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Nucleate boiling in bidistillate droplets
International Journal of Heat and Mass Transfer 71 (2014) 197–205
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Nucleate boiling in bidistillate droplets S.Ya. Misyura ⇑ Institute of Thermophysics Siberian Branch, Russian Academy of Sciences, 1. Akad. Lavrentyev Ave., Novosibirsk 630090, Russia
a r t i c l e
i n f o
Article history: Received 19 September 2013 Received in revised form 30 October 2013 Accepted 4 December 2013
Keywords: Water droplets Nucleate boiling Roughness Nucleation site Chaos
a b s t r a c t Dynamics of nucleate boiling in droplets of bidistillate on different wall surfaces was studied experimentally. These experiments were carried out on the rough copper and on the polished surface with plasma spraying of a golden film. The surface state was investigated by an electron microscope and 3D image processing software. Characteristic microroughness responsible for minimal superheating at nucleate boiling was determined. Heat transfer on the polished surface was significantly worse than on the rough wall. Thermal measurements were performed by means of a multiple increase in thermal imaging. When boiling on the polished surface, the self-organized ordered structures are formed there. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Boiling is widely used in devices with high density of energy. Nucleate boiling is applied for microelectronics cooling, space techniques, and cryobiology. A high heat flux is achieved due to evaporation of a liquid microlayer near the basis of a growing bubble [1]. Bubble separation and uplift cause liquid convection, which intensifies heat and mass transfer [2]. High-turbulent microconvective flow with a thin thermal layer is formed near the wall. Large-scale macroconvective transfer is observed along the whole height of the channel. Recently the applied interest to droplet boiling increased significantly; this boiling is generated both artificially for improvement of heat transfer efficiency and as a result of film and jet break-down. At a loss of stability a liquid film is divided into many jets and droplets of different sizes. Usually the theoretical models do not take into account film stability and as a result calculation of heat transfer can lead to significant errors. Initial studies dealt with determination of the averaged heat transfer characteristics: heat flux and heat transfer coefficient. Last decades many works that emphasize the dynamics of the behavior of individual bubbles have been published. However, the mechanistic models cause significant difficulties. The problem is not only a large number of degrees of freedom, but, first of all, the nonlinear nature of the interaction. Even bubble separation and uplift from one of the holes (without heat transfer, i.e., this is absolutely hydrodynamic factor) lead to the chaotic behavior of the whole
⇑ Address: Kutateladze Institute of Thermophysics SB RAS, Lavrentiev Ave. 1, 630090 Novosibirsk, Russia. Tel./fax: +7 (383) 335 65 77. E-mail address: [email protected] 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.12.013
system because of the nonlinear interaction between the wall, bubbles, and liquid [3]. The correct description of hydrodynamics requires consideration of the nonlinear interaction between the bubbles: transfer of perturbation from each bubble to liquid and from liquid to all bubbles. At that the motion of bubble surface has the oscillating character. Without doubt, if we add a thermal aspect to hydrodynamics, the scenario of bubble system behavior will become more complex. Nucleation site interaction relates both to liquid and bubble hydrodynamics and a solid wall of the heater [4]. Generation, development and separation of bubbles lead to a change in the wall temperature. Temperature pulsations on the wall switch on and off new sites of nucleation. This nucleation site interaction also causes the chaotic behavior and complicates the use of mechanistic models. Interaction of only two close bubbles on the wall will lead to chaos. The density of nucleation site distribution and boiling intensity depend on surface roughness [5–7]; thermal–physical properties of the heating wall [5–7,9,10]; fractal roughness [8]; the strong effect of the heater wall thickness also plays an important role [7,11]. Therefore, we have a complex multiparametric problem of nucleate boiling. At nucleate boiling liquid evaporates both from the liquid–vapor interface and bubble surface as well as from the near-wall microlayer of bubble base. The process of small droplets evaporation (with the diameter of up to 3 mm) without nucleate boiling and with the fixed contact line of a droplet is the most well studied now [12–19]. The experimental studies of the current paper relate to boiling of droplets of bidistillate in a wide range of wall superheat and at a large size of droplets. Geometrical characteristics of bubbles were measured at significantly nonstationary and non-uniform boiling. This boiling differs significantly from pool nucleate boiling.
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Nomenclature a D k l; x; h m N p rcr r; d S Sn Sd Ss t t1 T DTw V
thermal diffusivity (m2 s1) droplet diameter (m) specific heat of evaporation (J kg1) coordinate (m) the mass of droplet (kg) the number of vapor bubbles (–) pressure (Nm2) the critical radius micropore (m) bubble radius; bubble diameter (m) distance between bubbles (m) the area of bubble base surface (m2) the area of droplet base surface (m2) the area of droplet interfacial surface (liquid–gas) (m2) time (s) total time of droplet evaporation (s) temperature (°C) wall superheat (°C) the droplet volume (m3)
b1 b h k
q r
the function of the contact angle micropore angle (°) the contact angle (°) thermal conductivity (W m1 K1) density (kg m3) surface tension (Nm1)
Subscripts a the average value cr critical d droplet l liquid m the maximum value before the bubble collapse n bubble s droplet surface m vapor w wall 0 initial value (t = 0) i current value
Greek symbols a heat transfer coefficient (W m2 K1)
2. Experimental setup Synchronization of thermal imaging and high-speed digital filming allowed us to measure local characteristics for small droplets of liquid. Thermal images were measured by means of six-fold magnification using a high-accuracy measurement cell. The thermal field of droplet surface (Ts) was measured by the thermal imager (NEC-San Instruments). The wall temperature (Tw) was kept constant and it was determined by the readings of graduated thermocouple, located under the heated surface. The thermocouples were located at the distance of 0.5 mm from the wall surface. Four thermocouples were mounted at some distance from the center and one thermocouple was in the center of the cylinder. The wall temperature was kept constant automatically with the accuracy of ±0.5 °C. The batch of liquid was in the cylinder center. At droplet evaporation the wall temperature under the droplet decreased by 2 4 °C depending on superheat. The central thermocouple did not participate in automatic regulation; it measured the temperature only under the droplet. In every experiment the dosed batches of bidistillate were put on the heated surface by means of highprecision micro dispensers. Before the experiment bidistillate was degassed thoroughly by means of boiling, to reduce the amount of dissolved gas. For the sessile droplets the process of batch separation from the dosing device occurred without droplet fall, i.e., the dosing device was near the surface and it was located normally to the wall. The separated liquid volume had a short simultaneous contact with dosing device and wall surfaces. Time of separation was about 1 s, and then the dosing device was removed. This method of droplet separation excluded the droplet impact on the wall and its splitting. The moment of dosing device separation from the droplet surface corresponds to zero value of measurement time t = 0. To work with water droplets the working section was made of copper with metal spraying. The cylinder diameter was 84 mm and the height was 55 mm (Fig. 1). While studying nucleate boiling, the type of material, wall thickness, physical–chemical and geometrical properties of the heated surface are of a particular importance. Therefore, to exclude the additional factors effecting bubbles generation, the working section was made of the material with high heat conductivity (copper cylinder with low oxygen content), and the sizes of this section exceeded the diameter of liquid
droplets significantly. The cylinder surface was polished, and then a micron layer of chromium (to give the coating strength) and a golden film were deposited by means of plasma spraying. Polishing reduced significantly the roughness. Golden spraying excludes material aging completely (a change of properties with time). Moreover, exclusion of oxide film formation allowed us to keep high heat-conductive properties of section surface. A magnified image of the cylinder surface roughness obtained via an electron microscope is shown in Fig. 2. The rms roughness of mirrored gold-plated surface was of the order of 50 70 nm. Before every experiment the surface was thoroughly cleaned from dust. To exclude contamination of walls, the working section was put into the closed chamber at the constant ambient air temperature of 23 °C. Before the experiment air humidity in the chamber was decreased by means of a sorbent. All experiments were carried out at the atmospheric air pressure of 1 bar. Since the process of bubble nucleation in the droplet had an occasional character, every experiment was multiply repeated. The average characteristics were determined by 4 5 experiments under the same controlled conditions.
Fig. 1. The working section with mirrored gold-plated surface.
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Fig. 2. The 3D model of the wall surface obtained by means of an electron microscope.
