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Effect of contact angle on water droplet freezing process on a cold flat surface
Experimental Thermal and Fluid Science 40 (2012) 74–80
Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Effect of contact angle on water droplet freezing process on a cold flat surface Lingyan Huang a,b, Zhongliang Liu a,⇑, Yaomin Liu a, Yujun Gou a,b, Li Wang c a Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Ministry of Education, College of Environmental and Energy Engineering, Beijing University of Technology, Beijing 100124, PR China b Beijing Institute of Space Launch Technology, Beijing 100076, PR China c Tangshan University, Tangshan 063000, PR China
a r t i c l e
i n f o
Article history: Received 1 December 2010 Received in revised form 4 February 2012 Accepted 7 February 2012 Available online 16 February 2012 Keywords: Contact angle Water droplet Hydrophobic surface Crystal growth
a b s t r a c t The effect of contact angle on water droplet freezing process on a cold flat surface under natural convection conditions was experimentally investigated. A series of hydrophobic surfaces with different contact angles were prepared by solution immersion. The contact angles of these surfaces were varied from 97.2° to 154.9°. Comparative observations of water droplet freezing processes were carried out on both plain copper surface and these hydrophobic surfaces under the same conditions. The experimental results showed that the contact angle has a strong influence on the water droplet freezing time. The larger the contact angle is, the longer the freezing time. The frost crystals growth on the droplet surface that frozen on the hydrophobic surface is faster and presents a pattern that is more dendritic than that on the plain copper surface. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Frost formation on solid surface is commonly observed in cryogenic, refrigeration, air conditioning, and aerospace industries. It is a complicated transient process with simultaneous heat and mass transfer. Based on their experimental observations, Hayashi et al. [1] identified the frost formation process in three periods: the crystal growth, the frost layer growth, and the frost layer full growth period. The time of each period and the shape of frost crystals were found to strongly depend on the cold surface temperature and the vapor concentration difference between the mean stream and the cooling surface. Wu et al. [2] observed that the transition from water vapor to frost follows five independent stages: droplet condensation, droplet growth with coalescence of supercooled droplets, droplet freezing, formation of frost crystals on the frozen droplets, and crystal growth with simultaneous collapsing. The continuous and uncontrolled frost layer growth on heat transfer surfaces will adversely affect the performance of the refrigeration system due to the additional pressure drop and thermal resistance. Thus, numerous researchers have focused themselves on the investigation of frost formation mechanism and try to establish an effective defrosting method. The factors that influence the frost formation such as the ambient conditions, cold surface temperature and surface characteristics have been discussed repeatedly [3–5]. Lee et al. [6] and Liu et al. [7] have investigated the effect ⇑ Corresponding author. Tel.: +86 10 67391917; fax: +86 10 67391983. E-mail address: [email protected] (Z. Liu). 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2012.02.002
of surface energy on frost formation under free convection. They found that surface hydrophilicity is one of the more advanced and attractive methods to reduce frost formation on cold surfaces. Recently, enlightened by the super-hydrophobic characteristics of lotus leaf, some studies have been performed to investigate the anti-frosting performance of the hydrophobic surface with water contact angle higher than 150°. Wang et al. [8] fabricated a kind of super-hydrophobic coating with water contact angle of 155° by modifying CaCO3 and polyacrylate. Their experimental results showed that the frost formation on the super-hydrophobic surface was greatly retarded compared with that on the bare copper surface. The surface kept super hydrophobicity even after 10 freezing-thawing cycles. He et al. [9] observed the frost formation process on the hydrophobic and super-hydrophobic isotactic polypropylene (i-PP) films. Due to the micro-and-nanometer structures, the wettability of the super-hydrophobic film oscillates during the frost formation, this leads to the delay of the solidification of liquid water at the three-phase line (TPL) region. Liu et al. [10] studied the frost deposition on the cold super-hydrophobic surface with water contact angle of 162°. The frost deposition on the super-hydrophobic surface was delayed for 55 min compared with the plain copper surface under natural conditions. Furthermore, the frost structure on the superhydrophobic surface was looser, thin and shows a cluster of chrysanthemum-like pattern. The above research results have disclosed that the super-hydrophobic surface can retard the initial frost crystal formation; the contact angle of the solid surface has a direct effect on the water droplets condensation and thus frost deposition process. However,
