Dynamic Leidenfrost temperature increase of

International Journal of Heat and Mass Transfer 118 (2018) 1160–1168

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Dynamic Leidenfrost temperature increase of impacting droplets containing high-alcohol surfactant Hua Chen, Wen-long Cheng ⇑, Yu-hang Peng, Li-jia Jiang Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230027, PR China

a r t i c l e

i n f o

Article history: Received 5 August 2017 Received in revised form 25 October 2017 Accepted 18 November 2017 Available online 22 November 2017 Keywords: Droplet impact High-alcohol surfactant Surface tension Dynamic Leidenfrost temperature Spreading dynamics

a b s t r a c t Methods to avoid the dynamic Leidenfrost effect are of great importance for high heat flux spray cooling which needs an efficient contact of liquid and superheated surface. In this paper, a novel method of increasing dynamic Leidenfrost temperature is proposed through addition of high-alcohol surfactant (HAS). Effects of 1-Octanol and 2-ethyl-hexanol surfactants on dynamic Leidenfrost temperature and spreading dynamic of droplets impacting on superheated surface were investigated for the first time using high-speed photography. Empirical correlations of dynamic Leidenfrost temperature and maximum spreading factor were obtained based on our experimental data. A possible explanation for the dynamic Leidenfrost temperature increase caused by HAS was proposed based on bubble bursting and bubble coalescence. The results show that dynamic Leidenfrost temperature is significantly increased by addition of HAS because of surface tension reduction. The empirical correlations of dynamic Leidenfrost temperature and maximum spreading factor show good agreement with maximum error of 5% and 10% respectively. These empirical correlations could provide reference value for the future research. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Spray cooling and flash evaporation cooling [1,2] have attracted widespread attentions since they are effective heat removal technologies with high heat flux capacity. The cooling process is extremely complex involving numerous phenomena such as droplet impact, film convection and bubble boiling, however the underlying mechanism of these phenomena are poorly understood. Droplet impacting on hot solid surface plays a very important role during spray cooling process [3,4], and has attracted continuous research due to its relevance to a large number of applications, such as metal processing, fuel injection and fire suppression. Though there has been extensive research on droplet impact, many aspects of this phenomenon are still far from been fully understood due to the complexity of the phenomena involved [5]. To ensure the effective heat transfer of spray cooling and flash evaporation cooling, it requires the effective contact of the liquid and the hot surface. However, when the surface temperature is too high, a vapor layer forms immediately under the droplet and prevents the droplet making further contact with surface. This phenomenon is the so-called dynamic Leidenfrost effect [6,7], and the

⇑ Corresponding author. E-mail address: [email protected] (W.-l. Cheng). https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.100 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

minimum surface temperature at which the impacting droplet bouncing without splashing is identified as dynamic Leidenfrost temperature (TDL) [8]. Due to the poor thermal conductivity of vapor layer, the heat transfer is significantly reduced. Thus, efforts to avoid the Leidenfrost effect are of great importance for improving spray cooling heat transfer. Many researchers have studied methods of increasing dynamic Leidenfrost temperature, such as modified surface structure [9-13], electrostatic suppression [14], and low frequency vibration [15]. Among these methods, modified surface structure has received much attention. However, this method was not suitable for many applications in which the surface features are fixed such as metal processing. As a more convenient method, modifying the liquid property by additive is rare to be seen. Only Bertola et al. [16– 18] experimentally investigated the TDL of water droplets containing polymer additives and found that 200 ppm polyethylene oxide could reduce TDL of water droplets by 60 °C. As a reference, the effect of additives on static Leidenfrost temperature (TSL) have been studied by many researchers. Huang et al. [19] increased TSL by addition of dissolved salt and explained the increase effect by bubble coalescence suppression and salt deposition. Nagai et al. [20] increased TSL by adding emulsions into water and explained the increase effect caused by surface tension decrease. But there have been disparate conclusions regarding the effect of surfactant.

H. Chen et al. / International Journal of Heat and Mass Transfer 118 (2018) 1160–1168

1161

Nomenclature D0 D Dm d g H h N Oh TDL TSL Tsur

droplet initial diameter, m spreading diameter, m maximum spreading diameter, m needle diameter, m acceleration gravity, m/s2 impact height, m disk thickness, m nucleation site number Ohnesorge number dynamic Leidenfrost temperature, °C static Leidenfrost temperature, °C surface temperature, °C