3. Dynamics of vaporization inside a bidistillate droplet Let’s note some important differences of vaporization in droplet from pool boiling. Intensive droplet boiling is accompanied by continuous motion of a contact line: the area of droplet base and its shape change, the number of bubbles varies continuously as well as their average diameter and life time. The droplet migrates constantly over the surface changing the boundary conditions on the wall. Thus, in contrast to pool boiling, the vaporization in droplet is unstable, spatially unsteady and nonisothermal with a continuous change in conjugated boundary conditions, and all these complicate significantly experimental and theoretical studies. Distribution of the boiling sites in the droplet is also very non-uniform. Pool boiling is characterized by formation of bubble columns, vapor mushrooms and vapor clouds, depending on wall superheat [20]. There are no such structures in the droplet because of a small height of liquid. At low wall superheat DTw (less than 7 °C) the vapor bubble grows and can keep its stable shape, when reaching the droplet height. At superheat above 10 °C the bubble base diameter can significantly exceed the droplet height (Fig. 3(a)). Two spring forces effect the bubble motion: the force from the upper droplet surface (F1) and in horizontal direction (F2). At significant superheat the rate of bubble growth increases and force F2 disturbs the equilibrium at the droplet margins. The contact line slips periodically with velocity V and causes a significant change in the base area and height of the droplet, what, in turn, effects vaporization dynamics. As a result, in contrast to droplet evaporation without phase transition, there are five characteristic time regimes of F1
vapor
vapor
vapor F2
V V
(a)
(b)
Fig. 3. The scheme of nucleate boiling in a droplet.
boiling with a significant change in evaporation rate [7]. The contact line slipping generates considerable theoretical problems [21]. Actually, when the vapor bubble grows, the stability problem of two boundaries arises: droplet contact line and bubble contact line. When the film breaks vapor removes, and liquid fills a formed dry spot on the wall (Fig. 3(b)). It is evident that the heat flux on the wall will depend on frequency of bubble collapse. Heat and mass transfer in the droplet (Fig. 3(a)) depends on the rate of evaporation of a microlayer under the bubble, liquid evaporation from the outer surface of droplet (liquid–gas), microcirculation flows in liquid and non-uniform heat flux in the solid wall because of interaction between nucleation sites. Dynamics of nucleate boiling depends significantly on ratio S/ dm, where S is a distance between bubbles, and dm is the maximum value of diameter before the bubble collapse. If S/dm 3, the bubbles do not effect each other [4,22]. In the zone of 1 < S/dm < 3 the bubbles effect each other significantly. A growing bubble suppresses the adjacent active site. Transition from the active nucleation site to the nonactive one occurs both due to hydrodynamic perturbations and because of thermal pulsations in the wall (a growing bubble cools the nearby space of the wall). When S/dm approaches unity, we can observe a tendency towards adjacent bubbles merging. It is interesting to investigate ratio S/dm at boiling of the intermediate and large liquid batches (droplets). Most experiments on interaction of adjacent bubbles are carried out for a large water volume and for the artificial cavities. In the current study we did not form the cavities, and the bubbles were formed spontaneously. Distance S was determined as an average distance only for the adjacent bubbles, dm is the average diameter of all bubbles in the droplet at a given time moment. A change in values S/dm in time is shown in Fig. 4 for different initial superheat of the wall DTw, curve 1 presents initial superheat of 5 6 °C, and curve 2 shows DTw = 20 21 °C. The initial droplet diameter (without boiling) is 11 mm. Curve 1 corresponds to minimal superheating, when boiling started in the current study. The fixed contact line of a droplet is for curve 1 for the most part of evaporation time. Ratio S/dm is higher than 3 for the whole period of boiling, and this indicates a weak interconnection of bubbles,
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Fig. 4. A change in parameter S/dm with time for different initial superheat of the wall (initial droplet diameter is 11 103 m): curve 1 for DTw = 5 6 °C; curve 2 for DTw = 20 21 °C.
and we can consider the boiling model for each bubble separately. With time the size ratio increases because boiling cools the wall more intensively (the heat transfer coefficient increases), and as a result some part of active boiling sites is excluded, boiling degenerates (minimal superheat is insufficient to keep boiling stable). At high superheat (curve 2) ratio S/dm is less than 2 for the whole time range. The slipping contact line of a droplet corresponds to curve 2. This superheating is accompanied by a strong influence of bubbles on each other. With time S/dm tends to one. At that, we observe a drastic reduction in the number of bubbles because of their merging. The system (liquid–vapor bubbles–heater wall) is the complex open dissipative nonequilibrium system, which has a tendency both to the chaotic behavior [3,4] and to the fundamental property: self-organization [23], which is characterized by the principle of minimal entropy production [24]. The chaotic behavior is caused by the oscillating motion of the bubble surface and nonlinear interaction between the bubble surface and liquid [3] as well as by the nonlinear connection between a heat-conducting solid wall and boiling sites. If S/d < 3 chaos starts. Despite the fact that at high superheating S/dm < 2 (Fig. 4) and chaos should be observed, droplet boiling has a clear tendency to self-organization. In Fig. 5 there are the pictures of the ordered self-organized bubble structures for DTw = 17 18 °C at different moments of boiling. A change in dimensionless area of the droplet surface D2d =D2d0 vs. evaporation time is shown in Fig. 6 (Dd is the current diameter of droplet on the lower liquid–solid body interface, Dd0 is the initial diameter of droplet). With a rise of evaporation time not only the volume and surface of the droplet decrease, but also the number of nucleation sites, average bubble diameter, and total area of vapor changes. At a decrease in diameter it is necessary to taken into account non-isothermality in the wall under the droplet and inside this droplet. Non-isothermality in the wall is an additional key factor, which regulates the rate of evaporation and balance of heat fluxes from the wall and droplet surface at evaporation. According to thermal imaging measurements, the final stage of evaporation is
Fig. 6. A change in dimensionless area of bidistillate droplet surface vs. evaporation time (V0 = 1 107 m3; Dd is the current base diameter of droplet; Dd0 is the initial base diameter of droplet): curve 1 – Tw = 106 °C; curve 2 – Tw = 110 °C; curve 3 – Tw = 115 °C; curve 4 – Tw = 120 °C.
characterized by an insignificant growth of the droplet interface temperature by 1 3 °C. At short and intermediate times the upper surface of droplet has significantly nonuniform temperature field because of bubble nucleation. A change in the number of bubbles N in bidistillate droplet vs. evaporation time is shown in Fig. 7 for different wall temperatures. With time the droplet surface decreases (Fig. 6) and, respectively, the number of bubbles decreases for the whole range of nucleate boiling temperatures (Tw = 105 120 °C). The number of vapor bubbles N increases with a rise of temperature up to the maximal value (Tw about 115 °C) and then it decreases. A rise of N relates to the fact that with an increase in superheat DTw the microcavities of a smaller radius become active (1). As a result, the total number of cavities participating in vaporization increases
rcr ¼
2rRT 2s ; kpDT w
ð1Þ
where rcr is the minimal radius of micropore, which becomes active at given superheat DTw; R is universal gas constant; p is vapor pressure; k is specific heat of evaporation; r is surface tension; and Ts is temperature of vapor saturation. With a rise of superheat and approximation of parameter S/dm to 2, the boiling character changes: bubbles start joining (Tw is higher than 115 °C). Bubble merging leads to a following decrease in N. Similar bubble joining at high superheat DTw is also observed for a large water volume [20]. P A change in the average diameter of bubbles da vs. Tw (da = dai/ Ni) is shown in Fig. 8. With a rise of Tw superheat of a microlayer of the wall under vapor bubble increases, and this leads to a higher rate of microlayer evaporation and higher rate of bubble growth.
Fig. 5. The video images of the regular bubble structures in the droplet (Tw = 110 °C).
