Surface charge-induced EDL interaction on the contact angle of

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Surface charge-induced EDL interaction on the contact angle of surface nanobubbles Dalei Jing,*,† Dayong Li,‡,§ Yunlu Pan,*,‡ and Bharat Bhushan*,‡,∥ †

School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China School of Mechanical Engineering, Harbin Institute of Technology, Harbin, 150001, China § School of Mechanical Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China ∥ Nanoprobe Laboratory for Bio- & Nanotechnology and Biomimetics (NLB2), The Ohio State University, 201 West 19th Avenue, Columbus, Ohio 43210-1142, United States ‡

ABSTRACT: The contact angle (CA) of surface nanobubbles is believed to affect the stability of nanobubbles and fluid drag in micro/nanofluidic systems. The CA of nanobubbles is dependent on size and is believed to be affected by the surface chargeinduced electrical double layer (EDL). However, neither of these of attributes are well understood. In this paper, by introducing an EDL-induced electrostatic wetting tension, a theoretical model is first established to study the effect of EDLs formed near the solid− liquid interface and the liquid-nanobubble interface on the gas phase CA of nanobubbles. The size-dependence of this EDL interaction is studied as well. Next, by using atomic force microscopy (AFM), the effect of the EDL on nanobubbles’ gas phase CA is studied with variable electrical potential at the solid−liquid interface, which is adjusted by an applied voltage. Both the theoretical and the experimental results show that the EDLs formed near the solid−liquid interface and the liquid−nanobubble interface lead to a reduction of gas phase CA of the surface nanobubbles because of an electrostatic wetting tension on the nanobubble due to the attractive electrostatic interaction between the liquid and nanobubble within the EDL, which is in the nanobubbles’ outward direction. An EDL with a larger zeta potential magnitude leads to a larger gas phase CA reduction. Furthermore, the effect of EDL on the nanobubbles’ gas phase CA shows a significant size-dependence considering the size dependence of the electrostatic wetting tension. The gas phase CA reduction due to the EDL decreases with increasing nanobubble height and increases with the nanobubble’s increasing curvature radius, indicating that a surface charge-induced EDL could possibly explain the size dependence of the gas phase CA of nanobubbles.

1. INTRODUCTION Surface nanobubbles, which have drawn wide attention in micro/nano fluidic applications, are micro/nanoscale spherical cap-shaped gaseous domains formed at a solid−liquid interface.1−5 Since the first image of surface nanobubbles was obtained by Lou et al.6 and Ishida et al.7 using atomic force microscopy (AFM), various techniques have been used to image nanobubbles and study their properties. These techniques include AFM,1,2,6−13 optical microscopy,14,15 rapid cryofixation technique,16 and quartz crystal microbalance.17−19 The discovery and study of surface nanobubbles have made possible their wide use and potential applications in various fields including control of slippage and drag in micro/ nanofluidic systems,10 froth flotation,20 protein adsorption,21 and immersion lithography.22 Experimental and theoretical studies found that surface nanobubbles show some remarkable and unexpected properties. First, they have an abnormally long lifetime; they have stability up to several hours or even days.2,5,6,23 This deviates from the traditional prediction of their lifetime, which is in the range of microseconds considering the high Laplace pressure inside the nanobubbles. Extensive studies have been carried out to explain the remarkable stability of surface nanobubbles, and © 2016 American Chemical Society

various mechanisms have been proposed such as contamination theory,24 dynamic equilibrium theory,25 contact line pinning theory26−28 and even the combination of the above three theories.13 Second, they have a smaller contact angle (CA) on the gas side when compared to the macroscopic gas phase CA obtained by Young’s Equation, which suggests size-dependence of the CA.12,29−34 To explain the anomalously small gas phase CA of nanobubbles and its size-dependence, line tension is suggested to modify Young’s Equation as29,35 cos θ = cos θY −

τ γlgr

(1)

where θ is the CA on the gas side of the surface nanobubble, θY is the macroscopic CA on the gas side obtained by Young’s Equation, τ is the line tension, γlg is the liquid−gas surface tension, and r is the contact line radius. Special Issue: Nanobubbles Received: March 14, 2016 Revised: May 31, 2016 Published: June 3, 2016 11123

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nanobubbles due to the applied voltage is measured by using an AFM.

