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Effect of Gold Nanoparticles on the Dynamics of Gas Bubbles Saeid Vafaei and Dongsheng Wen* School of Engineering and Materials Science, Queen Mary University of London, London, U.K. Received September 24, 2009 The effect of gold nanoparticles on the formation of gas bubbles on top of a stainless steel tube is investigated in this work. Unlike other observations of bubble dynamics under evaporation or boiling conditions, which are caused by the surface modification due to particle sedimentation, this work reveals a unique phenomenon of enhanced pinning of the triple line and improved wetting by nanoparticles suspended in the liquid phase. Detailed characteristics related to bubble growth inside pure water and gold nanofluids, including the dynamics of the triple line, the variation of instantaneous contact angle, bubble height, and bubble volume expansion rate, are analyzed. The shape of the bubble is found to be in good agreement with predictions of the Young-Laplace equation by using experimental captured radius of contact line and bubble height as the two known inputs. The variation of surface tensions and the resultant force balance at the triple line are believed to be responsible for the modified dynamics of the triple line and subsequent bubble formation.
1. Introduction Bubbles are fundamental to many industries with extensive applications in power plants, chemical refineries, colloids engineering and pharmaceutical industry, and advanced medical and healthcare fields.1 An in-depth understanding of the bubble formation requires detailed knowledge at the interface of solidliquid-gas phases, especially the dynamics of triple lines and the variation of instantaneous contact angles, which are of interest to many practical applications such as surface coating and droplets drying. Extensive studies have been performed in the past to understand such processes. For an equilibrium system, a force balance method is usually proposed at the triple line to relate the macroscopic contact angle with material properties. A classical example is the Young’s equation, which is typically written as ð1Þ σlg cos θe ¼ σsg - σsl where θe is the equilibrium contact angle and σlg, σsg, and σsl are surface tensions at liquid-gas, solid-gas, and solid-liquid interfaces, respectively. While the liquid-gas surface tension is tabulated for a variety of materials, the solid-gas and solidliquid surface tensions are not easily available. Several independent approaches from both experimental and theoretical aspects have been employed to estimate solid surface tensions, i.e., through the measurement of interfacial forces, contact angles, capillary penetrations, particle sedimentations, solidification front interactions, and film flotation, as well as by gradient theory, Lifshitz theory, and van der Waals forces. In a straight way, the solid-liquid surface tension can be correlated as a function of liquid-gas and gas-solid surface tensions σsl ¼ f ðσ sg , σlg Þ
ð2Þ 2
and several correlations have been developed. The Young’s equation is associated with several restrictive conditions, and its applications are limited to equilibrium system *Corresponding author: e-mail
[email protected]; Tel 0044-20-78823232. (1) Wen, D. Int. J. Hyperthermia 2009, 25, 533. (2) Kwok, D. Y.; Neumann, A. W. Adv. Colloid Interface Sci. 1999, 81, 167. (3) Carey, V. P. Liquid-Vapor Phase-Change Phenomena, 2nd ed.; Hemisphere Publishing Corp.: Washington, DC, 2008.
6902 DOI: 10.1021/la1012022
where the substrate is ideal and the contact angle is size independent.3 Since the contact angle of axisymmetric bubbles and droplets are size dependent,4 the Young’s equation cannot be applied directly except for long droplets.5 In spite of that, the solid-gas, solid-liquid, and liquid-gas surface tensions acting on the triple line have a significant role on the shapes of bubbles and droplets in general, particularly the contact angle. To take the effect of size into the consideration, there were several attempts including the modified Young’s equation as (Figure 1) σ þ σ lg cos θe ¼ σsg - σ sl rd
ð3Þ