Contrary to Nagai’s conclusion, Qiao et al. [21] found that both TSL and surface tension of water droplets were decreased by adding SDS. Thus, whether the surfactant could increase the TDL of water droplets or not needs further study and new surfactant with better performance is need urgently. In our previous researches, high-alcohol surfactant (HAS) such as 1-Octanol and 2-ethyl-hexanol (2EH) was innovatively proposed to improve spray cooling heat transfer [22,23]. It was concluded that trace amount of 1-Octanol and 2EH could significantly enhance spray cooling heat transfer [22–24]. Also, 1-Octanol and 2EH could significantly enhance the heat and mass transfer of LiBr absorption chiller [25,26]. What’s more, compared with dissolved salt additives, HAS could avoid nozzle clogging and devices corrosion. Thus, HAS is a superior choice for heat transfer enhancement due to advantages of little additive amount and higher compatibility with devices. So, what is the effect of HAS on the dynamic behavior and TDL of water droplets? This issue is of great importance for spray cooling and flash evaporation cooling heat transfer enhancement. However, no public literature is found concerning the effect of HAS on dynamic Leidenfrost effect at present. To solve above problems, the present work is aimed at investigating the effect of HAS (1-Octanol and 2EH) on droplet behavior impacting on superheated surface, including the dynamic Leidenfrost effect and the spreading dynamic. The TDL and maximum spreading factor (bm) of Leidenfrost droplet is determined by high-speed photography. To understand how the surfactant affect the dynamic Leidenfrost effect, the surface tension and viscosity of water containing surfactant are measured. Considering the effect of surface tension and viscosity, Weber number (We) alone is not complete to describe the effect of surfactant, thus Ohnesorge number (Oh) is used to assistant the analysis. Then, the dependence of TDL and bm on We and Oh is studied, and the corresponding empirical correlations are obtained. Finally, a possible explanation for the increase effect of HAS on the TDL is proposed based on bubble bursting and bubble coalescence. 2. Experimental system 2.1. System description The experimental setup is illustrated in Fig. 1. Droplets are released from a syringe needle with inside diameter of 0.5 mm and then impact on the hot surface. The hot surface is the upper surface of a copper block (40 mm in length, 40 mm in width and 20 mm in thickness). The needle is positioned above the upper surface of copper block. The impact velocity of the droplet is controlled by varying the needle’s height. The heating equipment is provided by Shenzhen Fan and air electronical technology Co. Ltd. Two electric heating rods (total power of 2000 W) are fixed

Tsat V We

saturation temperature, °C droplet impact velocity, m/s Webber number

Greek letters ql liquid density, kg/m3 qv vapor density, kg/m3 r surface tension, N/m b spreading factor bm maximum spreading factor h contact angle

Fig. 1. Schematic diagram of experimental system.

inside the copper block at a distance of 10 mm from the bottom surface and 3 mm from the central axis. A dished groove is scooped in the center of the hot surface to restrict the droplets. The groove is 2 mm in depth and 20 mm in diameter. The temperature of the heated block is regulated by a temperature control system with PID controller and measured by a Type-K thermocouple placed 1 mm below the surface. As the thermocouple is very close to the surface, so the surface temperature is approximately equal to the temperature of thermocouple. The temperature control system keeps the temperature of the copper block at comparatively stable temperatures. The variation of the temperature is controlled within ±1 °C. The impact dynamic and boiling behavior of the droplet are recorded by a high-speed camera (Phantom VEO410) with frame rate of 4000 fps and resolution of 1280 800. A LED lamp of maximum 100 W (Superflash LED100A) is placed opposite to the camera to illuminate the droplets. During experiments, the LED lamp is bright enough at brightness of 20%. Thus, the heating effect of the lamp is negligible. 2.2. Procedure Before experiments, test solutions of water added by 1-Octanol and 2-ethyl-hexanol (2EH) surfactants are prepared with different concentrations from 100 ppm to 1000 ppm. The surface tension and viscosity of surfactant solutions at room temperature are measured by a surface tension meter (Shanghai Fangrui Instrument Co. Ltd) and a viscometer (Brookfield Inc), respectively. It should be noted that the quantity relevant to drop impact is the dynamic surface tension, since the droplet is in non-equilibrium state during the experiments. However, as the maximum falling time and impact time of droplet is less than 110 ms (impact height is 2–6 cm) and Cheng et al. [27] found that the change of dynamic surface tension during the first 110 ms is very small, the static surface tension values are used instead of dynamic surface tension to simplify the analysis. As shown in Fig. 2, the surfactants could dramatically