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Thermal dynamics of bubble is determined by the ratio of such parameters as thermal diffusivity, Fourier number, and Jacob number [25]. We have studied the behavior of vapor content near the droplet bottom, which has the different character of a change depending on time and wall superheat. A change in dimensionless total area
P P of bubbles Sgi/Sdi vs. evaporation time is shown in Fig. 9 ( Sgi the total area of the base surface of all bubbles at the measured moment of time t, Sdi is the area of base surface of a droplet at the measured moment of time). At Tw = 105 °C (curve 1) dimenP sionless area Sgi/Sdi decreases with a rise of time t, and this is explained by the cooling effect of the wall. With a rise of superheat, insignificant cooling of a metal surface does not effect the qualitative character of curve 2 (Fig. 9). With an increase in time of evaporation (curve 2) the total amount of generated vapor increases. The pictures of the droplet temperature (Ts) are shown in Fig. 10 for Tw = 105 °C; they are made by means of a thermal imager: (a) corresponds to evaporation time t = 5 s; (b) t = 10 s; (c) t = 15 s. The measured contact angle of a water droplet on the polished surface was 58°. The scale of 10 mm in Fig. 10 is the same as in Fig. 11. Before the experiment we have obtained dependences for the used materials of working sections on global emissivity of the water layer in the short wave range as a function of the optical thickness. Considering the droplet height (h) (Figs. 10 and 11(a)–(c)) the surface droplet temperature will be decreased by 8 10 °C, i.e., the actual droplet temperature will be 8 10 °C higher. It is reasonable to consider the surface temperatures only for the region of liquid without vapor bubbles because of a thin vapor film and we disregarded the temperature near the contact line (closer than 0.5 mm from edge of droplet). However, not the quantitative, but the qualitative character of temperature change in time is of a particular interest: boiling (bubble) degeneration at low superheat and bubble merging (the growth of vapor phase percentage) at high superheating. The thermal image shows that the process of vaporization causes nonisothermal and spatially nonuniform thermal conditions. According to Fig. 10, the number of bubbles decreases with time. The total area of vapor bubbles decreases also, and this corresponds to Fig. 9 (curve 1). A decrease in vapor area is caused by the cooling effect of the wall. Curve 2 in Fig. 9 has the different character: with time the total dimensionless area of vapor increases from 0.15 to 0.38, and this corresponds to the thermal images in Fig. 11 at Tw = 120 °C. Wall cooling by several degrees does not change boiling conditions: superheat is sufficient and high vapor output is kept. Therefore, to determine a change in vapor output in time, it is necessary to taken into account not only the effect of superheat, but the cooling effect on the walls. Volumetric content of vapor relative to the volume of a whole droplet is an important feature of boiling. According to experimental data of the current study, at Tw = 120 125 °C the vapor content is close to 40%. This temperature regime is the pre-critical one (at Tw = 129 °C the droplet separation occurs: the droplet separates from the wall and the vapor film is formed). Therefore, the boiling crisis of a droplet occurs at significantly lower vapor concentration
Fig. 8. A change in the average diameter (da) of bubble in bidistillate droplet vs. wall temperature (Tw) (the initial droplet diameter is 11 103 m): curve 1 for t = 5 s; curve 2 for t = 15 s.
Fig. 9. A change in dimensionless total area of bubbles surface vs. time of evaporation (V0 = 1 107 m3, Sn is the area of bubble base surface, Sd is the area of droplet base surface): curve 1 – Tw = 105 °C; curve 2 – Tw = 120 °C.
Fig. 7. A change in the number of bubbles N in bidistillate droplet vs. evaporation time at different Tw (V0 = 1 107 m3): curve 1 – Tw = 105 °C; curve 2 – Tw = 111 °C; curve 3 – Tw = 114 °C; curve 4 – Tw = 120 °C.
Labuntsov’s expression takes into account dependence of the shape of surface bubble on contact angle h. Evaporation occurs mainly through the microlayer surface [1] near the base of the growing bubble (2), where DT is superheating; k is specific heat of evaporation; k is thermal conductivity of the liquid; t is time; qv is vapor density, b1 is the function of the contact angle, shape and the ratio of the two characteristic scales. With a rise of superheat the rate of bubble diameter growth becomes higher. However, for the droplet there are significant differences: liquid subcooling and small height of the droplet, which lead to deformation of the bubble shape. The lift-off diameter of bubble can be much larger than the droplet height, and the bubble growth can be changed fast to the period of drastic decay because of subcooling. Moreover, expression (2) describes the growth of a single bubble and it does not take into account the effect of growing bubble on each other. The nonlinear interaction between the vapor phase and solid wall is not considered as well as the nonisothermal character of the ambient conditions and a change in droplet geometry with time.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b1 kDTt : d¼ kqv
ð2Þ
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bubble
liquid (a)
(b)
(c)
Fig. 10. The thermal imager pictures of nucleate boiling in the droplet (Tw = 105 °C, h is the average height droplet): (a) t = 5 s; h = 2.3 mm; (b) t = 10 s; h = 1.8 mm; (c) t = 15 s; h = 1.4 mm.
Fig. 11. The thermal imager pictures of nucleate boiling in the droplet (Tw = 120 °C, h is the average height droplet): (a) t = 5 s; h = 1.4 mm; (b) t = 10 s; h = 0.9 mm; (c) t = 15 s; h = 0.7 mm.
than that for the pool liquid. As it is known, pool boiling of water under the pre-critical conditions corresponds to very high vapor output, i.e., the ratio of vapor phase volume to liquid near the wall is up to 70 80%. It is also known that at liquid boiling above a micron wire the boiling crisis occurs abruptly because of a drastic growth of the separation zone. There is no the transitional zone of crisis. For the unlimited sizes of the heater (pool boiling) the separation zone of several millimeters can be formed locally, and it does not spread over the whole surface of the heater. From the point of vapor output and hydrodynamic and thermal instability the boiling crisis of droplet occupies an intermediate position between the micro- and mini-objects (filament) and macro-objects (the heaters of the large area).
4. Heat transfer on the polished and rough surfaces of a copper cylinder The experiments with heat transfer on the gold-plated surface and rough surface were carried out in the working section presented above. Geometry of the copper cylinder with rough surface is the same as for the polished one. The content of oxygen in copper was low to reduce surface oxidation in time. The method of determination of the heat flux and heat transfer coefficient is based on the measurement of current values of the droplet mass, wall temperature under the droplet, temperature of the upper droplet surface (liquid–gas) and droplet area [26]. Heat spent for droplet evaporation included droplet heating up to the maximal temperature with consideration of heat capacity. The droplet mass was
measured by means of scales. The upper surface temperature was measured by the thermal imager with consideration of data on global emissivity and current values of the droplet height. The wall temperature under the droplet was measured by a thermocouple. The droplet area was measured with application of video recording. The maximal measurement error a was within ±22%. On the basis of experimental data the values of heat transfer coefficient (local-temporal (ai) and averaged value during the whole period of evaporation (a)) can be determined respectively as
ai ¼
kDmi ; Ssi Dti ðT wi T si Þ
a¼
1 t1
Z
ai dt
1 X ai Dti ; t1
ð3Þ
ð4Þ
where k is specific heat of evaporation, mi is current value of droplet mass; Ssi is current area of droplet interfacial surface (liquid–gas), ti is current time, Twi is current wall temperature under droplet, Tsi is current temperature of the droplet interfacial surface (liquid–gas), t1 is total time of droplet evaporation. Subscript i relates to local values of parameters. According to Fig. 12, the polished section with gold deposition demonstrates a multiple reduction of heat transfer in comparison with the rough section. This result is really surprising and it can be explained by a significant decrease in the number of active nucleation sites. The experiments on the copper and stainless steel sections [5] showed an opposite result. Perhaps, surface polishing in [5] led to significant intensification of heat transfer because of an increase in the number of active nucleation sites and considerable
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Fig. 12. A relative change in the heat transfer coefficient vs. wall superheating DTw (a2 for the copper section with the polished surface and gold coating, a1 for the copper rough wall).
changes in surface energy of metal. The link between surface energy and wettability with a degree of vapor oversaturation is considered in the framework of the density functional theory [27]. With a rise of surface energy liquid superheating, required for heterogeneous phase transition, decreases. The polished section used in the current study essentially differs from that used in [5]. A gold layer of several microns was deposited on the polished surface via plasma spraying. Probably, the number of active boiling sites decreased significantly because of this coating. Therefore, to estimate the ability of material to intensify heat transfer, it is not sufficient to have information about roughness. It is also important to know the features of molecular interaction of molecules of a solid body and liquid. While studying heat transfer at pool boiling, contribution of two parameters is taken into account: heat transfer intensification via heat conductivity and convection in liquid as well as via evaporation from bubble surface and evaporation of a liquid microlayer near the bubble base. These two factors are interconnected and effect each other significantly, and this is one of complexities of theoretical analysis. Neglecting the motion of bubbles we do not obtain highly intensive convective turbulent mixing in liquid. If we consider only evaporation of a bubble microlayer, we will skip considerable heat transfer via the turbulized liquid. Heat transfer will depend on nucleation site density, bubble size, vapor phase volume and frequency of bubble detachment. The expression for boiling in a droplet will differ basically from pool boiling. There is no thick convective core in the droplet, and circulation occurs only near the wall (see Fig. 3(a)). Moreover, instead of bubble
203
detachment frequency we observe there frequency of bubble breaking, violation of droplet shape and interface relaxation back to the previous shape (Fig. 3(b)). It also follows from the experimental data that the boundary conditions change in time: droplet shape and size, size and number of bubbles. According to the density functional theory [27], heterogeneous phase transition for liquids with high wettability (metal wall) requires superheat of about 9 11 °C. Actually, minimal superheat of the wall, when nucleate boiling starts is 5 5.5 °C both for rough copper and polished copper. It turns out that stability of phase equilibrium is not considerably connected with the nucleation site distribution. We can make the estimates of cavities sizes using data obtained by the optical profilometer ‘‘Zygo’’ (uncertainty of measurement is ±15 nm). The rms roughness of copper was about 1.3 1.4 lm. There are three types of polished surface roughness (Fig. 13(a)): fine roughness with high concentration of cavities and rms roughness of the order of 50 70 nm; ledge above the surface with the average height of 100 150 nm; cavities with very low concentration and average height of about 150 200 nm. The work of nucleation on projections is higher than on a flat surface, and in a cavity it is lower than on a plane [28]. Therefore, it is reasonable to consider only large cavities. Expression (1) does not include contact angle h (Fig. 13(c)). Metals are characterized by good wettability by water (the contact angle between a solid wall and liquid h < 90°). Considering h and condition ql qv, expression (1) can be presented as (5), where ql is density of liquid; qv is density of vapor.
