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Experimental study on interfacial characteristics during bubble dissolution
G Model
ARTICLE IN PRESS
COLSUA-20557; No. of Pages 7
Colloids and Surfaces A: Physicochem. Eng. Aspects xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Experimental study on interfacial characteristics during bubble dissolution Xiaowei Hu a,∗ , Reinhard Miller b,∗ , Liejin Guo a a State Key Laboratory of Multiphase Flow in Power Engineering, International Research Center for Renewable Energy, Xi’an Jiaotong University, Xi’an, 710049, China b Max Planck Institute of Colloids & Interfaces, Potsdam-Golm, 14476, Germany
h i g h l i g h t s
g r a p h i c a l
a b s t r a c t
• A new setup based on Profile Analysis Tensiometry (PAT) for interfacial characteristics study is developed. • Surface tension decreases during bubble dissolution. • The interfacial equilibrium concentration state can be broken by the substance transfer across the interface.
a r t i c l e
i n f o
Article history: Received 31 October 2015 Received in revised form 27 March 2016 Accepted 31 March 2016 Available online xxx Keywords: Bubble dissolution Profile analysis tensiometry Interfacial mass transfer Surface tension
a b s t r a c t A new setup for interfacial characteristics study during bubble dissolution based on Profile Analysis Tensiometry (PAT) is developed. And the investigations on nitrogen and helium bubble are carried out. The experimental results indicate the decrease of surface tension during bubble dissolution, which means the equilibrium concentration state at the interface is broken by the substance transfer across the interface, and is determined by the molecules transfer rate into the liquid. © 2016 Elsevier B.V. All rights reserved.
1. Introduction
∗ Corresponding authors. E-mail addresses: [email protected] (X. Hu), [email protected] (R. Miller).
Gas transfer across bubble or droplet interface in twocomponent system is a typical interfacial mass transfer process, existing widely in chemical industry and biology process. As the crucial role of gas-liquid interface on the interphase substance
http://dx.doi.org/10.1016/j.colsurfa.2016.03.076 0927-7757/© 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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ARTICLE IN PRESS X. Hu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects xxx (2016) xxx–xxx
2
Fig. 1. Schematic diagram of Profile Analysis Tensiometry.
transfer, much work has been focused on the resistance effect of interface on the transfer process, i.e. how the interface affects the transfer process. Mass transfer coefficient ki is usually applied to describe its magnitude. The interfacial mass transfer rate per unit area could be expressed as Jm = ki (ci − c∞ )
(1)
where ci and c∞ are the gas molecules concentration at interface and in the liquid respectively. And many theories have been developed to model the coefficient ki [1–4]. The most classic theory for interfacial mass transfer is film theory, which was proposed by Nernst in 1904 first, describing the mass transfer resistance rooting in the stagnant film close to the interface. Based on the concept, two-film theory was developed, which considered steady state mass transfer processes in the gasfilm and liquid-film at the two sides of interface as the main mass transfer resistance [1]. And the mass transfer coefficient can be obtained by ki = Dg /Z
face tension describes the interfacial equilibrium property, and dynamic surface tension reflects how the interface behaves during dynamic interfacial process. The methodology based on profile analysis provides a possible way for dynamic interfacial characteristics study [5–8]. Especially with the development of computer technology in these decades, PCs are able to manage the job of image analysis and profile fitting. The profile analysis methodology could work in real-time including the image acquisition and data analysis so that the progress of an experiment can be followed easily, and study on thermodynamics, kinetics and rheology of interfacial layers has been fully carried out [9–12]. Based on the background, this paper presents an experimental study on interfacial characteristics during mass transfer. Bubble dissolution process was applied to represent the interfacial mass transfer process in experiment. The investigations on interfacial characteristics during bubble dissolution were conducted by Profile Analysis Tensiometry (PAT), and the effects of mass transfer on interfacial characteristics was discussed.