1162


decrease the surface tension and slightly increase the viscosity of water, which means the surface tension is more sensitive with the surfactant concentration. Moreover, the surface tension of surfactant solutions decreases significantly at first and then became stable with increasing surfactant concentration, and the effect of 1-Octanol surfactant is larger than 2EH. As the surface conditions (including surface roughness and oxide layer) will affect the dynamic behavior of impacting droplet [13,28], to maintain the same surface condition for all experiments, the surface is sanded by sandpaper and washed by distilled water and acetone several times before each impact experiment. After that, the surface is heated to a certain temperature. Droplets released from the syringe needle at different heights fall down and impact on the surface. The dynamic behavior of impacting droplet is captured by the high-speed camera and recorded in a computer. The droplet initial diameter (D0) and spreading diameter (D) can be obtained by the recorded images. Through images analysis, droplet diameter is 2.3 mm for water, 1.8–2.2 for 1-Octanol surfactant solution and 2.1–2.2 for 2EH surfactant solution. The impact velocity (V) is calculated by the free fall velocity pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V ¼ 2gðH D0 Þ. We can compare the droplet’s kinetic energy to its surface energy by evaluating the Weber number We ¼ ql V 2 D0 =r. Also, we can compare the viscous force to inertial and surface tension forces by evaluating the Ohnesorge number pffiffiffiffiffiffiffiffiffiffiffi Oh ¼ l= ql rD0 . In this study, the impact velocity is range from 0.5 m/s to 1.1 m/s and the Weber number is in the range of 8–36 for water, 22–50 for 1-Octanol surfactant solution and 14–41 for 2EH surfactant solution. The experiments are conducted at surface temperature ranging from 200 °C to 450 °C. This temperature range is well above the saturation temperature of water, where the nucleate boiling and film boiling occurs. Also, the transition from nucleate boiling to film boiling which is identified as TDL is in this temperature range. Through observation of images taken from high-speed camera, TDL is identified as the minimum temperature of the surface at which the impacting droplet bouncing without splashing. This definition is also adopted by many other researchers [5,17,18]. What’s more, the dynamic spreading characteristics of Leidenfrost droplets on the surface are also analyzed through the recorded images.

high-speed camera. Figs. 3–7 show a series of images captured during the impact of different droplets. The sequence occurrence during droplet impact can be described as: initial contact, spreading (with or without splashing), retraction, bouncing or disintegration. Different behavior is observed according to different impact Weber numbers and different surface temperatures. 3.1.1. Effect of surface temperature Firstly, droplet behavior at different surface temperature is shown in Fig. 3. With the increase of the surface temperature, the boiling behavior can be divided into three regimes: nucleate boiling (Fig. 3a), transition boiling (Fig. 3b) and film boiling (Fig. 3c). Nucleate boiling occurs when the surface temperature is higher than saturation temperature and lower than the Leidenfrost point. In this regime, nucleate bubble generation is so violent that the vapor bubbles burst abruptly on the free surface of the droplet, resulting in explosive ejection of tiny droplets. Transition boiling occurs when surface temperature is just below the Leidenfrost point, where the droplet is in partially contact with the surface. Film boiling occurs when the surface temperature is very high above the Leidenfrost point. At this high temperature, the number of activated nucleation site and the bubble generation rate increase rapidly. Thus, the bubble coalescence and the vapor layer formation becomes easily. So, in this regime, a vapor layer forms immediately after initial contact and prevents the droplet making further contact with surface. Due to poor conductivity of vapor layer, no boiling behavior is observed. Thus, the droplet is supported by its own vapor and bounce off the surface without ejecting tiny droplets. 3.1.2. Effect of impact momentum Next, droplet behavior at different impact height (impact momentum) is shown in Fig. 4. In the case of low impact momentum (Fig. 4a), the droplet bounces off the surface without splashing, which means it is in the Leidenfrost state. After initial contact, the droplet deforms and spreads out on the surface because of its kinetic energy. In the early stage impact, liquid at the bottom of the droplet spreads out horizontally at first, whereas

3. Results and discussion 3.1. Observation of droplet dynamic behavior Dynamic behavior (spreading dynamic and boiling behavior) of different droplets at different impact conditions are observed by 1.2

1.2

/

surfactant

Surface tension:

0.8

Surface tension: Viscosity: 1.1

1.0

/

surfactant

1.0

Viscosity:

water

1-Octanol 2-Ethyl-Hexanol

water

0.6 0.9 0.4 0

200

400

600

800

1000

1200

Surfactant concentration (ppm) Fig. 2. Surface tension and viscosity results of 1-Octanol and 2EH surfactant solutions.

Fig. 3. Boiling behaviors of water droplet impact on superheated surface with different temperatures in (a) nucleate boiling regime, (b) transition boiling regime, and (c) film boiling regime.


1163

Fig. 4. Dynamic behavior of water droplets with different impact height.

