Air bubble movement over and under hydrophobic surfaces in water

Air bubble movement over and under hydrophobic surfaces in water Ali Kibar 1, Ridvan Ozbay 2, Mohammad Amin Sarshar 2, Yong Tae Kang 3, Chang-Hwan Choi 2, 3 1 Department of Mechanical and Material Technologies, Kocaeli University, Kocaeli, Turkey 2 Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, New Jersey, USA 3 Department of Mechanical Engineering, Kyung Hee University, Yong In, Korea Keywords: Bubble, Hydrophobic, Buoyancy, Sliding angle, Contact angle hysteresis, Adhesion Abstract The movement of a single air bubble over and under a hydrophobic surface with an inclination was investigated, submerged in water. A Teflon sheet with an apparent contact angle of a sessile water droplet of 106 was used as a hydrophobic surface. The volume of a bubble and the inclination angle of a Teflon sheet were varied in the range of 5-40 µl and 0-45, respectively. The effects of the volume of a bubble on a sliding angle and contact angle hysteresis were examined in details on the top and the bottom of the hydrophobic surface, respectively, and compared. The result shows that the sliding angle has linear relationship with the bubble volume regardless of the location of the bubble. However, at the same given volume, a greater inclination angle is required for the bubble located on the downward facing surface to result in the sliding motion. It is attributed to the effect of a buoyancy force which causes the deformation of the bubble and the change of the adhesion force. Introduction Bubbles are important for many industrial processes and applications, such as boiling (Jo et al. 2011), cavitation (Plesset & Prosperetti 1977), electrolysis (Perron et al. 2006), water treatment (Demoyer et al. 2003), orifice plate (Xie et al. 2012), biomass energy (Qu et al. 2011), and hydrodynamic drag reduction (Aljallis et al. 2013). In such applications, the substrates often stand as inclined or their angles change over time. Although bubbles detach easily from a hydrophilic surface, they like to attach and spread over hydrophobic surfaces. Previously many studies were conducted on the bubble motions on hydrophilic surfaces both experimentally and theoretically. For example, Perron et al. (2006) studied the influence of a bubble volume and the inclination angle of a substrate on the terminal velocity of a bubble on the top of a surface in a hydrophilic condition (i.e., θ w <90, where θ w is a contact angle of a sessile droplet of water). In contrast, only a few studies have been made on hydrophobic surfaces. Sonoyama & Iguchis (2002) studied the bubble motion at both the top and the bottom sides of a hydrophobic surface (90 <θ w <130), and determined the detachment condition. However, the fundamental and systematic understanding of the effects of bubble volumes and inclination angles on the sliding motions and the contact angle hysteresis, especially both over and under a hydrophobic surface, has not yet been made much. In this work, we have studied the movement of an air bubble both over and under a hydrophobic surface submerged in water with the systematically varied air volumes and inclination angles. Herein, we report the analyzed results and show their effects on the sliding angles. Nomenclature Alphabets g Gravitational constant (ms -1 ) w Contact diameter (width) of a bubble (mm) V Bubble volume (μl) F B Buoyancy force (N) F adh Adhesion force (N) k Retentive force factor Greek letters α Inclination (sliding) angle ( ) L Liquid density (kg/m 3 ) A Air density (kg/m 3 ) θ Contact angle of a bubble ( ) Contact angle of a water droplet ( ) θ w θ a θ r γ Advancing contact angle of a bubble ( ) Receding contact angle of a bubble ( ) Coefficient of surface tension (N/m) Theoretical Models Figure 1 illustrates the theoretical models of forces acting on a bubble, including the cases on the top of a horizontal surface, on the bottom of a horizontal surface, on top of an inclined surface (c), and on the bottom of an inclined surface (d), respectively. There are primarily two factors that affect the bubble motion over an immersed surface in liquid, including the volume of a bubble (V) and the inclined angle of a surface (). The lateral sliding motion of a bubble along the surface is driven by the tangential component of the buoyancy force, such as: B L G F sin gv sin (1) where F B represents a vertical buoyant force. L and G 1