where σ and rd are the line tension and radius of contact line, respectively. There have been a number of experimental measurements of the line tension. Unfortunately, there is still no consistency in the reported value even on the force direction and orders of magnitude of the value of the line tension.6-12 For a dynamic system, the mechanisms of dynamics of triple line and wetting behavior of pure liquid on the solid are still not fully revealed; a few models have been proposed from both hydrodynamic and molecular kinetics aspects. The introduction of nanoparticles into a base liquid, or termed as nanofluids, makes it more complicated. Many experimental studies have been conducted to reveal the effects of nanoparticles on contact angles,13-16 (4) Gaydos, J.; Neumann, A. W. J. Colloid Interface Sci. 1987, 120, 76. (5) Vafaei, S.; Podowski, M. Z. Adv. Colloid Interface Sci. 2005, 113, 133. (6) Duncan, D.; Li, D.; Gaydos, J.; Neumann, A. W. J. Colloid Interface Sci. 1995, 169, 256. (7) Good, R. J.; Koo, M. N. J. Colloid Interface Sci. 1979, 71, 283. (8) Li, D.; Neumann, A. W. Colloids Surf. 1990, 43, 195. (9) Kwok, D. Y.; Lin, F. Y. H., Neumann, A. W. Adhesion Science and Technology Proceeding of the International Adhesion Symposium, Japan, 1994. (10) Amirfazli, A.; Neumann, A. W. Adv. Colloid Interface Sci. 2004, 110, 121. (11) Gershfeld, N. L.; Good, R. J. J. Theor. Biol. 1967, 17, 246. (12) Harkins, W. O. J. Chem. Phys. 1937, 5, 135. (13) Vafaei, S.; Borca-Tasciuc, T.; Podowski, M. Z.; Purkayastha, A.; Ramanath, G.; Ajayan, P. M. Nanotechnology 2006, 17, 2523. (14) Sefiane, K.; Skilling, J.; MacGillivray, J. Adv. Colloid Interface Sci. 2008, 138, 101. (15) Vafaei, S.; Wen, D.; Ramanath, G.; Borca-Tasciuc, T. 11th International Symposium on Gas-Liquid Two-Phase Flows, ASME, Aug 2-5, 2009, Vail, CO. (16) Coursey, J. S.; Kim, J. Int. J. Heat Fluid Flow 2008, 29, 1577.
Published on Web 04/15/2010
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Figure 1. Schematic of solid/gas, solid/liquid, and gas/liquid surface tensions at triple line.
structuring phenomenon,17,18 surface tension,19,20 and evaporation, boiling heat transfer coefficient, and critical heat flux.14,21-24 Among these studies, Wasan and Nikolov17 observed a particlestructuring phenomenon in the liquid film meniscus region for latex spherical particles of diameter ∼1 μm at 7% volume fraction with a surface charge of 0.8 μC/cm2, through a reflected-light digital video microscopy. The Brownian motion of colloidal particles along the solid surface was measured, and the period of oscillation was found to be around 2 Hz. In addition, the probability density distribution functions for disordered and ordered particles were plotted.17 Theoretically, some work has shown that particles could spread the triple line to a long distance of 20-50 times of the particle diameter through a structural disjoining pressure as a result of the self-ordering of particles in a confined wedge. However the structural disjoining force only becomes significant at relative high particle concentrations, i.e., over 20% volume fraction.25 The evaporation of nanoparticle laden droplets on top of a 1 μm thick PTFE layer on silicon wafer substrate was conducted by Sefiane et al.,14 where it was observed that the triple line exhibited a “stick-slip” behavior. It is postulated that such triple line dynamics was caused by deposited nanoparticles and/or increased effective viscosity due to high local nanoparticle concentrations. While in earlier studies, solids dispersed in a drying droplet were observed to migrate to the edge of the drop and form a solid ring due to an outward flow driven by the loss of solvent by evaporation.26 Nevertheless, no direct evidence of the influence of nanoparticles on the dynamics of bubble formation has ever been supplied so far, which forms the main motivation of this study. Using welldefined gold nanofluids as an example, this work will reveal the influence of nanoparticles on the formation of gas bubbles on top of a stainless steel tube, with a particular focus on the dynamics of triple lines and the variations of instantaneous contact angles. The experimental results will be compared with the predications from the Young-Laplace equation, and the influence of nanoparticles on other related parameters such as bubble volume and radius of at bubble apex will be revealed.
2. Experimental Setup The stainless steel tube has an internal diameter of 110 μm and outside diameter of 210 μm, which is submerged into a transparent (17) Wasan, D. T.; Nikolov, A. D. Nature 2003, 423, 156. (18) Chengara, A.; Nikolov, D.; Wasan, D. T.; Trokhymchuk, A.; Henderson, D. J. Colloid Interface Sci. 2004, 280, 192. (19) Kim, S. J.; Bang, I. C.; Buongiorno, J.; Hub, L. W. Int. J. Heat Mass Transfer 2007, 50, 4105. (20) Vafaei, S.; Purkayastha, A.; Jain, A.; Ramanath, G.; Borca-Tasciuc, T. Nanotechnology 2009, 20, 185702. (21) You, S. M.; Kim, J. H.; Kim, K. Appl. Phys. Lett. 2003, 83, 3374. (22) Wen, D S.; Ding, Y L.; Williams, R. J. Enhanced Heat Transfer 2006, 13, 231. (23) Wen, D. S. Int. J. Heat Mass Transfer 2008, 51, 4958. (24) Kim, S. J.; McKrell, T.; Buongiorno, J.; Hu, L. W. J. Heat Transfer 2009, 131, 043204. (25) Wen, D. J. Nanopart. Res. 2008, 10, 1129. (26) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827.