(2)
where Z is the film thickness/m, and Dg is the gas diffusion coefficient in liquid/m2 s−1 . But this theory can be only available at small Sc number due to the neglecting of the interfacial substance accumulating and convection mass transfer effects. Higbie proposed penetration theory with considering interphase mass transfer as a dynamic process [2]. This theory assumes the dynamic mass transfer process is caused by movement of the fluid elements from liquid phase and the contacting with the gas at the interface. During the period of fluid element’s exposure to the interface and the replacement, mass transfer happens. And ki = 2 Dg /(t) was obtained [2,3]. Danckwerts proposed surface renewal theory based on the penetration theory [4]. By introducing a time distribution function of fluid elements at the interface (t) = Se−st , S is the surface renewal rate, which is the ratio of the surface area increase rate to the surface area, ki = SDg can be obtained [4]. This theory is relatively close to the practical situation for the consideration of random time distribution of fluid elements at the interface. However, for the details how the gas transfer process influences the interface, little information especially available experimental data could be found. Surface tension is the most important parameter describing the interface characteristics, directly reflecting the intermolecular forces at the interface. Though interface itself is an “artificial” zone where two components co-exist, precisely because of the treatment, people can understand the composition and the interaction between the components in this co-existing area. Sur-
2. Experimental PAT was applied to acquire the interfacial information for bubble dissolution experiment. As a profile analysis method, PAT is based on the difference between the sample bubble/drop shape and the standard bubble/drop shape under gravity in principle. The schematic diagram of PAT is shown in Fig. 1. The key elements are a video camera with objective, a homogenous light source, and dosing system, and all of them are controlled by a computer. In our experiment, the gas was injected by the dosing system of PAT with a fixed volume, forming a bubble being hold by a flat metal surface. Once the bubble forms, the camera system could acquire the bubble outline and calculate the bubble area or volume in real-time. In this paper, the calculated bubble volume was applied for analysis, while the initial value of gas volume controlled by dosing system was used for labeling the experimental conditions. Fig. 2 is the SEM of the solid surface, with a tiny hole in the middle for a stable bubble attaching on the surface. Firstly, in order to ensure mass conservation, a sealed system was applied, which prevents the gas from the atmosphere dissolving in water. So before forming the bubble, one layer of MCT (medium-chain triglyceride) oil was injected on the top of the water by a needle tubing. Secondly, in order to ensure the largest concentration difference between the two sides of the bubble interface, which is one of the factors determining the mass transfer rate, and to enhance the possible effects of mass transfer on interfacial characteristics, the degassed water was applied during experiment. It
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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3
Fig. 2. SEM of solid metal surface.
was prepared from milli-Q water, with boiling first and using ultra sound to treat again for one hour just before the experiment. The application of degassed water could also eliminate the effect of gas adsorption from the liquid on the bubble interface at initial time, which could make bubble expand. Before measurement, milli-Q water and air bubble were used for calibration under the PAT working-mode of buoyant bubble, as shown in Fig. 3. After that, the investigations on bubble interfacial characteristics during bubble dissolution under different conditions were carried out. All the experiments were conducted under room temperature and atmosphere pressure. And each experimental condition was conducted for at least 3 times during experiment.
3. Results and discussions At first, bubble dissolution process of nitrogen bubble was studied. Fig. 4 shows the surface area, volume and surface tension variations of nitrogen bubble during its dissolution. We define J=
V (ti ) − V (ti−1 ) mm3 /s (ti − ti−1 )
(3)
as the bubble dissolution rate, where V(t) is the bubble volume in real-time. The profiles of nitrogen bubble dissolution rates are shown in Fig. 5. From the figures, we can see during bubble dissolution, surface tension decreases constantly, and decreases faster at smaller initial bubble size; furthermore, bubble dissolution rate J
Fig. 3. Calibration profile by milli-Q water and air bubble.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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Fig. 4. Variations of (a) surface area, (b) volume, and (c) surface tension, during nitrogen bubble dissolving in water at different bubble initial volumes.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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Fig. 5. Dissolution rate of nitrogen bubble.
