Jet Flows from Bubbles During Subcooled Pool Boiling on Micro Wires

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Science in China Ser. E Engineering & Materials Science 2005 Vol.48 No.4 385—402 385

Jet flows from bubbles during subcooled pool boiling on micro wires

WANG Hao, D. M. Christopher, PENG Xiaofeng & WANG Buxuan

Laboratory of Phase Change and Interfacial Transport Phenomena, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China Correspondence should be addressed to Peng Xiaofeng (email: [email protected]) Received January 4, 2005

Abstract An experimental investigation was conducted on subcooled nucleate boiling on ultra-small wires having diameters of 25―100 µm. High-speed photography and laser PIV (Particle Image Velocimetry) technology were used to visually observe the bubble dynamics. For highly subcooled boiling at moderate heat fluxes, the bubbles generally remained attached to the micro heating wires and bubble-top jet flows were clearly observed. Smaller bubbles usually had stronger bubble-top jet flows, while larger bubbles seemed to produce multi-jet flows. The structures of the bubble-top jet flows, as well as multi-jet flows, were proposed from the experimental observation. A model was developed to describe jet flow phenomena from bubbles on micro wires. Numerical simulations for bubbles having diameter of 0.03 and 0.06 mm showed that both the bubble-top and multi-jet flows were induced by a strong Marangoni effect due to high temperature gradients near the wire. The predicted velocity magnitudes and flow structures agreed very well with experimental measurements. The bubble size relative to the wire is an important factor affecting the jet flow structure. For a 0.03 mm bubble on a 0.1 mm wire, only a bubble-top jet flow forms, while a complex multi-jet flow pattern forms around the bubble with a weak bubble-top jet and two side jet flows for a 0.06 mm bubble. Keywords: subcooled boiling, bubble, multi-jet, jet flow, PIV, Marangoni, CFD.

DOI: 10.1360/ 04ye0052/53

NOMENCLATURE

Db, Vapor bubble diameter (m); Dw, heater wire diameter (m); hfg, latent heat (J/kg); hi, interface heat transfer 2 coefficient (W/m K); M , molecular weight of vapor (kg/kmol); R , universal gas constant (J/mol K); pl, liquid 2 2 2 3 pressure (N/m ); py, vapor pressure (N/m ); qw′′ , wire surface heat flux (W/m ); qw′′′ , wire volume heat flux (W/m ); 2 qi′′ , interfacial heat flux (W/m ); R, bubble radius (m); Tw, wire average temperature (K); Ti, liquid temperature at interface (K); Ts, saturated temperature under atmosphere (K); Tv, vapor temperature (K); v, velocity (m/s); λ, thermal conductivity (W/mK); β, liquid thermal expansivity (1/K); σ, surface tension coefficient (N/m); σˆ , accom- 3 3 modation coefficient; δ, liquid layer thickness (m); ρν, vapor density (kg/m ); ρl, liquid density (kg/m ); ν, kinetic viscosity (m2/s); µ, dynamic viscosity (Ns/m2). Subscripts: l, liquid; ν, vapor; I, interface; s, saturated.