represent the densities of surrounding liquid and immersed gas, respectively. g is a gravitational constant. Opposed to the lateral buoyant force, an adhesion force (F adh ) is applied along the three-phase contact line of a bubble, following: F kw (cos cos ) (2) adh r a where w is the contact diameter (or width) of a bubble on a surface and is the coefficient of surface tension. k is a retentive force factor which depends on the morphology of a contact line (shape and length) as well as the contact angle distribution along the contact line (Antonini et al. 2009). r and a represent the receding (or minimum) and the advancing (or maximum) contact angles of a bubble at the downhill and uphill sides, respectively (Extrand & Kumagai 1995). When the lateral buoyancy force (F B sin) overcomes the adhesion force (F adh ), the contact line of a bubble depins from the surface and starts to slide up along the surface at the sliding angle,, following: kw (cosr cos a ) sin ( ) gv L Equation 3 is physically the same as what Furmidge (1962) developed for a sliding liquid droplet on an inclined surface. (c) A (3) (d) Figure 1: Force balance for an air bubble. On the top of a horizontal surface. On the bottom of a horizontal surface. (c) On the top of an inclined surface. (d) On the bottom of an inclined surface. Experimental Figure 2a shows the experimental setup used for the measurement of the profiles and the sliding angle () of a bubble in movement. A goniometer system with an automated tilting stage (Model 590, Rame-hart) was used to measure the volume, width, contact angle, and sliding angle of an air bubble while the inclination angle of the stage was gradually increased. A Teflon sheet with an apparent contact angle of 106 for a sessile droplet of water was used as a hydrophobic surface. A custom-made rectangular acrylic tank (11 cm long, 8 cm wide, and 8 cm high) was attached on the stage of the goniometer and filled with distilled water by around a half. The Teflon sheet was fixed over an acrylic plate and mounted on the bottom of the tank in case of the experiment for an upward facing surface (Figure 2b). In case of the experiment for a downward facing surface, the Teflon sheet was mounted below the acrylic plate (Figure 2c). Then the acrylic plate was attached on the bottom of the tank with some gap for the loading of a bubble from the underneath. After the Teflon sheet is immersed in water, a single air bubble was loaded on the surface. When loading a bubble on the upward facing surface of the Teflon sheet, a single air bubble was carefully injected from above by using a micropipette until it touched the surface and became stable. In case of the experiments for the downward facing surface of the Teflon sheet, a bubble was injected under the Teflon sheet by using an inverted micro-needle. After a bubble was loaded on either surface horizontally, the stage of a goniometer was gradually tilted at the rage of 0.5 deg/s -1 for all experiments until it reached the point when the bubble started to slide up. While the stage was tilted, the images of the bubble were captured at ten frames per second (10 fps). These pictures were analyzed to determine the height, width, volume, and advancing/receding/sliding angles of the bubble, by using image processing software (DROPimage advanced v2.4, Rame-hart). The obtained experimental data were then compared with the theoretical models (Equation 3). To study the effects of a bubble volume on the dynamics, the different volumes of a bubble (5-40 µl) were tested. 2

dramatic on a upward facing surface than on a downward facing surface (Figure 4a). In contrast, the increase of a bubble width with the increase of a bubble volume is more dramatic on a downward facing surface than on a upward facing surface (Figure 4b). Upward facing Downward facing Figure 3: Profile of a bubble on an upward or downward facing surface of a Teflon sheet. In a horizontal position. At inclination. The bubble in each image has the same volume. (c) Figure 2: Experimental setup. Goniometer system and liquid chamber. (b-c) A Teflon sheet mounted on an acrylic plate for upward facing and downward facing (c) experiments. Results and Discussion Hata! Başvuru kaynağı bulunamadı.3 shows the example of the profile of a bubble of the same volume that was located on either the upward or downward facing surface, in both the initial horizontal position (Figure 3a) and at inclination (Figure 3b). Due to a vertical buoyant force, the bubble profile on the upward facing surface is different from that on the downward facing surface. When a bubble is located on the downward facing surface, the bubble gets compressed against the vertical buoyant force due to the obstruction of the surface. It results in the decrease of the height and the increase of the width, compared to the bubble located on the upward facing surface. It also affects the contact angles of a bubble. Figure 4 shows the height (Figure 4a) and width (Figure 4b) of a bubble on both upward and downward facing surfaces when they stand in a horizontal position. Figures 4a and 4b clearly show that the difference of the height and width of a bubble between the upward facing surface and the downward facing surface. The difference gets increased with the volume of a bubble since the buoyant force is proportional to the volume of a bubble. The increase of a bubble height with the increase of a bubble volume is more Figure 4: Variations of the height and width of a bubble of a different volume on the upward and the downward facing surfaces. Figure 5 shows the advancing/receding contact angles of a bubble at the moment when it started to slide up along the 3