decreases during dissolution, especially within the first 5000 s, and after that dissolution rate keeps relatively constant. Comparatively, bubble dissolution process of helium bubble was also studied. Fig. 6 shows the surface area, volume and surface tension variations of helium bubble during its dissolution. And Fig. 7 shows the corresponding dissolution rate. Similar to the results of nitrogen bubble, surface tension also decreases during bubble dissolution, and decreases faster at smaller initial bubble size. Compared to nitrogen, surface tension decreases much faster. For the bubble dissolution rate J, it decreases during dissolution continuously. But it takes longer time to reach the constant dissolution rate compared to that of nitrogen. In our experimental conditions, since the bubble interface shrinks at a low speed, there is almost no convection effect during dissolution process. The assumptions for film theory could be satisfied. It means the dissolution rate could be determined by Eqs. (1) and (2). At initial time, the gas concentration in the liquid is almost zero for the degassed water application. Therefore, the initial gas dissolution rate for the nitrogen and helium bubble is almost the same, as presented in Figs. 5 and 7. With the gas molecules dissolving in the liquid, gas concentration in the liquid will be above zero. Since the diffusion coefficient of helium in water is over three times than that of nitrogen, helium molecules moves faster than nitrogen molecules in water. So it takes a longer time for helium molecules to reach the same concentration of nitrogen molecules. Correspondingly, the time to reach the constant dissolution rate of helium is longer that of nitrogen as shown in Figs. 5 and 7. Surface tension is the result of the interfacial composition and its concentration. Once the gas-liquid interface exist, gas molecules from bubble or liquid can be adsorbed at the gas-liquid interface. Due to the diffusion velocity of molecules in gas phase is almost 10000 times of that in liquid phase, the net gas adsorption at the interface comes from the bubble. Meanwhile, the gas molecules will desorb from the interface and transfer into the liquid due to the dissolution tendency. The competition between the adsorption and
desorption at the interface causes a dynamic substance concentration at the interface, which may influence the interfacial structures, and the surface tension. So surface tension decreases during bubble dissolution in Figs. 4 and 6. Actually, gas molecules adsorbed at the interface also has the possibility to desorb into the bubble again. When there is no gas molecules transferring into the liquid, the adsorption from the bubble and the desorption into the bubble maintain a dynamic equilibrium state, keeping a constant substance concentration at the interface. However, the gas desorption into the liquid breaks the above “two-way” equilibrium state of the gas adsorption and desorption at the interface, and leads to a surface tension decrease. The ability of gas molecules transferring into the liquid, which is related to the gas diffusion ability, determines the influencing degree on surface tension. The diffusion coefficient of helium in water is over three times than that of nitrogen as mentioned, so the surface tension of helium-water decreases faster than that of nitrogen-water shown in Figs. 4(c) and 6(c).
4. Conclusions Based on the Profile Analysis Tensiometry, the experimental study on dynamic gas-liquid interfacial characteristics during bubble dissolution has been carried out. The dissolution experimental results could be supported the film theory of interfacial mass transfer. The experimental data on surface tension indicates its decrease during bubble dissolution. That is because the gas transfer across the interface breaks the dynamic equilibrium state of gas molecules adsorbing from the bubble at the surface and desorbing from the surface into the bubble, and makes a net substance concentration variation at the interface and surface tension decrease. And the decrease degree is related to the gas type and determined by the gas diffusion coefficient in the liquid.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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Fig. 6. Variations of (a) surface area, (b) volume, and (c) surface tension, during helium bubble dissolving in water at different bubble initial volumes.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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Fig. 7. Dissolution rate of helium bubble.
Conflict of interest There is no conflict of interest. Acknowledgements The authors gratefully acknowledge the financial support of National Natural Science Foundation of China (No. 51306147, No. 51236007, No. 51323011), Natural Science Foundation of Shaanxi Province (No. 2014JQ7260) and China Postdoctoral Science Foundation (No. 2014T70918). One of the authors (X. Hu) was supported by China Scholarship Council. References [1] W.G. Whitman, The two film theory of gas absorption, Int. J. Heat Mass Transf. 5 (1962) 429–433. [2] R. Higbie, The rate of absorption of a pure gas into still liquid during short periods of exposure, Trans. Am. Inst. Chem. Eng. 31 (1935) 365–389. [3] H.L. Toor, J.M. Marchello, Film-penetration model for mass and heat transfer, AIChE J. 4 (1958) 97–101.
