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Nucleation mechanism of nanofluid drops under acoustic levitation
Accepted Manuscript Nucleation mechanism of nanofluid drops under acoustic levitation Liu Yudong, Gao Yongkun, Wang Jiangqing, Geng Shichao, Su Chuangjian, Peng Quangui PII: DOI: Reference:
S1359-4311(17)31644-7 https://doi.org/10.1016/j.applthermaleng.2017.11.035 ATE 11405
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
11 March 2017 12 October 2017 5 November 2017
Please cite this article as: L. Yudong, G. Yongkun, W. Jiangqing, G. Shichao, S. Chuangjian, P. Quangui, Nucleation mechanism of nanofluid drops under acoustic levitation, Applied Thermal Engineering (2017), doi: https://doi.org/ 10.1016/j.applthermaleng.2017.11.035
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Nucleation mechanism of nanofluid drops under acoustic levitation Liu Yudonga,b,Gao Yongkunb,Wang Jiangqingb, Geng Shichaob, Su Chuangjianb, Peng Quanguib a
Key Laboratory of Low-Grade Energy Utilization Technologies and Systems of Ministry of Education ,Chongqing University, Chongqing 400030, China b College of Power Engineering, Chongqing University, Chongqing 400030, China
HIGHLIGHTS
The supercooling degree of nanofluid is significantly lower than that of deionized water.
The nucleation rate of nanofluid is greater than that of deionized water at the same supercooling degree.
The heterogeneous nucleation factor of nanofluid is less than that of deionized water at the same ultrasonic power.
Nucleation in levitated nanofluid drops includes both surface nucleation and volume nucleation.
ABSTRACT In this study, 0.03 wt.% graphene oxide nanofluid was prepared by adding graphene oxide nanosheets into deionized water, and nucleation experiments were conducted with levitated deionized water and graphene oxide nanofluid drops to study their supercooling degree distributions and nucleation mechanism. Results show that the supercooling degree of the nanofluid drop is significantly less than that of the deionized water drop, and that supercooling degree increases as ultrasonic power increases. The nucleation rates of the deionized water and nanofluid drops at two ultrasonic power levels was obtained according to the statistical nucleation theory, and heterogeneous nucleation factors and nucleation sites were calculated based on the classical nucleation theory. The nucleation rate of nanofluid is greater than that of deionized water at the same supercooling degree. The analysis of the heterogeneous nucleation factors revealed that levitated deionized water and nanofluid drops exhibit heterogeneous nucleation, and that heterogeneous nucleation factor decreases as ultrasonic power increases. The effects of ultrasonic power and nanoparticles on nucleation are coupled to each other. Comparing the nucleation site of drops at two power levels showed that the levitated deionized water drop exhibits surface-dominated nucleation and the levitated nanofluid drop exhibits both surface- and volume-dominated nucleation behaviors, which are affected by ultrasonic wave. Additionally, the surface nucleation site increases as ultrasonic power increases. Keywords: graphene oxide nanofluid, nucleation rate, nucleation site, volume nucleation, surface nucleation 1. Introduction Phase-change technology has always received research attention given the importance of phase-change materials (PCMs) in technology[1]. However, given that most PCMs exist under high supercooling degrees, liquid PCMs do not immediately solidify at freezing temperatures. Instead, PCMs will only crystallize at temperatures below the freezing temperature. Many scholars have studied various methods that decrease the degree of supercooling of PCMs such as adding nucleation catalyst and using ultrasonic technology. However, the effect of these methods is not ideal. The emergence of nanofluids provided an alternative. Nomenclature
C0
nucleation energy factor
Pn(t)
probability of observing no nucleation events
C’
sound speed in the air
KB
Boltzmann constant (J/K)
D
regional site of nucleation
S1
spherical drop surface site (mm2)
f
heterogeneous nucleation factor
S2
cylindrical drop surface site (mm2)
f0
angular frequency of incident sonic
Greek symbols
h
high of columnar drop (mm)
ΔH
phase change latent heat ( J/m )
J
nucleation rate (s−1)
ΔG*
heterogeneous nucleation critical energy (J)
Js
surface nucleation rate (s−1)
ΔT
supercooling degree (K)
Jv
volume nucleation rate (s−1)
conversion factor of transducer
kb
Boltzmann constant (J/K)
air density
Nu
Nusselt number
α0
air thermal diffusivity
Ntotal
total number of nucleated drops
ω
nucleation rate per drop (s−1)
Ny
number of non-nucleated drops
Subscript
P0
reference powers
1
20 W of ultrasonic power
Pe
sound pressure effective amplitude
2
32 W of ultrasonic power
3
Nanofluid is stable colloidal suspensions of mental or non-mental particle on a base fluid, which can enhance heat transfer of the solution and increase the storage capacity [2]. Many scholars have done a lot of research on the enhancement of heat transfer and supercooling degree of nanofluids. MM Sarafraz et al. [3] investigated the heat transfer coefficient of carbon nanotube water-based nanofluids inside the double pipe heat exchanger, and they found that presence of carbon nanotube can enhance the thermal conductivity up to 56% at wt.% = 0.3. They also investigated the fouling formation of CuO/water nanofluid inside a chevron type flat plate heat exchanger[4]. They used low frequency vibration to mitigate the fouling of nanoparticles and they found that thermal performance of the system is intensified. As for fouling formation of nanofluid in a gravity-assisted thermosyphon, they put forward a new fouling resistance model [5]. This model can predict the fouling resistance of nanofluid inside the thermosyphon with approximate deviation of 30%. Amirhossein Zamzamian et al[6] studied forced convective heat transfer coefficient of nanofluids of aluminum oxide and copper oxide with theory and experiment, and they evaluated the effects of particle concentration and operating temperature on the force convective heat transfer coefficient of the nanofluids. The results shows convective heat transfer coefficient of nanofluids enhances obviously and increases with increasing nanoparticles concentration and nanofluid temperature. MM Sarafraz et al.[7,8] studied nucleate pool boiling heat transfer of Al2O3 nanofluids and zirconium oxide nanofluids. They found nanoparticles improve the pool boiling heat transfer coefficient values and increased values of heat transfer are increased with increasing the concentration of nanoparticle. The pool boiling heat transfer coefficient of Al 2O3 and zirconium oxide nanofluids be enhanced to 25% and 12% incomparison with base liquid respectively. S. Harikrishnan et al. [9] added
50%CuO–50% TO2 hybrid nanoparticles into paraffin to prepare a new phase of solar-heating, energy-storage materials. Furthermore, they studied the thermal conductivity and phase transition properties of a PCM with mass fractions of 0.25%, 0.5%, 0.75%, and 1%, and found the melting and freezing time of mixed nano-phase change materials decreased by 27.7% and 29.8% respectively compared with paraffin. Deville et al.
[10]
studied the effect of the solidification
behavior of Al2O3/ distilled water nanofluid on supercooling degree. They reported that supercooling degree decreases as particle size decreases. Jia et al. [11] utilized X-ray photography and differential scanning calorimetry to study the effect of TiO2 nanoparticles with 0.2-3.4 micons on the supercooling degree of deionized water. They found that the supercooling degree of TiO2 nanofluids decreased by approximately 11.5% and supercooling degree is not much related to the concentration of nanofluids. The addition of surfactant can effectively reduce the supercooling degree. Zhao et al.
[12]
studied the supercooling and cold-energy storage characteristics of nanofluids and water-based nano-media in ball-packed porous structures by experimental methods. They found that its average and maximum supercooling degrees are lower than those of deionized water and nanofluid and nano-media can reduce the supercooling degree, shorten the cooling time and enhance heat transfer. Liu et al. [13,14,15] empirically studied the supercooling degree and nucleation sites of graphene oxide nanofluid. They found that graphene oxide nanoparticles are effective nucleating agents that dramatically reduce the supercooling degree of deionized water. Songping Mo [16] analyzed the combined effect of TiO 2 nanoparticles mass fraction, container wall roughness and wettability on the supercooling degree of nanofluid. They reported that the performance of the container wall mainly affected the supercooling degree and the supercooling degree of nanofluid at the same concentration in a glass container is higher than that in a plastic container. The container wall largely affects the nucleation of nanofluids, but acoustic suspension is a good way to avoid the effects of the container. Of course, ultrasound can also affect the nucleation of drops. M Saclier et al.[17] developed the modelling and simulation of ice nucleation triggered by acoustic cavitation. According to their study, the nucleation could be initiated with moderated acoustic pressure amplitude (around one bar) even at low supercooling levels (around few degrees). Although supercooling degree is an important feature of nanofluid crystallization nucleation, it is random and each measurement may attain different values. Therefore, only the study of supercooling degree can not fully understand the nucleation mechanism of nanofluids. The study of nucleation rate and nucleation sites is significant for revealing the mechanism of supercooling degree inhibited by nanoparticles. However, as nanofluid is a new colloidal solution, the theoretical calculation of nanofluid nucleation rate is imperfect. Therefore, limited research has been conducted on the nucleation rate and nucleation sites of nanofluids. Some researchers have calculated the nucleation rate of liquid water via the statistical probability method, which is based on nucleation statistical theory. Koop pointed out that drop nucleation is a random process and that nucleation rate follows Poisson distribution [18]. Koop then calculated the nucleation rate of H2SO4 and HNO3 aqueous solutions at different supercooling degrees. Kramer
[19]
measured the supercooling degree of thousands of suspended
droplets and analyzed the cooling process of those droplets. They calculated the homogeneous nucleation rate of water between 236–273 K, and nucleation energy and nucleation dimensions were determined by the classical nucleation theory. Seeley and Seidler
[20, 21]
encapsulated water drops with organic solvent to induce surface nucleation, thus obtaining
2D-nucelated water. They deduced the critical nucleation height and wetting angle by measuring nucleation rate. As the initial temperature of the drop increases, the supercooling degree of the drop increases; this behavior indicates that supercooling degree is determined only by the critical nucleation power. Heneghan et al.