L. Huang et al. / Experimental Thermal and Fluid Science 40 (2012) 74–80
75
Nomenclature T1 Tw
air temperature (°C) cold plate temperature (°C)
d h
frost crystal thickness (mm) contact angle (°)
Greek symbols u air relative humidity (%)
most research works reported in literature are on the frost layer growth and the frost layer full growth period, they studied influences of ambient conditions and cold surface temperature on frost growth. Few works have been completed on the water droplet freezing process on the cold surface. It has often been neglected since the freezing process is very fast. However, this period, i.e. the frost crystal nucleation period, is not only the starting point of the frost deposition process which should be fully understood as the initial condition for numerical simulation, but also relates to significant theoretical problems of nucleation and phase transition theory. Wang et al. [11] investigated the freezing processes of water droplet and peanut oil droplet on a cold surface. They found that only the base surface or the contact surface with the solid surface of the water droplet kept its initial shape and size, all the other part of the droplet showed an obvious growth along the direction normal to the base surface. They also observed a small sharppointed protrusion appeared on the top of the water droplet at the end of the freezing process. The cold surface they used is plain copper, and as far as we know there are no reports on the effects of different contact angles on the water droplet freezing process. In this paper, the influences of contact angle in a wide range on a single water droplet freezing process were studied experimentally. A set of copper surfaces with different contact angles were fabricated by means of a simple method suggested by Hou et al. [12]. Comparative observations of droplet freezing process were carried out on both plain copper surface and hydrophobic surfaces under the same conditions. Meanwhile the freezing time and crystals growth velocity on different surfaces are recorded and compared.
2. Experiments 2.1. Experimental apparatus Fig. 1 illustrates the experimental apparatus. The experimental setup mainly consists of a cooling system, microscopic image system, data acquisition system, a digital camera, optical fiber luminescence, air-conditioning system and humidity controller. The cooling system is basically a thermoelectric cooler that can provide cooling to maintain the cold plate temperature from 26 °C to 0 °C with a relative uncertainty of ±0.1 °C. The surface temperature of the cold plate is measured by four T-type thermocouples that are buried beneath the test surface through four holes of 1 mm in diameter and 13 mm in depth drilled into the plate. The temperature data is recorded by a HP data acquisition system and finally transferred to a personal computer for further analysis. The cold surface temperature is the average of the temperature readings of the four thermocouples. The thermocouples are all pre-calibrated and the maximum uncertainty of the surface temperature is estimated to be less than 0.5 °C, including those resulted from the location errors. The microscopic image system consists of a CCD camera, a microscope and a capture card. The system is used for the micro and transient observations of the frost deposition process. The CCD camera and microscope with a maximum magnification of 135 times are mounted parallel to the cooled surface to
take photographs and observe the droplet freezing process with the help of an optical fiber luminescence. A personal computer, equipped with image acquisition and processing software, receives the images taken by the microscopic image system, and then the height of droplet and crystal can be measured with an accuracy of ±0.001 mm. The test surfaces and the thermoelectric cooler are placed in a large Plexiglas enclosure with a dimension of 400 mm 400 mm 500 mm to maintain the constant natural convection condition during the test. The temperature and the humidity inside the enclosure are regulated at the given value by an air-conditioning system and a humidity controller. For all experiments in this paper, the air temperature (T1) inside the enclosure was maintained at 19.0 °C with an accuracy of ±0.1 °C, the relative humidity (u) was 45% with an accuracy of ±1%, respectively. An uncertainty analysis has been carried out and the results are summarized in Table 1.