DT w ¼
2rT s sin h rcr qv k
ð5Þ
Within the polished section the large cavities (pores) have average radius rcr of about 5 lm. The measured contact angle of a water droplet on the polished surface was 58°. With consideration of rcr and h, expression (5) gives superheating of 4.8 °C, and taking into account an experimental errors, this is close to superheat of 5.1 5.5, achieved in experiments and corresponded to boiling beginning. Therefore, we can assume that wettability of a large droplet is close to wettability of a microbubble, and the critical nucleuses relate to the large and deep cavities. Often, to estimate the radius of a critical nucleus an rms value of surface roughness is used. If we use rms roughness of the order of 70 nm as rcr in expression (2), superheat will be about 400 °C. Therefore, it is incorrect to use statistic averaging by all pores. Moreover, low heat transfer on the polished surface also demonstrates that the estimate of heat transfer at boiling requires consideration of the average radius of exactly typical cavities (pores) and density of their distribution. To let a vapor bubble to be on a flat surface, it should move over the walls of a microcavity from the bottom to the top
Fig. 13. Nucleate boiling on the polished surface.
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Table 1 Data on nucleation site density. No
Wall superheat DT, °C
Nucleation site density, qn, m2
1 2 3
6 12 22
1.7 105 2.9 105 3.5 105
(Fig. 13(b)). (V) indicates vapor; (L) is liquid; (1) is interface for good wettability; (2) is interface for poor wettability and (3) is interface for the contact angle, whose value is close to 90°. Average angle of the considered typical cavities b was 3 5°. At this b the upward motion of a vapor bubble is possible only, when h is close to 90°. For low (interface 2) and high wettability (interface 1) a micro or nanobubble will have very small radius and superheat of hundreds degrees will be required. Therefore, to achieve boiling on the polished golden-plated surface, two conditions should be implemented: neutral wettability inside the cavity (contact angle is close to 90°) and good wettability on a flat surface, which is close to that measured for a large droplet. Fig. 13 illustrates some different versions of surface wetting. For the large microcavities (Fig. 13(b)) both good and poorly wetting liquids penetrate inside the cavities. Fig. 13(d) presents poorly wetting liquids and small nanocavities. Liquid does not penetrate inside the cavities and the wetting angle on the heater surface is larger than 90°. The high wetting angle (according to (5)) decreases minimal superheat by tens times for boiling incipience. The case (c) corresponds to liquids with high wettability, e.g., water. According to Fig. 13(c) and expression (5), superheat decreases with a rise of wettability. However, Fig. 13(c) characterizes only the growth of bubble, whose size is higher than critical and which has already come to the heater surface from the cavity. Bubble inception and growth to the critical size occur not on the heater surface, but inside the cavity. High wettability in the cavity (Fig. 13(b)) increases superheat significantly. Therefore, to determine the density of active centers and the inception rate of the bubbles of a supercritical size, it is important to determine the surface free energy directly in the cavities and not only on the heater working surface. Data on nucleation site density (NSD) are shown in Table 1 depending on wall superheat DTw, where qn is nucleation site density for the polished surface. Maximal NSD (qmax) for the polished surface (according to the processed data of the electron microscope) is about 108. Density qmax was estimated only for cavities with radius rcr of about 5 lm, and it corresponds to superheat DTw of 5 6 °C by expression (3). Thus, only one microcavity of thousand cavities is active, despite geometry of other cavities also allows generation of micro bubbles. It is reasonable to relate this discrepancy with the features of local wettability inside the microcavities (Fig. 13(b)). It is known that the number of active nucleation sites is proportional to (DT)3. In this case NSD of about 107 will correspond to superheat of 22 °C, and this meets the data on maximal NSD [29]. However, in this case heat transfer on a polished surface will be close to that on the rough surface. Significant difference between heat transfers on two different surfaces (Fig. 12) shows that a will be the functions of nucleation site density and local wettability, which will depend on the type of mechanical processing of the surface and type of wall coating, considerably changing the surface energy of nano- and microcavities.
5. Conclusion Dynamics of nucleate boiling in the droplets of bidistillate was studied in the current work. These experiments were carried out on the copper rough surface as well as on the polished surface with plasma spraying of a golden film. The thermal field of droplet
surface was measured by the thermal imager (NEC-San Instruments). The 3D model of the wall surfaces obtained by means of an electron microscope. The following has been determined during the experiments and data analysis: 1. The ratio of an average distance between the bubbles to their diameter is less than 3, and this indicates the nonlinear interaction of bubbles and system inclination towards the chaotic behavior. Despite this fact, this complex open dissipative and nonlinear system has the obvious tendency to self-organization of the ordered structures. 2. At low superheat the contact line is fixed. At high superheat and high rate of bubble growth, the contact line of droplet moves continuously and the conjugated boundary conditions change (droplet surface, wall temperature). 3. While approaching the detachment point (boiling crisis at Leidenfrost temperature), total vapor concentration in the droplet is essentially lower than that for pool boiling of water. 4. Heat transfer on the polished golden-plated surface is significantly lower than that for the rough copper wall. When calculating the radius of a critical nucleus (for the surface studied in this work), it is necessary to consider not the root-meansquare value for all pores, but the cavities with characteristic geometry and neutral wettability (the contact angle is close to 90°).