In addition, the effect of surface charge at the solid−liquid interface or the liquid−nanobubble interface on the surface nanobubble is another scientific issue of surface nanobubbles, which has also been studied. When a solid surface is immersed in an electrolyte, the solid−liquid interface can become charged because of adsorption or deionization of ions.36−39 Then, the charged solid−liquid interface causes redistribution of ions in the electrolyte near the solid−liquid interface because of electrostatic interaction. This produces an electric double layer (EDL) with net local charge. Similarly, the liquid-nanobubble interface can be charged and produce an EDL near the liquidnanobubble interface.40 Attard et al.41 studied the effect of surface charge on surface nanobubbles and found that the EDL repulsion force between neighboring nanobubbles on a hydrophobic surface plays a role in their stability. Das42 modified Young’s Equation by introducing an electrostatic wetting tension induced by the EDL near the solid−liquid interface. Based on this modification, a scaling estimate was proposed to study the effect of the EDL on the gas phase CA of a nanobubble. Das and Mitra43 expanded the previous work and established a detailed analytical solution for the effect of the EDL on the gas phase CA of a nanobubble, based on a wedgelike assumption of the three-phases contact line (TPCL). Mazumder and Bhushan44 and Pan et al.11 experimentally studied and found the effect of pH of electrolyte and substrate bias on the propensity, geometrical distribution, and stability of surface nanobubbles on an ultrathin polystyrene (PS) film immersed in deionized (DI) water and saline solutions, and then tried to analyze the underlying mechanisms from the view of surface charge. However, Zhang et al.9 and Hampton and Nguyen20 reported unobvious effects of added salt on the stability and morphology of nanobubbles. Massive experimental and theoretical studies have been performed to investigate the remarkable stability and CA of surface nanobubbles. Nevertheless, they are still unsettled issues. Although Das42 and Das and Mitra43 theoretically analyzed the effect of a surface charge-induced EDL near the solid−liquid interface on the gas phase CA of surface nanobubbles, the surface charge at the liquid-nanobubble interface was neglected and a wedge-like assumption of the TPCL was used. Furthermore, the size-dependence of the EDL interaction on the gas phase CA of nanobubbles is missed, and the underlying mechanisms of the size-dependence of the gas phase CA of nanobubbles are still not well understood. For experimental studies, the effect of surface charge on the morphology of nanobubbles is still unclear. Additionally, there are no direct experimental results of the effect of surface charge on the gas phase CA of surface nanobubbles. To solve these problems, in this paper, a theoretical model is first established to study the effect of surface charge-induced EDLs near the solid−liquid interface and the liquid−nanobubble interface on the gas phase CA of surface nanobubbles. Next, based on the newly developed model, the sizedependence of the EDL interaction on the gas phase CA of nanobubbles is analyzed. Then, the size-dependence of the gas phase CA can be explained further from the perspective of surface charge. Finally, experimental studies of the effect of the EDL on the gas phase CA of surface nanobubbles formed on a hydrophobic PS sample immersed in oxygenated saline solution are carried out using an AFM technique. By applying a bias voltage, the electrical potential of the solid−liquid interface is adjusted. Then, the change in the gas phase CA of the

2. PROBLEM DESCRIPTION AND MATHEMATICAL MODEL In this section, a theoretical model is established to study the EDL interaction on the gas phase CA of surface nanobubbles by introducing an electrostatic wetting tension from the surface charge-induced EDL on the surface nanobubbles into Young’s Equation. In contrast to the work of Das42 and Das and Mitra,43 both the EDL formed near the solid−liquid interface as well as the EDL formed near the liquid−nanobubble interface are considered in the present work. The morphology of the nanobubble is kept as a spherical cap-shape without the employment of wedge-like assumption of the TPCL. Furthermore, the present work can be used to analyze the size-dependence of both the EDL interaction on the gas phase CA of nanobubbles and the gas phase CA of nanobubbles themselves, considering the dependence of electrostatic wetting tension on the nanobubble size. Figure 1 shows a schematic of a spherical cap-shaped surface nanobubble on a flat hydrophobic solid surface immersed in an

Figure 1. Schematic of a spherical cap-shaped surface nanobubble on a flat solid surface immersed inside an electrolyte solution, and the definition of variables.

