Air Bubble Departure on a Superhydrophobic Surface

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1 Air Bubble Departure on a Superhydrophobic Surface A. Kibar 1, R. Ozbay 2, C.H. Choi 2 1 Department of Mechanical and Material Technologies, Kocaeli University, 41285, Kocaeli, Turkey 2 Department of Mechanical Engineering, Stevens Institute of Technology, 07030, New Jersey, USA Abstract In this study, the departure of an air bubble on a Cassie State superhydrophobic surface is examined experimentally. A flat plexiglass sheet was covered with a superhydrophobic surface coating and submerged into the water horizontally. The superhydrophobic surface was oriented facing up. Air is pressured into the water throughout the hole with 1 mm in diameter on the surface. The growing and departure of the bubble is observed with a high speed camera. When the Cassie State superhydrophobic surface is submerged into the water, its surface is covered by a thin air layer. The bubble pinches off at a large diameter the Cassie state superhydrophobic surface IEESE. All rights reserved. 1. Introduction The departure of a gas bubble on a solid surface is one of the important parameter for industrial processes such as boiling. Heat and mass transfer are affected by the bubble departure diameter and volume [1]. Numerous studies have been performed about the bubble departure diameter. Fritz [2] introduced initially a predicted equation for maximum diameter of gas bubble based on the balance between the buoyancy and surface tension forces, as given in Eq. (1). ( ) (1) where θ is the contact angle of the surface as given in degree, g is gravitational acceleration, γ LG is the surface tension, ρ L and ρ G are the density of the liquid and gas, respectively. The contact angle is a common parameter to characterize the wetting of the solids, which is described by Young s equation [3] for the smooth and homogeneous surfaces, as defined in Eq (2). If the contact angle is lower than 90, the surface is called as hydrophilic which means that the surface can be wetted by liquid. If the contact angles are between 90 and 150, and bigger than 150, the surfaces are called as hydrophobic and superhydrophobic, respectively. They are also called non-wetted surfaces. In addition to surface chemistry, the surface topography (e.i. roughness) can be considered to describe the wetting [4]. Two states are possible for the rough surfaces, including the Wenzel and Cassie. The liquid penetrates into the structures on the surface in Wenzel state. In the case of Cassie state, the droplet stands on the surface with little points touching the surface and air pockets are forming between the structures. The Cassie state superhydrophobic surface has a low contact angle hysteresis and thus sliding angle. Therefore, the droplet can be moved away on the surface with a little external force such as gravity or wind. The contact angle hysteresis is related to capillary force at the three phase contact line (TPCL) of the droplet (or bubble) and is obtained by getting the difference between the advancing and receding contact angle [5]. 421 (2)

2 Huynh et al. [6] examined a captive bubble formation on a superhydrophobic surface and pointed out that superhydrophobic surfaces have the capability of transporting gas-phase samples using a large captive bubble. Kibar et al. [7] performed an experimental study about the sliding of an air bubble both upper and lower side of inclined hydrophobic surface. They indicated that sliding of the bubble was dependent on the adhesion force at the contact line which was affected by the vertical net force acting on bubble Forces Acting on a Growing Bubble There are several forces that act on an air bubble, such as the buoyancy, capillary tension, pressure, inertia and drag forces [8]. If the growing of a bubble is considered slow and steady, the inertia and drag forces can be neglected. When the Cassie state superhydrophobic surface is submerged into the water, the surface is covered by a thin air layer. This air layer stands on the surface by touching the tips of the structures. While the bubble grows, the air layer ruptures from the tips at the TPCL. The growing of the bubble is governed by the pressure inside the bubble. This pressure is balanced by the hydrostatic pressure of the water and surface tension [9]. The pressure differences between inside and outside of the bubble, which is determined by the Young-Laplace equation (Eq 3), produces force vertically upward (F P) acting on the projection area of the bubble [10] (spreading area for the superhydrophobic surface), as defined in Eq (4). ( ) (3) (4) where ΔP is the pressure difference between the inside and the outside of a bubble. R 1 and R 2 are the principal radii of curvatures of the bubble. The force, which is produced by the pressure differences, is balanced with the vertical capillary force at the TPCL, as defined in Eq (5). When the vertical net force exceeds the vertical capillary force, the bubble pinches-off from the surface. (5) Even though there have been numerous theoretical and empirical equations on bubble departure, all of them were in limited their experimental conditions since the bubble dynamics of the growing are very complex. The forces acting on the bubbles can be calculated by the profile of the bubble including: surface tension, buoyancy and contact pressure forces [8]. However the forces due to the dynamic of the bubble such as drag and inertia forces are very complex [7]. 2. Experimental Materials and Method A plexiglass sheet (100x50x5 mm in dimension) was coated with a superhydrophobic spray coating, and the contact angle of droplet on this surface was 161, as shown in Fig. 3a. The middle of the sheet was drilled with 1 mm hole. The superhydrophobic plexiglass sheet was submerged in the container, which was filled with distilled water, and placed horizontally so that superhydrophobic side was upward facing. An air pressure tank was used to obtain an air 422