2.2. Preparation of the surface with different contact angles The fabrication of super-hydrophobic surface is composed of two steps: creating the desired roughness on the metal surface and modifying the as-prepared rough surface with fluoroalkylsilane coating. Firstly, the copper foils (20 mm 10 mm 0.2 mm) which have been cleaned in HCl aqueous solution for 10 min and ultrasonically rinsed in de-ionized water, were immersed into a sealed vessel (total volume: 80 ml) containing an aqueous solution of 1.0 mol/l NaOH and 0.05 mol/lK2S2O8 at 60 °C. After 10–60 min, the copper foils were taken out from the solution and rinsed with distilled water, and then they were put into an oven and kept at 160 °C for 1 h. Thus, a dark film that covered uniformly on the copper foil was obtained. Secondly, the copper foils were modified by immersing into a pre-hydrolyzed ethanol–fluoroalkylsilane solution at room temperature for 1 h, followed by drying in the oven at 120 °C for another 1 h. Finally, the copper foil surfaces became super-hydrophobic by means of chemical etching and fluorination modification. The water contact angles of the surfaces were measured with the contact angle system (DCA, DSA100, KRUSS, Germany) at room temperature. The droplet volume was set using a burette with a 10 ll scale division; the average contact angle value was obtained by measuring five different positions of the same sample. The overall uncertainty for measured contact angle was ±5°. Fig. 2 shows copper surfaces with different contact angles. The plain copper surface has a contact angle of 76° as shown in Fig. 2a. The controlling factor that determines the value of the contact angle is the chemical etching time. The contact angles of 97.2°, 108.8° and 123.9° of the treated copper surfaces are obtained as the chemical etching time were set at 10 min, 20 min and 30 min respectively. After etching for 30 min and 60 min and modifying with the fluoroalkylsilane coating, the contact angles of the surfaces increase to 140.5° and 154.9°. Fig. 3 shows SEM images of the plain copper surfaces and surfaces treated with different time. The results showed that as the reaction time increased from 10 min to 30 min, thicker and longer CuO ribbons formed on the substrate, and the contact angles increased at the same time. However, when the reaction
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L. Huang et al. / Experimental Thermal and Fluid Science 40 (2012) 74–80
9
52
1 8
40
7
13 70
11
10 4 5
40
12
2
26
13 3
Unit:mm Thermocouples locations
6
cooling water source; 2. power source for thermoelectric cooler; 3. thermoelectric cooler; 4. cold plate; 5. T-type thermocouples; 6. HP data acquisition system; 7. microscope; 8. camera lens; 9. CCD; 10. computer; 11. power supply cable; 12. water inlet; 13. water outlet Fig. 1. Experimental system and apparatus.
Table 1 Uncertainty analysis for measured variables. Variable
Typical value
Uncertainty
Relative uncertainty (%)
Tw T1
26 to 0 °C 19.0 °C 45% 0–5.0 mm 0–180°
0.1 °C 0.1 °C 1% 0.001 mm 0.1°
3.8 – – 0.02 0.05
u d h
time increased from 30 min to 60 min, there was no significant change on the microstructure and the contact angles did not increase more. Hence one can infer that 30 min is an optimal reaction time under the present conditions. The water droplets show different shapes on these surfaces. The larger the contact angle is, the more spherical the water droplet presents on the surface. The water droplet presents a nearly perfect spherical shape on the super-hydrophobic surface, as shown in Fig. 2f. A stable cold plate surface temperature is needed to start an experiment. Therefore the cooling water system was turned on firstly to reduce the cold surface temperature and maintain at 12 °C. A 6 ll micro-syringe was used to place a droplet of distilled water on the testing cold surface. The microscope focus and image recording system were adjusted to work properly for observing the water droplet. After that the thermoelectric cooler was turned on and thus a gradual cooling process of the test surface was started
(time zero). During the test, the water droplet freezing process and crystal growth on its surface at different time were observed and recorded by the microscopic image system, the magnification was set 10. The cold plate temperature was set to be 8.5 °C which controlled by the power source. 3. Experimental results and discussion In our previous work [10], droplets freezing process on two different surfaces with contact angle of 72° (plain copper surface) and 162° (super-hydrophobic surface) were observed. It was found that the frost crystal growth on the frozen droplets that were dripped onto the super-hydrophobic surface and the copper surface shows a significant different pattern. The frost crystals grow on much larger portion of the frozen water droplet surface on the super-hydrophobic surface than that on the plain copper surface. And the frost crystal growth on the super-hydrophobic surface presents of much more dendritic growth. In this paper, close observations were made of the water droplet freezing process on a set of copper surfaces with contact angles varying from 97.2° to 154.9°. The freezing time and crystals growth velocity on the frozen droplet surface were also compared. The images of the droplet freezing process on five different samples were recorded per 5 min. Fig. 4 shows a group of typical pictures of droplet freezing process on the plain copper surface (h = 76.0°), hydrophobic surface (h = 123.9°) and super-hydrophobic
L. Huang et al. / Experimental Thermal and Fluid Science 40 (2012) 74–80
(a) CA=76.0° (Plain copper surface)
(b) CA=97.2°
(c) CA=108.8°
(d) CA=123.9°
(e) CA=140.5°
(f) CA=154.9°
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Fig. 2. Copper surfaces with different contact angles.
