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Bubble circling phenomena in subcooled nucleate pool boiling on microwires
International Journal of Heat and Mass Transfer 64 (2013) 945–951
Contents lists available at SciVerse ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Technical Note
Bubble circling phenomena in subcooled nucleate pool boiling on microwires Leping Zhou a,⇑, Longting Wei a,1, Yuanyuan Li a,1, Xiaoze Du a,⇑, Buxuan Wang b,2 a School of Energy, Power and Mechanical Engineering, Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, North China Electric Power University, Beijing 102206, China b Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 28 September 2012 Received in revised form 7 May 2013 Accepted 9 May 2013 Available online 7 June 2013 Keywords: Bubble circling Subcooled boiling Marangoni effect Viscous force
a b s t r a c t The interaction between adjacent bubbles plays an important role in boiling heat transfer on a micro heat source. In this paper, the visualizing bubble behaviors during subcooled pool boiling on microwires were revisited experimentally. Bubble circling phenomena, the circling of small bubble around a larger one for subcooled boiling on platinum microwires submerged in ultrapure water or self-rewetting fluid, were investigated. Different types of bubble circling phenomena, including small bubble sweeping, departing, rotating, returning or chasing at a larger bubble interface, were described in detail. The roles of Marangoni effect and viscous force were analyzed in the process of bubble circling to understand the mechanism of bubble behaviors on micro heated surface. The investigation on the bubble circling phenomenon can help verify the crucial factors that influence the bubble dynamics, bubble interaction and boiling heat transfer. The bubble dynamics in this phenomenon also makes it an interesting choice for many microscale applications. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Nucleate boiling phenomenon has been extensively investigated among boiling heat transfer problems since the boiling curve and the different heat transfer regimes for saturated pool boiling was first introduced by Nukiyama [1]. Bubble dynamics, bubble induced convection, thermocapillary flow, microlayer evaporation, nonlinear characteristics of boiling, etc., are possible mechanisms for the high heat transfer rate in nucleate boiling [2–5]. It is well recognized that the research on bubble dynamics is critical in boiling heat transfer mechanisms. However, there remain many unsolved problems in bubble dynamics and bubble interaction needed for further investigation [6–9]. Bubbles usually emerge from the active nucleate sites on a heating surface, grow up to a critical size, and then depart from the nucleate sites that can be easily observed with the naked eyes. When heater size scales down in recent years, e.g., nucleate boiling on microwires, many interesting phenomena could be observed in
⇑ Corresponding authors. Tel.: +86 10 5197 1316; fax: +86 10 5197 1328 (L. Zhou), tel.: +86 10 5197 1326; fax: +86 10 5197 1328 (X. Du). E-mail addresses: [email protected] (L. Zhou), [email protected] (L. Wei), [email protected] (Y. Li), [email protected] (X. Du), bxwang@mail. tsinghua.edu.cn (B. Wang). 1 Tel.: +86 10 5197 1316; fax: +86 10 5197 1328. 2 Tel.: +86 10 6278 9751; fax: +86 10 6277 0209. 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.05.023
the experiments. For example, Wang et al. [10–12] observed unusual bubble dynamics (such as bubble sweeping and bubbletop jet flow) and bubble interaction (including bubble collision, separation and coalescence) phenomena in subcooled nucleate boiling on microwires. Lu et al. [13–15] investigated experimentally and theoretically the bubble dynamics during subcooled nucleate boiling of water on platinum microwires. They pointed out that the temperature difference induced interfacial thermocapillary force and the bubble interactions are the most important forces during bubble collision and separation. Christopher et al. [16] further suggested that the unusual bubble dynamics can be explained by the asymmetric temperature, pressure or surface tension distribution on both sides of the bubble, since the relative motion between bubbles, bubble collision, coalescence and departure can actually affect the temperature and flow fields of the surrounding liquid. They established a model that balances the Marangoni force, the drag force, and the contact line force acting on a sweeping bubble and shows that when the sweeping bubble approaches an stationary bubble at moderate superheats, the reduced wire temperatures around the stationary bubble cause the sweeping bubble to decelerate and reverse direction before colliding with the stationary bubble [17]. Generally speaking, the Marangoni effect is a crucial factor that influences the bubble interactions. Besides the prominent effect of Marangoni convection, fluid viscosity (or drag force) can also apparently affect bubble dynamics, especially in the rising process [18,19]. Therefore, the fluid viscous
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Nomenclature db E fV h q R
small bubble diameter (m) viscosity temperature coefficient (J mol1) viscous force (N) heat transfer coefficient (W m2 k1) heat flux (W m2) bubble diameter (m)
universal t T u
gas constant (J mol1 K1) time (s) temperature (K) velocity (m s1)