electrolyte solution. hb is the height of the nanobubble, R is its curvature radius, and L is the radius of the TPCL. As shown in Figure 1, there are three different phases: the nanobubble (phase 1), the surrounding electrolyte (phase 2), and the solid substrate (phase 3). Correspondingly, the volumes inside these three different phases are denoted as Ω1, Ω2, and Ω3, respectively. The interface between any two phases i and j is denoted as Sij. Thus, two closed surfaces Σ1 = S12 ∪ S13 ∪ S11 and Σ2 = S21 ∪ S22 ∪ S23 ∪ S2∞ are introduced to enclose the nanobubble and the surrounding electrolyte, respectively. To establish the mathematical formulation describing the effect of the surface charge-induced EDL on the gas phase CA of surface nanobubbles, the liquid-nanobubble interface and the solid−liquid interface are assumed to be negatively charged. Thus, two separate EDLs near the solid−liquid interface and liquid-nanobubble interface are formed on the liquid side and overlap with each other. Here, the zeta potential rather than the surface potential at the interface are used to characterize the surface charge densities of the solid−liquid interface and the liquid−nanobubble interface considering the following reasons. (1) Compared to the surface potential, the zeta potential can be experimentally measured and there are lots of reported experimental data of zeta potential; (2) although there is difference between the surface potential and the zeta potential, sometimes, this difference is small enough to be neglected.45 Meanwhile, the zeta potentials of the two EDLs formed near the solid−liquid interface and the liquid−nanobubble interface 11124

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schematic describing the effect of surface charge-induced EDL on a nanobubble, where the nanobubble in the dashed line is the one considering the effect of EDL, and the nanobubble in the solid line is the one neglecting the effect of EDL. As shown in Figure 2, the electrostatic wetting tension applied on the nanobubble due to the EDL, which is in the outward direction of the nanobubble, pulls the nanobubble and leads to a displacement of the liquid−nanobubble interface toward the liquid side. This leads to a change in the gas phase CA of the nanobubble. Based on the schematic shown in Figure 2 and the conservation of energy after the change of the nanobubble, the effect of surface charge-induced EDL on the gas phase CA of the nanobubble can be expressed as42,43,48

are assumed to be constant and small enough that the EDLs can be simplified using the linear Poisson−Boltzmann equation based on the Debye−Hückel approximation. In addition, it is assumed that there are no free ions in the nanobubble; thus, no electrostatic field inside the nanobubble. It should be noted that, although the linear Poisson− Boltzmann equation is only valid with a small error for the small magnitude of zeta potential, up to 50−80 mV,46 the zeta potentials at the most solid−liquid interfaces or liquidnanobubble interfaces are in the range of tens of millivolts. Thus, this assumption presented here can successfully be used for most practical applications and analyze the effect of EDL on the CA of nanobubbles. When the zeta potential at any interface goes beyond the range of small zeta potential to validate the linear Poisson−Boltzmann equation, the theoretical model presented here can still be used to analyze the EDL interface on the gas phase CA of nanobubbles qualitatively. To accurately study the EDL interaction on the gas phase CA of nanobubles in the case of high magnitude of zeta potential, the method to establish the theoretical model can be modified by introducing the electrical potential within the EDL obtained from solving the nonlinear Poisson−Boltzmann equation. The previous experimental studies on nanobubbles showed that the size of nanobubbles formed on a PS sample immersed in DI water or saline solution increases with the increasing pH of the solution and an increasing applied voltage.11,44 This indicates a spreading nanobubble. However, this is different from the electrowetting phenomenon of a macroscopic liquid droplet11 or a macrobubble,47 which show a decreasing CA on the aqueous side of the liquid droplet or a shrinking macrobubble with an increasing voltage because of the decreasing surface tension of the solid−liquid interface based on the Young’s equation and Lippman effect. As such, the theory of the conventional electrowetting theory cannot simply be used to analyze the effect of surface charge or an applied voltage on the nanobubble. In this paper, an electromechanical method is used to analyze the effect of surface charge on the nanobubble.42,43,48 Based on this method, the effect of surface charge on the nanobubble is attributed to an electrostatic force. This electrostatic force is believed to be in the outward direction from the nanobubble, which can be proved by the experimental results of an increasing nanobubble with increasing electrical potential adjusted by an increasing pH or an increasing applied voltage.11,44 The mechanism for the electrostatic force in the outward direction of the nanobubble is the agglomeration of electrical charge with positive sign near the negatively charged interface and the resulting electrostatic attractive force between the liquid and the nanobubble. Thus, the surface charge-induced EDL will introduce an electrostatic wetting tension, Wel, on the nanobubble, affecting the CA of the nanobubbles. Figure 2 shows a simplified

cos θ = cos θ0 +

Wel γlg

(2)

where θ is the gas phase CA of a nanobubble with the effect of surface charge, θ0 is the gas phase CA of a nanobubble without the effect of surface charge, Wel is the EDL-induced electrostatic wetting tension, and γlg is the surface tension of the liquidnanobubble interface. The EDL-induced electrostatic wetting tension on the nanobubble can be expressed as42,48 Wel = −ex ·

∫S +S 12

T · ( − n) dS

(3)