bubble. The flow rate was adjusted using a pressure regulator and a precision valve. Growing of the bubbles were observed with a high speed camera and recorded in a computer.

. a) b) Fig. 3. The appearance of a) the standing droplet and b) detaching bubble on the superhydrophobic surface. 3. Results and Discussions In this study, departure of an air bubble on a superhydrophobic surface is studied experimentally.

The surface is covered by a thin air layer and the water touches to the surface with less points (tips of the rough structures).

3 bubble. The flow rate was adjusted using a pressure regulator and a precision valve. Growing of the bubbles were observed with a high speed camera and recorded in a computer. The images were analyzed to determine the volume, spreading diameter (D) and neck angle (α) of the bubble with respect to time, as shown in Fig. 3b. a) b) Fig. 3. The appearance of a) the standing droplet and b) detaching bubble on the superhydrophobic surface. 3. Results and Discussions In this study, departure of an air bubble on a superhydrophobic surface is studied experimentally. Fig. 4 shows an air bubble on a superhydrophobic surface submerged in water. The surface is covered by a thin air layer and the water touches to the surface with less points (tips of the rough structures). The hydraulic (hydrostatic) pressure is a dominant parameter for the sustainability of the air layer [11]. Fig. 4. Appearance of a submerged superhydrophobic surface in water. Fig. 5 shows a bubble growing and pinching-off from a superhydrophobic surface. The bubble is pulled by an upward force due to pressure differences between the inside and outside of the bubble acting on the projection area and it is held from the surface due to capillary force, which is linked to the contact boundary of the bubble and contact angle [8]. However, the superhydrophobic surface is covered by an air layer in the case of Cassie state. Therefore, the bubble stands with a continuous contact touching the surface with very few points. If the inside pressure of the bubble increases, the bubble volume increases. Because, the outer hydrostatic pressure is the same during growing processes since the level of the water is almost the same. However, the pressure difference between the inside and outside of the bubble produces the excess force. Therefore, the bubble size (curvature and projection area of the bubble) increases in order to balance this excess force. With further increasing the inside pressure, the capillary force does not overcome the net upward force and the bubble pinches-off from the surface at a critical diameter. This diameter is called departure diameter [2]. The bubble departures at ~

mm in diameter, as shown in Fig. 5. This value should be 8.8 mm according to theory suggested by Fritz [2]. 2.4 14.3 28.6 42.9 57.1 71.

Several images of bubble growing and departure on a superhydrophobic surface. The widths of the images are 15 mm wide.

5, the departure of bubble starts at time ~100 ms. The bubble is held on the surface by the capillary force up to this time.

The top shape of the bubble becomes perfect spherical during the pinching off process.

5. Fig. 6a shows the volume and spreading diameter of the bubble with respect to the time.

However, the spreading diameter increases at first during the bubble growing.