surface (h = 154.9°). It was found that the droplet presents different shape on different surfaces before the experiment starts. The water droplet spreading on the plain copper surface is of spherical crown shape due to the small contact angle and good wettability of the surface, while the water droplet presents hemispherical and nearly perfect spherical shape on the hydrophobic and super-hydrophobic surfaces, respectively. Some typical Parameters of the water droplet on different surface are showed in Table 2. The water droplet height is 1.23 mm, 1.73 mm and 2.08 mm, respectively on these three different surfaces measured by the image processing software, the contact area on the cold surface is 7.74 mm2, 2.66 mm2 and 0.67 mm2, respectively. The water droplets are transparent before freezing takes place. As the cold surface temperature was reduced from 12 °C to 8.5 °C, the droplets lose their transparency gradually and remain supercooled for a period of time. After the test started about 196 s, 310 s and 458 s respectively, the water droplets begin to freeze on these three different surfaces. The freezing of the water droplets starts from the bottom surface of the droplet that contacts with the cold surface, and propagates upwards and finally reaches to the top of the droplet. The whole processes last 10 s, 16 s and 27 s on the three different surfaces respectively. At the end of the freezing process the droplet becomes fully opaque and a small sharp-pointed protrusion appears on the top of the droplet. It is postulated that the effects of surface tension and volume dilatation
resulted from liquid-to-solid phase change caused the shape change and protrusions formation [11]. The water density decreases during freezing process, and the conservation of mass requires that its volume expands. This may at least partially explain the appearance of the protrusion of water droplet freezing. The numerical modeling results by Wang et al. [11] supported this postulation. Another possible reason is resulted from Hindmarsh’s experimental observation [13]. They videoed the freezing process of a suspended water droplet in the cold air stream, and observed many gas bubbles during the freezing process and a bulge appears at the top of the droplet after it completely frozen. Therefore, it may be well presumed that the droplet generally nucleated from the outward surface and formed a solid shell around the droplet. The bulging observed at the surface was due to the shell being pushed out by a pressure build up inside the droplet from the formation of gas bubbles and the density change of water to ice. The exterior surface of the droplet is very smooth except for a protrusion on the top after it freezes into ice solid. It is observed that columnar frost crystals appear at the protrusion first and some smaller frost crystals form around these columnar frost crystals subsequently. This phenomenon may be attributed to the small surface energy of the protrusion, it acts just like a mini particle with small nucleation potential barrier, and therefore the nucleation and condensation of air vapor may occur at the protrusion
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(a) Plain copper surface
(b) Etching for 10 min
(c) Etching for 20 min
(d) Etching for 30 min
Fig. 3. SEM images of different surfaces.