[22]
used ALTA equipment to
measure the supercooling degree of hundreds of pure water drops and drops that contained AgI particle solution. The respective nucleation curves of the two liquids were obtained. They showed that the supercooling degree of AgI solution is significantly less than that of pure water and the limitation of classical nucleation theory is revealed. Kuhn [23] studied the volume and surface nucleation of water drops in a cryogenic laminar aerosol flow tube. Their results showed that the
contribution from nucleation at the drop surface increases with decreasing drop radius and dominates over nucleation in the bulk droplet volume for drops with radii smaller than approximately 5 µm. Yongjun Lv [24] studied the law that governs the supercooling degree distribution of a large volume of water under acoustic suspension. Yongjun Lv found that the maximum supercooling degree of suspended drops is 32 K. He then utilized statistical methods to elucidate the nucleation law of suspended water drops. He found that drop nucleation is heterogeneous and that nucleation occurs mainly on the drop surface.
Liu et al.
[25]
calculated the theoretical nucleation rates of deionized water and different
concentrations of graphene oxide nanofluid. They found that the nucleation rate of nanofluid is higher than that of deionized water at the same supercooling degree, and nanofluid nucleation occurs mainly on the surface of nanoparticles. As the classical nucleation theory is not perfect and the supercooling degree is random, the theoretical value is slightly different from the actual value. However, there are few studies on the nucleation rate of nanofluid drops under acoustic suspension, and there is no research on the nucleation sites of nanofluid drops. In the present study, graphene oxide nanofluid was prepared. Then, the supercooling degrees of the deionized water and nanofluid drops were measured via the single drop method. The nucleation rates of the drops were calculated using the statistical nucleation theory, and the nucleation sites of nanofluid drops was studied.
2. Experiments 2.1 Preparation and stability of graphene oxide nanofluid
The base fluid is deionized water. The suspension additive is graphene oxide. The experimental procedure is as follows: first, 30 mg graphene oxide nanosheets and 100 ml deionized water are measured with an electronic balance and a measuring cylinder, respectively, and then added to a small beaker. Next, the beaker is placed in a larger beaker with ice and water. The distance between the bottoms of the ultrasonic horn and large beaker is adjusted. Finally, the power of the ultrasonic oscillator is set at 300 W with 8-s pulse mode for 150 min. The ice–water mixtures in the large beaker are replaced every 30 min. The preparation of 30 mg/(100 ml) nanofluid is thus completed. The preparation of nanofluid is shown in Fig. 2.1. Fig2.2 is the STEM image of graphene oxide nanosheets. In this paper, only one concentration of graphene oxide nanofluids is prepared in order to exclude the effect of concentration on nucleation rate and nucleation site.
Suspension stability is an important factor in the practical application of nanofluids. The prepared graphene oxide nanofluid is stable, as indicated by the absence of aggregation and precipitation when left to sit for 30 days. P article size distribution and zeta potential were obtained by Laser Size and Zeta Potential Analyzer (Nano ZS90). Fig.2.3 shows the particle size and the zeta distribution of the graphene oxide nanofluid. The particle diameters are 37–74 nm and the average particle size is 52 nm. The zeta distribution of the nanofluid is distributed in 0–70 mV with an average potential of −38 mV. These results further indicate that the prepared nanofluid [26] is stable.
Fig.2.1 Schematic of the nanofluid preparation system 1. Ultrasonic transducer 2. Ultrasonic horn 3. Small beaker 4. Large beaker 5. Adjustable holder 6. Electric wire 7. Ultrasonic generator
Fig2.2 STEM image of graphene oxide nanosheets
Tatal Counts
300000
200000
100000
0 -200
-100
0
100
Zeta Potential (mV)
Fig2.3 Particle size and Zeta potential distribution of 0.03% graphene oxide nanofluid (150 min)
200
2.2 Deionized water and nanofluid drop suspension system
An experimental system for acoustic levitation was constructed in this study. The system comprises an acoustic levitator system, cooling system, and data acquisition system, as shown in Fig.2.4. The basic working principle of the system is as follows: first, a low-temperature environment is prepared using the cooling system. Then, a drop is suspended by the acoustic levitator. The temperature change of the drop is measured by copper-konjoc T thermocouple during the cooling process and is recorded by an agent. The precision of the thermocouple was ±0.2℃ and the average relative error was less than 3% when the temperature changing from -25℃ to 15℃. The thermocouple was calibrated by a high precision thermometer. The drop volume is determined by the pipette. The pipette was calibrated with a electronic balance, and the average relative error was less than 4% with a calibration range of 20µL to100µL.
Fig.2.4 Structure of the experimental system 1. Data acquisition module 2. Computer 3. Ultrasonic generator 4. Power cord 5. Ultrasonic horn 6. Emitter 7. Thermocouple 8. Reflector 9. Operation window 10. Height adjuster and transducer 12. Bracket 13. Levitated drop 14. Radiant cooler 15. Connecting pipe 16. Control box 17. Cooling medium 18. Cryostat circulator First, the cryostat circulator starts working. The ambient temperature of the cooling box is maintained at −21 °C. Then, 30-µL drops of deionized water and graphene oxide nanofluid are levitated at 20 W and 32 W of the acoustic levitator power. The phase transition supercooling is measured. The experiment is repeated 500 times at each power to obtain the supercooling distributions of the deionized water and graphene oxide nanofluid drops.
3. Experimental results and discussion 3.1 Supercooling degree of acoustically levitated deionized water and nanofluid drop
The supercooling degree of the deionized water and nanofluid drops at two power levels are statistically analyzed at the unit temperature interval. The temperature interval is [T−0.5, T+0.5]. The results are shown in Fig.3.1. In this figure, the coordinate ΔT is the supercooling degree of the drops and the ordinate is the number of experiments. As shown in the figure, the supercooling degree of the nanofluid drop at the same power is significantly lower than that of the
deionized water drop, thus indicating that nanoparticles effectively inhibit supercooling degree. The supercooling degree of one kind of fluid at 32 W is less than that at 20 W. Therefore, acoustic power affects supercooling degree, and the greater the power, the higher the supercooling degree. However, the effect of acoustic power on supercooling is considerably less than that of nanoparticles. The supercooling degree of different fluids at different powers is shown in Table 3.1.
20W deionized water 32W deionized water
140
20W nanofluid 32W nanofluid
Expriment number
120 100 80 60 40 20 0 2
4
6
8
10
12
14
16
ΔT/K Fig.3.1 Distribution of the supercooling degree of deionized water and nanofluid drops
Table 3.1 Supercooling degree of two fluids Minimum Power
Fluid
Maximum
Average
Supercooling
supercooling
supercooling degree
supercooling
degree range
degree (K)
(K)
degree (K)
(K)
deionized water
3.7
16.4
11.54
11–14
nanofluid
2.7
13.4
8.28
6–10
deionized water
2.8
15.2
10.27
9–13
nanofluid
2.1
11.2
7.16
5–9
20 W
32 W
According to Fig.3.1, the probability of observing no nucleation event at a fixed temperature T within the time t is calculated by freezing 500 sets of deionized water and nanofluid drops. As shown in Fig.3.2, Ny represents the number of non-nucleated drops at a certain supercooling degree and Ntotal represents the total number of nucleated drops within the total measured time. The nucleation rates of the unit supercooling degree of the deionized water and nanofluid drops are calculated later in the unit temperature interval. Although the supercooling degree of nanofluid at the acoustic power of 20 W and that of deionized water at the acoustic power of 32 W are both −3 °C, the supercooling degree of nanofluid is
mainly distributed in the 6°C –10 °C, and that of deionized water is mainly distributed in the 9°C –13 °C. A small number of deionized water drops have a low supercooling degree, but the vast majority of deionized water drops have a higher supercooling degree. Therefore, the crystallization of deionized water is random but its supercooling degree is within a certain range. The crystallization of graphene oxide nanofluid drops is also random.