effect should also be an important contributor for the bubble dynamics. In this paper, a unique bubble behavior that is closely related with the above-mentioned bubble dynamics and bubble interaction is observed. The phenomenon is named as bubble circling, for which an interaction between bubbles during subcooled nucleate boiling of ultrapure water or high-carbon alcohol aqueous solution (self-rewetting fluid) on microwires is recorded using highspeed CCD camera system. Different types of bubble circling phenomena, accompanied by small bubble sweeping, departing, rotating, returning or chasing at a larger bubble interface, are described in detail. The possible mechanisms of these bubble behaviors on micro heated surface are discussed, and the effects of Marangoni convection and viscous force are further analyzed for the observed bubble circling phenomenon. The investigation on the bubble circling phenomenon can help verify the crucial factors that influence the bubble dynamics, bubble interaction and boiling heat transfer. The bubble dynamics in this phenomenon also makes it an interesting choice for many microscale applications, such as microchannel and microflow. 2. Experimental set-up The schematics of the experimental set-up for visualizing the subcooled nucleate pool boiling of ultrapure water on microscale platinum wire is shown in Fig. 1. The wire was horizontally installed at the bottom of the glass container, and was connected on the electric connectors and heated by a DC Power Supply (Dahua DH1720A-3). The power supply provided direct current to the wire, generating Joule heat as the applied heat flux. The heater was replaced by different platinum wires, namely 30 lm, 50 lm or 60 lm in diameter and 65 mm in length. The ends of the wire are connected to the DC power. The size of the glass container is 25 25 25 cm. The images of bubble behaviors during subcooled nucleate boiling on these microwires were recorded with a highspeed CCD (Luster LightTech MC1310, 500 fps) and a data acquisition module (Agilent 34970). The heating wire was fixed on an adjustable bracket, recording the voltage and the current at the ends of it, so as to calculate the heat flux with the electric resistance. The testing liquid being heated and to be observed was ultrapure water or alcohol aqueous solution, with an initial temperature at around 289 K. The water was deaerated by an auxiliary copper heater with power output 150 W to heat the water for about 60 min before the boiling experiment. The bulk temperature of the testing liquid was measured using a thermocouple located 1 cm apart from the microwire. The heat flux can be calculated by using the resistance-temperature formula for the electric
Greek symbols l dynamic viscosity (Pa s) h angle r surface tension (N m1) s shear force (N m2) Subscripts 0 reference point b bubble w wire
resistor and the error for the heat flux was estimated to be less than 0.1%. The error for the average wall temperature was estimated to be less than 5 K. The container was kept in an environment at atmospheric pressure. An observation area of 2 2 mm around the center of the wire was selected for observation. 3. Results and discussions Experimental observation of the bubble dynamics of nucleate pool boiling on the microwire was conducted using the device described in the previous section. Several interesting phenomena were observed, especially the bubble circling phenomenon. Small bubble, with or without jet flow at its top, can circle a larger stationary bubble that it meets, when it is sweeping on or departing from the microwire. Bubble circling phenomenon is diverse and complex. During the process of circling, small bubble can be accompanied with a jet flow; it can also depart, rotate, return or chase at the interface of a larger bubble. A detailed discussion on the bubble circling phenomena is given as follows. 3.1. Bubble sweeping and circling Bubble sweeping can be observed frequently in the experiment when heat flux is relatively high [11,17]. In the experimental investigation, it happens at heat flux, for example, higher than 1.6 106 W/m2. When it occurs, the bubble moves back and forth along the microwire, accompanied with the bubble growth. There exists single or multiple jet flows on the top of the reciprocating bubble. In addition to the single bubble sweeping, the sweeping bubbles nearby can also influence each other by collision. For
DC Power Supply
Computer Data Acquisition
Pure Water Transparent container
CCD Camera
Thermocouple
Heating wire
Bracket
Fig. 1. Schematics of experimental set-up.
L. Zhou et al. / International Journal of Heat and Mass Transfer 64 (2013) 945–951
example, two sweeping bubbles can collide and merge into a larger sweeping bubble. Two sweeping bubbles can also collide and move along the same direction or move oppositely. A sweeping bubble can collide with a stationary bubble and the bubble collision process is just like an elastic collision – for example, for a platinum wire (100 lm in diameter, and the heat flux is 0.6 106 W/m2) immersed in water (subcooling degree is 70 K), a large bubble moves with a velocity of 40 mm/s and collides with an stationary bubble; after about 0.024 s, the bubble decelerates to zero as it approaches to the stationary bubble; then the sweeping bubble began to return and accelerate [13]. The bubble sweeping phenomenon was frequently observed in the experiment, but few report mentioned the circling phenomenon after the bubble sweeping along the thin wire. Besides the above-mentioned various forms of sweeping of two bubbles, a small sweeping bubble can also circle a larger bubble that is stationary yet has no prominent jet flow at its top. When the diameter of the heating wire is 30 lm and the heat flux is 2.35 106 W/m2, the measured temperature of the ultrapure water is 290.35 K and the measured temperature of the wire is 337.09 K. Under this condition, the small bubble can sweep towards the larger bubble, and then circle the latter for a short distance before it collapses into the subcooled water near the bubble-top, as shown in Fig. 2. The complete time for the sweeping and circling is about 0.03 s. For bubble circling phenomenon, there may