[4] P. Danckwerts, Significance of liquid-film coefficients in gas absorption, Ind. Eng. Chem. Res. 43 (1951) 1460–1467. [5] Y. Rotenberg, L. Boruvka, A.W. Neumann, Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces, J. Colloid Interface Sci. 93 (1983) 169–183. [6] P. Cheng, D. Li, L. Boruvka, Y. Rotenberg, A.W. Neumann, Colloids Surf. 43 (1990) 151. [7] R. Miller, A. Hofmann, R. Hartmann, K.H. Schano, A. Halbig, Measuring dynamic surface and interfacial-tensions, Adv. Mater. 4 (1992) 370–374. [8] S.A. Zholob, A.V. Makievski, R. Miller, V.B. Fainennan, Optimisation of calculation methods for determination of surface tensions by drop profile analysis tensiometry, Adv. Colloid. Interface 134–35 (2007) 322–329. [9] Y.Y. Zuo, D.Q. Li, E. Acosta, P.N. Cox, A.W. Neumann, Effect of surfactant on interfacial gas transfer studied by axisymmetric drop shape analysis-captive bubble (ADSA-cB), Langmuir 21 (2005) 5446–5452. [10] N. Wüstneck, R. Wüstneck, U. Pison, H. Möhwald, On the dissolution of vapors and gases, Langmuir 23 (2007) 1815–1823. [11] C. Kotsmar, V. Pradines, V.S. Alahverdjieva, E.V. Aksenenko, V.B. Fainerman, V.I. Kovalchuk, J. Kragel, M.E. Leser, B.A. Noskov, R. Miller, Thermodynamics, adsorption kinetics and rheology of mixed protein-surfactant interfacial layers, Adv. Colloid. Interface 150 (2009) 41–54. [12] B. Fainerman, S.V. Lylyk, E.V. Aksenenko, A.V. Makievski, J.T. Petkov, J. Yorke, R. Miller, Adsorption layer characteristics of Triton surfactants 1. Surface tension and adsorption isotherms, Colloid. Surf. A. 334 (2009) 1–7.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
ARTICLE IN PRESS
COLSUA-20557; No. of Pages 7
Colloids and Surfaces A: Physicochem. Eng. Aspects xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Experimental study on interfacial characteristics during bubble dissolution Xiaowei Hu a,∗ , Reinhard Miller b,∗ , Liejin Guo a a State Key Laboratory of Multiphase Flow in Power Engineering, International Research Center for Renewable Energy, Xi’an Jiaotong University, Xi’an, 710049, China b Max Planck Institute of Colloids & Interfaces, Potsdam-Golm, 14476, Germany
h i g h l i g h t s
g r a p h i c a l
a b s t r a c t
• A new setup based on Profile Analysis Tensiometry (PAT) for interfacial characteristics study is developed. • Surface tension decreases during bubble dissolution. • The interfacial equilibrium concentration state can be broken by the substance transfer across the interface.
a r t i c l e
i n f o
Article history: Received 31 October 2015 Received in revised form 27 March 2016 Accepted 31 March 2016 Available online xxx Keywords: Bubble dissolution Profile analysis tensiometry Interfacial mass transfer Surface tension
a b s t r a c t A new setup for interfacial characteristics study during bubble dissolution based on Profile Analysis Tensiometry (PAT) is developed. And the investigations on nitrogen and helium bubble are carried out. The experimental results indicate the decrease of surface tension during bubble dissolution, which means the equilibrium concentration state at the interface is broken by the substance transfer across the interface, and is determined by the molecules transfer rate into the liquid. © 2016 Elsevier B.V. All rights reserved.
1. Introduction
∗ Corresponding authors. E-mail addresses: [email protected] (X. Hu), [email protected] (R. Miller).
Gas transfer across bubble or droplet interface in twocomponent system is a typical interfacial mass transfer process, existing widely in chemical industry and biology process. As the crucial role of gas-liquid interface on the interphase substance
http://dx.doi.org/10.1016/j.colsurfa.2016.03.076 0927-7757/© 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
G Model COLSUA-20557; No. of Pages 7
ARTICLE IN PRESS X. Hu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects xxx (2016) xxx–xxx
2
Fig. 1. Schematic diagram of Profile Analysis Tensiometry.
transfer, much work has been focused on the resistance effect of interface on the transfer process, i.e. how the interface affects the transfer process. Mass transfer coefficient ki is usually applied to describe its magnitude. The interfacial mass transfer rate per unit area could be expressed as Jm = ki (ci − c∞ )
(1)
where ci and c∞ are the gas molecules concentration at interface and in the liquid respectively. And many theories have been developed to model the coefficient ki [1–4]. The most classic theory for interfacial mass transfer is film theory, which was proposed by Nernst in 1904 first, describing the mass transfer resistance rooting in the stagnant film close to the interface. Based on the concept, two-film theory was developed, which considered steady state mass transfer processes in the gasfilm and liquid-film at the two sides of interface as the main mass transfer resistance [1]. And the mass transfer coefficient can be obtained by ki = Dg /Z
face tension describes the interfacial equilibrium property, and dynamic surface tension reflects how the interface behaves during dynamic interfacial process. The methodology based on profile analysis provides a possible way for dynamic interfacial characteristics study [5–8]. Especially with the development of computer technology in these decades, PCs are able to manage the job of image analysis and profile fitting. The profile analysis methodology could work in real-time including the image acquisition and data analysis so that the progress of an experiment can be followed easily, and study on thermodynamics, kinetics and rheology of interfacial layers has been fully carried out [9–12]. Based on the background, this paper presents an experimental study on interfacial characteristics during mass transfer. Bubble dissolution process was applied to represent the interfacial mass transfer process in experiment. The investigations on interfacial characteristics during bubble dissolution were conducted by Profile Analysis Tensiometry (PAT), and the effects of mass transfer on interfacial characteristics was discussed.