4 mm in diameter, as shown in Fig. 5. This value should be 8.8 mm according to theory suggested by Fritz [2] ms Fig. 5. Several images of bubble growing and departure on a superhydrophobic surface. The widths of the images are 15 mm wide. The top surface of the bubble is not a spherical until the departure starts. As seen in Fig. 5, the departure of bubble starts at time ~100 ms. The bubble is held on the surface by the capillary force up to this time. Then, the upward force overcomes the capillary force and bubble starts to detach from the surface. The top shape of the bubble becomes perfect spherical during the pinching off process. The bubble is pinched off at a large diameter the Cassie state superhydrophobic surface, as seen in Fig. 5. Fig. 6a shows the volume and spreading diameter of the bubble with respect to the time. While the inside pressure increases, the bubble volume increases continuously. However, the spreading diameter increases at first during the bubble growing. After a certain time, the spreading diameter starts to decrease. This decreasing continues until the bubble departures from the surface. During the bubble growing, the contact angle of the bubble is almost the same as its contact angle. However, the contact angle changes continuously for bubble departure from the hydrophilic surface. It is attributed that it is due to the air layer on the surface in the case of Cassie state superhydrophobic surface. The bubble has a neck during the pinching-off and the neck angle decreases fast during the departure, as shown in Fig. 6b. 424

5 a) b) Fig. 6. Sizes of the bubble with respect the time, a) volume and spreading area, b) volume and neck angle. 5. Conclusion In this study, departure of an air bubble from the superhydrophobic surface has been examined experimentally. The bubble stands with a continuous contact with a thin layer on the Cassie state superhydrophobic surface by touching the surface with a very few points. The departure of the bubble is governed by the force due to pressure differences between inside and outside pressure of the bubble. This force is compensated by the vertical capillary force at the spreading boundary of the bubble. As a result, the large bubble can be obtained on the Cassie state superhydrophobic surface. References [1] M. T. Islam, P. B. Ganesan, J. N. Sahu, and S. C. Sandaran, Effect of orifice size and bond number on bubble formation characteristics: A CFD study, Can. J. Chem. Eng., vol. 93, no. 10, pp , [2] W. Fritz, Maximum volume of vapour bubbles, Physic Zeitschr, vol. 36, pp , 425

6 1935. [3] T. Young, An Essay on the Cohesion of Fluids, Philos. Trans. R. Soc. London, vol. 95, no. 0, pp , [4] A. Marmur, Wetting on hydrophobic rough surfaces: To be heterogeneous or not to be?, Langmuir, vol. 19, no. 20, pp , [5] J. H. Snoeijer and B. Andreotti, Moving Contact Lines: Scales, Regimes, and Dynamical Transitions, Annu. Rev. Fluid Mech., vol. 45, no. 1, pp , [6] S. H. Huynh, A. A. A. Zahidi, M. Muradoglu, B. H.-P. Cheong, and T. W. Ng, Plastron- Mediated Growth of Captive Bubbles on Superhydrophobic Surfaces, Langmuir, vol. 31, no. 24, pp , [7] A. Kibar, R. Ozbay, M. A. Sarshar, Y. T. Kang, and C. Choi, Air bubble movement over and under hydrophobic surfaces in water, in 8th International Conference on Multiphase Flow ICMF, 2013, no. 1, pp [8] S. Di Bari and A. J. Robinson, Experimental study of gas injected bubble growth from submerged orifices, Exp. Therm. Fluid Sci., vol. 44, pp , [9] A. Kibar, An Investigation of Droplet Bubble and Liquid Jet Dynamics on Superhydrophobic and Hydrophobic Surfaces, Pamukkale Univ. J. Eng. Sci., doi: /pajes [10] R. Ozbay, A. Kibar, and C. H. Choi, Bubble Adhesion to Superhydrophilic Surfaces, in Advances in Contact Angle, Wettability and Adhesion, Volume Two, 2015, pp [11] X. Sheng and J. Zhang, Air layer on superhydrophobic surface underwater, Colloids Surfaces A Physicochem. Eng. Asp., vol. 377, no. 1 3, pp ,

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,