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1 Introduction Nucleate boiling is widely encountered in a variety of practical applications, such as energy conversion, manufacturing process and chemical processing. However, because of their extreme complexity, many boiling phenomena still remained to be understood with no general theoretical models available to accurately predict boiling heat and mass transfer[1,2]. After his comprehensive review of the available investigations in the literature, Dhir[1] appealed to investigators to investigate boiling phenomena with renewed or unconventional ideas. In recent years, many investigators have paid more attention to the nonlinear interaction in boiling processes. Henley and Hummel[3] mentioned the interactions among nucleation sites. Sadasivan et al.[4―6] further indicated that available investigations normally ignored the nonlinear characteristics of boiling processes, which is the most seri- ous shortcoming of conventional theories. Eddington and Kenning[7] conducted an investigation on the interaction among bubble productions occurring at adjacent sites. Kenning et al.[8,9] investigated the temperature field on a boiling surface using a liquid crystal layer on the bottom of the boiling surface and concluded that a comprehensive model for nucleate boiling ought to have the following features: Consideration of local superheats to determine the activity of sites and their contribution to the heat transfer; specification of sites by their properties of activation and cessation; accounting for the effect of intermittency of the overall heat flux. These investigations provide more fundamental understanding of nucleate boiling. However, most of these investigations have only qualitatively illustrated the nonlinear and dynamic behavior, lacking accurate mathematical descriptions of the interactions among nucleation sites during nucleation processes. Therefore, many unsolved problems and unrecognized phenomena still re- main. More recently, the development of digitally enhanced measurement and visualization techniques and the urgent need to predict the heat transfer for boiling in unconventional environments, especially microscale and microgravity environments, has resulted in more comprehensive investigations of boiling processes. Some interesting phenomena and dynamic processes were observed in the open literature. Lin et al.[10, 11] observed microscale homogeneous nucleation. Glod et al.[12] investigated the explosive vaporization of water close to its superheat limit at the microscale level. Nucleation jets and bubble-sweeping on micro wires were investigated in a sequence of experiments conducted by the authors’ group[13―15]. The PIV technique was used to visually observe flow fields around micro bubbles with intensive jet flows[16]. These studies have given an additional insight into the fundamental mechanisms controlling the boiling process and the complexity of nucleate boiling. Bubble-top jet flows, jet-like flows from the bubble top surface into the bulk liquid, are interesting phenomena observed in downward-facing subcooled boiling[17―19]. These jet flows represent important mechanisms in more accurate boiling heat transfer models,

Copyright by Science in China Press 2005 中国科技论文在线 http://www.paper.edu.cn Jet flows from bubbles during subcooled pool boiling on micro wires 387 especially by clarifying the balance between microlayer evaporation and heat removal by the liquid phase, and both are widely recognized as key boiling heat transfer mechanisms. Many investigators sought to observe these phenomena and provide more experimental and theoretical evidence for better understanding of the physical nature of bubble-top jet flows. Various investigators suggested that the interfacial mass flux due to evaporation and condensation, Marangoni effect induced by the surface tension gradient and the surface pressure gradient resulting from evaporation all contribute to the jet flows. The present paper presents photographic and quantitative measurements data on bubble-top jet flows and multi-jet flows for subcooled pool boiling on ultrathin platinum wires. The structures of the bubble-top jet and multi-jet flows were proposed from the experimental observations and measurements. The various jet flow structures and the measured velocity profiles were independent of the orientation relative to gravity. A physical model was developed to describe the jet flow phenomena from bubbles on micro wires. 2 Experimental description The experimental facility employed in the present investigation consisted of three parts, the test section, the power supply and the high-speed photographic system, as shown in Fig. 1. The test section was a transparent vessel with a platinum heating wire inside the vessel. The wire could be placed horizontally or inclined. The platinum wires used in the experiments were 49 mm long having diameters of 0.1 mm or 0.025 mm. The photographic system included a high-speed CCD camera, a high-resolution image acquisition card, and zoom lenses. The frame speed was 30―1000 frames per second. The power supply provided direct current to the platinum wire for Joule heating. The ends of the wires were connected tightly to copper posts. The pressure in the vessel was kept at atmospheric pressure. The current and voltage to the platinum wire were measured to determine the input power and the wire resistance. The average wire temperature was estimated using a calibrated resistance-temperature correlation. The bulk liquid temperature was measured using thermocouples and ther- mometers placed in the bulk liquid. The back lighting with some angle inclined to the wire was used. Detailed measurements of the jet flow field were obtained using a 2-D particle image velocimetry (PIV) system. The PIV system includes an imaging subsystem, an image capture subsystem and an analysis and display subsystem. The PIV system and experimental facility are illustrated in Fig. 2 and Fig. 3. Because the bubbles on the heater wire were very small (the heater wires were 0.1 or 0.025 mm in diameter), the CCD camera was equipped with a series of zoom lens. 1 µm aluminum particles were used as tracing particles.

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Fig. 1. Experiment setup.