have a thin liquid film that could protect them from coalescence between the bubbles. A thin liquid film between a small bubble and the lager bubble was observed by Jiang et al. [20] in the sub-cooled boiling experiment of deaerated water, where a small bubble rotated slowly at the top of a larger bubble staying on a 10 mm diameter steel cylinder heater (but they did not report the bubble circling process). This may help explain why in this investigation the two bubbles did not coalesce during the circling process. It may also explain why in Section 3.3 a small bubble rotating at the top of a larger bubble did not coalesce with the latter. The thermocapillary force (Marangoni effect) is essentially a critical factor in bubble behaviors, including bubble-top jet flow, bubble movement, and bubble interaction. For example, the Marangoni effect drives the surrounding liquid to flow toward the bubble-top (the pumping effect) and thus forms jet flow [12]. When the heat flux or the temperature gradient on the bubble is relatively small, the bubble diameters could be large (usually about 1 mm in our experimental observation), which is in good
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agreement with previous investigations [11–13,21–24]. In these studies, the diameters of the heating wire and the bubble were usually less than 1 mm, and consequently, both the interfacial force and the thermocapillary force are important for bubble top jets. The interfacial flow at the interface induces a shear force s in the liquid phase and s0 in the vapor phase [25]. These shear forces are balanced by the surface tension gradient for a steady flow. The vapor viscosity is very small (s0 0), thus the boundary condition corresponding to the interfacial effect is s + dr/(Rdh = 0, where R is bubble diameter and h angle. Therefore, the fluid flow along the bubble interface caused by the surface tension gradient, or the induced bubble top jets, may not be prominent for larger bubble. Besides the prominent effect of Marangoni convection, the viscous force also plays an important role in bubble interaction, especially the bubble circling. When a small bubble is circling a larger bubble, the involved forces include the buoyancy force, the viscous force, the surface tension and the driving force caused by Marangoni effect. For a bubble moving slowly in an infinite liquid pool, the viscous force on it is given by the Hadamard–Rybczynski law or fV = 3pldbu [26,27], and the fluid viscosity can be expressed in the form of an Arrhenius-type viscosity–temperature empirical equation or l = l0e–E/(RT) [28]. Here fV is the viscous force, db is the small bubble diameter, u is the small bubble velocity, l0 is the viscosity at some reference temperature, E is the viscosity temperature coefficient or the activation energy, R is the universal gas constant, and T is the absolute temperature. When the heat flux is high or the small bubble diameter is small, the viscous force on the moving bubble is consequently small. Bubble circling can happen when the viscous force is relatively small and hence the buoyancy force and driving force by the Marangoni effect play important roles in the bubble movement. 3.2. Bubble circling and rotating When the testing fluid is ultrapure water, the circling bubble may rotate and coalesce with another small bubble at the top of a larger bubble and then depart from it. Fig. 3 gives an example for this phenomenon, while the heat flux is 2.83 106 W/m2, the superheat is 55 K, the wire diameter is 60 lm, the small bubble diameters are about 1.6 mm, and the circling velocity is about 93 mm/s. These small bubbles rotate slowly at the bubble-top for about 5 s before they coalesce and depart.
0.000s
0.014s
0.018s
0.022s
0.026s
0.030s
Fig. 2. Bubble sweeping towards and circling around a stationary bubble.
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0.000s
0.020s
0.006s
0.022s
0.016s
0.024s
Fig. 3. Small bubbles circling and rotating at the top of a big bubble.
The bubble circling phenomenon is due to the Marangoni convection of liquid near the interface of the larger bubble. A liquid pumping effect can be created by the vertical Marangoni convection, as discussed in a proposed structure of the bubble-top jet flow [17]. The small bubble could be dragged by the liquid pumping effect. However, the Marangoni convection is weak near the top of the larger bubble, since the temperature gradient is small comparing with the lower part of the bubble and a stagnation point (low flow region) can be formed near the bubble-top due to the symmetry of the liquid velocity along the bubble interface. The liquid flow near the top is almost stagnant which reduces the (condensation) heat transfer at the top, resulting in a higher temperature at the top and the coldest region is slightly lower to the top of the bubble [12,29,30]. This may help explain why the small bubbles rotate and not completely condense at the top of the larger bubble.
1.75 mm, and the circling velocity is about 101 mm/s. It stays at the bubble-top for about 0.5 s before it departs. As discussed in the above subsection, bubble circling phenomenon could be due to the Marangoni convection along the larger bubble interface. Our recent analysis on the simulation of velocity field for bubble-top jet flow in water indicates that the Marangoni convection at the bottom of the larger bubble could lead the surrounding liquid moving to the heated surface [31]. Depending on the balance of the buoyancy force on the small bubble, the viscous force, the surface tension and the driving force caused by the Marangoni effect, the circling bubble could continue to circle to the top, as shown in Fig. 4, or leave the larger bubble part way up the surface and then return to the wire, as shown in the next subsection.