(2)
where Z is the film thickness/m, and Dg is the gas diffusion coefficient in liquid/m2 s−1 . But this theory can be only available at small Sc number due to the neglecting of the interfacial substance accumulating and convection mass transfer effects. Higbie proposed penetration theory with considering interphase mass transfer as a dynamic process [2]. This theory assumes the dynamic mass transfer process is caused by movement of the fluid elements from liquid phase and the contacting with the gas at the interface. During the period of fluid element’s exposure to the interface and the replacement, mass transfer happens. And ki = 2 Dg /(t) was obtained [2,3]. Danckwerts proposed surface renewal theory based on the penetration theory [4]. By introducing a time distribution function of fluid elements at the interface (t) = Se−st , S is the surface renewal rate, which is the ratio of the surface area increase rate to the surface area, ki = SDg can be obtained [4]. This theory is relatively close to the practical situation for the consideration of random time distribution of fluid elements at the interface. However, for the details how the gas transfer process influences the interface, little information especially available experimental data could be found. Surface tension is the most important parameter describing the interface characteristics, directly reflecting the intermolecular forces at the interface. Though interface itself is an “artificial” zone where two components co-exist, precisely because of the treatment, people can understand the composition and the interaction between the components in this co-existing area. Sur-
2. Experimental PAT was applied to acquire the interfacial information for bubble dissolution experiment. As a profile analysis method, PAT is based on the difference between the sample bubble/drop shape and the standard bubble/drop shape under gravity in principle. The schematic diagram of PAT is shown in Fig. 1. The key elements are a video camera with objective, a homogenous light source, and dosing system, and all of them are controlled by a computer. In our experiment, the gas was injected by the dosing system of PAT with a fixed volume, forming a bubble being hold by a flat metal surface. Once the bubble forms, the camera system could acquire the bubble outline and calculate the bubble area or volume in real-time. In this paper, the calculated bubble volume was applied for analysis, while the initial value of gas volume controlled by dosing system was used for labeling the experimental conditions. Fig. 2 is the SEM of the solid surface, with a tiny hole in the middle for a stable bubble attaching on the surface. Firstly, in order to ensure mass conservation, a sealed system was applied, which prevents the gas from the atmosphere dissolving in water. So before forming the bubble, one layer of MCT (medium-chain triglyceride) oil was injected on the top of the water by a needle tubing. Secondly, in order to ensure the largest concentration difference between the two sides of the bubble interface, which is one of the factors determining the mass transfer rate, and to enhance the possible effects of mass transfer on interfacial characteristics, the degassed water was applied during experiment. It
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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3
Fig. 2. SEM of solid metal surface.
was prepared from milli-Q water, with boiling first and using ultra sound to treat again for one hour just before the experiment. The application of degassed water could also eliminate the effect of gas adsorption from the liquid on the bubble interface at initial time, which could make bubble expand. Before measurement, milli-Q water and air bubble were used for calibration under the PAT working-mode of buoyant bubble, as shown in Fig. 3. After that, the investigations on bubble interfacial characteristics during bubble dissolution under different conditions were carried out. All the experiments were conducted under room temperature and atmosphere pressure. And each experimental condition was conducted for at least 3 times during experiment.
3. Results and discussions At first, bubble dissolution process of nitrogen bubble was studied. Fig. 4 shows the surface area, volume and surface tension variations of nitrogen bubble during its dissolution. We define J=
V (ti ) − V (ti−1 ) mm3 /s (ti − ti−1 )
(3)
as the bubble dissolution rate, where V(t) is the bubble volume in real-time. The profiles of nitrogen bubble dissolution rates are shown in Fig. 5. From the figures, we can see during bubble dissolution, surface tension decreases constantly, and decreases faster at smaller initial bubble size; furthermore, bubble dissolution rate J
Fig. 3. Calibration profile by milli-Q water and air bubble.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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Fig. 4. Variations of (a) surface area, (b) volume, and (c) surface tension, during nitrogen bubble dissolving in water at different bubble initial volumes.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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Fig. 5. Dissolution rate of nitrogen bubble.