1.0
20W deionized water 32W deionized water 20W nanofluid 32W nanofluid
Ny/Ntotal
0.8 0.6 0.4 0.2 0.0 2
4
6
8
10
12
14
16
18
20
ΔT/K Fig.3.2 Relationship between non-nucleation probability and supercooling degree The average freezing curves of the deionized water and nanofluid drops are obtained, then the relationship between supercooling degree and time is established, as shown in Fig.3.3. Bigg [27] found that freezing rate affects the supercooling degree of drops. In the present experiment, the difference in freezing rates is contributed by nanoparticles and ultrasound. Fig.3.3 indicates that the freezing curves of the two fluids at different ultrasonic powers follow the same trend, but the freezing rate of the graphene oxide nanofluid is slightly higher. Given that the volume of drops in the experiment is 30 µL, the surface site of the levitated deionized water and nanofluid drops negligibly changes. So the freezing curves of the two fluid drops are the same in a short time. However, enlarging Part A in Fig.3.3 reveals that the freezing rate of the nanofluid is significantly higher than that of the deionized water, and that the freezing rate at the ultrasonic power of 32 W is greater than that at 20 W. The large cooling rate of drops indicates good heat transfer performance. Some scholars [28] have reported that adding nanoparticles to water effectively enhances the heat transfer of the liquid. The average freezing curve in the experiment also shows that the heat transfer coefficient of the nanofluid is greater than that of the deionized water. As shown in the enlarged view of Part B, the temperature of the deionized water drop at the ultrasonic power of 32 W is lower than that at the 20 W, which also indicates that the strength of the ultrasonic waves affects the freezing rate of the deionized water drop. Yairn[29] proposed the relationship between the sound pressure and Nusselt number Nu near the surface of spherical drop under ultrasonic suspended: (3.1)
Where the sound pressure effective amplitude Pe is determined by the sound pressure definition:
.
is air thermal diffusivity,
f0 is angular frequency of incident sonic,
relationship between Pe and power P is
is air density,
, where
is sound speed in the air. The
is reference powers, and
is conversion
factor of transducer.So the relationship between Nu and P is: (3.2) It can be seen from the above formula that Nu is related to P and Nu , and the decreasing P and the increasing
. The increasing P and the decreasing
will reduce Nu. In the experiment,
will increase
of the acoustic suspension device
is constant, so Nu is only related to power P. The convective heat transfer coefficient between drop and air increase with increasing power, and the cooling rate of drop also increases, as shown in Fig3.3. -8 -9 20W deionized water 32W deionized water
4
20W nanofluid 32W nanofluid
T/℃
-10
6
2
-12
0
-13 -14 25 30 35 40 45 50 55 60 65
-2
T/℃
-11
-4 -6
t/s
-14.0
-8
T/℃
-10 -12 -14
-15.0
a
-16 -18 -20
b 0
20
40
-14.5
60
-15.5 93
80 100 120 140 160 180
96
99 102 105 108 111 114 117
t/s
t/s Fig.3.3 Cooling curves of deionized water and nanofluid
3.2 Nucleation rates and heterogeneous nucleation factors of deionized water and graphene oxide nanofluid drops
According to the statistical nucleation theory proposed by Koop et al. [18], the probability of observing a non-nucleation event at a fixed temperature T and time t is described by
Pnt e T t , where
is the nucleation rate
per drop. According to the relation between the supercooling degree and the time established by the average freezing curve of deionized water and nanofluid fluid, the nucleation rate for a given volume can be expressed as:
T
ln N y T Nt o t
t a l
(3.3)
Using Eq. 3.3, the unfrozen probability in Fig.3.2 and the freezing curve in Fig.3.3 can be transformed into the nucleation rates of deionized water and nanofluid drops. According to the classical nucleation theory [30], the nucleation rate is given by:
T A exp
B T 2 273.15 T
where A and B are temperature-independent parameters [24] and are written in detail as:
(3.4)
A C0 D B f
(3.5)
3 16 iw Tm2
(3.6)
3H v k b 2
where C0 is the nucleation energy factor, which is the ability of water molecules to transition to the surface of the crystal embryo; D is the regional size of nucleation; f is the heterogeneous nucleation factor;
iw is
the interface energy
between ice and water; Tm is the phase transition temperature; H v is the phase change latent heat; and kb is the Boltzmann constant. Table 3.2 shows the relevant physical properties.
Table 3.2 Physical properties
iw （J/m2）
H v （J/m3）
kb（J/K）
0.02343
3.06634 × 108
1.38 × 10−23
The nucleation rate curve with supercooling degree is obtained based on Eq. 3.3 and 3.4. Fig.3.4 and Fig.3.5 represent the nucleation rate curves of deionized water and nanofluid, respectively. In these figures, the scattered points indicate the experimental values and the solid line represents the nucleation rate curve as a function of supercooling degree.
0.09 20W deionized water 32W deionized water 32W deionized water 20W deionized water Data in Ref.24 Data in Ref.24
0.08 0.07 0.06
ω/s-1
0.05 0.04 0.03
Model
zuichu (User)
Equation
y = A*exp(-B/(x^2*(273.15-x
0.02
Reduced Chi-Sqr
1.06943 E-5
0.01
Adj. R-Squ
0.98416 Value
0.00
B
-0.01 2
4
6
8
10
12
14
16
ΔT/K
Fig.3.4 Nucleation rate of deionized water drop According to the fitting results, when the ultrasonic power is 20 W, A1 is 0.2415 and B1 is 92306.56. When the ultrasonic power is 32 W, A1 is 0.3332 and B1 is 74487.28. The subscripts 1 and 2 represent 20 and 32 W, respectively. The nucleation rates of deionized water are expressed as:
A
0.33317
B
74487.28
92306.56 J1 T 0.2415 exp T 2 273.15 T
74487.28 J 2 T 0.3332 exp T 2 273.15 T
(3.7)
(3.8)
The fitting curve presents the nucleation rate of 30 µL deionized water, not unit volume, as with the case of nanofluid. Given that C0 is dependent only on physical properties and does not change with acoustic pressure, then according to Eq. 3.5, A2/A1 = D2/D1 = 1.38. This indicates that the nucleation area of the deionized water drop at 32 W is 1.38 times that at 20 W. The heterogeneous nucleation factors of deionized water at two power levels were calculated using the physical parameters in Table 3.1 and Eq.3.6. The values of f1 and f2 are 0.0074 and 0.0060, respectively, which indicate that levitated deionized water drops exhibit a heterogeneous nucleation process and that the ultrasonic wave promotes rapid nucleation. According to the classical nucleation theory, the heterogeneous nucleation critical work [31] is expressed as:
G f
3 16 iw Tm2 1 2 3H v T 2
(3.9)
In addition to the heterogeneous nucleation factor, the rest of the parameters are the constants in Eq.3.9. Thus, critical nucleation work is only determined by the heterogeneous nucleation factor f:
G2 G1 f 2 f1 0.81
(3.10)
The critical nucleation work of deionized water at 32 W is only 81% of that at 20 W, which indicates that nucleation work decreases as ultrasonic power increases. The nucleation rate in this paper compares with Lv Yongjuns’ results[24]. As shown in Fig 3.4, the difference between the two results in an order of magnitude, indicating that the experimental results are correct. The main reason for the difference is that the ultrasonic pressure amplitude, the cooling rate and the location of temperature measurement are different in the two papers. 0.14 20W 32W 32W 20W
0.12 0.10
nanofluid nanofluid nanofluid nanofluid
ω/s-1
0.08 0.06 0.04 0.02 0.00 2
4
6
8
10
12
ΔT/K Fig3.5 Nucleation rate of graphene oxide nanofluid drop According to the fitting results, when the ultrasonic power is 20 W, A1 is 0.3276 and B1 is 41785.93. When the
ultrasonic power is 32 W, A1 is 0.3628 and B1 is 28968.33. The nucleation rates of the nanofluid are expressed as:
41785.93 J1 T 0.3276 exp T 2 273 .15 T
(3.11)
28968.33 J 2 T 0.3628 exp T 2 273 .15 T
(3.12)
According to Eq. 3.5, A2/A1 = D2/D1 = 1.11, indicating that the nucleation site of the nanofluid drop at 32 W is 1.11 times that at 20 W. The values of f 1 and f2 of the nanofluid are 0.0034 and 0.0023, respectively, indicating that nucleation process is heterogeneous. Based on Eq. 3.9, the critical nucleation work of the nanofluid drop at 32 W is 68% at 20 W. By comparing the fitting parameters, it can be concluded that: 1. The nucleation rate of the nanofluid is considerably larger than that of the deionized water at the same supercooling degree. Furthermore, the greater the ultrasonic power, the greater the nucleation rate; 2. The nucleation sites of deionized water and nanofluid at 32 W are greater than those at 20 W, indicating that increasing ultrasonic power increases nucleation sites. However, nucleation site, which depends on the number of critical crystal nuclei in the drop, does not directly determine supercooling degree. The ratio of the nucleation site of the deionized water is larger than that of the nanofluid; this indicates that the ultrasonic power has a greater effect on the nucleation site of deionized water; 3. Compared with the heterogeneous nucleation factors of deionized water and graphene oxide nanofluid, the greater the ultrasonic power, the smaller the heterogeneous nucleation factor. And the heterogeneous nucleation factors of nanofluid are less than those of deionized water at two levels of ultrasonic power, indicating the effects of ultrasonic and nanoparticles on nucleation can be superimposed; 4. The critical nucleation work of deionized water and nanofluid at 32 W is 0.80 times and 0.68 times, respectively, that at 20 W. The effect of ultrasonic wave on nanofluid nucleation work is greater than that on deionized water nucleation. The nucleation rate obtained by the experiment is different from the nucleation rate calculated by theory in the previous paper[25]. Caused by the following reasons: 1.In the previous paper, the nucleation rate of nanofluid is calculated by the classical nucleation theory, and the cooling rate is not taken into account. Bigg E K[27] found that the cooling rate affects supercooling degree of liquid, and the greater cooling rate, the greater supercooling degree. In this paper, the nucleation rate of nanofluid is obtained by statistical nucleation theory, and the cooling rate is considered. 2.There are tiny bubbles inside the levitation drop, and the surface of the drop under the acoustic suspension can undergo ultrasonic cavitation. When ultrasonic cavitation [32] on the drop occurs, the pressure of bubble in the compression phase can reach hundreds of atmospheric pressure, and it can reach more than 5GP a in crack finally, accompanied by sonogenic phenomenon. The freezing point of the water will change at high pressure, and the solidification temperature increases with increasing pressure, so that the drops are more likely to have large supercooling degree[33]. 3.In the ultrasonic field, the drops rotate around the z-axis and the surface vibrates. The internal flow and shock of the drops increase the collision of the internal crystal embryos and particles, and it is easy to form larger crystal embryos and particles. So the nucleation rate increases. These three reasons cause the difference between the theoretical and experimental values.