3.3. Bubble circling and departing
3.4. Bubble circling and returning
When the testing fluid is ultrapure water, bubble coalescence can cause oscillation or departure of neighbor bubbles, which may circle a larger bubble that it meets, as shown in Fig. 4. The circling bubble accelerates and then decelerates along the interface of the larger bubble. The time for a bubble circling process before it departs at the bubble-top is about 0.024 s, while the heat flux is 1.41 106 W/m2, the wire diameter is 60 lm, the small bubble diameter is about 0.73 mm, the big bubble diameter is about
When the testing fluid is ultrapure water, the circling bubble may return to its initial position after circling a short distance, as shown in Fig. 5. It is noticed that bubble returning happens when the small bubble circles for a short distance, separating from the larger bubble at t = 0.026 s and being attracted to the interface of the larger bubble at t = 0.046 s, while the heat flux is 1.42 106 W/m2, the wire diameter is 60 lm, the diameter of the merged bubble is about 0.17 mm, the diameter of the larger
L. Zhou et al. / International Journal of Heat and Mass Transfer 64 (2013) 945–951
0.000s
0.018s
0.010s
0.022s
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0.014s
0.028s
Fig. 4. Small bubble circling a larger bubble and departing from its top.
bubble is about 1.38 mm, and the complete time for the bubble returning is about 0.090 s. Small bubble (less than 50 lm in diameter) can be generated from bubble collapse and be observed returning to the wire
0.000s
0.080s
surface; small bubble (up to 200 lm in diameter) can also be observed departing from and then returning to the heating wire, when it was at the end of a liquid–vapor jet issuing from the wire – the vapor in the jet appears to feed the small bubble which
0.002s
0.084s
0.046s
0.090s
Fig. 5. Small bubble circling for a short distance and returning near the bottom of a larger bubble.
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L. Zhou et al. / International Journal of Heat and Mass Transfer 64 (2013) 945–951
increased in size and evolved into a larger bubble [32]. In our experimental observation, small bubble can circle along the interface of a larger bubble for a short distance and then return to the heated wire. This phenomenon is probably due to the Marangoni convection along the larger bubble interface, the buoyancy force on the small bubble, the viscous force, and the surface tension [31], as discussed in the previous subsection.
like other working liquids. Therefore, it is necessary to improve the heat flux to reveal the phenomenon at different heat transfer regimes. It also notes that these bubbles are small in size and are not tended to coalesce, making them an interesting choice for microscale applications, such as microchannel, microflow, micromixer, micropump, and microactuator. 4. Conclusions
3.5. Bubble circling and chasing Self-rewetting working fluids, i.e., dilute alcohol aqueous solutions, have unique surface tension property in the higher temperature region that increases with temperature, and can exhibit a reverse Marangoni flow along the bubble interface, resulting in a strong liquid flow towards the hot side. When a self-rewetting fluid, namely 3.0 wt% n-butanol aqueous solution, is used as testing fluid, bubble circling phenomenon can also be observed, only that the diameter of the circling bubbles are extremely small, e.g., one order of magnitude lower than those of the ultrapure water. The small bubbles can chase each other along the bubble interface, as shown in Fig. 6, while the heat flux is 2.0 106 W/m2, the superheat is 102 K, the wire diameter is 30 lm, the diameter of the stationary larger bubble is about 0.84 mm, the small bubble diameters are about 0.03 mm. The small bubbles depart from the microwire with velocity at about 82.5 mm/s, and then change their directions along the interface of the larger bubble. The circling velocity is about 6.5 mm/s before the small bubbles arrive at the middle part of the larger bubble, then the small bubbles decelerate and move upwards with extremely slow velocity. The experiment shows that no sweeping, rotating, or returning happens during the bubble circling process when the self-rewetting fluid was employed. However, simultaneous circling of multiple bubbles at the interface of a larger stationary bubble was observed. This is possibly because that the fluid temperature is not too high and the surface tension decreases with temperature
0.000s
0.200s
Bubble circling phenomenon is observed in the experiment of subcooled nucleate boiling of ultrapure water or alcohol aqueous solution on platinum microwires. Small bubble can sweep with jet flow along the microwire and circle at a larger bubble interface. It can also depart, rotate, return or chase at the interface of a larger bubble. The possible mechanisms that influence the observed phenomena are discussed. The observation shows that small bubble circling around a larger bubble, bubble-top rotating, bubble returning and bubble chasing are due to the balance of the Marangoni force along the larger bubble interface, the buoyancy force on the small bubble, the viscous force, and the surface tension. The investigation on the bubble circling phenomenon can help verify the crucial factors that influence the bubble dynamics, bubble interaction and boiling heat transfer. The bubble dynamics in this phenomenon also makes it an interesting choice for many microscale applications. Conflict of interest statement I have read the statement of policy regarding conflict of interest. No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. I would like to declare on behalf of my coauthors that the submission is original work and is not under review at any other publication. All the authors listed have approved the manuscript that is enclosed.
0.060s
0.534s
Fig. 6. Small bubble circling and chasing at a big bubble interface.