Fig. 5. Dynamic behavior of 1-Octanol surfactant droplets in: (a) nucleate boiling regime, (b) transition boiling regime, and (c) film boiling regime.

the upper part remains spherical. At time of 3.5 ms, the droplet spreads to a maximum spreading and forms a disk (or liquid film) on the surface. At this time, the kinetic energy of initial droplet has been totally transformed into surface energy. After that, the disk retracts and the surface energy is transformed back to the kinetic energy. Finally, the droplet bounces off the surface after the retraction of the disk is completed. In the case of high impact momentum (Fig. 4b), splashing occurs during the contact of the droplet and the surface, which means the droplet is in violent boiling state. In this case, a large amount of tiny droplets jet out from the bottom of the disk as shown in the images taken at time larger than 2 ms. These jetting droplets may be caused by the boiling bubbles bursting out

Fig. 6. Dynamic behavior of 2EH surfactant droplets in: (a) nucleate boiling regime, (b) transition boiling regime, and (c) film boiling regime.

from the liquid-vapor interface. After that, the droplet will break down into smaller droplets. It is found that TDL increases with the increase of impact momentum. This can be explained by the comparison of vapor pressure and kinetic pressure. A higher kinetic pressure requires higher vapor pressure of vapor layer (corresponding to higher surface temperature) to support the droplet. Moreover, with higher impact momentum, the kinetic energy of spreading droplet is higher, so the liquid disk formed on the surface is thinner. Thus, nucleate bubbles are easier to burst out from the disk and break the Leidenfrost state.

1164


Fig. 7. Maximum spreading of water droplets and surfactant droplets in Leidenfrost state with different impact We.

3.1.3. Effect of surfactants In particular, comparison study between surfactant droplets and water droplet is conducted. Figs. 5 and 6 show the dynamic behavior of impacting droplets containing 1-Octanol and 2EH surfactants at different surface temperatures, respectively. The dynamic behaviors of surfactant droplets and the effect of surface temperature and Weber number are similar to that of water droplets (Fig. 3). Compared with water droplets, droplet initial diameter is decreased by addition of surfactant due to the surface tension reduction. Through images analysis, droplet initial diameter is 2.3 mm for water, 1.8–2.2 mm for 1-Octanol surfactant solution and 2.1–2.2 mm for 2EH surfactant solution. Moreover, for water droplets, the droplet is transparent after initial contact with the surface. However, for surfactant droplets, the droplet becomes opaque after initial contact. This indicates that massive tiny bubbles are generated homogeneously inside surfactant Leidenfrost droplets. However, the mechanism of this novel phenomenon is still obscure and should be investigated in the future research. Fig. 7(a–g) are images showing the maximum spreading of Leidenfrost droplets at different impact height. For a certain solution, TDL increases with the increase of impact height (or impact We). This has been explained in Section 3.1.2. The maximum spreading diameter increases and the time to reach maximum spreading decreases with the increase of We. This is the result of a balance between the surface energy and the kinetic energy. Let us discuss the difference of Leidenfrost dynamic between droplets containing different surfactants and water droplet. Firstly, at the same impact height, the spreading dynamic of different solutions is different. The maximum spreading diameter and time to reach the maximum spreading are reduced by the addition of surfactants. This indicates surfactant has a great influence on spreading dynamic of Leidenfrost droplets and the influence effect will be discussed in detail in the following section. Secondly, at the same impact height, TDL of surfactant droplets are higher than water droplets and TDL of 1-Octanol surfactant droplet is the highest. Finally, for surfactant droplets, a higher We leads to a higher TDL, and a higher surface temperature will result in a more opaque droplet. This means surfactant could increases the bubble numbers inside the droplet, and bubble numbers increase with the increase of surface temperature.

3.2. Spreading dynamic of Leidenfrost droplet Through observation, it is clear that surfactants have great effect on the spreading dynamic of Leidenfrost droplets. As both the maximum spreading diameter (Dm) and the droplet initial diameter (D0) are decreased by the addition of surfactant, a dimen-