3.3 Volume nucleation and surface nucleation of two levitated fluids
The nucleation rate of a drop that contains a free-liquid surface should include both surface and volume nucleation rates. Specifically, J T J v T V J s T S , where Jv is the volume nucleation rate and Js is the surface nucleation rate [34] . The nucleation of deionized water and nanofluid drops may occur only within the drop (volume nucleation) or only on the surface (surface nucleation), or both of them. According to Eq. 3.5, parameter A is related to the nucleation dynamics factor C0 and the nucleation site size D. C0 does not vary with ultrasonic wave. On the other hand, given that the volume of the drop in the experiment is maintained at 30 µL and the evaporation of the liquid during freezing is negligible, the volume of the drop is approximately constant before nucleation. Fig.3.6 and Fig.3.7 show the geometric dimensions of deionized water and nanofluid drops at both powers.
Fig.3.6 Geometric dimension of deionized water drop at different power levels
Fig.3.7 Geometric dimension of nanofluid drop at different power levels
If the nucleation of the levitated drop is volume-dominated, then, according to the classical nucleation theory, the nucleation site inside the drop should remain constant at different power levels. According to the experimental data, the ratio of the nucleation site of the deionized water drop at two power levels is A2/A1 = D2 /D1 = 1.38. Thus, the nucleation sites increased by a factor of 1.38. This result is clearly inconsistent with the classical nucleation theory and indicates that
the nucleation of the deionized water drop is not volume-dominated. The ratios of the nucleation site of the graphene oxide nanofluid drop at two power levels are A2/A1 = D2/D1 = 1.11. Although the ratio of the nanofluid is smaller than that of deionized water, it is also inconsistent with the classical nucleation theory. Therefore, the nucleation of the nanofluid drop is also not volume-dominated. If the nucleation of the levitated drop is surface-dominated, then volume nucleation is negligible and the nucleation sites on the drop surface remains constant. As shown in Fig.3.7 and Fig.3.6, when the ultrasonic power is 20 W, the shape of the drop is spherical. When the ultrasonic power is 32 W, the shape of the drop is cylindrical. The size of levitated drops can be calculated proportionally by experimentally measuring the distance between the emitter and the reflector. The superficial sites of the drop at two power levels are calculated in terms of spherical and cylindrical shapes. The surface site ratios of the drops at different power levels are expressed as:
S2 d 2 h 2 d 2 2 2 S1 4 d1 2 2
(3.13)
According to the sizes of the deionized water and nanofluid drops, the surface site ratio of the deionized water drop is 1.30 and that of the nanofluid drop is 1.28. In the light of the surface nucleation hypothesis, when the nucleation of the deionized water drop is surface-dominated, the nucleation site ratio of the deionized water drop at two power levels is 1.30. Based on the experimental results, the nucleation site ratio of the deionized water drop is 1.38. These two values differ by only 6%, indicating that nucleation occurs mainly on the drop surface. The conclusion is the same as that of Ref.24.There are two main reasons, one is that the ultrasonic cavitation on the surface of the drop promotes the nucleation of the drop surface; the other is the drop surface temperature is lower than the dropt internal temperature, so the critical nucleation energy of the drop surface is less than that of the drop internal[33].
Fig.3.8 Measurement of the surface and internal temperature of the nanofluid drop
4 surface temperature internal temperature
2
T/K
0 -2 -4 -6 -8 -10 0
10
20
30
40
t/s Fig.3.9 Surface temperature and internal temperature of the nanofluid drop The theoretical nucleation area ratio of the nanofluid drop at two power levels is 1.28. However, the experimentally calculated nucleation site ratio of the nanofluid is 1.11. The difference between these two values is relatively large, which indicates that nanofluid nucleation is not surface-dominated but is dominated by both volume and surface nucleation. A previous article[25] indicate that nanofluids nucleation occurs mainly on the surface of nanoparticles. But ultrasonic waves cause drop rotation[35], and some nanoparticles are closer on the surface. This part of nanoparticles-induced heterogeneous nucleation can directly contribute to the drop surface nucleation, and the other part is volume nucleation. As the drop volume and the nanoparticle concentration is the same, so the nucleation site of nanoparticles surface in the drop is the same. The nucleation site of nanofluid drop at 32W is larger than that at 20W, indicating that increased ultrasonic power increases the drop surface nucleation site. The higher the ultrasonic power, the higher the perturbation of the ultrasonic wave on the nanofluid drop, the more particles in the drop near the surface, and the larger the drop surface nucleation site. The internal and near-surface temperatures of the levitated nanofluid drop were measured with thermocouple at an ultrasonic power of 20 W, as shown in Fig.3.8. Fig.3.9 shows that the difference between the near-surface and internal temperatures changes with time. It can be seen that the surface temperature of the nanofluid drops is lower than the internal temperature of drops and the maximum temperature difference is 1.2 °C. Nucleation is more likely to occur on nanoparticles near the drop surface, which induces drop surface nucleation. Fig3.9 shows that the surface temperature and the internal temperature of nanofluid drop suddenly become 0℃from supercooled state at the same time, indicating that nanofluid drop nucleate is both surface nucleation and volume nucleation. When the surface temperatures of the nanofluid drop become 0℃, the drop is removed. It is found that the whole nanofluid drop is frozen, but the deionized water drop is both ice and water. 4. Conclusion (1) At 20 W of ultrasonic power, the average supercooling degree of deionized water is 11.54 K and that of nanofluid
is 8.28 K. At 32 W of ultrasonic power, the average supercooling degree of deionized water is 10.27 K and that of nanofluid is 7.16 K. The supercooling degree of nanofluid drops is significantly less than that of deionized water. The higher the ultrasonic power, the lower the supercooling degree. The freezing rate of nanofluid is slightly higher than that of deionized water, and the higher the ultrasonic power, the faster the freezing rate. (2) The experimentally calculated nucleation rate of nanofluid is considerably higher than that of deionized water at the same supercooling degree. Moreover, the nucleation rates at 32 W are greater than those at 20 W. Levitated nanofluid and deionized water drops exhibit heterogeneous nucleation. The heterogeneous nucleation factors of nanofluid are lower than those of deionized water. The higher the ultrasonic power, the lower the heterogeneous nucleation factor. The nucleation sitess of the two fluid drops at 32 W are larger than those at 20 W, and the nucleation sites of deionized water at the two power levels are larger than those of nanofluid. (3) Comparing the nucleation sites of deionized water and nanofluid drops at two different power levels revealed that the nucleation of the levitated deionized water drops is mainly surface-dominated, whereas that of the levitated nanofluid drops is both surface-dominated and volume-dominated. Ultrasonic cavitation and lower surface temperature promote the surface nucleation of deionized water drop. The graphene oxide particles induce the drop volume nucleation, and the nanoparticles also induce the surface nucleation of the drop due to the internal flow of the drop. Acknowledgments The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 51276204).
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List of figures: Fig.2.1 Schematic of the nanofluid preparation system Fig2.2 STEM image of graphene oxide nanosheets Fig2.3 Particle size and Zeta potential distribution of 0.03% graphene oxide nanofluid (150 min) Fig.2.4 Structure of the experimental system Fig.3.1 Distribution of the supercooling degree of deionized water and nanofluid drops Fig.3.2 Relationship between non-nucleation probability and supercooling degree Fig.3.3 Cooling curves of deionized water and nanofluid Fig.3.4 Nucleation rate of deionized water drop Fig3.5 Nucleation rate of graphene oxide nanofluid drop Fig.3.6 Geometric dimension of deionized water drop at different power levels Fig.3.7 Geometric dimension of nanofluid drop at different power levels Fig.3.8 Measurement of the surface and internal temperature of the nanofluid drop Fig.3.9 Surface temperature and internal temperature of the nanofluid drop List of tables:
Table 3.1 Supercooling degree of two fluids Table 3.2 Physical properties
Highlights The supercooling degree of nanofluid is significantly lower than that of deionized water. The nucleation rate of nanofluid is greater than that of deionized water at the same supercooling degree. The heterogeneous nucleation factor of nanofluid is less than that of deionized water at the same ultrasonic power. Nucleation in levitated nanofluid drops includes both surface nucleation and volume nucleation .