0.160s
0.996s
L. Zhou et al. / International Journal of Heat and Mass Transfer 64 (2013) 945–951
Acknowledgements Project 50906024 supported by National Natural Science Foundation of China, Project 3102026 supported by Beijing Natural Science Foundation, Project 12ZX02 supported by the Fundamental Research Funds for the Central Universities, and Project NCET-120845 supported by the Program for New Century Excellent Talents in University. The authors gratefully appreciate the reviewers for their comments.
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Contents lists available at SciVerse ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Technical Note
Bubble circling phenomena in subcooled nucleate pool boiling on microwires Leping Zhou a,⇑, Longting Wei a,1, Yuanyuan Li a,1, Xiaoze Du a,⇑, Buxuan Wang b,2 a School of Energy, Power and Mechanical Engineering, Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, North China Electric Power University, Beijing 102206, China b Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 28 September 2012 Received in revised form 7 May 2013 Accepted 9 May 2013 Available online 7 June 2013 Keywords: Bubble circling Subcooled boiling Marangoni effect Viscous force
a b s t r a c t The interaction between adjacent bubbles plays an important role in boiling heat transfer on a micro heat source. In this paper, the visualizing bubble behaviors during subcooled pool boiling on microwires were revisited experimentally. Bubble circling phenomena, the circling of small bubble around a larger one for subcooled boiling on platinum microwires submerged in ultrapure water or self-rewetting fluid, were investigated. Different types of bubble circling phenomena, including small bubble sweeping, departing, rotating, returning or chasing at a larger bubble interface, were described in detail. The roles of Marangoni effect and viscous force were analyzed in the process of bubble circling to understand the mechanism of bubble behaviors on micro heated surface. The investigation on the bubble circling phenomenon can help verify the crucial factors that influence the bubble dynamics, bubble interaction and boiling heat transfer. The bubble dynamics in this phenomenon also makes it an interesting choice for many microscale applications. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Nucleate boiling phenomenon has been extensively investigated among boiling heat transfer problems since the boiling curve and the different heat transfer regimes for saturated pool boiling was first introduced by Nukiyama [1]. Bubble dynamics, bubble induced convection, thermocapillary flow, microlayer evaporation, nonlinear characteristics of boiling, etc., are possible mechanisms for the high heat transfer rate in nucleate boiling [2–5]. It is well recognized that the research on bubble dynamics is critical in boiling heat transfer mechanisms. However, there remain many unsolved problems in bubble dynamics and bubble interaction needed for further investigation [6–9]. Bubbles usually emerge from the active nucleate sites on a heating surface, grow up to a critical size, and then depart from the nucleate sites that can be easily observed with the naked eyes. When heater size scales down in recent years, e.g., nucleate boiling on microwires, many interesting phenomena could be observed in
⇑ Corresponding authors. Tel.: +86 10 5197 1316; fax: +86 10 5197 1328 (L. Zhou), tel.: +86 10 5197 1326; fax: +86 10 5197 1328 (X. Du). E-mail addresses: [email protected] (L. Zhou), [email protected] (L. Wei), [email protected] (Y. Li), [email protected] (X. Du), bxwang@mail. tsinghua.edu.cn (B. Wang). 1 Tel.: +86 10 5197 1316; fax: +86 10 5197 1328. 2 Tel.: +86 10 6278 9751; fax: +86 10 6277 0209. 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.05.023
the experiments. For example, Wang et al. [10–12] observed unusual bubble dynamics (such as bubble sweeping and bubbletop jet flow) and bubble interaction (including bubble collision, separation and coalescence) phenomena in subcooled nucleate boiling on microwires. Lu et al. [13–15] investigated experimentally and theoretically the bubble dynamics during subcooled nucleate boiling of water on platinum microwires. They pointed out that the temperature difference induced interfacial thermocapillary force and the bubble interactions are the most important forces during bubble collision and separation. Christopher et al. [16] further suggested that the unusual bubble dynamics can be explained by the asymmetric temperature, pressure or surface tension distribution on both sides of the bubble, since the relative motion between bubbles, bubble collision, coalescence and departure can actually affect the temperature and flow fields of the surrounding liquid. They established a model that balances the Marangoni force, the drag force, and the contact line force acting on a sweeping bubble and shows that when the sweeping bubble approaches an stationary bubble at moderate superheats, the reduced wire temperatures around the stationary bubble cause the sweeping bubble to decelerate and reverse direction before colliding with the stationary bubble [17]. Generally speaking, the Marangoni effect is a crucial factor that influences the bubble interactions. Besides the prominent effect of Marangoni convection, fluid viscosity (or drag force) can also apparently affect bubble dynamics, especially in the rising process [18,19]. Therefore, the fluid viscous
