreased monotonically with the tilted angle, indicating the increment of the hydrodynamic resistance associated with shape distortion. The hydrodynamic resistance

quantified

by

the

drag

coefficient

of

sliding

bubbles

below

superhydrophobic surfaces was comparable to that of freely rising ones. Consequently, the small drag force associated with sliding bubbles was attributed to their substantially small frontal areas on superhydrophobic surfaces. Our finding reveals that tiny bubbles can be readily removed to avoid clogging problems by small gravity if superhydrophobic surfaces are used in the system such as narrow microfluidic passages.

AUTHOR IMFORMATION

Corresponding Authors *E-mail: [email protected] *E-mail: [email protected]

ACKNOWLEDGMENTS

This research work is supported by Ministry of Science and Technology of Taiwan and Industrial Technology Research Institute of Taiwan.

ASSOCIATED CONTENT Supporting information is available free of charge http//:pubs.acs.org/.

REFERENCES 14


via the Internet at

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Extraordinarily Rapid Rise of Tiny Bubbles Sliding beneath Superhydrophobic Surfaces

Cyuan-Jhang Wu,† Cheng-Chung Chang,‡ Yu-Jane Sheng,*,‡ and Heng-Kwong Tsao*,†,§

Tiny bubbles under an inclined superhydrophobic surface ascend faster than freely rising ones.

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Extraordinarily Rapid Rise of Tiny Bubbles Sliding beneath

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