of the frozen droplet surface easier. During this period, droplet freezing and the frost crystals appearance on the three surfaces are very similar. However, after 20 min the phenomena happening on the three frozen droplet surfaces are quite different. On the plain copper surface the frost crystals grow mainly on the top of the ice droplet and along the vertical direction, the frost crystals are short and thick. On the hydrophobic and super-hydrophobic surfaces the frost crystals grow on almost every position of the droplet surface, they flourish on the frozen droplets surface and are thinner and more slender than that of the plain copper surface. At about 60 min some of frost crystals on the upper position of the droplet thaw and fall down onto the crystals of the lower part of the droplet on the super-hydrophobic surface. This phenomenon was not observed on the copper surface and would certainly enhance the growth of the frost crystals in the horizontal direction. Based on the recorded images, the average height of the frost crystals grow on the frozen droplets was measured at different times. Fig. 5 compares the frost crystals height on five different surfaces. From this figure, it can be seen that the frost crystals height increases from 1.08 mm, 1.11 mm, 1.17 mm to 1.19 mm only on the frozen droplets as the contact angle increases from 97.2°, 123.9°, 140.5° to 154.9° of the cold surfaces. However, it should be pointed out that the frost crystals height on the frozen droplet that grow on the plain copper surface is only 0.86 mm. This indicates that the frost crystals growth velocity on the hydrophobic surface is larger than that on the plain copper surface. The present results well explain the observation of Liu et al. [7] that the influence of surface hydrophobicity is limited to the very initial period of the frost deposition process. After a continuous frost layer formed on the surface, the frost formation behavior on both the hydrophobic and the hydrophilic surface shows no significant differences. Therefore a hydrophobic surface does not actually restrain frost deposition as effectively as it is expected and it has
no recognizable influence on the frost thickness growth for long test runs. From the above experimental observation and measurements, it is found that the water droplet freezing process and the frost crystals formed on the frozen ice droplets were completely different on the hydrophobic and the plain copper surfaces. The freezing time of the water droplet is defined as the time from the turning on of the thermoelectric cooler to the completion of the droplet freezing. Fig. 6 depicts the variation of droplet freezing time with the contact angle under the same environmental conditions. One can see clearly from the figure, the droplet freezing time increases with the contact angle very quickly. For example, on the plain copper surface with contact angle of 76.0°, the freezing time is only 206 s. As the surface contact angle increases from 76.0° to 154.9°, i.e. the cold surface changes from the plain copper to the super-hydrophobic surface, the freezing time increased to 485 s which is more than doubled the time of the plain copper surface. As mentioned above, the contact angle has an obvious effect on the water droplet shape on the surface. The larger the contact angle is, the smaller the contact area with the cold surface. The smaller contact area weakens the heat transfer from the cold surface to the water droplet, and therefore slows the cooling and freezing process of the water droplet on the hydrophobic surface. From the observation of the freezing process of the water droplets, it was found that the frost crystals appeared at the protrusion of the frozen droplet surface both on the plain copper surface and the hydrophobic surfaces. However, the frost crystals growth on the water droplets that frozen on the hydrophobic surface and the copper surface shows a significant difference. The frost crystals present much more dendritic growth of the frozen water droplet surface on the super-hydrophobic surface than that on the plain copper surface.
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Time (min)
θ =76.0°
θ =123.9°
θ =154.9°
0
Frozen
20
60
Fig. 4. Water droplet freezing process and crystal growth on different surfaces.
Table 2 Parameters of the water droplet on different surface. Variable of the water Height Surface area in contact with air (A1) Surface area in contact with the cold surface (A2) Volume (V) Surface/Volume (A1/V) Surface/Volume (A2/V) Time for starting freeze Time for freezing
h = 76.0° 1.23 mm 1.62 mm2 7.74 mm2 6 ll 0.27 m1 1.29 196 s 10 s
For dendritic growth from a subcooled solution, the dendrite growth velocity and morphology are dependent largely upon the behavior of the tip region. Karma [14] considered for simplicity the solidification of a pure melt, in which case the rate of crystallization is governed by the transport of heat away from the growing solid. According to the Gibbs–Thomson theory, the translational speed of liquid–solid phase transition is closely related to the super-cooling degree of the medium and the curvature of the phase interface. For liquid–solid phase transition, the growth velocity of a
h = 123.9° 1.73 mm 4.53 mm2 2.66 mm2 6 ll 0.75 m1 0.38 310 s 16 s
h = 154.9° 2.08 mm 21.54 mm2 0.67 mm2 6 ll 3.59 m1 0.11 458 s 27 s
solid–liquid interface increases with the increasing super-cooling degree and the curvature of the phase interface. The experimental observation shows that a water droplet on a superhydrophobic surface is more close to a perfect sphere, that is, its sphericity is large. Therefore, the curvature of the frozen ice droplet surface that is formed on the superhydrophobic surface from the same amount of water is large. The water droplet on the plain copper surface is more closer to a spherical crown, the droplet surface is flat and with a smaller curvature after freezing.