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Nomenclature db E fV h q R
small bubble diameter (m) viscosity temperature coefficient (J mol1) viscous force (N) heat transfer coefficient (W m2 k1) heat flux (W m2) bubble diameter (m)
universal t T u
gas constant (J mol1 K1) time (s) temperature (K) velocity (m s1)
effect should also be an important contributor for the bubble dynamics. In this paper, a unique bubble behavior that is closely related with the above-mentioned bubble dynamics and bubble interaction is observed. The phenomenon is named as bubble circling, for which an interaction between bubbles during subcooled nucleate boiling of ultrapure water or high-carbon alcohol aqueous solution (self-rewetting fluid) on microwires is recorded using highspeed CCD camera system. Different types of bubble circling phenomena, accompanied by small bubble sweeping, departing, rotating, returning or chasing at a larger bubble interface, are described in detail. The possible mechanisms of these bubble behaviors on micro heated surface are discussed, and the effects of Marangoni convection and viscous force are further analyzed for the observed bubble circling phenomenon. The investigation on the bubble circling phenomenon can help verify the crucial factors that influence the bubble dynamics, bubble interaction and boiling heat transfer. The bubble dynamics in this phenomenon also makes it an interesting choice for many microscale applications, such as microchannel and microflow. 2. Experimental set-up The schematics of the experimental set-up for visualizing the subcooled nucleate pool boiling of ultrapure water on microscale platinum wire is shown in Fig. 1. The wire was horizontally installed at the bottom of the glass container, and was connected on the electric connectors and heated by a DC Power Supply (Dahua DH1720A-3). The power supply provided direct current to the wire, generating Joule heat as the applied heat flux. The heater was replaced by different platinum wires, namely 30 lm, 50 lm or 60 lm in diameter and 65 mm in length. The ends of the wire are connected to the DC power. The size of the glass container is 25 25 25 cm. The images of bubble behaviors during subcooled nucleate boiling on these microwires were recorded with a highspeed CCD (Luster LightTech MC1310, 500 fps) and a data acquisition module (Agilent 34970). The heating wire was fixed on an adjustable bracket, recording the voltage and the current at the ends of it, so as to calculate the heat flux with the electric resistance. The testing liquid being heated and to be observed was ultrapure water or alcohol aqueous solution, with an initial temperature at around 289 K. The water was deaerated by an auxiliary copper heater with power output 150 W to heat the water for about 60 min before the boiling experiment. The bulk temperature of the testing liquid was measured using a thermocouple located 1 cm apart from the microwire. The heat flux can be calculated by using the resistance-temperature formula for the electric
Greek symbols l dynamic viscosity (Pa s) h angle r surface tension (N m1) s shear force (N m2) Subscripts 0 reference point b bubble w wire
resistor and the error for the heat flux was estimated to be less than 0.1%. The error for the average wall temperature was estimated to be less than 5 K. The container was kept in an environment at atmospheric pressure. An observation area of 2 2 mm around the center of the wire was selected for observation. 3. Results and discussions Experimental observation of the bubble dynamics of nucleate pool boiling on the microwire was conducted using the device described in the previous section. Several interesting phenomena were observed, especially the bubble circling phenomenon. Small bubble, with or without jet flow at its top, can circle a larger stationary bubble that it meets, when it is sweeping on or departing from the microwire. Bubble circling phenomenon is diverse and complex. During the process of circling, small bubble can be accompanied with a jet flow; it can also depart, rotate, return or chase at the interface of a larger bubble. A detailed discussion on the bubble circling phenomena is given as follows. 3.1. Bubble sweeping and circling Bubble sweeping can be observed frequently in the experiment when heat flux is relatively high [11,17]. In the experimental investigation, it happens at heat flux, for example, higher than 1.6 106 W/m2. When it occurs, the bubble moves back and forth along the microwire, accompanied with the bubble growth. There exists single or multiple jet flows on the top of the reciprocating bubble. In addition to the single bubble sweeping, the sweeping bubbles nearby can also influence each other by collision. For
DC Power Supply
Computer Data Acquisition
Pure Water Transparent container
CCD Camera
Thermocouple
Heating wire
Bracket
Fig. 1. Schematics of experimental set-up.