surface at inclination. In case of the upward facing surface, the advancing/receding contact angles do not change much with the volume of a bubble. In case of the downward facing surface, a significant decrease of both the advancing and receding contact angles with a bubble volume was observed. Despite such differences, the receding contact angles on both the upward and the downward facing surfaces are overall similar. However, the advancing contact angles on the downward facing surface are significantly higher than on the upward facing surface. It suggests that the adhesion force of a bubble on the downward facing surface would be greater than that on the upward facing surface, according to Equation 2, because of the larger contact width (w) and contact angle hysteresis (cos r - cos a ) on the downward facing surface. Then, according to Equation 3, a larger sliding angle () would be required for a bubble attached on the downward facing surface. Figure 6: Results of sliding angles of bubbles of different volumes on upward and downward facing surfaces. The data with solid lines represent the experimental measurement data, while the data with dotted lines represent the theoretical expectation based on Equation 3. Conclusions Figure 5: Variations of the advancing and receding contact angles (CA) of a bubble of a different volume on the upward and the downward facing surfaces. Figure 6 shows the results of the sliding angles of the bubbles. The data with solid lines represent the experimental measurement data, while the data with dotted lines represent the theoretical expectation based on Equation 3. For the theoretical values, the retentive force factor (k) was obtained for the upward and the downward facing surfaces, respectively, by using a least squares fitting method to the experimental values. The obtained values for the retentive force factor (k) are 2/Π and 1/2 for the upward and the downward facing surfaces, respectively. With the estimated values of the retentive force factors, the results show that the experimental data agree well with the theoretical prediction on both the upward and downward facing surfaces. As predicted by the theoretical model (Equation 3), the results also show that a higher inclination angle () was required to result in the movement of a bubble on the downward facing surface than on the upward facing surface at the same given volume of a bubble. It is because of the larger contact width and the larger contact angle hysteresis (i.e., adhesion force) of a bubble when attached on the downward facing surface. In this work, the sliding angle of a bubble on an inclined hydrophobic surface has been studied experimentally, especially to investigate the effects of the buoyant force on the sliding behavior when a bubble is placed over and under the surface, respectively. Compared to a bubble on the upward facing surface, a bubble on the downward facing surface needs a greater inclination angle for the sliding motion. It is attributed to the increased contact area (width) and the contact angle hysteresis on the downward facing surface, which result in the larger adhesion force of a bubble on the surface. When comparing the experimental results to those of theoretical models, it is found that different retentive force factors should be used for the different facings, which are 2/Π and 1/2 for the upward and the downward facing surfaces, respectively. Acknowledgements This work was supported by the Scientific and Technical Research Council of Turkey (TUBITAK) BIDEB-2219 and the US Office of Naval Research (ONR) under the Young Investigator Program (YIP). References Aljallis, E., Sarshar, M., Datla, R., Sikka, V., Jones, A., and Choi, C.-H. Experimental Study of Skin Friction Drag Reduction on Superhydrophobic Flat Plates in High Reynolds Number Boundary Layer Flow. Phys. Fluids, Vol: 25, 025103 (2013) Antonini, C., Carmona F. J., Pierce E., Marengo M., and Amirfazli, A. General Methodolgy for Evaluating the Adhesion force of Drops and Bubbles on Solid Surfaces. Langmuir, Vol: 25, 6143-6154, (2009) 4

Demoyer, C. D., Schierholz, E. L, Gulliver, J. S., Wilhelms, S. C. Impact of Bubble and Free Surface Oxygen Transfer on Diffused Aeration Systems. Water Research, Vol: 37, 1890-1904 (2003) Extrand, C. & Kumagai, Y. Liquid Drop on an Inclined Plane: The Relation between Contact Angles, Drop Shape, and Retentive Force. J. Colloid Interface Sci, Vol: 170, 515-521, (1995) Furmidge C. G. L. The Sliding of Liquid Drops on Solid Surfaces and a Theory for Spray Retention, J. Colloid Interface Sci., Vol: 17, 309-324, (1962) Jo, H. J., Ahn, H. S., Kong, S. H., Kim, M. H. A Study of Nucleate Boiling Heat Transfer on Hydrophilic, Hydrophobic and Heterogeneous Wetting Surfaces. Int. J. Heat Mass Tran., Vol: 54, 5643-5652, (2011) Perron, A., Kiss, L. I., Poncsak, S. An Experimental Investigation of the Motion of Single Bubbles Under a Slightly Inclined Surface. Int. J. Multiphase Flow, Vol: 32, 606-622 (2006) Plesset, M. S. & Prosperetti, A. Bubble Dynamics and Cavitation. Annu. Rev. Fluid Mech., Vol: 9, 145-185, (1977) Qu, X. F., Wang, Y. Z., Zhu, X., Liao, Q., Li, J., Ding, Y., Lee, D. J. Bubble Behavior and Photo-Hydrogen Production Performance of Photosynthetic Bacteria in Microchannel Photobioreactor. Int. J. Hydrogen Energy, Vol: 36, 14111-14119, (2011) Sonoyama, N. & Iguchi, M. Bubble Formation and Detachment on Nonwetted Surfaces. Metall. Mater. Trans. B, Vol: 33, 155-162, (2002) Xie, J., Zhu, X., Liao, Q., Wang, H., Ding, Y. D. Dynamics of Bubble Formation and Detachment from an Immersed Micro-Orifice on a Plate. Int. J. Heat Mass Tran., Vol: 55, 3205-3213, (2012) 5