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to the smaller contact area between the droplet and the cold surface. It is observed that a small sharp-pointed protrusion appears on the top of the droplet at the end of the freezing process, the frost crystals appear at this protrusion first. The reason for the protrusion formation might be closely related to the density change of water freezing and the dissolved air discharge in water. The measured frost crystal growth velocity on the hydrophobic surfaces is larger than that on the plain copper surface. Moreover, the frost crystal growth velocity slightly increases with the contact angle of the hydrophobic surfaces. This revealed although the hydrophobic surface can effectively retard the water droplet freezing time and thus crystal nucleation, it will lose anti-frosting performance as the frost formation. Therefore, the hydrophobicity of a surface has a very weak influence on the frost deposition process, especially during the late stage of the process. Fig. 5. Variations of crystal height with different contact angles.
Acknowledgements This work is supported by the Beijing Natural Science Foundation Project (No. 3073014), Beijing Outstanding Scholar Program (No. 20061D0501500186) and Beijing Science and Technology Plan Project of Beijing Science and Technology Commission (No. Z07020600290793). References
Fig. 6. Variations of water droplet freezing time with different contact angles.
Therefore, we may conclude that the frost crystals growth on the water droplet that freezes on a hydrophobic surface is faster than that on the plain copper surface. 4. Conclusions In summary, a set of hydrophobic surfaces with different contact angles were successfully fabricated on the copper foil substrate by chemical etching and fluorination modification method. The largest contact angle obtained is 156.2° and water droplets on the superhydrophobic surfaces present a nearly perfect spherical shape. A series of micro-observations of the water droplet freezing processes and the frost crystals formation on the frozen water droplets were carried out on both the hydrophobic surfaces and the plain copper surface. The experimental results showed that the contact angle has a direct influence on the water droplet freezing time and frost crystal growth velocity. For a water droplet of 6 ll, the larger the contact angle of the copper surface is, the larger the sphericity of the water droplet. The freezing process of the water droplet on the large contact angle surfaces begins later due
[1] Y. Hayashi, A. Aoki, S. Adachi, K. Hori, Study of frost properties correlating with frost formation types, ASME Journal of Heat Transfer 99 (1977) 239–245. [2] X.M. Wu, W.T. Dai, W.C. Wang, L.M. Tang, Visual and theoretical analyses of the early stage of frost formation on cold surfaces, Journal of Enhanced Heat Transfer 14 (3) (2007) 257–268. [3] C.H. Cheng, C.C. Shiu, Frost formation and frost crystal growth on a cold plate in atmospheric air flow, International Journal of Heat and Mass Transfer 45 (2002) 4289–4303. [4] Y.B. Lee, S.T. Ro, Analysis of the frost growth on a flat plate by simple models of saturation and supersaturation, Experimental Thermal and Fluid Science 29 (2005) 685–696. [5] D.K. Yang, K.S. Lee, D.J. Cha, Frost formation on a cold surface under turbulent flow, International Journal of Refrigeration 29 (2006) 164–469. [6] H. Lee, J. Shin, S. Ha, B. Choi, J. Lee, Frost formation on a plate with different surface hydrophilicity, International Journal of Heat and Mass Transfer 47 (2004) 4881–4893. [7] Z.L. Liu, X.H. Zhang, H.Y. Wang, S. Meng, S.Y. Cheng, Influences of surface hydrophilicity on frost formation on a vertical cold plate under natural convection conditions, Experimental Thermal and Fluid Science 31 (2007) 789–794. [8] H. Wang, L.M. Tang, X.M. Wu, W.T. Dai, Y.P. Qiu, Fabrication and anti-frosting performance of super hydrophobic coating based on modified nano-sized calcium carbonate and ordinary polyacrylate, Applied Surface Science 253 (2007) 8818–8824. [9] M. He, J.X. Wang, H.L. Li, X.L. Jin, J.J. Wang, B.Q. Liu, Y.L. Song, Superhydrophobic film retards frost formation, Soft Matter 6 (11) (2010) 2396– 2399. [10] Z.L. Liu, Y.J. Gou, J.T. Wang, S.Y. Cheng, Frost formation on a super-hydrophobic surface under natural convection conditions, International Journal of Heat and Mass Transfer 51 (2008) 5975–5982. [11] J.T. Wang, Z.L. Liu, Y.J. Gou, X.H. Zhang, S.Y. Cheng, Deformation of freezing water droplets on a cold copper surface, Science in China Series E: Technological Sciences 49 (5) (2006) 590–600. [12] H.W. Hou, Y. Xie, Q. Ling, Large-scale synthesis of single-crystalline quasialigned submicrometer CuO ribbons, Crystal Growth & Design 5 (1) (2005) 201–205. [13] J.P. Hindmarsh, A.B. Russell, X.D. Chen, Experimental and numerical analysis of the temperature transition of a suspended freezing water droplet, International Journal of Heat and Mass Transfer 46 (2003) 1199–1213. [14] A. Karma, W.J. Rappel, Quantitative phase-field modeling of dendritic growth in two and three dimensions, Physical Review E. 57 (4) (1998) 4323–4349.
Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Effect of contact angle on water droplet freezing process on a cold flat surface Lingyan Huang a,b, Zhongliang Liu a,⇑, Yaomin Liu a, Yujun Gou a,b, Li Wang c a Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Ministry of Education, College of Environmental and Energy Engineering, Beijing University of Technology, Beijing 100124, PR China b Beijing Institute of Space Launch Technology, Beijing 100076, PR China c Tangshan University, Tangshan 063000, PR China
a r t i c l e
i n f o
Article history: Received 1 December 2010 Received in revised form 4 February 2012 Accepted 7 February 2012 Available online 16 February 2012 Keywords: Contact angle Water droplet Hydrophobic surface Crystal growth
a b s t r a c t The effect of contact angle on water droplet freezing process on a cold flat surface under natural convection conditions was experimentally investigated. A series of hydrophobic surfaces with different contact angles were prepared by solution immersion. The contact angles of these surfaces were varied from 97.2° to 154.9°. Comparative observations of water droplet freezing processes were carried out on both plain copper surface and these hydrophobic surfaces under the same conditions. The experimental results showed that the contact angle has a strong influence on the water droplet freezing time. The larger the contact angle is, the longer the freezing time. The frost crystals growth on the droplet surface that frozen on the hydrophobic surface is faster and presents a pattern that is more dendritic than that on the plain copper surface. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Frost formation on solid surface is commonly observed in cryogenic, refrigeration, air conditioning, and aerospace industries. It is a complicated transient process with simultaneous heat and mass transfer. Based on their experimental observations, Hayashi et al. [1] identified the frost formation process in three periods: the crystal growth, the frost layer growth, and the frost layer full growth period. The time of each period and the shape of frost crystals were found to strongly depend on the cold surface temperature and the vapor concentration difference between the mean stream and the cooling surface. Wu et al. [2] observed that the transition from water vapor to frost follows five independent stages: droplet condensation, droplet growth with coalescence of supercooled droplets, droplet freezing, formation of frost crystals on the frozen droplets, and crystal growth with simultaneous collapsing. The continuous and uncontrolled frost layer growth on heat transfer surfaces will adversely affect the performance of the refrigeration system due to the additional pressure drop and thermal resistance. Thus, numerous researchers have focused themselves on the investigation of frost formation mechanism and try to establish an effective defrosting method. The factors that influence the frost formation such as the ambient conditions, cold surface temperature and surface characteristics have been discussed repeatedly [3–5]. Lee et al. [6] and Liu et al. [7] have investigated the effect ⇑ Corresponding author. Tel.: +86 10 67391917; fax: +86 10 67391983. E-mail address: [email protected] (Z. Liu). 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2012.02.002
of surface energy on frost formation under free convection. They found that surface hydrophilicity is one of the more advanced and attractive methods to reduce frost formation on cold surfaces. Recently, enlightened by the super-hydrophobic characteristics of lotus leaf, some studies have been performed to investigate the anti-frosting performance of the hydrophobic surface with water contact angle higher than 150°. Wang et al. [8] fabricated a kind of super-hydrophobic coating with water contact angle of 155° by modifying CaCO3 and polyacrylate. Their experimental results showed that the frost formation on the super-hydrophobic surface was greatly retarded compared with that on the bare copper surface. The surface kept super hydrophobicity even after 10 freezing-thawing cycles. He et al. [9] observed the frost formation process on the hydrophobic and super-hydrophobic isotactic polypropylene (i-PP) films. Due to the micro-and-nanometer structures, the wettability of the super-hydrophobic film oscillates during the frost formation, this leads to the delay of the solidification of liquid water at the three-phase line (TPL) region. Liu et al. [10] studied the frost deposition on the cold super-hydrophobic surface with water contact angle of 162°. The frost deposition on the super-hydrophobic surface was delayed for 55 min compared with the plain copper surface under natural conditions. Furthermore, the frost structure on the superhydrophobic surface was looser, thin and shows a cluster of chrysanthemum-like pattern. The above research results have disclosed that the super-hydrophobic surface can retard the initial frost crystal formation; the contact angle of the solid surface has a direct effect on the water droplets condensation and thus frost deposition process. However,