21

⎛ 1 ⎞ T = −ΠI + ε0ε⎜EE − E2 I⎟ ⎝ 2 ⎠

(4)

where T is the electrostatic stress tensor, ex is the unit vector in the positive x-direction, n is the outward unit normal vector at the surfaces, Π is the osmotic pressure, ε0 is the vacuum permittivity, ε is the dielectric constant of the electrolyte, E = −∇φ (φ is the electrostatic potential) is the electrical field vector, E is the magnitude of the electrical field, and I is the second-order isotropic tensor. The osmotic pressure can be obtained by the Poisson’s Equation as42,48 ∇Π = ε0ε(∇·E)E

(5)

Based on the assumption of no electrical field inside the nanobubble, the electrostatic wetting tension in eq 3 can be simplified as Wel = −ex ·

∫S

T · ( − n) dS

(6)

21

Then, considering ∫ T·( −n) dS = 0, the electrostatic Σ 2

wetting tension in eq 6 can be expressed further as42,46 Wel = ex ·

∫S

T · ( − n) dS 22 + S23 + S2 ∞

(7)

To obtain the electrostatic wetting tension, the electrical field vectors at three surface S22, S23, and S2∞ (denoted as E22, E23, and E2∞, respectively) are needed. The electrical field vector at each surface is the sum of the electrical fields formed by both the charged solid−liquid interface and the charged liquidnanobubble interface (denoted as Esl and Elg, respectively, for example, E22= E22sl + E22lg). For the electrical field E2∞ at the surface S2∞, because S2∞ is far from the liquid−air interface, the contribution of E2∞lg to

Figure 2. Schematic of the surface charge-induced EDL interaction on the gas phase CA of a nanobubble. 11125

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Langmuir E2∞ can be neglected. That is, E2∞ consists only of E2∞sl and is in the direction of the y-axis. Thus, ex·E2∞ = 0 and the integration over S2∞ in eq 7 can be simplified as Wel′ = ex ·

∫S

T · ( − n) dS 2∞

∫S

= ex·

E 22 =

⎡ ⎛ ε0ε 2⎞ ⎤ E ⎟I⎥ ·( −n) dS ⎢⎣ −⎜⎝Π + 2 ⎠⎦ 2∞

κ −1 =

(8)

Wel″ = ex ·

(10)

Esl = −∇φsl = κζ1e−κy ·ey

(11)

Wel‴ = ex · =

Wel =

(12)

ε εκζ 2 ⎛ ε0ε 2⎞ ⎜− E ⎟I·( −n) dS = 0 1 (1 − e−2κhb) ⎝ 2 ⎠ 2 2∞

where hb is the height of the nanobubble. Similarly, the electrical field E22 at the surface S22 can be expressed as, E 22 = E 22 sl + E 22 lg

(14)

For the EDL formed by the charged liquid-nanobubble interface with small zeta potential ζ2, the electrical potential and the electrical field of the EDL are given by39

+

ζ2R(1 + κr )

ζ2R(1 + κr ) r2

r e

−κ(r − R )

ε0εζ2R2 ⎡ 2ζ2(1 + κR )2 (1 + κR )κ πζ1 ⎤ ⎥ ⎢ + 4 ⎦ (R − hb) ⎣ 15(R − hb)2 R

e−κ(r − R) cos α ·ex

sin α ·ey

⎤ ε εζ R2 πζ1 (1 + κR )κe−κhb⎥ + 0 2 4 ( R − h b) ⎦ (20)

The nanobubbles formed on a hydrophobic PS sample immersed in an oxygen-saturated saline solution were imaged by AFM operating in tapping mode (TM-AFM). The saline solution used in the present work is an oxygen-saturated saline solution (RNS60, Revalesio Corporation, Tacoma, WA), consisting of 0.9% saline in water and 55 ± 5 ppm oxygen without any active pharmaceutical ingredients. The detailed process to prepare RNS60 is described in our previous work.49 The process to prepare the PS sample was the same as our previous method11 and is as follows. First, a 1 cm × 1 cm substrate of Si wafer (Silicon Quest International) with 300 nm thick silicon oxide coating was first immersed in a piranha solution of a 3:1 (volume ratio) mixture of 98% sulfuric acid and 30% hydrogen peroxide for 30 min, and then rinsed by DI water followed by ethanol at least five times and dried with clean compressed air. Second, the PS pellets (Sigma-Aldrich) with a molecular weight of 35 000 was dissolved in

(15)

r

2

T · ( − n) dS 23

3. EXPERIMENTAL SECTION

−κ(r − R )

Elg = −∇φ lg =

(18)

By introducing the electrostatic wetting tension (eq 20) into eq 2, the effect of surface charge-induced EDL on the gas phase CA of the surface nanobubble can be studied. It should be noted that constant zeta potentials at the interfaces are assumed here, so the theoretical model can be expressed as eq 19. However, the present theoretical work can be expanded easily to the case of constant surface charge density at the interfaces and the case of a nanobubble formed at the dielectric substrate immersed in an electrolyte under the condition of an applied electrical voltage (similar to the electrowetting effect on the liquid droplet). In addition, when the zeta potential of the solid−liquid interface is much larger than that of the liquidnanobubble interface (this is the common case), eq 20 can be approximated as eq 13.