Fig. 2. PIV system. Fig. 3. PIV experimental equipment. 3 Experimental observations 3.1 Bubble-top jet flows For highly subcooled boiling at moderate heat fluxes, the bubbles generally remained attached to the micro heating wire for a long time, with clearly observed bubble-top jet flows. Fig. 4 shows several well-developed bubble-top jet flows recorded with the CCD camera. More detailed information was obtained from the PIV measurements, as shown in Fig. 5 in which the arrows represent the direction and magnitude of the local velocity vectors. The left picture in Fig. 5 is the real photo superimposed with the flow field vectors. The bubble-top jet flows had a stable structure and intensity which pumped liquid into the bulk region. The gravity had little effect on the jet flow velocities. In Fig. 4(b) and Fig. 5, the downward facing bubbles had strong jet flows from their top. Accordingly, the structure scheme of the bubble-top jet flow is illustrated in Fig. 6. Hot liquid near the wire is pumped through the neck region and ejected into the bulk liquid.

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Fig. 4. CCD photographs of bubble-top jet flows. (a) Inclined wire, heat flux 5. 3×105 W/m2, average superheat 5℃, subcooling 43℃; (b) horizontal wire, heat flux 1.4×106W/m2, average superheat 21℃, subcooling 60℃.

Fig. 5. PIV measurements of bubble-top jet flows. 0.1 mm wire, heat flux 5. 5×105 W/m2, average superheat 6℃; water, subcooling 50℃.

One of significant characteristics is that smaller bubbles usually had more concen- trated and stronger jet flows than larger bubbles. In experiments with subcooled water on a 0.1 mm platinum wire, the jet flow velocities in the expanding region ranged from 10 mm/s to about 140 mm/s.

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Fig. 6. The structure of a bubble-top jet flow. 3.2 Multi-jet flows In the side-view experimental observations, several quite different bubble-top jet flows structures were observed, as illustrated in Fig. 7(a). One bubble seemed to produce more than one jet, which is termed as the “multi-jet phenomenon” here. In Fig. 7(a), the bubble strode aslant on the wire and two jets were observed. As Fig. 7(b) illustrates, the experiments were conducted to observe from the top, and the multi-jet flows were then clearly observed in the subcooled boiling. Normally, small bubbles (diameters less than 0.04 mm) did not have multi-jet flows while larger bubbles were more likely to have multi-jet flows. Higher subcoolings also increased the possibility of multi-jet flows.

Fig. 7. Multi-jet flow phenomena. (a) Stable bubble (side-view); (b) stable bubble (top-view).

The multi-jet structure is schematically illustrated in Fig. 8. A two-jet structure includes two symmetrical sub jets with each sub jet having a stable angle, α , relative to a plane through the wire axis and the bubble center. When the angle, α , was close to 90°, the two sub jets were almost horizontal and hard to observe for the side view. Forα = 0° , the two sub jets would combine into one bubble-top jet flow. Usually smaller bubbles

Copyright by Science in China Press 2005 中国科技论文在线 http://www.paper.edu.cn Jet flows from bubbles during subcooled pool boiling on micro wires 391 had smallerα value. That is why the smaller bubbles often had stronger bubble-top jet flows than larger bubbles. Fig. 9 shows two images of bubble I as it rotated around the wire as observed from the top. Bubble I was initially attached to the side of the wire, so its two vertical sub jet flows were invisible, as shown in Fig. 9(a). Driven by the buoyancy the bubble moved to the top of the wire, and Fig. 8. Multi-jet structure. the two sub jets were immediately visible (Fig. 9(b)).

Fig. 9. Top view of bubble I as it quickly rotated around the wire. (a) t = 0 s, sub jets not visible; (b) t = 0.16 s, sub jets visible. 4 Simulation 4.1 Description For a single bubble attached to the heating wire, the symmetry of the wire and bubble geometry allowed only one fourth to be taken for the simulation, as shown in Fig. 10(a). The entire calculational domain is illustrated in Fig. 10(b). The bubble diameters were 0.03 or 0.06 mm, the wire diameter was 0.1 mm, and the out boundary diameter was 2 mm. The microlayer between the bubble bottom and the wire surface will have a thickness of 0.5―2.5 µm as noted by Sharp [20]. In our experiments, the bubbles were not attached to the wire very tightly. There is a relatively thick liquid layer under the bubble. The thinnest part of the liquid layer is settled to be 2 µm in the simulations. From the experimental observations, the developed jet flows can be stable. Here steady state simulation is carried out for jet flows, and a 3-dimensional steady laminar model was used to model the fluid flow and heat transfer in the liquid region around the wire and bubble. The governing equations are

∇ ()0,ρV = (1)

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Fig. 10. Geometry and mesh for numerical simulations. (a) Bubble and wire; (b) calculational domain.