decreases during dissolution, especially within the first 5000 s, and after that dissolution rate keeps relatively constant. Comparatively, bubble dissolution process of helium bubble was also studied. Fig. 6 shows the surface area, volume and surface tension variations of helium bubble during its dissolution. And Fig. 7 shows the corresponding dissolution rate. Similar to the results of nitrogen bubble, surface tension also decreases during bubble dissolution, and decreases faster at smaller initial bubble size. Compared to nitrogen, surface tension decreases much faster. For the bubble dissolution rate J, it decreases during dissolution continuously. But it takes longer time to reach the constant dissolution rate compared to that of nitrogen. In our experimental conditions, since the bubble interface shrinks at a low speed, there is almost no convection effect during dissolution process. The assumptions for film theory could be satisfied. It means the dissolution rate could be determined by Eqs. (1) and (2). At initial time, the gas concentration in the liquid is almost zero for the degassed water application. Therefore, the initial gas dissolution rate for the nitrogen and helium bubble is almost the same, as presented in Figs. 5 and 7. With the gas molecules dissolving in the liquid, gas concentration in the liquid will be above zero. Since the diffusion coefficient of helium in water is over three times than that of nitrogen, helium molecules moves faster than nitrogen molecules in water. So it takes a longer time for helium molecules to reach the same concentration of nitrogen molecules. Correspondingly, the time to reach the constant dissolution rate of helium is longer that of nitrogen as shown in Figs. 5 and 7. Surface tension is the result of the interfacial composition and its concentration. Once the gas-liquid interface exist, gas molecules from bubble or liquid can be adsorbed at the gas-liquid interface. Due to the diffusion velocity of molecules in gas phase is almost 10000 times of that in liquid phase, the net gas adsorption at the interface comes from the bubble. Meanwhile, the gas molecules will desorb from the interface and transfer into the liquid due to the dissolution tendency. The competition between the adsorption and
desorption at the interface causes a dynamic substance concentration at the interface, which may influence the interfacial structures, and the surface tension. So surface tension decreases during bubble dissolution in Figs. 4 and 6. Actually, gas molecules adsorbed at the interface also has the possibility to desorb into the bubble again. When there is no gas molecules transferring into the liquid, the adsorption from the bubble and the desorption into the bubble maintain a dynamic equilibrium state, keeping a constant substance concentration at the interface. However, the gas desorption into the liquid breaks the above “two-way” equilibrium state of the gas adsorption and desorption at the interface, and leads to a surface tension decrease. The ability of gas molecules transferring into the liquid, which is related to the gas diffusion ability, determines the influencing degree on surface tension. The diffusion coefficient of helium in water is over three times than that of nitrogen as mentioned, so the surface tension of helium-water decreases faster than that of nitrogen-water shown in Figs. 4(c) and 6(c).
4. Conclusions Based on the Profile Analysis Tensiometry, the experimental study on dynamic gas-liquid interfacial characteristics during bubble dissolution has been carried out. The dissolution experimental results could be supported the film theory of interfacial mass transfer. The experimental data on surface tension indicates its decrease during bubble dissolution. That is because the gas transfer across the interface breaks the dynamic equilibrium state of gas molecules adsorbing from the bubble at the surface and desorbing from the surface into the bubble, and makes a net substance concentration variation at the interface and surface tension decrease. And the decrease degree is related to the gas type and determined by the gas diffusion coefficient in the liquid.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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Fig. 6. Variations of (a) surface area, (b) volume, and (c) surface tension, during helium bubble dissolving in water at different bubble initial volumes.
Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076
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7
Fig. 7. Dissolution rate of helium bubble.
Conflict of interest There is no conflict of interest. Acknowledgements The authors gratefully acknowledge the financial support of National Natural Science Foundation of China (No. 51306147, No. 51236007, No. 51323011), Natural Science Foundation of Shaanxi Province (No. 2014JQ7260) and China Postdoctoral Science Foundation (No. 2014T70918). One of the authors (X. Hu) was supported by China Scholarship Council. References [1] W.G. Whitman, The two film theory of gas absorption, Int. J. Heat Mass Transf. 5 (1962) 429–433. [2] R. Higbie, The rate of absorption of a pure gas into still liquid during short periods of exposure, Trans. Am. Inst. Chem. Eng. 31 (1935) 365–389. [3] H.L. Toor, J.M. Marchello, Film-penetration model for mass and heat transfer, AIChE J. 4 (1958) 97–101.
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Please cite this article in press as: X. Hu, et al., Experimental study on interfacial characteristics during bubble dissolution, Colloids Surf. A: Physicochem. Eng. Aspects (2016), http://dx.doi.org/10.1016/j.colsurfa.2016.03.076