(13)

Re

∫S

⎡ 2ζ (1 + κR )2 (1 + κR )κ πζ1 ⎤ ⎥ ×⎢ 2 + 2 4 ⎦ R ⎣ 15(R − hb)

Thus, eq 8 can be expressed as

φ lg = ζ2

ε0ε EE·( −n) dS 22

⎡ 2ζ (1 + κR )2 ε0εκζ12 (1 − e−2κhb) + ε0εζ2⎢ 2 2 R ⎣ 15 +

2

∫S

∫S

Thus, the total electrostatic wetting tension can be expressed using eqs 13, 18, and 19 as

where κ is the Debye length of the EDL, which is a parameter to characterize the thickness of the EDL, kb is the Boltzmann constant, T is the absolute temperature, n0 is the bulk ionic concentration of the electrolyte, z is the valence of the ions, e is the elementary charge, and ey is the unit vector in the positive y-direction. Based on eq 5, the osmotic pressure Π can be expressed as

Wel′ = ex ·

T·( −n)dS = ex· 22

(19)

−1

ε0εE 2

(17)

Similarly, there is

εε0k bT 2 2

∫S

⎤ ⎡ 2ζ (1 + κR )2 πζ = ε0εζ2⎢ 2 + 1 (1 + κR )κ e−κhb⎥ R 4 ⎦ ⎣ 15

(9)

2n0z e

Π∼

e−κ(r − R) cos α ·ex r2 ⎡ ζ R(1 + κr ) −κ(r − R) ⎤ e sin α + κζ1e−κhb⎥ ·ey +⎢ 2 2 ⎣ ⎦ r

By using the one-order approximation of Taylor expansion, 1 + κR that is, e−κ(r − R) ≈ 1 + κr , there is

To obtain the electrical field at any surface, the electrical potential of the EDL is needed. For the EDL formed by the charged solid−liquid interface with small zeta potential ζ1, the electrical potential and the electrical field of the EDL are given by39

φsl = ζ1e−κy

ζ2R(1 + κr )

(16)

where R is the curvature radius of the surface nanobubble, r and α are the parameters labeled in Figure 1, and cos α = (r 2 − R2)/r 2 . Combining eqs 11, 14, and 16, E22 can be expressed as 11126

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Langmuir toluene (Mallinckrodt Chemical) to prepare a PS formulation with a concentration of 1% (w/w). Third, a thin film of PS was spin-coated on the clean Si substrate at a speed of 2,000 rpm. Finally, the PS sample was heated in an oven at 53 ± 2 °C for 4 h to remove the remaining solvent. The liquid phase CA of a 5 μL droplet of DI water on the newly prepared PS sample was measured as 96 ± 2° by a 290F4 Ramé-Hart goniometer. A Dimension 3000 AFM (Bruker Instruments) operating in tapping mode was used to image the surface nanobubble. A polychlorotrifluoroethylene (PCTFE) fluid cell cantilever holder (DTFML-DD, Bruker) with a piezo was used to keep the aqueous environment. A silicon nitride cantilever (PNPTR, Nanoworld) with a tip radius less than 10 nm and a stiffness of 0.32 N·m−1 was used to image the nanobubble. The set point was 95% of the free amplitude to minimize the force applied on the nanobubble. All experiments were carried out in ambient conditions (temperature of 22 ± 1 °C and humidity of 45− 55% RH). To experimentally investigate the effect of the EDL on the gas phase CA of the surface nanobubbles, the experimental setup shown in Figure 3 was used. The PS coated sample, which consists of PS film on

Table 1. Properties of Saline Solution and Parameters Used in Simulation properties

symbol

value

zeta potential of the solid−liquid interface (mV) zeta potential of the liquid−nanobubble interface (mV) vacuum permittivity (F/m)50 dielectric constant of saline solution50 bulk ionic concentration (mM) surface tension of the liquid−air interface (N/m)42 height of the surface nanobubble (nm) curvature radius of the surface nanobubble (nm) temperature (K)