sionless parameter to characterize the spreading scale is introduced as spreading factor (b = D/D0). Fig. 8 shows the experimental data measured for different impacting droplets in Leidenfrost state (with different solution at different impact conditions) based on images taken by high-speed camera. It is evident that the droplet spreads firstly on the surface, reaches the maximum spreading and retracts as time goes by. With the increase of impact height, the We increases, and the spreading factor increases as a consequence. This is because the greater the kinetic energy of impacting droplet, the easier it is to overcome the surface energy and to spread on the surface. Fig. 8(a) shows the variation of spreading factor over time for water droplets and Fig. 8(b) shows the variation trend of droplets containing different surfactants at the concentration of 1000 ppm. Compared with water droplet, the maximum spreading factor is increased and the time to reach the maximum spreading is reduced by the addition of surfactants. What’s more, the maximum spreading factor of 1-Octanol surfactant droplet is slightly higher than 2EH surfactant droplet, while the time to reach the maximum spreading of 1-Octanol surfactant droplet is much shorter than 2EH surfactant droplet. This different effect of two surfactants is mainly caused by the difference of surface tension. As the surface tension of 1-Octanol solution is much lower 2EH solution, the initial diameter of 1-Octanol surfactant droplet is much smaller than 2EH surfactant droplet. As shown in Figs. 5–7, both the initial diameter (D0) and maximum spreading diameter (Dm) of 1-Octanol surfactant droplet are smaller than 2EH surfactant droplet. Thus, at the same impact height (i.e. the same kinetic energy), the time to reach the maximum spreading of 1Octanol surfactant droplet is shorter than 2EH surfactant droplet. The effect of surfactant concentration on the maximum spreading factor (bm) is also studied as shown in Fig. 9. bm increases with the increase of surfactant concentration for all surfactants at any impact height due to the surface tension decrease caused by surfactants. With the decrease of surface energy, the droplet spreads more easily on the superheated surface. Combined with the effect of impact height (Fig. 8), it is concluded that bm increases with the increase of We, since We increases with the increase of impact height and the decrease of surface tension. This conclusion is also obtain by many other researchers [5,8,12]. Spreading scale is commonly studied by many researchers [5,8,10,12]. However, no public literature is found on studying the spreading scale of droplets containing HAS. The Weber number is widely used to characterize the effect of droplet velocity. Fig. 10 shows the variation of maximum spreading factor over Weber number for Leidenfrost droplets of all solutions. It is evident that bm increases with the increase of We for all solution droplets. At the same We, bm of surfactant droplets is lower than water droplets and decreases with the increase of surfactant concentration. However, Fig. 9 obviously shows that bm of surfactant droplets is higher than water droplets at the same impact height. Moreover, all the experimental data in Fig. 10 cannot be generalized into one curve. These facts indicate that We alone is not complete to describe the effect of surfactant. This is because both the surface tension and viscosity are changed by surfactants. Thus, to better express the effect of surfactants, we use the Oh to assist the impact analysis and obtain the empirical correlation. According to the theoretical derivation of Tran et al. [12], the dependence of maximum spreading diameter (Dm) on impact velocity (V), surface tension (r) and droplet initial diameter (D0) is as follows:

Dm V 0:6 D01:2 r0:4

ð1Þ

The dependence of D0 on surface tension is obtained by balancing surface energy and droplet gravity of droplet from the needle:

1 6

rpd pD30 ql g

ð2Þ

1165


3.0

Impact height: 2cm 3cm 4cm 5cm 6cm

2.5

2.0

1.5

(a)

1.0 0

1

Surfactant: Impact height: 2cm 4cm

Water droplet

2

3

4

5

Spreading factor, =D/D0

Spreading factor, =D/D0

3.0

2.5

1-Octanol

2-Ethyl-Hexanol

2.0

1.5

(b)

1.0 0

6

1

2

3

4

5

6

Time (ms)

Time (ms)

Fig. 8. Spreading factor variation over time. (a) water droplets, (b) 1-Octanol and 2EH surfactant droplets.

0:2

bm We0:3 Oh Surfactant: Impact height: 2cm 3cm 4cm

2.4

1-Octanol

2EH

0:2

bm ¼ 0:14We0:3 Oh 2.2

2.0

ð4Þ

1.8

3.3. Dynamic Leidenfrost temperature 200

400

600

800

1000

Surfactant concentration (ppm) Fig. 9. Maximum spreading factor variation over surfactant concentration of 1Octanol and 2EH surfactant droplets in Leidenfrost state.

2.5 2.4 2.3

The variation of dynamic Leidenfrost temperature over surfactant concentration is shown in Fig. 12. Both 1-Octanol and 2EH surfactants could significantly increase TDL, and the maximum TDL increase caused by surfactant is as high as 65 °C. For a certain surfactant, TDL increases with the increase of surfactant concentration or the decrease of surface tension at the same impact height. This increase effect caused by surfactants can be explained by the decrease of surface tension in two ways. On one hand, from bubble bursting point of view, a lower surface tension results in a larger spreading factor (as concluded in Section 3.2) which corresponds

2.2 2.5 2.1 2.4

water 1-Octanol 2-Ethyl-Hexanol 200ppm 200ppm 400ppm 400ppm 600ppm 600ppm 800ppm 800ppm 1000ppm 1000ppm

2.0 1.9 1.8

m

m

þ 0:85

Eq. (4) is obtained based on our experimental data and could reflect the effect of both impact kinetic energy and the surfactants. As shown in Fig. 11, this correlation provides very good predictions against our experimental results, with all the data falling within ±5% error bands. Although the experiment data is limited, it can provide some reference value for the future research.