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example, two sweeping bubbles can collide and merge into a larger sweeping bubble. Two sweeping bubbles can also collide and move along the same direction or move oppositely. A sweeping bubble can collide with a stationary bubble and the bubble collision process is just like an elastic collision – for example, for a platinum wire (100 lm in diameter, and the heat flux is 0.6 106 W/m2) immersed in water (subcooling degree is 70 K), a large bubble moves with a velocity of 40 mm/s and collides with an stationary bubble; after about 0.024 s, the bubble decelerates to zero as it approaches to the stationary bubble; then the sweeping bubble began to return and accelerate [13]. The bubble sweeping phenomenon was frequently observed in the experiment, but few report mentioned the circling phenomenon after the bubble sweeping along the thin wire. Besides the above-mentioned various forms of sweeping of two bubbles, a small sweeping bubble can also circle a larger bubble that is stationary yet has no prominent jet flow at its top. When the diameter of the heating wire is 30 lm and the heat flux is 2.35 106 W/m2, the measured temperature of the ultrapure water is 290.35 K and the measured temperature of the wire is 337.09 K. Under this condition, the small bubble can sweep towards the larger bubble, and then circle the latter for a short distance before it collapses into the subcooled water near the bubble-top, as shown in Fig. 2. The complete time for the sweeping and circling is about 0.03 s. For bubble circling phenomenon, there may have a thin liquid film that could protect them from coalescence between the bubbles. A thin liquid film between a small bubble and the lager bubble was observed by Jiang et al. [20] in the sub-cooled boiling experiment of deaerated water, where a small bubble rotated slowly at the top of a larger bubble staying on a 10 mm diameter steel cylinder heater (but they did not report the bubble circling process). This may help explain why in this investigation the two bubbles did not coalesce during the circling process. It may also explain why in Section 3.3 a small bubble rotating at the top of a larger bubble did not coalesce with the latter. The thermocapillary force (Marangoni effect) is essentially a critical factor in bubble behaviors, including bubble-top jet flow, bubble movement, and bubble interaction. For example, the Marangoni effect drives the surrounding liquid to flow toward the bubble-top (the pumping effect) and thus forms jet flow [12]. When the heat flux or the temperature gradient on the bubble is relatively small, the bubble diameters could be large (usually about 1 mm in our experimental observation), which is in good
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agreement with previous investigations [11–13,21–24]. In these studies, the diameters of the heating wire and the bubble were usually less than 1 mm, and consequently, both the interfacial force and the thermocapillary force are important for bubble top jets. The interfacial flow at the interface induces a shear force s in the liquid phase and s0 in the vapor phase [25]. These shear forces are balanced by the surface tension gradient for a steady flow. The vapor viscosity is very small (s0 0), thus the boundary condition corresponding to the interfacial effect is s + dr/(Rdh = 0, where R is bubble diameter and h angle. Therefore, the fluid flow along the bubble interface caused by the surface tension gradient, or the induced bubble top jets, may not be prominent for larger bubble. Besides the prominent effect of Marangoni convection, the viscous force also plays an important role in bubble interaction, especially the bubble circling. When a small bubble is circling a larger bubble, the involved forces include the buoyancy force, the viscous force, the surface tension and the driving force caused by Marangoni effect. For a bubble moving slowly in an infinite liquid pool, the viscous force on it is given by the Hadamard–Rybczynski law or fV = 3pldbu [26,27], and the fluid viscosity can be expressed in the form of an Arrhenius-type viscosity–temperature empirical equation or l = l0e–E/(RT) [28]. Here fV is the viscous force, db is the small bubble diameter, u is the small bubble velocity, l0 is the viscosity at some reference temperature, E is the viscosity temperature coefficient or the activation energy, R is the universal gas constant, and T is the absolute temperature. When the heat flux is high or the small bubble diameter is small, the viscous force on the moving bubble is consequently small. Bubble circling can happen when the viscous force is relatively small and hence the buoyancy force and driving force by the Marangoni effect play important roles in the bubble movement. 3.2. Bubble circling and rotating When the testing fluid is ultrapure water, the circling bubble may rotate and coalesce with another small bubble at the top of a larger bubble and then depart from it. Fig. 3 gives an example for this phenomenon, while the heat flux is 2.83 106 W/m2, the superheat is 55 K, the wire diameter is 60 lm, the small bubble diameters are about 1.6 mm, and the circling velocity is about 93 mm/s. These small bubbles rotate slowly at the bubble-top for about 5 s before they coalesce and depart.
0.000s
0.014s
0.018s
0.022s
0.026s
0.030s
Fig. 2. Bubble sweeping towards and circling around a stationary bubble.
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0.000s
0.020s
0.006s
0.022s
0.016s
0.024s
Fig. 3. Small bubbles circling and rotating at the top of a big bubble.
The bubble circling phenomenon is due to the Marangoni convection of liquid near the interface of the larger bubble. A liquid pumping effect can be created by the vertical Marangoni convection, as discussed in a proposed structure of the bubble-top jet flow [17]. The small bubble could be dragged by the liquid pumping effect. However, the Marangoni convection is weak near the top of the larger bubble, since the temperature gradient is small comparing with the lower part of the bubble and a stagnation point (low flow region) can be formed near the bubble-top due to the symmetry of the liquid velocity along the bubble interface. The liquid flow near the top is almost stagnant which reduces the (condensation) heat transfer at the top, resulting in a higher temperature at the top and the coldest region is slightly lower to the top of the bubble [12,29,30]. This may help explain why the small bubbles rotate and not completely condense at the top of the larger bubble.
1.75 mm, and the circling velocity is about 101 mm/s. It stays at the bubble-top for about 0.5 s before it departs. As discussed in the above subsection, bubble circling phenomenon could be due to the Marangoni convection along the larger bubble interface. Our recent analysis on the simulation of velocity field for bubble-top jet flow in water indicates that the Marangoni convection at the bottom of the larger bubble could lead the surrounding liquid moving to the heated surface [31]. Depending on the balance of the buoyancy force on the small bubble, the viscous force, the surface tension and the driving force caused by the Marangoni effect, the circling bubble could continue to circle to the top, as shown in Fig. 4, or leave the larger bubble part way up the surface and then return to the wire, as shown in the next subsection.