ζ1 ζ2

−50−0 −20−0

ε0 ε n0 γlg hb R T

8.85 × 10−12 ∼76 1 or 10 ∼0.072 10−100 100−1000 298

4.1. Variation of the Electrostatic Wetting Tension. The Effect of Zeta Potential. Figure 4 shows the effect of zeta potentials of the solid−liquid interface and the liquid− nanobubble interface on the calculated electrostatic wetting tension applied on a surface nanobubble with fixed dimensions. From Figure 4, it can be found that the electrostatic wetting tension has a positive sign, which means it is in the outward direction from the nanobubble, as shown in Figure 2. The mechanism for the electrostatic wetting tension in the outward direction of the nanobubble is the agglomeration of electrical charge having the opposite sign with that of the negatively charged interface near the interface and the resulting electrostatic attractive force between the liquid and the nanobubble. Further, the increasing magnitude of zeta potentials of both the solid−liquid interface and the liquid− nanobubble interface leads to an increase in the electrostatic wetting tension. The mechanisms of this phenomena are as following. A larger zeta potential magnitude leads to a larger electrical potential magnitude within the EDL and a stronger electrical field induced by the surface charge based on eq 11 and eq 16, and the negatively charged interface attracts much more electrical charge having the opposite sign to close to the interface; furthermore, a larger zeta potential refers to a larger surface charge density at the liquid-nanobubble interface. Those lead to a larger electrostatic attractive force applied on the surface nanobubble based on the Coulomb’s law, which is in the outward direction of the nanobubble, and a larger electrostatic wetting tension on the surface nanobubble. In addition, the electrostatic wetting tension applied on the surface nanobubble increases with the increasing ionic concentration. The Effect of Nanobubble Dimensions. As mentioned above, the gas phase CA of nanobubbles shows an obvious sizedependence with the height and curvature radius of the nanobubble. Furthermore, the dimensions of the nanobubble inevitably affect the EDL-related interaction between the solid− liquid interface and the nanobubble, and affect the electrostatic wetting tension applied on the nanobubble. Therefore, it is essential to analyze the effect of nanobubble dimensions on the electrostatic wetting tension and the gas phase CA. Figure 5 shows the variation of the calculated electrostatic wetting tension with the nanobubble height and the curvature radius under the condition of fixed zeta potentials. It can be found from Figure 5 that the electrostatic wetting tension first decreases followed by an increase with the increasing height of nanobubbles. Meanwhile, the electrostatic wetting tension always increases with the increasing curvature radius of nanobubble. The size-dependence of the electrostatic wetting

Figure 3. Experimental schematic to measure the effect of the EDL on the gas phase CA of surface nanobubbles (adapted from ref 11). a Si substrate, was first glued onto a steel plate (SD-101, Bruker) using conductive silver paint. Next, the steel plate was connected to the positive electrode of a DC power supply by a stainless steel wire. Meanwhile, another stainless steel wire inserted into the droplet of experimental liquid was connected to the negative electrode of the DC power supply. In this way, the Si substrate was electrically connected to the DC power supply, and a positive voltage was applied on the PS film. The electrical potential of the solid−liquid interface then could be adjusted by changing the applied voltage. Because of the existence of a dielectric layer consisting of PS film and SiO2 on the Si wafer, it is believed that the applying of voltage cannot lead to the occurrence of water electrolysis, which can produce the H2 and O2 and then affect the formation of nanobubbles. During the experiment, the chosen voltages were continuously applied, and scanning at least three times at the same location was performed to image nanobubbles for each voltage. After imaging the surface nanobubble, the height (hb) of the nanobubble and the radius of the TPCL (L) can be obtained. Then, the gas phase CA of the nanobubble can be calculated by θ = 2arctan(hb/L).

4. RESULTS AND DISCUSSION After establishing both a model for the surface charge-induced EDL interaction on the CA of the surface nanobubbles and an experimental setup, theoretical analysis and experiments are carried out. Saline solution with different ionic concentrations is used as the electrolyte in the theoretical analysis. Some properties of the saline solution were chosen. Table 1 shows the properties and parameters used in the theoretical analysis. 11127

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Figure 4. Effect of zeta potential of (a) the solid−liquid interface and (b) the liquid−nanobubble interface on the calculated electrostatic wetting tension.

Figure 5. Variation of the calculated electrostatic wetting tension with (a) the height and (b) the curvature radius of the surface nanobubble.

Figure 6. Effect of the EDL on (a) the calculated gas phase CA reduction and (b) calculated gas phase CA of surface nanobubbles and their heightdependence.