0

Maximum spreading factor,

ð3Þ

Finally, through fitting our experimental data according to Tran’s results and Eq. (3), the empirical correlations of bm is obtained:

1.7 0

10

20

30

40

50

60

70

80

Weber number, We Fig. 10. Maximum spreading factor variation over Weber number of Leidenfrost droplets.

Calculated spreading factor,

Maximum spreading factor,

m

=Dm/D0

2.6

2.3 2.2

Experimental results water 1-Octanol 2-Ethyl-Hexanol 200ppm 200ppm 400ppm 400ppm 600ppm 600ppm 800ppm 800ppm 1000ppm 1000ppm

+5

%

%

-5

2.1 2.0 1.9

Correlation 0.3 -0.2 =0.14We Oh +0.85 m

1.8 1.7

where d is the diameter of needle. Thus, it can be derived that: D0 r1=3 . Then we can rewrite Eq. (1) in dimensionless form with relevant dimensionless numbers We and Oh as follows:

1.7

1.8

1.9

2.0

2.1

2.2

Experimental spreading factor,

2.3

2.4

2.5

=Dm/D0 m

Fig. 11. Comparison between calculated and experimental maximum spreading factor.


500 Surfactant: Impact height: 2cm 3cm 4cm

o

Dynamic Leidenfrost temperature ( C)

1166

450

1-Octanol

2EH

400 350 300 250 200 0

200

400

600

800

1000

Surfactant concentration (ppm) Fig. 12. Dynamic Leidenfrost temperature variation over surfactant concentration of 1-Octanol and 2EH surfactant droplets.

N ðT sur T sat Þ5:3

Dd h

350 water 1-Octanol 2-Ethyl-Hexanol 200ppm 200ppm 400ppm 400ppm 600ppm 600ppm 800ppm 800ppm 1000ppm 1000ppm

300

250

200 0

10

20

30

40

50

60

70

80

Weber number, We Fig. 13. Dynamic Leidenfrost temperature variation over Weber number of all solution droplets.

r

1=2 ð6Þ

gðql qv Þ

where h is the contact angle between liquid and surface. In addition, Siedel et al. [29] found that Dd is almost independent of surface superheat while the bubble growth rate and bubble detachment frequency increase significantly with surface superheat. Thus, the reduction in surface tension will reduce bubble departure Dd, which makes it difficult for bubble coalescence and vapor layer formation. Thus, a higher surface temperature is needed to active more nucle-

500

o

400

ð5Þ

The bubble departure diameter (Dd) is obtained by Fritz [35] as follows:


450

o


to a thinner liquid disk. It is easier for vapor bubbles to burst out from the thinner disk and break the Leidenfrost state. Thus, Leidenfrost state is difficult to achieve with lower surface tension. On the other hand, from bubble coalescence point of view, a lower surface tension results in a lower bubble departure diameter [29], which makes it difficult for the bubble coalescence and vapor layer formation. Thus, a higher surface temperature is required to accelerate bubble generation and vapor layer formation. The dependence of TDL on We for all solution droplets is presented in Fig. 13. It is shown that TDL increases with the increase of We for all solution droplets. Compared with Fig. 12 which obviously shows the increase effect of surfactant, Fig.13 is not able to reflect this increase effect. This indicates that We alone is not complete to describe the effect of surfactant. Thus, similar to the analysis of bm, Oh is introduced to express the effect of surfactants on TDL. The variation of dynamic Leidenfrost temperature with Ohnesorge number is given in Fig. 14. Similar to the effect of surfactant concentration (Fig. 12), Fig. 14 clearly shows that TDL increases with the increase of Oh at the same impact height. The comparison between Figs. 14 and 12 indicates that the variation trend of TDL with Oh is similar to that of surfactant concentration, which means Oh could appropriately reflect the effect of surfactants. Through above analysis, a possible explanation for the trigger mechanism of dynamic Leidenfrost phenomenon is proposed