2 ∇p VV ∇=∇−ν V −g j, (2) ρ

1 2 (3) V ∇=∇()cTp λ T . ρ

The natural convection was modeled using the Boussinesq approximation, or

ρρβ=−ref(),TT ref (4)

where β is the thermal expansion coefficient of water. The out domain boundary was modeled as an inflow/outflow boundary with a speci- fied bulk liquid temperature and atmospheric pressure. The outside diameter of 2 mm,

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20 times the wire diameter, is sufficiently large to remove any effect of the out boundary on the flow. Some calculations with a solid surface at the out boundary gave essentially the same results, which demonstrates that the assumption is reasonable. The wire had the temperature Tw, measured in the experiments. The flow boundary condition at the wire surface was non-slip. The main difficulty in the simulation was the boundary conditions at the bubble interface, including the heat transfer and the interfacial mass flux. 4.2 Phase change heat transfer at the bubble interface The vapor temperature inside a spherical bubble is obtained from the Laplace and Clausius-Clapeyron equations,

2σTs 2σTs TTvs=+ . TTvs=+ . (5) hRfgvbρ hRfgvbρ

The heat transfer between the vapor inside the bubble and the interface is

qi′′ = hi (Tv − Ti ) , (6) where the interfacial heat transfer coefficient due to evaporation or condensation is[21]

1/2 ˆ h2 ρ ⎛⎞⎡ p ⎤ 2σ fg v M v (7) hi =−⎜⎟⎢1.⎥ ˆ 22−σπTRThvv⎝⎠⎣⎢ 2 fgv ρ⎦⎥ Paul[22] experimentally measured the accommodation coefficient, σˆ, ranging from

0.02 to 0.04. Here σˆ was assumed to be 0.03.

When the local interfacial temperature Ti>Tv, qi′′ <0, which means that liquid evapo- rates from the surface into the bubble and the bubble absorbs heat. When Ti0, which means condensation occurs at the surface. A bubble very near a wire surface as in

Fig. 10 absorbs energy from the bubble bottom (Ti>Tv,) and releases energy from its top

(Ti

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1dσ ∂T τ + + τ ′ =0. (8) Rθ RTd ∂θ Rθ

Because the vapor viscosity is very small, τ R′θ ≈0, the boundary condition corre- sponding to the interfacial effect is

⎡⎤∂∂uθ 1dσ T µ ⎢⎥r ()+ = 0. (9) ⎣⎦∂∂rrrR= RTd θ

The bubble interfacial parameters used in eqs. (5)―(9) are listed in Table 1.

Table 1 Bubble and interfacial parameters –2 –1 –1 –1 Db/mm Tν /K σˆ hi/W·m · K dσ/dT/N · m · K 0.03 375 0.03 2.3E+5 −1.8E-4 0.06 373 0.03 2.3E+5 −1.8E-4

In addition to the tangential flow along the interface caused by the surface tension gradient, a mass flux normal to the bubble surface occurs due to the evaporation and condensation. The heat transfer in the microlayer would be mainly conduction and the maximum heat flux would be TT− TT− q′′ ≈

62 In the experiments, qi′′ <×2.04 10 W/m , so the maximum liquid velocity normal to −4 the surface would be wl<8.5×10 m/s. Compared with the jet flows whose maximum measured velocities were 0.01 to 0.14 m/s, this velocity is very small. So the associated mass transfer was neglected when calculating the flow field around the bubble, even though the heat transfer due to the evaporation and condensation was included. 4.4 Numerical method The mesh geometry is illustrated in Fig. 10 and summarized in Table 2. The mesh geometry for the 0.06 mm bubble was similar. The discretization methods for the advec- tion terms, the pressure equations and the pressure-velocity coupling are listed in Table 3 with the convergence criteria in Table 4. The commercial CFD software FLUENT was used for the calculations.