Figure 7. Effect of the EDL on (a) the calculated gas phase CA reduction and (b) calculated gas phase CA of surface nanobubbles and their curvature radius dependence. 11128

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Figure 8. 3D images showing the size-dependence of (a) the calculated gas phase CA and (b) the calculated gas phase CA reduction of the surface nanobubbles under the effect of the EDL.

the height of the bubble reaches the range of macroscale, the gas phase CA of the bubble can be explained by conventional theory. However, there is a larger gas phase CA reduction for a nanobubble with a larger curvature radius when the nanobubble height is kept constant, as shown in Figure 7a. This means that the gas phase CA of the nanobubbles has a more obvious trend to decrease with the increasing curvature radius, as shown in Figure 7b. Considering the coupling relationship between the dimensions of nanobubbles and the gas phase CA, two threedimensional images in Figure 8 are given to describe the sizedependence of gas phase CA and gas phase CA reduction with the effect of surface charge-induced EDL. The results shown in Figures 6−8 indicate that the size of the nanobubble will affect the electrostatic wetting tension applied on it. Thus, the size of the nanobubble generates a different surface charge effect on the gas phase CA of the nanobubble. Therefore, the nanobubble size affects not only the electrostatic wetting tension applied on it, but also its gas phase CA. That is, the gas phase CA of nanobubble is dependent on the size of the nanobubble. Thus, our theory indicates that, besides line tension,29 surface charge is another possible explanation for the size dependence of gas phase CA of nanobubbles. From the above analysis, it can be found that the zeta potential of the interfaces ionic concentration of the electrolyte, and the dimensions of the nanobubble can affect the gas phase CA reduction relating to the EDL. The finding of sizedependence of the EDL interaction on the gas phase CA in the present work is helpful to the understanding of the sizedependence of the gas phase CA with the height and curvature radius of the nanobubble. However, it should be noted that under some conditions, such as small zeta potential, small ionic concentration, large nanobubble height, or small curvature radius of the nanobubble, the gas phase CA reduction induced by the EDL is negligible. This may be used to explain the unobvious effect of added salt and solution pH on the morphology of nanobubbles in the works of Zhang et al.9 and Hampton and Nguyen.20 4.4. The effect of applied voltage on the gas phase CA of nanobubbles. To prove the effect of the EDL on the gas phase CA of nanobubbles, an experimental study was carried out and the electrical potential at the solid−liquid interface was adjusted by changing the applied voltage. However, the electrical potential of the liquid-nanobubble interface was assumed to be constant. Figure 9 shows AFM images of nanobubbles formed on a PS sample immersed in an oxygenated saline solution under different applied voltages. From the results shown in Figure 9, it can be found that the

force means that the effect of surface charge-induced EDL on the nanobubbles’ gas phase CA is size-dependent based on eq 2. Further, nanobubbles with different dimensions will show different changes in gas phase CA due to the surface charge. The corresponding studies are described in the following section. 4.2. The EDL Interaction on Gas Phase CA. With the calculated electrostatic wetting tension applied on the surface nanobubbles, the surface charge-induced EDL interaction on the gas phase CA of surface nanobubbles can be analyzed based on eq 2. Figures 6 and 7 show the effect of the EDL on the calculated gas phase CA of surface nanobubbles. θ0−θ is the gas phase CA reduction of the nanobubbles; that is, the difference between the gas phase CA without the effect of surface charge and the gas phase CA considering the effect of surface charge. It can be found from both Figure 6 and Figure 7 that the surface charge-induced EDL can reduce the gas phase CA because of the electrostatic wetting force on the nanobubbles, which is in the outward direction from the nanobubble. The generation of this force due to surface charge pulls the nanobubble, enlarges its diameter, and reduces its gas phase CA. For a nanobubble with fixed dimensions, an increase in the zeta potential magnitude of the solid−liquid interface or the liquid− nanobubble interface leads to a larger gas phase CA reduction. This is consistent with the increasing electrostatic wetting tension on the nanobubbles with increasing zeta potential magnitude. This means that a larger zeta potential magnitude leads to a smaller CA for a nanobubble with fixed dimensions, as shown in Figure 6b and Figure 7b. Additionally, a larger ionic concentration can lead to a larger gas phase CA reduction, which is consistent with the effect of ionic concentration on the electrostatic wetting force. 4.3. The Size Dependence of EDL Interaction on Gas Phase CA. The gas phase CA reduction caused by the EDLs formed near the solid−liquid interface and liquid−nanobubble interface with the fixed zeta potentials is size-dependent. Figure 6a shows that, under the condition of fixed zeta potentials at the two interfaces, when nanobubbles have the same curvature radius, the gas phase CA reduction of the nanobubbles with larger height is smaller. Furthermore, the gas phase CA of the nanobubble increases with increasing nanobubble height, as shown in Figure 6b. This is consistent with the results of Kameda and Nakabayashi31 and Li and Zhao.12 Due to the decreasing gas phase CA reduction with increasing nanobubble height shown in Figure 6a, the gas phase CA of the nanobubble has a tendency toward macroscopic gas phase CA (the results in the solid line with zero zeta potential). This is because when 11129

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Figure 10. Effect of applied voltage on the average gas phase CA of surface nanobubbles formed on a PS sample.