S1359-4311(17)31644-7 https://doi.org/10.1016/j.applthermaleng.2017.11.035 ATE 11405
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
11 March 2017 12 October 2017 5 November 2017
Please cite this article as: L. Yudong, G. Yongkun, W. Jiangqing, G. Shichao, S. Chuangjian, P. Quangui, Nucleation mechanism of nanofluid drops under acoustic levitation, Applied Thermal Engineering (2017), doi: https://doi.org/ 10.1016/j.applthermaleng.2017.11.035
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Nucleation mechanism of nanofluid drops under acoustic levitation Liu Yudonga,b,Gao Yongkunb,Wang Jiangqingb, Geng Shichaob, Su Chuangjianb, Peng Quanguib a
Key Laboratory of Low-Grade Energy Utilization Technologies and Systems of Ministry of Education ,Chongqing University, Chongqing 400030, China b College of Power Engineering, Chongqing University, Chongqing 400030, China
HIGHLIGHTS
The supercooling degree of nanofluid is significantly lower than that of deionized water.
The nucleation rate of nanofluid is greater than that of deionized water at the same supercooling degree.
The heterogeneous nucleation factor of nanofluid is less than that of deionized water at the same ultrasonic power.
Nucleation in levitated nanofluid drops includes both surface nucleation and volume nucleation.
ABSTRACT In this study, 0.03 wt.% graphene oxide nanofluid was prepared by adding graphene oxide nanosheets into deionized water, and nucleation experiments were conducted with levitated deionized water and graphene oxide nanofluid drops to study their supercooling degree distributions and nucleation mechanism. Results show that the supercooling degree of the nanofluid drop is significantly less than that of the deionized water drop, and that supercooling degree increases as ultrasonic power increases. The nucleation rates of the deionized water and nanofluid drops at two ultrasonic power levels was obtained according to the statistical nucleation theory, and heterogeneous nucleation factors and nucleation sites were calculated based on the classical nucleation theory. The nucleation rate of nanofluid is greater than that of deionized water at the same supercooling degree. The analysis of the heterogeneous nucleation factors revealed that levitated deionized water and nanofluid drops exhibit heterogeneous nucleation, and that heterogeneous nucleation factor decreases as ultrasonic power increases. The effects of ultrasonic power and nanoparticles on nucleation are coupled to each other. Comparing the nucleation site of drops at two power levels showed that the levitated deionized water drop exhibits surface-dominated nucleation and the levitated nanofluid drop exhibits both surface- and volume-dominated nucleation behaviors, which are affected by ultrasonic wave. Additionally, the surface nucleation site increases as ultrasonic power increases. Keywords: graphene oxide nanofluid, nucleation rate, nucleation site, volume nucleation, surface nucleation 1. Introduction Phase-change technology has always received research attention given the importance of phase-change materials (PCMs) in technology[1]. However, given that most PCMs exist under high supercooling degrees, liquid PCMs do not immediately solidify at freezing temperatures. Instead, PCMs will only crystallize at temperatures below the freezing temperature. Many scholars have studied various methods that decrease the degree of supercooling of PCMs such as adding nucleation catalyst and using ultrasonic technology. However, the effect of these methods is not ideal. The emergence of nanofluids provided an alternative. Nomenclature
C0
nucleation energy factor
Pn(t)
probability of observing no nucleation events
C’
sound speed in the air
KB
Boltzmann constant (J/K)
D
regional site of nucleation
S1
spherical drop surface site (mm2)
f
heterogeneous nucleation factor
S2
cylindrical drop surface site (mm2)
f0
angular frequency of incident sonic
Greek symbols
h
high of columnar drop (mm)
ΔH
phase change latent heat ( J/m )
J
nucleation rate (s−1)
ΔG*
heterogeneous nucleation critical energy (J)
Js
surface nucleation rate (s−1)
ΔT
supercooling degree (K)
Jv
volume nucleation rate (s−1)
conversion factor of transducer
kb
Boltzmann constant (J/K)
air density
Nu
Nusselt number
α0
air thermal diffusivity
Ntotal
total number of nucleated drops
ω
nucleation rate per drop (s−1)
Ny
number of non-nucleated drops
Subscript
P0
reference powers
1
20 W of ultrasonic power
Pe
sound pressure effective amplitude
2
32 W of ultrasonic power
3
Nanofluid is stable colloidal suspensions of mental or non-mental particle on a base fluid, which can enhance heat transfer of the solution and increase the storage capacity [2]. Many scholars have done a lot of research on the enhancement of heat transfer and supercooling degree of nanofluids. MM Sarafraz et al. [3] investigated the heat transfer coefficient of carbon nanotube water-based nanofluids inside the double pipe heat exchanger, and they found that presence of carbon nanotube can enhance the thermal conductivity up to 56% at wt.% = 0.3. They also investigated the fouling formation of CuO/water nanofluid inside a chevron type flat plate heat exchanger[4]. They used low frequency vibration to mitigate the fouling of nanoparticles and they found that thermal performance of the system is intensified. As for fouling formation of nanofluid in a gravity-assisted thermosyphon, they put forward a new fouling resistance model [5]. This model can predict the fouling resistance of nanofluid inside the thermosyphon with approximate deviation of 30%. Amirhossein Zamzamian et al[6] studied forced convective heat transfer coefficient of nanofluids of aluminum oxide and copper oxide with theory and experiment, and they evaluated the effects of particle concentration and operating temperature on the force convective heat transfer coefficient of the nanofluids. The results shows convective heat transfer coefficient of nanofluids enhances obviously and increases with increasing nanoparticles concentration and nanofluid temperature. MM Sarafraz et al.[7,8] studied nucleate pool boiling heat transfer of Al2O3 nanofluids and zirconium oxide nanofluids. They found nanoparticles improve the pool boiling heat transfer coefficient values and increased values of heat transfer are increased with increasing the concentration of nanoparticle. The pool boiling heat transfer coefficient of Al 2O3 and zirconium oxide nanofluids be enhanced to 25% and 12% incomparison with base liquid respectively. S. Harikrishnan et al. [9] added
50%CuO–50% TO2 hybrid nanoparticles into paraffin to prepare a new phase of solar-heating, energy-storage materials. Furthermore, they studied the thermal conductivity and phase transition properties of a PCM with mass fractions of 0.25%, 0.5%, 0.75%, and 1%, and found the melting and freezing time of mixed nano-phase change materials decreased by 27.7% and 29.8% respectively compared with paraffin. Deville et al.
[10]
studied the effect of the solidification
behavior of Al2O3/ distilled water nanofluid on supercooling degree. They reported that supercooling degree decreases as particle size decreases. Jia et al. [11] utilized X-ray photography and differential scanning calorimetry to study the effect of TiO2 nanoparticles with 0.2-3.4 micons on the supercooling degree of deionized water. They found that the supercooling degree of TiO2 nanofluids decreased by approximately 11.5% and supercooling degree is not much related to the concentration of nanofluids. The addition of surfactant can effectively reduce the supercooling degree. Zhao et al.
[12]
studied the supercooling and cold-energy storage characteristics of nanofluids and water-based nano-media in ball-packed porous structures by experimental methods. They found that its average and maximum supercooling degrees are lower than those of deionized water and nanofluid and nano-media can reduce the supercooling degree, shorten the cooling time and enhance heat transfer. Liu et al. [13,14,15] empirically studied the supercooling degree and nucleation sites of graphene oxide nanofluid. They found that graphene oxide nanoparticles are effective nucleating agents that dramatically reduce the supercooling degree of deionized water. Songping Mo [16] analyzed the combined effect of TiO 2 nanoparticles mass fraction, container wall roughness and wettability on the supercooling degree of nanofluid. They reported that the performance of the container wall mainly affected the supercooling degree and the supercooling degree of nanofluid at the same concentration in a glass container is higher than that in a plastic container. The container wall largely affects the nucleation of nanofluids, but acoustic suspension is a good way to avoid the effects of the container. Of course, ultrasound can also affect the nucleation of drops. M Saclier et al.[17] developed the modelling and simulation of ice nucleation triggered by acoustic cavitation. According to their study, the nucleation could be initiated with moderated acoustic pressure amplitude (around one bar) even at low supercooling levels (around few degrees). Although supercooling degree is an important feature of nanofluid crystallization nucleation, it is random and each measurement may attain different values. Therefore, only the study of supercooling degree can not fully understand the nucleation mechanism of nanofluids. The study of nucleation rate and nucleation sites is significant for revealing the mechanism of supercooling degree inhibited by nanoparticles. However, as nanofluid is a new colloidal solution, the theoretical calculation of nanofluid nucleation rate is imperfect. Therefore, limited research has been conducted on the nucleation rate and nucleation sites of nanofluids. Some researchers have calculated the nucleation rate of liquid water via the statistical probability method, which is based on nucleation statistical theory. Koop pointed out that drop nucleation is a random process and that nucleation rate follows Poisson distribution [18]. Koop then calculated the nucleation rate of H2SO4 and HNO3 aqueous solutions at different supercooling degrees. Kramer
[19]
measured the supercooling degree of thousands of suspended
droplets and analyzed the cooling process of those droplets. They calculated the homogeneous nucleation rate of water between 236–273 K, and nucleation energy and nucleation dimensions were determined by the classical nucleation theory. Seeley and Seidler
[20, 21]
encapsulated water drops with organic solvent to induce surface nucleation, thus obtaining
2D-nucelated water. They deduced the critical nucleation height and wetting angle by measuring nucleation rate. As the initial temperature of the drop increases, the supercooling degree of the drop increases; this behavior indicates that supercooling degree is determined only by the critical nucleation power. Heneghan et al.