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square-sized glass container of the size of 20 20 mm and a height of 72 mm. The glass container is filled with quiescent deionized water or gold nanofluids to a height of 20 mm and open to the atmosphere under ambient conditions. The gas flow is supplied by compressed air in a cylinder, which is connected to a highly accurate gas flow controller through a pressure reduction valve. The gas is controlled in the range of 0.015-0.83 mL/min with an accuracy of (0.5% of its reading. Detailed bubble formation process is captured by a high-speed camera (1200 frame/s) equipped with an optical microscope head. The resolution of the camera is 5 μm/pixel, and later image processing in commercial software at pixel resolution renders reliable bubble parameters such as transient radius of contact line and bubble height. The gold nanoparticle dispersions are custom ordered from a commercial company that contain only deionizer water and gold nanoparticles. Independent studies, including equilibrium contact angle measurement of the top layer liquid after particle separation and chemical element analysis by energy dispersive X-ray spectroscopy (EDS), have been performed to confirm that there is no any surfactants or dispersants presence in the gold nanofluids. Good stability of nanoparticles is achieved through random Brownian motions. The particles have a narrow size distribution and an average diameter of 5 nm (Figure 2). Separate measurements of particle size in liquid dispersions by dynamic light scattering (DLS) method show a uniform size distribution, consistent with that observed by TEM, which also confirms the good stability of gold particles. The nanoparticle concentration of nanofluid is controlled at 0.01% by weight in this study. The static equilibrium contact angle of water on stainless-steel surface is also measured by a goniometer, which shows a consistent result with other published studies for a given droplet volume. The captured images of bubble formation are imported into the software of a drop shape analysis (DSA) system to measure the surface tension of gold nanofluid and water. The accuracy of surface tension measurement of the device is 0.01 mN/m. The nanofluid and water surface tensions are measured using six different bubble images. The surface tension of water and nanofluid are determined as 0.07238 ( 0.0041 and 0.06753 ( 0.0066 N/m, respectively, under room temperature.
3. Axisymmetric Bubble Shape Prediction For small flow rates as in the experiments, bubble formation takes place in a quasi-steady-state manner; i.e., a force balance is reached between the surface tension and external forces. Mathematically, the Young-Laplace equation represents a mechanical equilibrium condition between two fluids separated by an interface. The Young-Laplace equation shows that the pressure difference across the interface is equal to the product of the curvature multiplied by the gas-liquid surface tension. The Young-Laplace equation has been solved to predict the shape of axisymmetric liquid pendants and sessile drops on ideal solid surfaces.27,28,5 In addition, the prediction of axisymmetric bubble shapes by the Young-Laplace equation under quasi-steady-state conditions has been examined by experiments27,29 and numerical simulations based on the volume of fluid method,30 with good agreement reached. In this paper, the Young-Laplace equation will be applied to predict the bubble formation on a submerged orifice based on the running angle and curvature system, and the predictive results will be compared with experimental studies. Similar to the experimental setup, the solid surface is assumed to (27) del Rio, O. I.; Neumann, A. W. J. Colloid Interface Sci. 1997, 196, 136. (28) Vafaei, S.; Podowski, M. Z. The Modeling of Liquid Droplet Shape on Horizontal and Inclined Surfaces, 5th ICMF, Yokohama, Japan, May 30-June 4, 2004. (29) Gerlach, D.; Biswas, G.; Durst, F.; Kolobaric, V. Int. J. Heat Mass Transfer 2005, 48, 425–438. (30) Gerlach, D.; Tomar, G.; Biswas, G.; Durst, F. Int. J. Heat Mass Transfer 2006, 49, 740.
DOI: 10.1021/la1012022
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Figure 2. TEM image of gold nanoparticles.