3.3. Bubble circling and departing
3.4. Bubble circling and returning
When the testing fluid is ultrapure water, bubble coalescence can cause oscillation or departure of neighbor bubbles, which may circle a larger bubble that it meets, as shown in Fig. 4. The circling bubble accelerates and then decelerates along the interface of the larger bubble. The time for a bubble circling process before it departs at the bubble-top is about 0.024 s, while the heat flux is 1.41 106 W/m2, the wire diameter is 60 lm, the small bubble diameter is about 0.73 mm, the big bubble diameter is about
When the testing fluid is ultrapure water, the circling bubble may return to its initial position after circling a short distance, as shown in Fig. 5. It is noticed that bubble returning happens when the small bubble circles for a short distance, separating from the larger bubble at t = 0.026 s and being attracted to the interface of the larger bubble at t = 0.046 s, while the heat flux is 1.42 106 W/m2, the wire diameter is 60 lm, the diameter of the merged bubble is about 0.17 mm, the diameter of the larger
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0.000s
0.018s
0.010s
0.022s
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0.014s
0.028s
Fig. 4. Small bubble circling a larger bubble and departing from its top.
bubble is about 1.38 mm, and the complete time for the bubble returning is about 0.090 s. Small bubble (less than 50 lm in diameter) can be generated from bubble collapse and be observed returning to the wire
0.000s
0.080s
surface; small bubble (up to 200 lm in diameter) can also be observed departing from and then returning to the heating wire, when it was at the end of a liquid–vapor jet issuing from the wire – the vapor in the jet appears to feed the small bubble which
0.002s
0.084s
0.046s
0.090s
Fig. 5. Small bubble circling for a short distance and returning near the bottom of a larger bubble.
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increased in size and evolved into a larger bubble [32]. In our experimental observation, small bubble can circle along the interface of a larger bubble for a short distance and then return to the heated wire. This phenomenon is probably due to the Marangoni convection along the larger bubble interface, the buoyancy force on the small bubble, the viscous force, and the surface tension [31], as discussed in the previous subsection.
like other working liquids. Therefore, it is necessary to improve the heat flux to reveal the phenomenon at different heat transfer regimes. It also notes that these bubbles are small in size and are not tended to coalesce, making them an interesting choice for microscale applications, such as microchannel, microflow, micromixer, micropump, and microactuator. 4. Conclusions
3.5. Bubble circling and chasing Self-rewetting working fluids, i.e., dilute alcohol aqueous solutions, have unique surface tension property in the higher temperature region that increases with temperature, and can exhibit a reverse Marangoni flow along the bubble interface, resulting in a strong liquid flow towards the hot side. When a self-rewetting fluid, namely 3.0 wt% n-butanol aqueous solution, is used as testing fluid, bubble circling phenomenon can also be observed, only that the diameter of the circling bubbles are extremely small, e.g., one order of magnitude lower than those of the ultrapure water. The small bubbles can chase each other along the bubble interface, as shown in Fig. 6, while the heat flux is 2.0 106 W/m2, the superheat is 102 K, the wire diameter is 30 lm, the diameter of the stationary larger bubble is about 0.84 mm, the small bubble diameters are about 0.03 mm. The small bubbles depart from the microwire with velocity at about 82.5 mm/s, and then change their directions along the interface of the larger bubble. The circling velocity is about 6.5 mm/s before the small bubbles arrive at the middle part of the larger bubble, then the small bubbles decelerate and move upwards with extremely slow velocity. The experiment shows that no sweeping, rotating, or returning happens during the bubble circling process when the self-rewetting fluid was employed. However, simultaneous circling of multiple bubbles at the interface of a larger stationary bubble was observed. This is possibly because that the fluid temperature is not too high and the surface tension decreases with temperature
0.000s
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Bubble circling phenomenon is observed in the experiment of subcooled nucleate boiling of ultrapure water or alcohol aqueous solution on platinum microwires. Small bubble can sweep with jet flow along the microwire and circle at a larger bubble interface. It can also depart, rotate, return or chase at the interface of a larger bubble. The possible mechanisms that influence the observed phenomena are discussed. The observation shows that small bubble circling around a larger bubble, bubble-top rotating, bubble returning and bubble chasing are due to the balance of the Marangoni force along the larger bubble interface, the buoyancy force on the small bubble, the viscous force, and the surface tension. The investigation on the bubble circling phenomenon can help verify the crucial factors that influence the bubble dynamics, bubble interaction and boiling heat transfer. The bubble dynamics in this phenomenon also makes it an interesting choice for many microscale applications. Conflict of interest statement I have read the statement of policy regarding conflict of interest. No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. I would like to declare on behalf of my coauthors that the submission is original work and is not under review at any other publication. All the authors listed have approved the manuscript that is enclosed.
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Fig. 6. Small bubble circling and chasing at a big bubble interface.
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Acknowledgements Project 50906024 supported by National Natural Science Foundation of China, Project 3102026 supported by Beijing Natural Science Foundation, Project 12ZX02 supported by the Fundamental Research Funds for the Central Universities, and Project NCET-120845 supported by the Program for New Century Excellent Talents in University. The authors gratefully appreciate the reviewers for their comments.
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