References [1] D.A. Labuntsov, Physical Foundation of Power Engineering, Selected Works on Heat Transfer, Hydrodynamics, Thermodynamics, MEI, Moscow, 2000. [2] S.S. Kutateladze, Fundamentals of Heat Transfer Theory, Atomizdat, Moscow, 1979. [3] R. Mosdorf, M. Shoji, Chaos in bubbling-nonlinear analysis and modeling, Chem. Eng. Sci. 58 (2003) 3837–3846. [4] M. Shoji, Studies of boiling chaos: a review, Int. J. Heat Mass Transfer 47 (2004) 1105–1128. [5] B. Bon, C.-K. Guan, J.F. Klausner, Heterogeneous nucleation on ultra smooth surfaces, Exp. Therm. Fluid Sci. 35 (2011) 746–752. [6] R.J. Benjamin, A.R. Balakrishnan, Nucleation site density in boiling of saturated pure liquids: effect of surface microroughness and surface and liquid physical properties, Exp. Therm. Fluid Sci. 15 (1) (1997) 33–42. [7] V.E. Nakoryakov, S.Y. Misyura, S.L. Elistratov, The behavior of water droplets on the heated surface, Int. J. Heat Mass Transfer 55 (2012) 6609–6617. [8] R.W. L Fong et al., Correlation between the critical heat flux and the fractal surface roughness of Zirconium alloy tubes, J. Enhance Heat Transfer 8 (2001) 137–146. [9] Y. Qi, J.F. Klausner, Heterogeneous nucleation with artificial cavities, J. Heat Transfer 127 (2005) 1189–1196. [10] Y. Qi, J.F. Klausner, Comparison of nucleation site density for pool boiling and gas nucleation, J. Heat Transfer 128 (2006) 13–20. [11] L.H. Chai, X.F. Peng, B.X. Wang, Nucleation site interaction during boiling, Int. J. Heat Mass Transfer 43 (2000) 4249–4258. [12] D. Brutin, B. Sobac, F. Rigollet, C. Le-Niliot, Infrared visualization of thermal motion inside a sessile drop deposited onto a heated surface, Exp. Therm. Fluid Sci. 35 (2011) 521–530. [13] K. Sefiane, S.K. Wilson, S. David, G.J. Dunn, B.R. Duffy, On the effect of the atmosphere on the evaporation of sessile droplets of water, J. Phys. Fluids 21 (2009). [14] N. Shahidzadeh-Bonn, S. Rafaı, A. Azouni, D. Bonn, Evaporating droplets, Fluid Mech. 549 (2006) 307–313. [15] R. Mollaret, K. Serfiane, I.R. Christy, D. Veyret, Experimental and numerical investigation of the evaporation into air of drop on a heated surface, Chem. Eng. Res. Des. 82 (4) (2004) 471–480. [16] G.J. Dunn, S.K. Wilson, B.R. Duffy, S. David, K. Seffiane, The strong influence of substrate conductivity on droplet evaporation, J. Fluid Mech. 623 (2009) 329. [17] Mebrouk Ait Saada, Salah Chikh, Lounes Tadrist, Numerical investigation of heat mass transfer of an evaporating sessile drop on a horizontal surface, J. Phys. Fluids 22 (2010) 112115. [18] N. Murisic, L. Kondic, On evaporation of sessile drops with moving contact lines, J. Fluid. Mech. 679 (2011) 219–246. [19] S. David, K. Sefiane, L. Tadrist, Experimental investigation of the effect of thermal properties of the substrate in the wetting and evaporation of sessile drops, Colloids Surfaces 298 (2007) 108–114. [20] R.F. Gaertner, Trans. ASME C87 (1) (1965) 20. [21] V.I. Pukhnachev, V.A. Solonnikov, To the problem of dynamic contact angle, Appl. Math. Mech. 46 (6) (1982) 961–971.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Nucleate boiling in bidistillate droplets S.Ya. Misyura ⇑ Institute of Thermophysics Siberian Branch, Russian Academy of Sciences, 1. Akad. Lavrentyev Ave., Novosibirsk 630090, Russia
a r t i c l e
i n f o
Article history: Received 19 September 2013 Received in revised form 30 October 2013 Accepted 4 December 2013
Keywords: Water droplets Nucleate boiling Roughness Nucleation site Chaos
a b s t r a c t Dynamics of nucleate boiling in droplets of bidistillate on different wall surfaces was studied experimentally. These experiments were carried out on the rough copper and on the polished surface with plasma spraying of a golden film. The surface state was investigated by an electron microscope and 3D image processing software. Characteristic microroughness responsible for minimal superheating at nucleate boiling was determined. Heat transfer on the polished surface was significantly worse than on the rough wall. Thermal measurements were performed by means of a multiple increase in thermal imaging. When boiling on the polished surface, the self-organized ordered structures are formed there. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Boiling is widely used in devices with high density of energy. Nucleate boiling is applied for microelectronics cooling, space techniques, and cryobiology. A high heat flux is achieved due to evaporation of a liquid microlayer near the basis of a growing bubble [1]. Bubble separation and uplift cause liquid convection, which intensifies heat and mass transfer [2]. High-turbulent microconvective flow with a thin thermal layer is formed near the wall. Large-scale macroconvective transfer is observed along the whole height of the channel. Recently the applied interest to droplet boiling increased significantly; this boiling is generated both artificially for improvement of heat transfer efficiency and as a result of film and jet break-down. At a loss of stability a liquid film is divided into many jets and droplets of different sizes. Usually the theoretical models do not take into account film stability and as a result calculation of heat transfer can lead to significant errors. Initial studies dealt with determination of the averaged heat transfer characteristics: heat flux and heat transfer coefficient. Last decades many works that emphasize the dynamics of the behavior of individual bubbles have been published. However, the mechanistic models cause significant difficulties. The problem is not only a large number of degrees of freedom, but, first of all, the nonlinear nature of the interaction. Even bubble separation and uplift from one of the holes (without heat transfer, i.e., this is absolutely hydrodynamic factor) lead to the chaotic behavior of the whole
⇑ Address: Kutateladze Institute of Thermophysics SB RAS, Lavrentiev Ave. 1, 630090 Novosibirsk, Russia. Tel./fax: +7 (383) 335 65 77. E-mail address: [email protected] 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.12.013
system because of the nonlinear interaction between the wall, bubbles, and liquid [3]. The correct description of hydrodynamics requires consideration of the nonlinear interaction between the bubbles: transfer of perturbation from each bubble to liquid and from liquid to all bubbles. At that the motion of bubble surface has the oscillating character. Without doubt, if we add a thermal aspect to hydrodynamics, the scenario of bubble system behavior will become more complex. Nucleation site interaction relates both to liquid and bubble hydrodynamics and a solid wall of the heater [4]. Generation, development and separation of bubbles lead to a change in the wall temperature. Temperature pulsations on the wall switch on and off new sites of nucleation. This nucleation site interaction also causes the chaotic behavior and complicates the use of mechanistic models. Interaction of only two close bubbles on the wall will lead to chaos. The density of nucleation site distribution and boiling intensity depend on surface roughness [5–7]; thermal–physical properties of the heating wall [5–7,9,10]; fractal roughness [8]; the strong effect of the heater wall thickness also plays an important role [7,11]. Therefore, we have a complex multiparametric problem of nucleate boiling. At nucleate boiling liquid evaporates both from the liquid–vapor interface and bubble surface as well as from the near-wall microlayer of bubble base. The process of small droplets evaporation (with the diameter of up to 3 mm) without nucleate boiling and with the fixed contact line of a droplet is the most well studied now [12–19]. The experimental studies of the current paper relate to boiling of droplets of bidistillate in a wide range of wall superheat and at a large size of droplets. Geometrical characteristics of bubbles were measured at significantly nonstationary and non-uniform boiling. This boiling differs significantly from pool nucleate boiling.
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Nomenclature a D k l; x; h m N p rcr r; d S Sn Sd Ss t t1 T DTw V
thermal diffusivity (m2 s1) droplet diameter (m) specific heat of evaporation (J kg1) coordinate (m) the mass of droplet (kg) the number of vapor bubbles (–) pressure (Nm2) the critical radius micropore (m) bubble radius; bubble diameter (m) distance between bubbles (m) the area of bubble base surface (m2) the area of droplet base surface (m2) the area of droplet interfacial surface (liquid–gas) (m2) time (s) total time of droplet evaporation (s) temperature (°C) wall superheat (°C) the droplet volume (m3)
b1 b h k
q r
the function of the contact angle micropore angle (°) the contact angle (°) thermal conductivity (W m1 K1) density (kg m3) surface tension (Nm1)
Subscripts a the average value cr critical d droplet l liquid m the maximum value before the bubble collapse n bubble s droplet surface m vapor w wall 0 initial value (t = 0) i current value
Greek symbols a heat transfer coefficient (W m2 K1)
2. Experimental setup Synchronization of thermal imaging and high-speed digital filming allowed us to measure local characteristics for small droplets of liquid. Thermal images were measured by means of six-fold magnification using a high-accuracy measurement cell. The thermal field of droplet surface (Ts) was measured by the thermal imager (NEC-San Instruments). The wall temperature (Tw) was kept constant and it was determined by the readings of graduated thermocouple, located under the heated surface. The thermocouples were located at the distance of 0.5 mm from the wall surface. Four thermocouples were mounted at some distance from the center and one thermocouple was in the center of the cylinder. The wall temperature was kept constant automatically with the accuracy of ±0.5 °C. The batch of liquid was in the cylinder center. At droplet evaporation the wall temperature under the droplet decreased by 2 4 °C depending on superheat. The central thermocouple did not participate in automatic regulation; it measured the temperature only under the droplet. In every experiment the dosed batches of bidistillate were put on the heated surface by means of highprecision micro dispensers. Before the experiment bidistillate was degassed thoroughly by means of boiling, to reduce the amount of dissolved gas. For the sessile droplets the process of batch separation from the dosing device occurred without droplet fall, i.e., the dosing device was near the surface and it was located normally to the wall. The separated liquid volume had a short simultaneous contact with dosing device and wall surfaces. Time of separation was about 1 s, and then the dosing device was removed. This method of droplet separation excluded the droplet impact on the wall and its splitting. The moment of dosing device separation from the droplet surface corresponds to zero value of measurement time t = 0. To work with water droplets the working section was made of copper with metal spraying. The cylinder diameter was 84 mm and the height was 55 mm (Fig. 1). While studying nucleate boiling, the type of material, wall thickness, physical–chemical and geometrical properties of the heated surface are of a particular importance. Therefore, to exclude the additional factors effecting bubbles generation, the working section was made of the material with high heat conductivity (copper cylinder with low oxygen content), and the sizes of this section exceeded the diameter of liquid
droplets significantly. The cylinder surface was polished, and then a micron layer of chromium (to give the coating strength) and a golden film were deposited by means of plasma spraying. Polishing reduced significantly the roughness. Golden spraying excludes material aging completely (a change of properties with time). Moreover, exclusion of oxide film formation allowed us to keep high heat-conductive properties of section surface. A magnified image of the cylinder surface roughness obtained via an electron microscope is shown in Fig. 2. The rms roughness of mirrored gold-plated surface was of the order of 50 70 nm. Before every experiment the surface was thoroughly cleaned from dust. To exclude contamination of walls, the working section was put into the closed chamber at the constant ambient air temperature of 23 °C. Before the experiment air humidity in the chamber was decreased by means of a sorbent. All experiments were carried out at the atmospheric air pressure of 1 bar. Since the process of bubble nucleation in the droplet had an occasional character, every experiment was multiply repeated. The average characteristics were determined by 4 5 experiments under the same controlled conditions.