based on the relative impact of bubble bursting and bubble coalescence. When bubble bursting is dominant, violent boiling occurs and Leidenfrost state is suppressed. When bubble coalescence is dominant, vapor layer forms quickly under the droplet and Leidenfrost state is achieved. Firstly, the bubble bursting is discussed. Through observation, it is found that bubble bursting is highly dependent on the spreading dynamic. At high Webber number (Fig. 4(b), time = 2 ms), bursting occurs when droplet spreads into a very thin disk. If the disk thickness (h) is the same order of the size of nucleate bubbles, the bubbles will burst through the disk instead of coalesce. Thus, TDL increases with the decrease of h. Considering bm We0.3Oh0.2, and pD2h pD30, it is obtained that h We0.3Oh0.3. As TDL increases with the decrease of h, it is easy to explain the increase trend of TDL with increasing We and Oh shown in Figs. 13 and 14. Next, the bubble coalescence is discussed. Bubble coalescence has been considered as the trigger mechanism of CHF (Critical heat flux) by many researchers [30,31]. In this model, the dryout of the pre-existing liquid beneath coalesced bubbles just before the departure of coalesced bubbles from the heated surface triggers the CHF. Bernardin [32,33] also presented a model for Leidenfrost temperature based on bubble nucleation, growth, and coalescence. The basis principle of this model is that enough nucleation site is activated and enough bubble is generated to form a vapor layer between the surface and the droplet. If the bubble radius exceeds half of the distance of the adjacent nucleation sites, the bubbles will coalesce. The nucleation site density (N) is determined by surface superheat and surface characteristic Basu [34]. As the same surface condition is maintained for all experiments, N is mainly dependent on surface superheat (the difference between surface temperature Tsur and saturation temperature Tsat) as follows [34]:

450 400

H=2 cm 3 cm 4 cm 5 cm 6 cm

350 300 250 200 0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0.0050

Ohnesorge number, Oh Fig. 14. Dynamic Leidenfrost temperature variation over Ohnesorge number of all solution droplets.

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Through least squares fitting, the empirical correlation of TDL with We and Oh is obtained as follows: 0:2

T DL ¼ ð13We0:5 þ 22ÞOh

þ 48;

R2 ¼ 0:91

ð8Þ

As shown in Fig. 15, the corresponding coefficient of determination R2 values are relatively high and all the experimental data are falling within ±10% error band. This means the prediction accuracy of this empirical correlation is relatively high and could provide some reference value for the future research on this issue. To verify the universality of the empirical correlations (Eqs. (4) and (8)) obtained in this paper, the comparison study with experimental data in Refs. [8,10,16,17] are presented in Figs. 16 and 17. It is found that the calculation results of bm by Eq. (4) are lower than the experimental results in other references, while the calculation results of TDL by Eq. (8) are higher than the experimental results in other references. This deviation is possibly because the solid surfaces used in different studies are different (silicon, aluminum and structured surfaces were used in the references). This indicates that the Leidenfrost phenomenon is not only related to the properties of fluid but also related to the properties of solid surface. Moreover, the experimental system and measurement method were arranged differently in the references. Thus, the influencing mechanism of Leidenfrost phenomenon is very complex and needs further in-depth studies. 4. Conclusions

o

Calculated Leidenfrost temperature ( C)

400

m

3.0

2.5

2.0

1.5

Correlation 0.3 -0.2 =0.14We Oh +0.85 m

1.0 1.0

Experimental results water 1-Octanol 2-Ethyl-Hexanol 200ppm 200ppm 400ppm 400ppm 600ppm 600ppm 800ppm 800ppm 1000ppm 1000ppm

+1

0%

0%

-1

350

300 Correlation 0.5 -0.2 TDL=(13We +22)Oh +48 2

250

R =0.91

250

300

350

400

450 o

Experimental Leidenfrost temperature ( C) Fig. 15. Comparison between calculated and experimental dynamic Leidenfrost temperature.

1.5

2.0

2.5

3.0

Experimental spreading factor,

3.5

=Dm/D0 m

Fig. 16. Empirical correlation of bm: comparison with experimental data in reference [8,10,17].

600

Data in present work water/surfactant droplet impact on copper surface Data in Ref.[8] water droplet impact on silicon surface Data in Ref.[10]: FC-72 droplet impact on aluminium surface Data in Ref.[16]: water droplet impact on aluminium surface

500 400 300 200 100

Correlation 0.5 -0.2 TDL=(13We +22)Oh +48

0 0

In this study, high-alcohol surfactant (HAS) was proposed to increase dynamic Leidenfrost temperature (TDL). The effect of HAS (1-Octanol and 2EH) on droplet behavior impacting on superheated surface was studied experimentally. The TDL is determined as the minimum temperature of the surface at which the impacting droplet bouncing without splashing through observation of images taken from high-speed camera. It is exciting that both 1-Octanol and 2EH surfactants could significantly increase the TDL and 1-

450

Calculated spreading factor,

ð7Þ

Data in present work water/surfactant droplet impact on copper surface Data in Ref.[8] water droplet impact on silicon surface Data in Ref.[10]: FC-72 droplet impact on aluminium surface Data in Ref.[17]: water droplet impact on aluminium surface

o

d

T DL ¼ ðaWeb þ cÞOh þ e

3.5

Calculated Leidenfrost temperature ( C)

ation sites and enhance the bubble generation and finally achieve the Leidenfrost state. In summary, the dynamic Leidenfrost temperature is highly dependent on the Weber number and the Ohnesorge number. Noticing that TDL tends to Static Leidenfrost temperature (TSL) when We ? 0 and that TSL is independent of We, the experimental results of TDL are fitted as the following pattern:

100

200

300

400

500

600

o

Experimental Leidenfrost temperature ( C) Fig. 17. Empirical correlations of TDL: comparison with experimental data in reference [8,10,16].