Figure 9. AFM images of nanobubbles formed on a PS sample immersed in oxygenated saline solution under different applied voltages (adapted from ref 49).

the PS−saline solution interface is believed to increase with increasing applied voltage. This means that the increasing magnitude of the electrical potential of the solid−liquid interface will lead to a decrease in the gas phase CA of nanobubbles, which is consistent with our theoretical analysis. The increasing magnitude of the electrical potential of the solid−liquid interface adjusted by an applied voltage increases the electrostatic wetting tension on the nanobubble, which is in the outward direction from the nanobubble. Then, this tension pulls the nanobubble, enlarges its size, and decreases its gas phase CA. The results in the present work shed light on the understanding of the size-dependence of the gas phase CA of nanobubbles and the stability of nanobubbles. Furthermore, it provides a potential means to control boundary slip and fluid drag in micro/nanofluidic systems by adjusting the gas phase CA of nanobubbles using applied voltage.

applied voltage on the substrate has an obvious effect on the morphology and geometrical distribution of the surface nanobubbles. With increasing applied voltage, the diameter of the nanobubbles shows an increasing trend. However, the number of nanobubbles shows a decreasing trend. Based on theoretical analysis, the surface charge-induced EDL applies an electrostatic wetting tension on the surface nanobubble, which is in the outward direction from the nanobubble. Then, this electrostatic wetting tension pulls the nanobubble and leads to increasing diameters of the nanobubbles. When a voltage is applied on the PS-saline solution system, the electrical potential of the solid−liquid interface is changed. A higher voltage causes a higher electrical potential, leading to a larger electrostatic wetting tension on the nanobubbles and generating larger-sized bubbles. In addition, as the nanobubbles extend due to the electrostatic wetting tension, some adjacent nanobubbles coalesce with each other, leading to a further increase in the diameter of the nanobubbles and a decreasing number of nanobubbles on the solid−liquid interface. Based on the morphology of nanobubbles obtained by AFM, as shown in Figure 9, the height hb, and the radius of the TPCL L of surface nanobubbles can be determined, and the gas phase CA of surface nanobubbles can be calculated by θ = 2 arctan(hb/L). Figure 10 shows the effect of applied voltage on the average gas phase CA of nanobubbles formed on a PS sample immersed in oxygenated saline solution. The results in Figure 10 show that an increasing applied voltage results in a decreasing average gas phase CA of nanobubbles. In the present experimental study, the magnitude of the electrical potential of

5. CONCLUSION In this paper, the effect of the surface charge-induced EDL on the gas phase CA of surface nanobubbles was theoretically and experimentally studied. By introducing electrostatic wetting tension due to surface charge, which is in the outward direction from a nanobubble, a theoretical model was first established to investigate the effect of the EDLs formed near the solid−liquid interface and liquid−nanobubble interface on the gas phase CA of surface nanobubbles, and the size-dependence of the EDL interaction on the gas phase CA of nanobubbles. The theoretical results showed that the EDL formed near the solid−liquid interface or the liquid−nanobubble interface led to a gas phase CA reduction of surface nanobubbles because of the outward electrostatic wetting tension due to the surface charge. Further, an EDL with a larger zeta potential magnitude generated a larger electrostatic wetting tension and led to a larger gas phase CA reduction. Furthermore, the effect of the EDL on the gas phase CA of nanobubbles showed a significant size-dependence. The EDL-induced gas phase CA reduction decreased with the increasing nanobubble height, but increased with the increasing curvature radius of the nanobubble. This results suggest that, besides line tension, surface charge is another reason to explain the size-dependence of nanobubble. Furthermore, the effect of the EDL formed near the solid− liquid interface on the gas phase CA of nanobubbles on a PS film immersed in oxygenated saline solution was experimentally studied using an AFM while the electrical potential of the EDL was adjusted by an applied electrical field. The experimental results showed that the EDL led to a gas phase CA reduction of 11130

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nanobubbles and an EDL with a larger magnitude of electrical potential resulted in a larger gas phase CA reduction of surface nanobubbles.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The first author gratefully acknowledges the financial support of the National Natural Science Foundation of China (No. 51505292). The authors would like to thank Revalesio Corporation, Tacoma, WA for providing RNS60 for this study.

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