Fig. 1. The working section with mirrored gold-plated surface.
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Fig. 2. The 3D model of the wall surface obtained by means of an electron microscope.
3. Dynamics of vaporization inside a bidistillate droplet Let’s note some important differences of vaporization in droplet from pool boiling. Intensive droplet boiling is accompanied by continuous motion of a contact line: the area of droplet base and its shape change, the number of bubbles varies continuously as well as their average diameter and life time. The droplet migrates constantly over the surface changing the boundary conditions on the wall. Thus, in contrast to pool boiling, the vaporization in droplet is unstable, spatially unsteady and nonisothermal with a continuous change in conjugated boundary conditions, and all these complicate significantly experimental and theoretical studies. Distribution of the boiling sites in the droplet is also very non-uniform. Pool boiling is characterized by formation of bubble columns, vapor mushrooms and vapor clouds, depending on wall superheat [20]. There are no such structures in the droplet because of a small height of liquid. At low wall superheat DTw (less than 7 °C) the vapor bubble grows and can keep its stable shape, when reaching the droplet height. At superheat above 10 °C the bubble base diameter can significantly exceed the droplet height (Fig. 3(a)). Two spring forces effect the bubble motion: the force from the upper droplet surface (F1) and in horizontal direction (F2). At significant superheat the rate of bubble growth increases and force F2 disturbs the equilibrium at the droplet margins. The contact line slips periodically with velocity V and causes a significant change in the base area and height of the droplet, what, in turn, effects vaporization dynamics. As a result, in contrast to droplet evaporation without phase transition, there are five characteristic time regimes of F1
vapor
vapor
vapor F2
V V
(a)
(b)
Fig. 3. The scheme of nucleate boiling in a droplet.
boiling with a significant change in evaporation rate [7]. The contact line slipping generates considerable theoretical problems [21]. Actually, when the vapor bubble grows, the stability problem of two boundaries arises: droplet contact line and bubble contact line. When the film breaks vapor removes, and liquid fills a formed dry spot on the wall (Fig. 3(b)). It is evident that the heat flux on the wall will depend on frequency of bubble collapse. Heat and mass transfer in the droplet (Fig. 3(a)) depends on the rate of evaporation of a microlayer under the bubble, liquid evaporation from the outer surface of droplet (liquid–gas), microcirculation flows in liquid and non-uniform heat flux in the solid wall because of interaction between nucleation sites. Dynamics of nucleate boiling depends significantly on ratio S/ dm, where S is a distance between bubbles, and dm is the maximum value of diameter before the bubble collapse. If S/dm 3, the bubbles do not effect each other [4,22]. In the zone of 1 < S/dm < 3 the bubbles effect each other significantly. A growing bubble suppresses the adjacent active site. Transition from the active nucleation site to the nonactive one occurs both due to hydrodynamic perturbations and because of thermal pulsations in the wall (a growing bubble cools the nearby space of the wall). When S/dm approaches unity, we can observe a tendency towards adjacent bubbles merging. It is interesting to investigate ratio S/dm at boiling of the intermediate and large liquid batches (droplets). Most experiments on interaction of adjacent bubbles are carried out for a large water volume and for the artificial cavities. In the current study we did not form the cavities, and the bubbles were formed spontaneously. Distance S was determined as an average distance only for the adjacent bubbles, dm is the average diameter of all bubbles in the droplet at a given time moment. A change in values S/dm in time is shown in Fig. 4 for different initial superheat of the wall DTw, curve 1 presents initial superheat of 5 6 °C, and curve 2 shows DTw = 20 21 °C. The initial droplet diameter (without boiling) is 11 mm. Curve 1 corresponds to minimal superheating, when boiling started in the current study. The fixed contact line of a droplet is for curve 1 for the most part of evaporation time. Ratio S/dm is higher than 3 for the whole period of boiling, and this indicates a weak interconnection of bubbles,
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Fig. 4. A change in parameter S/dm with time for different initial superheat of the wall (initial droplet diameter is 11 103 m): curve 1 for DTw = 5 6 °C; curve 2 for DTw = 20 21 °C.
and we can consider the boiling model for each bubble separately. With time the size ratio increases because boiling cools the wall more intensively (the heat transfer coefficient increases), and as a result some part of active boiling sites is excluded, boiling degenerates (minimal superheat is insufficient to keep boiling stable). At high superheat (curve 2) ratio S/dm is less than 2 for the whole time range. The slipping contact line of a droplet corresponds to curve 2. This superheating is accompanied by a strong influence of bubbles on each other. With time S/dm tends to one. At that, we observe a drastic reduction in the number of bubbles because of their merging. The system (liquid–vapor bubbles–heater wall) is the complex open dissipative nonequilibrium system, which has a tendency both to the chaotic behavior [3,4] and to the fundamental property: self-organization [23], which is characterized by the principle of minimal entropy production [24]. The chaotic behavior is caused by the oscillating motion of the bubble surface and nonlinear interaction between the bubble surface and liquid [3] as well as by the nonlinear connection between a heat-conducting solid wall and boiling sites. If S/d < 3 chaos starts. Despite the fact that at high superheating S/dm < 2 (Fig. 4) and chaos should be observed, droplet boiling has a clear tendency to self-organization. In Fig. 5 there are the pictures of the ordered self-organized bubble structures for DTw = 17 18 °C at different moments of boiling. A change in dimensionless area of the droplet surface D2d =D2d0 vs. evaporation time is shown in Fig. 6 (Dd is the current diameter of droplet on the lower liquid–solid body interface, Dd0 is the initial diameter of droplet). With a rise of evaporation time not only the volume and surface of the droplet decrease, but also the number of nucleation sites, average bubble diameter, and total area of vapor changes. At a decrease in diameter it is necessary to taken into account non-isothermality in the wall under the droplet and inside this droplet. Non-isothermality in the wall is an additional key factor, which regulates the rate of evaporation and balance of heat fluxes from the wall and droplet surface at evaporation. According to thermal imaging measurements, the final stage of evaporation is
Fig. 6. A change in dimensionless area of bidistillate droplet surface vs. evaporation time (V0 = 1 107 m3; Dd is the current base diameter of droplet; Dd0 is the initial base diameter of droplet): curve 1 – Tw = 106 °C; curve 2 – Tw = 110 °C; curve 3 – Tw = 115 °C; curve 4 – Tw = 120 °C.
characterized by an insignificant growth of the droplet interface temperature by 1 3 °C. At short and intermediate times the upper surface of droplet has significantly nonuniform temperature field because of bubble nucleation. A change in the number of bubbles N in bidistillate droplet vs. evaporation time is shown in Fig. 7 for different wall temperatures. With time the droplet surface decreases (Fig. 6) and, respectively, the number of bubbles decreases for the whole range of nucleate boiling temperatures (Tw = 105 120 °C). The number of vapor bubbles N increases with a rise of temperature up to the maximal value (Tw about 115 °C) and then it decreases. A rise of N relates to the fact that with an increase in superheat DTw the microcavities of a smaller radius become active (1). As a result, the total number of cavities participating in vaporization increases
rcr ¼
2rRT 2s ; kpDT w
ð1Þ
where rcr is the minimal radius of micropore, which becomes active at given superheat DTw; R is universal gas constant; p is vapor pressure; k is specific heat of evaporation; r is surface tension; and Ts is temperature of vapor saturation. With a rise of superheat and approximation of parameter S/dm to 2, the boiling character changes: bubbles start joining (Tw is higher than 115 °C). Bubble merging leads to a following decrease in N. Similar bubble joining at high superheat DTw is also observed for a large water volume [20]. P A change in the average diameter of bubbles da vs. Tw (da = dai/ Ni) is shown in Fig. 8. With a rise of Tw superheat of a microlayer of the wall under vapor bubble increases, and this leads to a higher rate of microlayer evaporation and higher rate of bubble growth.