Octanol surfactant could increase TDL more. The TDL increases with the increase of surfactant concentration because of surface tension reduction. At a fixed concentration, the TDL increases with increasing impact momentum. Also, the spreading dynamic in the Leidenfrost state was studied. The maximum spreading factor (bm) is increased and time to reach the maximum spreading is reduced by the addition of surfactants. bm increases with the increase of surfactant concentration at a fixed impact height. At a fixed surfactant concentration, bm increases with increasing impact momentum. Moreover, Weber number (We) and Ohnesorge number (Oh) were used to analyze the effect of impact height and surfactant. The scaling law of bm We0.3Oh0.2 derived from Tran shows a favorable accordance with all our experimental data falling within ±5% error bands. The empirical correlation of TDL (TDL We0.5 and Oh0.2) generalized by our experimental data provides very good prediction with maximum error of 10%. Finally, a possible explanation of the effect of HAS on TDL is proposed based on bubble bursting and bubble coalescence. On one hand, a lower surface tension results in a larger spreading factor which corresponds to a thinner liquid disk. Thus, vapor bubbles are easier to burst out from the disk and break the Leidenfrost state. On the other hand, a lower surface tension results in a lower

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bubble departure diameter, which makes it difficult for the bubble coalescence and vapor layer formation. Thus, it will increase the dynamic Leidenfrost temperature. Conflicts of interest There are no conflicts of interest to declare. Acknowledgement The authors would like to thank the National Natural Science Foundation of China (Grant No. 51376169) for the financial support. References [1] W.L. Cheng, W.W. Zhang, H. Chen, et al., Spray cooling and flash evaporation cooling: the current development and application, Renew. Sustain. Energy Rev. 55 (2016) 614–628. [2] J. Kim, Spray cooling heat transfer: the state of the art, Int. J. Heat Fluid Flow 28 (4) (2007) 753–767. [3] R. Zhao, W.L. Cheng, Q.N. Liu, et al., Study on heat transfer performance of spray cooling: model and analysis, Heat Mass Transf. 46 (8–9) (2010) 821–829. [4] W.L. Cheng, H. Chen, L. Hu, et al., Effect of droplet flash evaporation on vacuum flash evaporation cooling: modeling, Int. J. Heat Mass Transf. 84 (2015) 149– 157. [5] G. Liang, I. Mudawar, Review of drop impact on heated walls, Int. J. Heat Mass Transf. 106 (2017) 103–126. [6] M. Shirota, M.A. van Limbeek, C. Sun, et al., Dynamic Leidenfrost effect: relevant time and length scales, Phys. Rev. Lett. 116 (6) (2016) 064501. [7] D. Quéré, Leidenfrost dynamics, Annu. Rev. Fluid Mech. 45 (2013) 197–215. [8] T. Tran, H.J. Staat, A. Prosperetti, et al., Drop impact on superheated surfaces, Phys. Rev. Lett. 108 (3) (2012) 036101. [9] H.M. Kwon, J.C. Bird, K.K. Varanasi, Increasing Leidenfrost point using micronano hierarchical surface structures, Appl. Phys. Lett. 103 (20) (2013) 201601. [10] H. Nair, H.J. Staat, T. Tran, et al., The Leidenfrost temperature increase for impacting droplets on carbon-nanofiber surfaces, Soft Matter 10 (13) (2014) 2102–2109. [11] M.A.J. van Limbeek, M. Shirota, P. Sleutel, et al., Vapour cooling of poorly conducting hot substrates increases the dynamic Leidenfrost temperature, Int. J. Heat Mass Transf. 97 (2016) 101–109. [12] T. Tran, H.J. Staat, A. Susarrey-Arce, et al., Droplet impact on superheated micro-structured surfaces, Soft Matter 9 (12) (2013) 3272–3282. [13] M. Chabicˇovsky´, M. Hnízdil, A.A. Tseng, et al., Effects of oxide layer on Leidenfrost temperature during spray cooling of steel at high temperatures, Int. J. Heat Mass Transf. 88 (2015) 236–246. [14] A. Shahriari, J. Wurz, V. Bahadur, Heat transfer enhancement accompanying Leidenfrost state suppression at ultrahigh temperatures, Langmuir 30 (40) (2014) 12074–12081. [15] B.T. Ng, Y.M. Hung, M.K. Suppression of the Leidenfrost effect via low frequency vibrations, Soft Matter 11 (4) (2015) 775–784.

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