be perfectly smooth and homogeneous without any contact angle hysteresis, and the gas flow rate is assumed to be steady and slow enough to ignore the gas-liquid shear stress. Under such conditions, the equilibrium of the surface pressure and gravitational forces on the bubble surface can be described by the YoungLaplace equation. Assuming that the bubble is growing in a quasi-steady state, the Young-Laplace equation on the interfacial surface can be written as 1 1 Δp ¼ σlg þ ð4Þ R1 R2 where R1 and R2 are the radii of curvatures; i.e., R1 is the radius of curvature describing the latitude as it rotates, and R2 is the radius of curvature in a vertical section of the bubble describing the longitude as it rotates. The centers of R1 and R2 are on the same line but different location. Δp is the pressure difference between the gas, pg, and liquid phase, pl (see Figure 3), which can be written as pg ðzÞ ¼
2σlg þ P0 þ Fg gz þ Fl gh R0
ð5Þ
pl ðzÞ ¼ P0 þ Fl gðh þ zÞ
ð6Þ
R1 ¼ ds=dθ and R2 ¼ r=sin θ
ð7Þ
where P0 is the ambient pressure, h is the hydrostatic head, and θ is the running angle. Substituting eqs 5-7 into eq 4, the YoungLaplace equation is obtained as dθ 2 gz sin θ ¼ - ðFl - Fg Þds R0 σ lg r
ð8Þ
The Young-Laplace equation can be solved, with the following system of ordinary differential equations for axisymmetric interfaces, to obtain the bubble shape. dr ¼ cos θ ds
ð9Þ
dz ¼ sin θ ds
ð10Þ
6904 DOI: 10.1021/la1012022
Figure 3. Schematics of an axisymmetric bubble.
dV ¼ πr2 sin θ ds
ð11Þ
This system of ordinary differential equations avoids the usual singularity problem at the bubble apex in a Cartesian coordinate, since sin θ 1 ð12Þ ¼ r R0 s¼0
Knowing two parameters of a bubble shape (such as contact angle, radius of contact line, bubble volume, or location of the apex), the system of ordinary differential eqs 8-11 can be solved to obtain the axisymmetric bubble shape, using the following boundary conditions.27,29 rð0Þ ¼ zð0Þ ¼ θð0Þ ¼ Vð0Þ ¼ 0
ð13Þ
In this study, the accurately determined experimental value of the radius of contact line and the height of bubble are used as the only two inputs to solve above equations at each time step to predict the bubble shape and other related parameters. The set of firstorder differential equations are solved in Version 7 of Matlab environment using the fourth-order Runge-Kutta method. The simultaneous bubble volume expansion rate is also calculated by solving the Young-Laplace equation to predict the variation of bubble volume over time. The average gas flow rate is calculated by multiplying the bubble frequency with the bubble detachment volume, Qav = fV, which is the summation of last bubble volume predicted by Young-Laplace equation and extra R volume added during the detachment period, tltdQ dt. The detachment time, td, is determined experimentally.
4. Results and Discussion 4.1. General Observation. In the experiments, many differences on the characteristics of bubble formation in water and in gold nanofluids are observed. In general, bubbles forming in gold Langmuir 2010, 26(10), 6902–6907
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nanofluids are developed earlier, and the bubble departure volume is smaller but at increased bubble departure frequency. For instance, a reduction in bubble departure volume by 25% and an increase of ∼1/3 in bubble frequency is observed for bubbles forming in gold nanofluids under a gas flow rate of 0.249 mL/min. It is believed that such differences are partly associated with the modification of surface tension due to the presence of gold nanoparticles, i.e. a 7% reduction in the surface tension is measured for gold nanofluids comparing with that of deionized water. It might also be influenced by the dynamics of the triple line as described in section 4.3. It is observed that with the increase of gas flow rates, the bubble frequency increases but the departure volume exhibits a weak dependence on the flow rate for both pure water and nanofluids. For bubbles forming in gold nanofluids, the detached volume varies only ∼5% of the average value within the whole range (0.015-0.83 mL/min). It is believed that such a weak bubble volume dependence on flow rate is due to the dual roles that the flow rate may play here. At one side, increasing flow rate contributes to the increase of the flow amount into the bubble; however at the other side, it would contribute to the necking process, which has a tendency of reducing the bubble volume. The gas flow rate effect on the departure volume appears to be a combination of these two effects. 4.2. Comparison of Bubble Shapes. As presented in section 3, the prediction of bubble shape requires two known parameters such as contact angle, radius of contact line, bubble volume, bubble height, or location of the apex. Within these parameters, the radius of contact line and bubble height can be reliably determined by high-speed imaging and are used as two inputs to solve eqs 8-12. Figure 4 compares the prediction of bubble shape inside nanofluid and pure water with experimental data for a gas flow rate of 0.249 mL/min. Apart from the necking and detachment periods, where the bubble starts being stretched and the effect of viscosity and inertia becomes important, the Young-Laplace equation predicts bubble shape reliably for both pure liquids and nanofluids. The only exception is for bubbles forming in nanofluids in a short period between t = 0.414-0.581 s, when the contact angle reaches the minimum and starts being increased. Within this period, there is slight difference (