[22]
used ALTA equipment to
measure the supercooling degree of hundreds of pure water drops and drops that contained AgI particle solution. The respective nucleation curves of the two liquids were obtained. They showed that the supercooling degree of AgI solution is significantly less than that of pure water and the limitation of classical nucleation theory is revealed. Kuhn [23] studied the volume and surface nucleation of water drops in a cryogenic laminar aerosol flow tube. Their results showed that the
contribution from nucleation at the drop surface increases with decreasing drop radius and dominates over nucleation in the bulk droplet volume for drops with radii smaller than approximately 5 µm. Yongjun Lv [24] studied the law that governs the supercooling degree distribution of a large volume of water under acoustic suspension. Yongjun Lv found that the maximum supercooling degree of suspended drops is 32 K. He then utilized statistical methods to elucidate the nucleation law of suspended water drops. He found that drop nucleation is heterogeneous and that nucleation occurs mainly on the drop surface.
Liu et al.
[25]
calculated the theoretical nucleation rates of deionized water and different
concentrations of graphene oxide nanofluid. They found that the nucleation rate of nanofluid is higher than that of deionized water at the same supercooling degree, and nanofluid nucleation occurs mainly on the surface of nanoparticles. As the classical nucleation theory is not perfect and the supercooling degree is random, the theoretical value is slightly different from the actual value. However, there are few studies on the nucleation rate of nanofluid drops under acoustic suspension, and there is no research on the nucleation sites of nanofluid drops. In the present study, graphene oxide nanofluid was prepared. Then, the supercooling degrees of the deionized water and nanofluid drops were measured via the single drop method. The nucleation rates of the drops were calculated using the statistical nucleation theory, and the nucleation sites of nanofluid drops was studied.
2. Experiments 2.1 Preparation and stability of graphene oxide nanofluid
The base fluid is deionized water. The suspension additive is graphene oxide. The experimental procedure is as follows: first, 30 mg graphene oxide nanosheets and 100 ml deionized water are measured with an electronic balance and a measuring cylinder, respectively, and then added to a small beaker. Next, the beaker is placed in a larger beaker with ice and water. The distance between the bottoms of the ultrasonic horn and large beaker is adjusted. Finally, the power of the ultrasonic oscillator is set at 300 W with 8-s pulse mode for 150 min. The ice–water mixtures in the large beaker are replaced every 30 min. The preparation of 30 mg/(100 ml) nanofluid is thus completed. The preparation of nanofluid is shown in Fig. 2.1. Fig2.2 is the STEM image of graphene oxide nanosheets. In this paper, only one concentration of graphene oxide nanofluids is prepared in order to exclude the effect of concentration on nucleation rate and nucleation site.
Suspension stability is an important factor in the practical application of nanofluids. The prepared graphene oxide nanofluid is stable, as indicated by the absence of aggregation and precipitation when left to sit for 30 days. P article size distribution and zeta potential were obtained by Laser Size and Zeta Potential Analyzer (Nano ZS90). Fig.2.3 shows the particle size and the zeta distribution of the graphene oxide nanofluid. The particle diameters are 37–74 nm and the average particle size is 52 nm. The zeta distribution of the nanofluid is distributed in 0–70 mV with an average potential of −38 mV. These results further indicate that the prepared nanofluid [26] is stable.
Fig.2.1 Schematic of the nanofluid preparation system 1. Ultrasonic transducer 2. Ultrasonic horn 3. Small beaker 4. Large beaker 5. Adjustable holder 6. Electric wire 7. Ultrasonic generator
Fig2.2 STEM image of graphene oxide nanosheets
Tatal Counts
300000
200000
100000
0 -200
-100
0
100
Zeta Potential (mV)
Fig2.3 Particle size and Zeta potential distribution of 0.03% graphene oxide nanofluid (150 min)
200
2.2 Deionized water and nanofluid drop suspension system
An experimental system for acoustic levitation was constructed in this study. The system comprises an acoustic levitator system, cooling system, and data acquisition system, as shown in Fig.2.4. The basic working principle of the system is as follows: first, a low-temperature environment is prepared using the cooling system. Then, a drop is suspended by the acoustic levitator. The temperature change of the drop is measured by copper-konjoc T thermocouple during the cooling process and is recorded by an agent. The precision of the thermocouple was ±0.2℃ and the average relative error was less than 3% when the temperature changing from -25℃ to 15℃. The thermocouple was calibrated by a high precision thermometer. The drop volume is determined by the pipette. The pipette was calibrated with a electronic balance, and the average relative error was less than 4% with a calibration range of 20µL to100µL.
Fig.2.4 Structure of the experimental system 1. Data acquisition module 2. Computer 3. Ultrasonic generator 4. Power cord 5. Ultrasonic horn 6. Emitter 7. Thermocouple 8. Reflector 9. Operation window 10. Height adjuster and transducer 12. Bracket 13. Levitated drop 14. Radiant cooler 15. Connecting pipe 16. Control box 17. Cooling medium 18. Cryostat circulator First, the cryostat circulator starts working. The ambient temperature of the cooling box is maintained at −21 °C. Then, 30-µL drops of deionized water and graphene oxide nanofluid are levitated at 20 W and 32 W of the acoustic levitator power. The phase transition supercooling is measured. The experiment is repeated 500 times at each power to obtain the supercooling distributions of the deionized water and graphene oxide nanofluid drops.
3. Experimental results and discussion 3.1 Supercooling degree of acoustically levitated deionized water and nanofluid drop
The supercooling degree of the deionized water and nanofluid drops at two power levels are statistically analyzed at the unit temperature interval. The temperature interval is [T−0.5, T+0.5]. The results are shown in Fig.3.1. In this figure, the coordinate ΔT is the supercooling degree of the drops and the ordinate is the number of experiments. As shown in the figure, the supercooling degree of the nanofluid drop at the same power is significantly lower than that of the
deionized water drop, thus indicating that nanoparticles effectively inhibit supercooling degree. The supercooling degree of one kind of fluid at 32 W is less than that at 20 W. Therefore, acoustic power affects supercooling degree, and the greater the power, the higher the supercooling degree. However, the effect of acoustic power on supercooling is considerably less than that of nanoparticles. The supercooling degree of different fluids at different powers is shown in Table 3.1.
20W deionized water 32W deionized water
140
20W nanofluid 32W nanofluid
Expriment number
120 100 80 60 40 20 0 2
4
6
8
10
12
14
16
ΔT/K Fig.3.1 Distribution of the supercooling degree of deionized water and nanofluid drops
Table 3.1 Supercooling degree of two fluids Minimum Power
Fluid
Maximum
Average
Supercooling
supercooling
supercooling degree
supercooling
degree range
degree (K)
(K)
degree (K)
(K)
deionized water
3.7
16.4
11.54
11–14
nanofluid
2.7
13.4
8.28
6–10
deionized water
2.8
15.2
10.27
9–13
nanofluid
2.1
11.2
7.16
5–9
20 W
32 W
According to Fig.3.1, the probability of observing no nucleation event at a fixed temperature T within the time t is calculated by freezing 500 sets of deionized water and nanofluid drops. As shown in Fig.3.2, Ny represents the number of non-nucleated drops at a certain supercooling degree and Ntotal represents the total number of nucleated drops within the total measured time. The nucleation rates of the unit supercooling degree of the deionized water and nanofluid drops are calculated later in the unit temperature interval. Although the supercooling degree of nanofluid at the acoustic power of 20 W and that of deionized water at the acoustic power of 32 W are both −3 °C, the supercooling degree of nanofluid is
mainly distributed in the 6°C –10 °C, and that of deionized water is mainly distributed in the 9°C –13 °C. A small number of deionized water drops have a low supercooling degree, but the vast majority of deionized water drops have a higher supercooling degree. Therefore, the crystallization of deionized water is random but its supercooling degree is within a certain range. The crystallization of graphene oxide nanofluid drops is also random.