Table 2 Mesh (0.03 mm bubble) Type Number Nodes 13969 Cells 61526

Table 3 Discretization methods Momentum Second order upwind Energy Second order upwind Pressure Standard Pressure-velocity coupling SIMPLE

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Table 4 Fluent convergence criterion Continuity 1E-5 Energy 1E-8 Velocity 1E-5

5 Results and discussions 5.1 Jet flow and pumping effect The numerical results for a 0.03 mm bubble are presented in Fig. 11. The flow field and flow structure agree well with the experimental measurements. In Fig. 11(b), the flow at the bubble top is very slow because the temperature distribution is quite uniform there compared to the region close to the wire causing very weak Marangoni effect. The PIV measurements in Fig. 5 show that the fastest flow was not at the bubble’s top, but some distance away from the top surface, referred to as the “neck” of the jet flow in Fig. 6. The slow region observed experimentally verifies that the bubble-top jet flow is not induced by the mass flux from condensation or breaking out of vapor inside the bubble. Fig. 11(c) shows that the jet flow region in fact forms around the bubble because of the Marangoni flow which accelerates the fluid all around the lower half of the bubble. However, the flow near the vapor bubble directly above the wire is obstructed by the wire so the flow velocities in the regions not directly above the wire are relatively high. The flows from all sides of the bubble concentrate above the top of the bubble to form the observed bubble-top jet phenomenon. Hot liquid is sucked from the pumped region and pumped into the expanding region, where there is a significant temperature difference between the jet flow and the surrounding liquid, as shown in Fig. 11(d). The density difference allowed the jet flow to be observed by light refraction in the CCD photographs. The pumping effect of the jet flow is the key heat transfer mechanism connected with the bubble. The experiments showed that the gravity had little effect on the jet flows. The numerical results in Fig. 12 show the velocity and temperature fields for a reversed gravity. The velocity distributions are namely identical with only slightly slower velocities in the jet flow when the buoyancy is opposing the jet flow. The temperature distribution in Fig. 12(b) is also similar to Fig. 11(d), only with the hot liquid layer somewhat thinner around the bubble in Fig. 12(b) because the natural convection is reversed. If the flow is analyzed with only natural convection and no Marangoni flow, the jet flow does not form, as shown in Fig. 13. 5.2 Multi-jet flows The predicted flow structure for a bubble diameter of 0.06 mm is shown in Fig. 14 for the same superheat and subcooling conditions as in Fig. 11. The flow in the central plane parallel to the wire axis is shown in Fig. 14(a). The shape is similar to the bubble-top jet flow around the 0.03 mm bubble (Fig. 11(b)). However, the velocities accordingly

www.scichina.com 中国科技论文在线 http://www.paper.edu.cn z - — 396 Science in China Ser. E Engineering & Materials Science 2005 Vol.48 No.4y 385 402 plane

z . - ) y

K (

lanes p

z - y and y

- x planes (m/s); (d) temperature (d) (m/s); planes z - y and

y le-top jet flow (bubble diameter 0.03 lane (m/s);(c)velocity magnitudes in - 11. Fig. bub- the for results Simulation b p x mm, wiresuperheat K, 7 subcooling 43 on vectors (a) Velocity K). contours in in contours (m/s); (b) velocity magnitudes on magnitudes (b) velocity (m/s);

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Fig. 12. Gravitational effect on the jet flow. (a) Velocity magnitudes in x-y and y-z planes (m/s); (b) temperature in x-y and y-z planes (K). are much smaller. The velocity at the neck in Fig. 11(b) is about 50 mm/s but just 20 mm/s in Fig. 14(a). This is consistent with the experimental observations that smaller bubbles had stronger jet flows than larger bubbles. The flow in the x-y plane perpendicular to the wire axis exhibits a butterfly-like flow structure (as seen in Fig. 14(b)) of two symmetrical sub jets around the wire and bubble, which is just consistent with the multi-jet flows observed in the experiments. The highest flow velocities are not above the bubble because the two sub jets do not coalesce there, but occur beside the bubble where the sub jets flows are driven by the Marangoni effect. Fig. 14(c) and (d) illustrate the very complex multi-jet flow structure around a bubble. The pumping effect of the multi-jet flows spreads the high temperature fluid over a larger region than the bubble-top jet. Comparison of the flow in Fig. 11 with Fig. 14 shows that the bubble size significantly affects the jet flow structure. Actually, the flow struc-