Fig. 5. The video images of the regular bubble structures in the droplet (Tw = 110 °C).
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Thermal dynamics of bubble is determined by the ratio of such parameters as thermal diffusivity, Fourier number, and Jacob number [25]. We have studied the behavior of vapor content near the droplet bottom, which has the different character of a change depending on time and wall superheat. A change in dimensionless total area
P P of bubbles Sgi/Sdi vs. evaporation time is shown in Fig. 9 ( Sgi the total area of the base surface of all bubbles at the measured moment of time t, Sdi is the area of base surface of a droplet at the measured moment of time). At Tw = 105 °C (curve 1) dimenP sionless area Sgi/Sdi decreases with a rise of time t, and this is explained by the cooling effect of the wall. With a rise of superheat, insignificant cooling of a metal surface does not effect the qualitative character of curve 2 (Fig. 9). With an increase in time of evaporation (curve 2) the total amount of generated vapor increases. The pictures of the droplet temperature (Ts) are shown in Fig. 10 for Tw = 105 °C; they are made by means of a thermal imager: (a) corresponds to evaporation time t = 5 s; (b) t = 10 s; (c) t = 15 s. The measured contact angle of a water droplet on the polished surface was 58°. The scale of 10 mm in Fig. 10 is the same as in Fig. 11. Before the experiment we have obtained dependences for the used materials of working sections on global emissivity of the water layer in the short wave range as a function of the optical thickness. Considering the droplet height (h) (Figs. 10 and 11(a)–(c)) the surface droplet temperature will be decreased by 8 10 °C, i.e., the actual droplet temperature will be 8 10 °C higher. It is reasonable to consider the surface temperatures only for the region of liquid without vapor bubbles because of a thin vapor film and we disregarded the temperature near the contact line (closer than 0.5 mm from edge of droplet). However, not the quantitative, but the qualitative character of temperature change in time is of a particular interest: boiling (bubble) degeneration at low superheat and bubble merging (the growth of vapor phase percentage) at high superheating. The thermal image shows that the process of vaporization causes nonisothermal and spatially nonuniform thermal conditions. According to Fig. 10, the number of bubbles decreases with time. The total area of vapor bubbles decreases also, and this corresponds to Fig. 9 (curve 1). A decrease in vapor area is caused by the cooling effect of the wall. Curve 2 in Fig. 9 has the different character: with time the total dimensionless area of vapor increases from 0.15 to 0.38, and this corresponds to the thermal images in Fig. 11 at Tw = 120 °C. Wall cooling by several degrees does not change boiling conditions: superheat is sufficient and high vapor output is kept. Therefore, to determine a change in vapor output in time, it is necessary to taken into account not only the effect of superheat, but the cooling effect on the walls. Volumetric content of vapor relative to the volume of a whole droplet is an important feature of boiling. According to experimental data of the current study, at Tw = 120 125 °C the vapor content is close to 40%. This temperature regime is the pre-critical one (at Tw = 129 °C the droplet separation occurs: the droplet separates from the wall and the vapor film is formed). Therefore, the boiling crisis of a droplet occurs at significantly lower vapor concentration
Fig. 8. A change in the average diameter (da) of bubble in bidistillate droplet vs. wall temperature (Tw) (the initial droplet diameter is 11 103 m): curve 1 for t = 5 s; curve 2 for t = 15 s.
Fig. 9. A change in dimensionless total area of bubbles surface vs. time of evaporation (V0 = 1 107 m3, Sn is the area of bubble base surface, Sd is the area of droplet base surface): curve 1 – Tw = 105 °C; curve 2 – Tw = 120 °C.
Fig. 7. A change in the number of bubbles N in bidistillate droplet vs. evaporation time at different Tw (V0 = 1 107 m3): curve 1 – Tw = 105 °C; curve 2 – Tw = 111 °C; curve 3 – Tw = 114 °C; curve 4 – Tw = 120 °C.
Labuntsov’s expression takes into account dependence of the shape of surface bubble on contact angle h. Evaporation occurs mainly through the microlayer surface [1] near the base of the growing bubble (2), where DT is superheating; k is specific heat of evaporation; k is thermal conductivity of the liquid; t is time; qv is vapor density, b1 is the function of the contact angle, shape and the ratio of the two characteristic scales. With a rise of superheat the rate of bubble diameter growth becomes higher. However, for the droplet there are significant differences: liquid subcooling and small height of the droplet, which lead to deformation of the bubble shape. The lift-off diameter of bubble can be much larger than the droplet height, and the bubble growth can be changed fast to the period of drastic decay because of subcooling. Moreover, expression (2) describes the growth of a single bubble and it does not take into account the effect of growing bubble on each other. The nonlinear interaction between the vapor phase and solid wall is not considered as well as the nonisothermal character of the ambient conditions and a change in droplet geometry with time.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b1 kDTt : d¼ kqv
ð2Þ
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bubble
liquid (a)
(b)
(c)
Fig. 10. The thermal imager pictures of nucleate boiling in the droplet (Tw = 105 °C, h is the average height droplet): (a) t = 5 s; h = 2.3 mm; (b) t = 10 s; h = 1.8 mm; (c) t = 15 s; h = 1.4 mm.
Fig. 11. The thermal imager pictures of nucleate boiling in the droplet (Tw = 120 °C, h is the average height droplet): (a) t = 5 s; h = 1.4 mm; (b) t = 10 s; h = 0.9 mm; (c) t = 15 s; h = 0.7 mm.
than that for the pool liquid. As it is known, pool boiling of water under the pre-critical conditions corresponds to very high vapor output, i.e., the ratio of vapor phase volume to liquid near the wall is up to 70 80%. It is also known that at liquid boiling above a micron wire the boiling crisis occurs abruptly because of a drastic growth of the separation zone. There is no the transitional zone of crisis. For the unlimited sizes of the heater (pool boiling) the separation zone of several millimeters can be formed locally, and it does not spread over the whole surface of the heater. From the point of vapor output and hydrodynamic and thermal instability the boiling crisis of droplet occupies an intermediate position between the micro- and mini-objects (filament) and macro-objects (the heaters of the large area).
4. Heat transfer on the polished and rough surfaces of a copper cylinder The experiments with heat transfer on the gold-plated surface and rough surface were carried out in the working section presented above. Geometry of the copper cylinder with rough surface is the same as for the polished one. The content of oxygen in copper was low to reduce surface oxidation in time. The method of determination of the heat flux and heat transfer coefficient is based on the measurement of current values of the droplet mass, wall temperature under the droplet, temperature of the upper droplet surface (liquid–gas) and droplet area [26]. Heat spent for droplet evaporation included droplet heating up to the maximal temperature with consideration of heat capacity. The droplet mass was
measured by means of scales. The upper surface temperature was measured by the thermal imager with consideration of data on global emissivity and current values of the droplet height. The wall temperature under the droplet was measured by a thermocouple. The droplet area was measured with application of video recording. The maximal measurement error a was within ±22%. On the basis of experimental data the values of heat transfer coefficient (local-temporal (ai) and averaged value during the whole period of evaporation (a)) can be determined respectively as
ai ¼
kDmi ; Ssi Dti ðT wi T si Þ
a¼
1 t1
Z
ai dt
1 X ai Dti ; t1
ð3Þ
ð4Þ
where k is specific heat of evaporation, mi is current value of droplet mass; Ssi is current area of droplet interfacial surface (liquid–gas), ti is current time, Twi is current wall temperature under droplet, Tsi is current temperature of the droplet interfacial surface (liquid–gas), t1 is total time of droplet evaporation. Subscript i relates to local values of parameters. According to Fig. 12, the polished section with gold deposition demonstrates a multiple reduction of heat transfer in comparison with the rough section. This result is really surprising and it can be explained by a significant decrease in the number of active nucleation sites. The experiments on the copper and stainless steel sections [5] showed an opposite result. Perhaps, surface polishing in [5] led to significant intensification of heat transfer because of an increase in the number of active nucleation sites and considerable
S.Ya. Misyura / International Journal of Heat and Mass Transfer 71 (2014) 197–205
Fig. 12. A relative change in the heat transfer coefficient vs. wall superheating DTw (a2 for the copper section with the polished surface and gold coating, a1 for the copper rough wall).