1.0
20W deionized water 32W deionized water 20W nanofluid 32W nanofluid
Ny/Ntotal
0.8 0.6 0.4 0.2 0.0 2
4
6
8
10
12
14
16
18
20
ΔT/K Fig.3.2 Relationship between non-nucleation probability and supercooling degree The average freezing curves of the deionized water and nanofluid drops are obtained, then the relationship between supercooling degree and time is established, as shown in Fig.3.3. Bigg [27] found that freezing rate affects the supercooling degree of drops. In the present experiment, the difference in freezing rates is contributed by nanoparticles and ultrasound. Fig.3.3 indicates that the freezing curves of the two fluids at different ultrasonic powers follow the same trend, but the freezing rate of the graphene oxide nanofluid is slightly higher. Given that the volume of drops in the experiment is 30 µL, the surface site of the levitated deionized water and nanofluid drops negligibly changes. So the freezing curves of the two fluid drops are the same in a short time. However, enlarging Part A in Fig.3.3 reveals that the freezing rate of the nanofluid is significantly higher than that of the deionized water, and that the freezing rate at the ultrasonic power of 32 W is greater than that at 20 W. The large cooling rate of drops indicates good heat transfer performance. Some scholars [28] have reported that adding nanoparticles to water effectively enhances the heat transfer of the liquid. The average freezing curve in the experiment also shows that the heat transfer coefficient of the nanofluid is greater than that of the deionized water. As shown in the enlarged view of Part B, the temperature of the deionized water drop at the ultrasonic power of 32 W is lower than that at the 20 W, which also indicates that the strength of the ultrasonic waves affects the freezing rate of the deionized water drop. Yairn[29] proposed the relationship between the sound pressure and Nusselt number Nu near the surface of spherical drop under ultrasonic suspended: (3.1)
Where the sound pressure effective amplitude Pe is determined by the sound pressure definition:
.
is air thermal diffusivity,
f0 is angular frequency of incident sonic,
relationship between Pe and power P is
is air density,
, where
is sound speed in the air. The
is reference powers, and
is conversion
factor of transducer.So the relationship between Nu and P is: (3.2) It can be seen from the above formula that Nu is related to P and Nu , and the decreasing P and the increasing
. The increasing P and the decreasing
will reduce Nu. In the experiment,
will increase
of the acoustic suspension device
is constant, so Nu is only related to power P. The convective heat transfer coefficient between drop and air increase with increasing power, and the cooling rate of drop also increases, as shown in Fig3.3. -8 -9 20W deionized water 32W deionized water
4
20W nanofluid 32W nanofluid
T/℃
-10
6
2
-12
0
-13 -14 25 30 35 40 45 50 55 60 65
-2
T/℃
-11
-4 -6
t/s
-14.0
-8
T/℃
-10 -12 -14
-15.0
a
-16 -18 -20
b 0
20
40
-14.5
60
-15.5 93
80 100 120 140 160 180
96
99 102 105 108 111 114 117
t/s
t/s Fig.3.3 Cooling curves of deionized water and nanofluid
3.2 Nucleation rates and heterogeneous nucleation factors of deionized water and graphene oxide nanofluid drops
According to the statistical nucleation theory proposed by Koop et al. [18], the probability of observing a non-nucleation event at a fixed temperature T and time t is described by
Pnt e T t , where
is the nucleation rate
per drop. According to the relation between the supercooling degree and the time established by the average freezing curve of deionized water and nanofluid fluid, the nucleation rate for a given volume can be expressed as:
T
ln N y T Nt o t
t a l
(3.3)
Using Eq. 3.3, the unfrozen probability in Fig.3.2 and the freezing curve in Fig.3.3 can be transformed into the nucleation rates of deionized water and nanofluid drops. According to the classical nucleation theory [30], the nucleation rate is given by:
T A exp
B T 2 273.15 T
where A and B are temperature-independent parameters [24] and are written in detail as:
(3.4)
A C0 D B f
(3.5)
3 16 iw Tm2
(3.6)
3H v k b 2
where C0 is the nucleation energy factor, which is the ability of water molecules to transition to the surface of the crystal embryo; D is the regional size of nucleation; f is the heterogeneous nucleation factor;
iw is
the interface energy
between ice and water; Tm is the phase transition temperature; H v is the phase change latent heat; and kb is the Boltzmann constant. Table 3.2 shows the relevant physical properties.
Table 3.2 Physical properties
iw （J/m2）
H v （J/m3）
kb（J/K）
0.02343
3.06634 × 108
1.38 × 10−23
The nucleation rate curve with supercooling degree is obtained based on Eq. 3.3 and 3.4. Fig.3.4 and Fig.3.5 represent the nucleation rate curves of deionized water and nanofluid, respectively. In these figures, the scattered points indicate the experimental values and the solid line represents the nucleation rate curve as a function of supercooling degree.
0.09 20W deionized water 32W deionized water 32W deionized water 20W deionized water Data in Ref.24 Data in Ref.24
0.08 0.07 0.06
ω/s-1
0.05 0.04 0.03
Model
zuichu (User)
Equation
y = A*exp(-B/(x^2*(273.15-x
0.02
Reduced Chi-Sqr
1.06943 E-5
0.01
Adj. R-Squ
0.98416 Value
0.00
B
-0.01 2
4
6
8
10
12
14
16
ΔT/K
Fig.3.4 Nucleation rate of deionized water drop According to the fitting results, when the ultrasonic power is 20 W, A1 is 0.2415 and B1 is 92306.56. When the ultrasonic power is 32 W, A1 is 0.3332 and B1 is 74487.28. The subscripts 1 and 2 represent 20 and 32 W, respectively. The nucleation rates of deionized water are expressed as:
A
0.33317
B
74487.28
92306.56 J1 T 0.2415 exp T 2 273.15 T
74487.28 J 2 T 0.3332 exp T 2 273.15 T
(3.7)
(3.8)
The fitting curve presents the nucleation rate of 30 µL deionized water, not unit volume, as with the case of nanofluid. Given that C0 is dependent only on physical properties and does not change with acoustic pressure, then according to Eq. 3.5, A2/A1 = D2/D1 = 1.38. This indicates that the nucleation area of the deionized water drop at 32 W is 1.38 times that at 20 W. The heterogeneous nucleation factors of deionized water at two power levels were calculated using the physical parameters in Table 3.1 and Eq.3.6. The values of f1 and f2 are 0.0074 and 0.0060, respectively, which indicate that levitated deionized water drops exhibit a heterogeneous nucleation process and that the ultrasonic wave promotes rapid nucleation. According to the classical nucleation theory, the heterogeneous nucleation critical work [31] is expressed as:
G f
3 16 iw Tm2 1 2 3H v T 2
(3.9)
In addition to the heterogeneous nucleation factor, the rest of the parameters are the constants in Eq.3.9. Thus, critical nucleation work is only determined by the heterogeneous nucleation factor f:
G2 G1 f 2 f1 0.81
(3.10)
The critical nucleation work of deionized water at 32 W is only 81% of that at 20 W, which indicates that nucleation work decreases as ultrasonic power increases. The nucleation rate in this paper compares with Lv Yongjuns’ results[24]. As shown in Fig 3.4, the difference between the two results in an order of magnitude, indicating that the experimental results are correct. The main reason for the difference is that the ultrasonic pressure amplitude, the cooling rate and the location of temperature measurement are different in the two papers. 0.14 20W 32W 32W 20W
0.12 0.10
nanofluid nanofluid nanofluid nanofluid
ω/s-1
0.08 0.06 0.04 0.02 0.00 2
4
6
8
10
12
ΔT/K Fig3.5 Nucleation rate of graphene oxide nanofluid drop According to the fitting results, when the ultrasonic power is 20 W, A1 is 0.3276 and B1 is 41785.93. When the
ultrasonic power is 32 W, A1 is 0.3628 and B1 is 28968.33. The nucleation rates of the nanofluid are expressed as:
41785.93 J1 T 0.3276 exp T 2 273 .15 T
(3.11)
28968.33 J 2 T 0.3628 exp T 2 273 .15 T
(3.12)
According to Eq. 3.5, A2/A1 = D2/D1 = 1.11, indicating that the nucleation site of the nanofluid drop at 32 W is 1.11 times that at 20 W. The values of f 1 and f2 of the nanofluid are 0.0034 and 0.0023, respectively, indicating that nucleation process is heterogeneous. Based on Eq. 3.9, the critical nucleation work of the nanofluid drop at 32 W is 68% at 20 W. By comparing the fitting parameters, it can be concluded that: 1. The nucleation rate of the nanofluid is considerably larger than that of the deionized water at the same supercooling degree. Furthermore, the greater the ultrasonic power, the greater the nucleation rate; 2. The nucleation sites of deionized water and nanofluid at 32 W are greater than those at 20 W, indicating that increasing ultrasonic power increases nucleation sites. However, nucleation site, which depends on the number of critical crystal nuclei in the drop, does not directly determine supercooling degree. The ratio of the nucleation site of the deionized water is larger than that of the nanofluid; this indicates that the ultrasonic power has a greater effect on the nucleation site of deionized water; 3. Compared with the heterogeneous nucleation factors of deionized water and graphene oxide nanofluid, the greater the ultrasonic power, the smaller the heterogeneous nucleation factor. And the heterogeneous nucleation factors of nanofluid are less than those of deionized water at two levels of ultrasonic power, indicating the effects of ultrasonic and nanoparticles on nucleation can be superimposed; 4. The critical nucleation work of deionized water and nanofluid at 32 W is 0.80 times and 0.68 times, respectively, that at 20 W. The effect of ultrasonic wave on nanofluid nucleation work is greater than that on deionized water nucleation. The nucleation rate obtained by the experiment is different from the nucleation rate calculated by theory in the previous paper[25]. Caused by the following reasons: 1.In the previous paper, the nucleation rate of nanofluid is calculated by the classical nucleation theory, and the cooling rate is not taken into account. Bigg E K[27] found that the cooling rate affects supercooling degree of liquid, and the greater cooling rate, the greater supercooling degree. In this paper, the nucleation rate of nanofluid is obtained by statistical nucleation theory, and the cooling rate is considered. 2.There are tiny bubbles inside the levitation drop, and the surface of the drop under the acoustic suspension can undergo ultrasonic cavitation. When ultrasonic cavitation [32] on the drop occurs, the pressure of bubble in the compression phase can reach hundreds of atmospheric pressure, and it can reach more than 5GP a in crack finally, accompanied by sonogenic phenomenon. The freezing point of the water will change at high pressure, and the solidification temperature increases with increasing pressure, so that the drops are more likely to have large supercooling degree[33]. 3.In the ultrasonic field, the drops rotate around the z-axis and the surface vibrates. The internal flow and shock of the drops increase the collision of the internal crystal embryos and particles, and it is easy to form larger crystal embryos and particles. So the nucleation rate increases. These three reasons cause the difference between the theoretical and experimental values.