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Fig. 13. Natural convection velocity magnitudes with no Marangoni flow (m/s). ture was a function of both the bubble size and the ratio of the bubble diameter (0.03 mm or 0.06 mm) to the wire diameter (0.1 mm). A smaller bubble was small enough that it did not extend far into the subcooled liquid, while a larger bubble extended farther into the subcooled liquid resulting in more non-uniform temperature distribution on the bubble. The ratio of the bubble diameter to the wire diameter also affected the flow structure. The smaller bubble was so much smaller than the wire that the obstruction due to the wire was more uniform. The larger bubble diameter was similar to that of the wire, so the flow in the region beside the wire moving up past the bubble was less obstructed than the flow immediately above the wire. The temperature distribution on the bubble surface helps understand the multi-jet flow phenomenon. Since a smaller bubble (d =0.03 mm) is mostly within hot liquid layer where there is great temperature gradient, the temperature distribution of the smaller bubble surface decreases fairly uniformly from the bottom to the top, as shown in Fig. 15(a). For a larger bubble (d =0.06 mm), the top and much area of the two sides stretch into the cold bulk liquid. Both the bubble-top jet and side jets pump hot the liquid up past the bubble. Additionally, since the flow is relatively slow and there are vortices above the bubble (Fig. 16), the fluid above the bubble is not cooled by the incoming subcooled liquid while condensation along the bubble upper surface heats the liquid (Fig. 17). Furthermore, since the larger bubble extends farther out into the flow, the flow passes the bubble along the lower half of the bubble and the colder liquid cools the interface, which creates a higher heat transfer rate there, and hence lower temperature. Therefore, the coolest parts of the 0.06 mm bubble would be the two sides stretching into the cold bulk liquid, as shown in Fig. 15(b). The specific location of the coolest region would be a function of the bubble and wire sizes, the hot liquid layer thickness, the temperature of the wire, the subcooling degree and the condensation and evaporation agree on the bubble surface.

z Jet flows from bubbles during subcooled pool boiling on micro wires - 399 y planes and z y - - y

and y - x

plane perpendicular the to wire y

- x

bcooling 43 K). (a) Flow in the central plane central in the (a) K). Flow 43 bcooling arallelto thewire axis: bubble-topjet; (b)flow in vectors velocity (d) lanes; u observed in the observed axis: multi-jet; (c) velocity magnitudes in Fig. 14. magnitude of multi-jet flow (m/s) Velocity (bubble diameter 0.06 mm, wire superheat 7 K, s p p (m/s).

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Fig. 15. Contours of temperature on bubble surfaces (K). (a) 0.03 mm bubble; (b) 0.06 mm bubble.

Fig. 16 . Vortices above the 0.06 mm bubble (m/s). 6 Conclusions Experimental and theoretical simulations were conducted to investigate the jet flows from a bubble on micro wires during subcooled boiling. Top-view observation on the bubbles demonstrates that one bubble could own more than one jet flow or display multi-jet flow phenomenon. Numerical simulations for 0.03 and 0.06 mm diameter bubbles on a 0.1 mm diameter wire clearly reproduced the observed phenomena. The results showed that both the bubble-top and the multi-jet flows were induced by a strong Ma- rangoni effect due to high temperature gradient along the bubble surface. The predicted velocity magnitudes and the flow structures were all consistent with the experimental observations. The bubble size relative to the wire is an important factor affecting the jet flow structures. The 0.03 mm bubble had only a bubble-top jet flow structure, while the 0.06 mm bubble had a complex multi-jet flow structure with two sub jets. The analytical results also confirmed the experimentally observed phenomena that gravity had little effect on the flow field with the jet flow in the downward direction be-

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Fig. 17. Detailed temperature distribution around the 0.06 mm bubble [K]. (a) x-y plane; (b) y-z plane. ing only slightly slower than in the upward direction. Therefore, the Marangoni flow is far more significant than natural convection. The temperature distribution along the upper part of the bubble surface was fairly uniform caused by the very low velocities on the top surface of the bubble and an essentially stagnant region above the bubble.

Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 59976016) and the Graduate Foundation of Tsinghua University. References

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