changes in surface energy of metal. The link between surface energy and wettability with a degree of vapor oversaturation is considered in the framework of the density functional theory [27]. With a rise of surface energy liquid superheating, required for heterogeneous phase transition, decreases. The polished section used in the current study essentially differs from that used in [5]. A gold layer of several microns was deposited on the polished surface via plasma spraying. Probably, the number of active boiling sites decreased significantly because of this coating. Therefore, to estimate the ability of material to intensify heat transfer, it is not sufficient to have information about roughness. It is also important to know the features of molecular interaction of molecules of a solid body and liquid. While studying heat transfer at pool boiling, contribution of two parameters is taken into account: heat transfer intensification via heat conductivity and convection in liquid as well as via evaporation from bubble surface and evaporation of a liquid microlayer near the bubble base. These two factors are interconnected and effect each other significantly, and this is one of complexities of theoretical analysis. Neglecting the motion of bubbles we do not obtain highly intensive convective turbulent mixing in liquid. If we consider only evaporation of a bubble microlayer, we will skip considerable heat transfer via the turbulized liquid. Heat transfer will depend on nucleation site density, bubble size, vapor phase volume and frequency of bubble detachment. The expression for boiling in a droplet will differ basically from pool boiling. There is no thick convective core in the droplet, and circulation occurs only near the wall (see Fig. 3(a)). Moreover, instead of bubble
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detachment frequency we observe there frequency of bubble breaking, violation of droplet shape and interface relaxation back to the previous shape (Fig. 3(b)). It also follows from the experimental data that the boundary conditions change in time: droplet shape and size, size and number of bubbles. According to the density functional theory [27], heterogeneous phase transition for liquids with high wettability (metal wall) requires superheat of about 9 11 °C. Actually, minimal superheat of the wall, when nucleate boiling starts is 5 5.5 °C both for rough copper and polished copper. It turns out that stability of phase equilibrium is not considerably connected with the nucleation site distribution. We can make the estimates of cavities sizes using data obtained by the optical profilometer ‘‘Zygo’’ (uncertainty of measurement is ±15 nm). The rms roughness of copper was about 1.3 1.4 lm. There are three types of polished surface roughness (Fig. 13(a)): fine roughness with high concentration of cavities and rms roughness of the order of 50 70 nm; ledge above the surface with the average height of 100 150 nm; cavities with very low concentration and average height of about 150 200 nm. The work of nucleation on projections is higher than on a flat surface, and in a cavity it is lower than on a plane [28]. Therefore, it is reasonable to consider only large cavities. Expression (1) does not include contact angle h (Fig. 13(c)). Metals are characterized by good wettability by water (the contact angle between a solid wall and liquid h < 90°). Considering h and condition ql qv, expression (1) can be presented as (5), where ql is density of liquid; qv is density of vapor.
DT w ¼
2rT s sin h rcr qv k
ð5Þ
Within the polished section the large cavities (pores) have average radius rcr of about 5 lm. The measured contact angle of a water droplet on the polished surface was 58°. With consideration of rcr and h, expression (5) gives superheating of 4.8 °C, and taking into account an experimental errors, this is close to superheat of 5.1 5.5, achieved in experiments and corresponded to boiling beginning. Therefore, we can assume that wettability of a large droplet is close to wettability of a microbubble, and the critical nucleuses relate to the large and deep cavities. Often, to estimate the radius of a critical nucleus an rms value of surface roughness is used. If we use rms roughness of the order of 70 nm as rcr in expression (2), superheat will be about 400 °C. Therefore, it is incorrect to use statistic averaging by all pores. Moreover, low heat transfer on the polished surface also demonstrates that the estimate of heat transfer at boiling requires consideration of the average radius of exactly typical cavities (pores) and density of their distribution. To let a vapor bubble to be on a flat surface, it should move over the walls of a microcavity from the bottom to the top
Fig. 13. Nucleate boiling on the polished surface.
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Table 1 Data on nucleation site density. No
Wall superheat DT, °C
Nucleation site density, qn, m2
1 2 3
6 12 22
1.7 105 2.9 105 3.5 105
(Fig. 13(b)). (V) indicates vapor; (L) is liquid; (1) is interface for good wettability; (2) is interface for poor wettability and (3) is interface for the contact angle, whose value is close to 90°. Average angle of the considered typical cavities b was 3 5°. At this b the upward motion of a vapor bubble is possible only, when h is close to 90°. For low (interface 2) and high wettability (interface 1) a micro or nanobubble will have very small radius and superheat of hundreds degrees will be required. Therefore, to achieve boiling on the polished golden-plated surface, two conditions should be implemented: neutral wettability inside the cavity (contact angle is close to 90°) and good wettability on a flat surface, which is close to that measured for a large droplet. Fig. 13 illustrates some different versions of surface wetting. For the large microcavities (Fig. 13(b)) both good and poorly wetting liquids penetrate inside the cavities. Fig. 13(d) presents poorly wetting liquids and small nanocavities. Liquid does not penetrate inside the cavities and the wetting angle on the heater surface is larger than 90°. The high wetting angle (according to (5)) decreases minimal superheat by tens times for boiling incipience. The case (c) corresponds to liquids with high wettability, e.g., water. According to Fig. 13(c) and expression (5), superheat decreases with a rise of wettability. However, Fig. 13(c) characterizes only the growth of bubble, whose size is higher than critical and which has already come to the heater surface from the cavity. Bubble inception and growth to the critical size occur not on the heater surface, but inside the cavity. High wettability in the cavity (Fig. 13(b)) increases superheat significantly. Therefore, to determine the density of active centers and the inception rate of the bubbles of a supercritical size, it is important to determine the surface free energy directly in the cavities and not only on the heater working surface. Data on nucleation site density (NSD) are shown in Table 1 depending on wall superheat DTw, where qn is nucleation site density for the polished surface. Maximal NSD (qmax) for the polished surface (according to the processed data of the electron microscope) is about 108. Density qmax was estimated only for cavities with radius rcr of about 5 lm, and it corresponds to superheat DTw of 5 6 °C by expression (3). Thus, only one microcavity of thousand cavities is active, despite geometry of other cavities also allows generation of micro bubbles. It is reasonable to relate this discrepancy with the features of local wettability inside the microcavities (Fig. 13(b)). It is known that the number of active nucleation sites is proportional to (DT)3. In this case NSD of about 107 will correspond to superheat of 22 °C, and this meets the data on maximal NSD [29]. However, in this case heat transfer on a polished surface will be close to that on the rough surface. Significant difference between heat transfers on two different surfaces (Fig. 12) shows that a will be the functions of nucleation site density and local wettability, which will depend on the type of mechanical processing of the surface and type of wall coating, considerably changing the surface energy of nano- and microcavities.
5. Conclusion Dynamics of nucleate boiling in the droplets of bidistillate was studied in the current work. These experiments were carried out on the copper rough surface as well as on the polished surface with plasma spraying of a golden film. The thermal field of droplet
surface was measured by the thermal imager (NEC-San Instruments). The 3D model of the wall surfaces obtained by means of an electron microscope. The following has been determined during the experiments and data analysis: 1. The ratio of an average distance between the bubbles to their diameter is less than 3, and this indicates the nonlinear interaction of bubbles and system inclination towards the chaotic behavior. Despite this fact, this complex open dissipative and nonlinear system has the obvious tendency to self-organization of the ordered structures. 2. At low superheat the contact line is fixed. At high superheat and high rate of bubble growth, the contact line of droplet moves continuously and the conjugated boundary conditions change (droplet surface, wall temperature). 3. While approaching the detachment point (boiling crisis at Leidenfrost temperature), total vapor concentration in the droplet is essentially lower than that for pool boiling of water. 4. Heat transfer on the polished golden-plated surface is significantly lower than that for the rough copper wall. When calculating the radius of a critical nucleus (for the surface studied in this work), it is necessary to consider not the root-meansquare value for all pores, but the cavities with characteristic geometry and neutral wettability (the contact angle is close to 90°).
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