3.3 Volume nucleation and surface nucleation of two levitated fluids
The nucleation rate of a drop that contains a free-liquid surface should include both surface and volume nucleation rates. Specifically, J T J v T V J s T S , where Jv is the volume nucleation rate and Js is the surface nucleation rate [34] . The nucleation of deionized water and nanofluid drops may occur only within the drop (volume nucleation) or only on the surface (surface nucleation), or both of them. According to Eq. 3.5, parameter A is related to the nucleation dynamics factor C0 and the nucleation site size D. C0 does not vary with ultrasonic wave. On the other hand, given that the volume of the drop in the experiment is maintained at 30 µL and the evaporation of the liquid during freezing is negligible, the volume of the drop is approximately constant before nucleation. Fig.3.6 and Fig.3.7 show the geometric dimensions of deionized water and nanofluid drops at both powers.
Fig.3.6 Geometric dimension of deionized water drop at different power levels
Fig.3.7 Geometric dimension of nanofluid drop at different power levels
If the nucleation of the levitated drop is volume-dominated, then, according to the classical nucleation theory, the nucleation site inside the drop should remain constant at different power levels. According to the experimental data, the ratio of the nucleation site of the deionized water drop at two power levels is A2/A1 = D2 /D1 = 1.38. Thus, the nucleation sites increased by a factor of 1.38. This result is clearly inconsistent with the classical nucleation theory and indicates that
the nucleation of the deionized water drop is not volume-dominated. The ratios of the nucleation site of the graphene oxide nanofluid drop at two power levels are A2/A1 = D2/D1 = 1.11. Although the ratio of the nanofluid is smaller than that of deionized water, it is also inconsistent with the classical nucleation theory. Therefore, the nucleation of the nanofluid drop is also not volume-dominated. If the nucleation of the levitated drop is surface-dominated, then volume nucleation is negligible and the nucleation sites on the drop surface remains constant. As shown in Fig.3.7 and Fig.3.6, when the ultrasonic power is 20 W, the shape of the drop is spherical. When the ultrasonic power is 32 W, the shape of the drop is cylindrical. The size of levitated drops can be calculated proportionally by experimentally measuring the distance between the emitter and the reflector. The superficial sites of the drop at two power levels are calculated in terms of spherical and cylindrical shapes. The surface site ratios of the drops at different power levels are expressed as:
S2 d 2 h 2 d 2 2 2 S1 4 d1 2 2
(3.13)
According to the sizes of the deionized water and nanofluid drops, the surface site ratio of the deionized water drop is 1.30 and that of the nanofluid drop is 1.28. In the light of the surface nucleation hypothesis, when the nucleation of the deionized water drop is surface-dominated, the nucleation site ratio of the deionized water drop at two power levels is 1.30. Based on the experimental results, the nucleation site ratio of the deionized water drop is 1.38. These two values differ by only 6%, indicating that nucleation occurs mainly on the drop surface. The conclusion is the same as that of Ref.24.There are two main reasons, one is that the ultrasonic cavitation on the surface of the drop promotes the nucleation of the drop surface; the other is the drop surface temperature is lower than the dropt internal temperature, so the critical nucleation energy of the drop surface is less than that of the drop internal[33].
Fig.3.8 Measurement of the surface and internal temperature of the nanofluid drop
4 surface temperature internal temperature
2
T/K
0 -2 -4 -6 -8 -10 0
10
20
30
40
t/s Fig.3.9 Surface temperature and internal temperature of the nanofluid drop The theoretical nucleation area ratio of the nanofluid drop at two power levels is 1.28. However, the experimentally calculated nucleation site ratio of the nanofluid is 1.11. The difference between these two values is relatively large, which indicates that nanofluid nucleation is not surface-dominated but is dominated by both volume and surface nucleation. A previous article[25] indicate that nanofluids nucleation occurs mainly on the surface of nanoparticles. But ultrasonic waves cause drop rotation[35], and some nanoparticles are closer on the surface. This part of nanoparticles-induced heterogeneous nucleation can directly contribute to the drop surface nucleation, and the other part is volume nucleation. As the drop volume and the nanoparticle concentration is the same, so the nucleation site of nanoparticles surface in the drop is the same. The nucleation site of nanofluid drop at 32W is larger than that at 20W, indicating that increased ultrasonic power increases the drop surface nucleation site. The higher the ultrasonic power, the higher the perturbation of the ultrasonic wave on the nanofluid drop, the more particles in the drop near the surface, and the larger the drop surface nucleation site. The internal and near-surface temperatures of the levitated nanofluid drop were measured with thermocouple at an ultrasonic power of 20 W, as shown in Fig.3.8. Fig.3.9 shows that the difference between the near-surface and internal temperatures changes with time. It can be seen that the surface temperature of the nanofluid drops is lower than the internal temperature of drops and the maximum temperature difference is 1.2 °C. Nucleation is more likely to occur on nanoparticles near the drop surface, which induces drop surface nucleation. Fig3.9 shows that the surface temperature and the internal temperature of nanofluid drop suddenly become 0℃from supercooled state at the same time, indicating that nanofluid drop nucleate is both surface nucleation and volume nucleation. When the surface temperatures of the nanofluid drop become 0℃, the drop is removed. It is found that the whole nanofluid drop is frozen, but the deionized water drop is both ice and water. 4. Conclusion (1) At 20 W of ultrasonic power, the average supercooling degree of deionized water is 11.54 K and that of nanofluid
is 8.28 K. At 32 W of ultrasonic power, the average supercooling degree of deionized water is 10.27 K and that of nanofluid is 7.16 K. The supercooling degree of nanofluid drops is significantly less than that of deionized water. The higher the ultrasonic power, the lower the supercooling degree. The freezing rate of nanofluid is slightly higher than that of deionized water, and the higher the ultrasonic power, the faster the freezing rate. (2) The experimentally calculated nucleation rate of nanofluid is considerably higher than that of deionized water at the same supercooling degree. Moreover, the nucleation rates at 32 W are greater than those at 20 W. Levitated nanofluid and deionized water drops exhibit heterogeneous nucleation. The heterogeneous nucleation factors of nanofluid are lower than those of deionized water. The higher the ultrasonic power, the lower the heterogeneous nucleation factor. The nucleation sitess of the two fluid drops at 32 W are larger than those at 20 W, and the nucleation sites of deionized water at the two power levels are larger than those of nanofluid. (3) Comparing the nucleation sites of deionized water and nanofluid drops at two different power levels revealed that the nucleation of the levitated deionized water drops is mainly surface-dominated, whereas that of the levitated nanofluid drops is both surface-dominated and volume-dominated. Ultrasonic cavitation and lower surface temperature promote the surface nucleation of deionized water drop. The graphene oxide particles induce the drop volume nucleation, and the nanoparticles also induce the surface nucleation of the drop due to the internal flow of the drop. Acknowledgments The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 51276204).
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List of figures: Fig.2.1 Schematic of the nanofluid preparation system Fig2.2 STEM image of graphene oxide nanosheets Fig2.3 Particle size and Zeta potential distribution of 0.03% graphene oxide nanofluid (150 min) Fig.2.4 Structure of the experimental system Fig.3.1 Distribution of the supercooling degree of deionized water and nanofluid drops Fig.3.2 Relationship between non-nucleation probability and supercooling degree Fig.3.3 Cooling curves of deionized water and nanofluid Fig.3.4 Nucleation rate of deionized water drop Fig3.5 Nucleation rate of graphene oxide nanofluid drop Fig.3.6 Geometric dimension of deionized water drop at different power levels Fig.3.7 Geometric dimension of nanofluid drop at different power levels Fig.3.8 Measurement of the surface and internal temperature of the nanofluid drop Fig.3.9 Surface temperature and internal temperature of the nanofluid drop List of tables:
Table 3.1 Supercooling degree of two fluids Table 3.2 Physical properties
Highlights The supercooling degree of nanofluid is significantly lower than that of deionized water. The nucleation rate of nanofluid is greater than that of deionized water at the same supercooling degree. The heterogeneous nucleation factor of nanofluid is less than that of deionized water at the same ultrasonic power. Nucleation in levitated nanofluid drops includes both surface nucleation and volume nucleation .