L. Huang et al. / Experimental Thermal and Fluid Science 40 (2012) 74–80
75
Nomenclature T1 Tw
air temperature (°C) cold plate temperature (°C)
d h
frost crystal thickness (mm) contact angle (°)
Greek symbols u air relative humidity (%)
most research works reported in literature are on the frost layer growth and the frost layer full growth period, they studied influences of ambient conditions and cold surface temperature on frost growth. Few works have been completed on the water droplet freezing process on the cold surface. It has often been neglected since the freezing process is very fast. However, this period, i.e. the frost crystal nucleation period, is not only the starting point of the frost deposition process which should be fully understood as the initial condition for numerical simulation, but also relates to significant theoretical problems of nucleation and phase transition theory. Wang et al. [11] investigated the freezing processes of water droplet and peanut oil droplet on a cold surface. They found that only the base surface or the contact surface with the solid surface of the water droplet kept its initial shape and size, all the other part of the droplet showed an obvious growth along the direction normal to the base surface. They also observed a small sharppointed protrusion appeared on the top of the water droplet at the end of the freezing process. The cold surface they used is plain copper, and as far as we know there are no reports on the effects of different contact angles on the water droplet freezing process. In this paper, the influences of contact angle in a wide range on a single water droplet freezing process were studied experimentally. A set of copper surfaces with different contact angles were fabricated by means of a simple method suggested by Hou et al. [12]. Comparative observations of droplet freezing process were carried out on both plain copper surface and hydrophobic surfaces under the same conditions. Meanwhile the freezing time and crystals growth velocity on different surfaces are recorded and compared.
2. Experiments 2.1. Experimental apparatus Fig. 1 illustrates the experimental apparatus. The experimental setup mainly consists of a cooling system, microscopic image system, data acquisition system, a digital camera, optical fiber luminescence, air-conditioning system and humidity controller. The cooling system is basically a thermoelectric cooler that can provide cooling to maintain the cold plate temperature from 26 °C to 0 °C with a relative uncertainty of ±0.1 °C. The surface temperature of the cold plate is measured by four T-type thermocouples that are buried beneath the test surface through four holes of 1 mm in diameter and 13 mm in depth drilled into the plate. The temperature data is recorded by a HP data acquisition system and finally transferred to a personal computer for further analysis. The cold surface temperature is the average of the temperature readings of the four thermocouples. The thermocouples are all pre-calibrated and the maximum uncertainty of the surface temperature is estimated to be less than 0.5 °C, including those resulted from the location errors. The microscopic image system consists of a CCD camera, a microscope and a capture card. The system is used for the micro and transient observations of the frost deposition process. The CCD camera and microscope with a maximum magnification of 135 times are mounted parallel to the cooled surface to
take photographs and observe the droplet freezing process with the help of an optical fiber luminescence. A personal computer, equipped with image acquisition and processing software, receives the images taken by the microscopic image system, and then the height of droplet and crystal can be measured with an accuracy of ±0.001 mm. The test surfaces and the thermoelectric cooler are placed in a large Plexiglas enclosure with a dimension of 400 mm 400 mm 500 mm to maintain the constant natural convection condition during the test. The temperature and the humidity inside the enclosure are regulated at the given value by an air-conditioning system and a humidity controller. For all experiments in this paper, the air temperature (T1) inside the enclosure was maintained at 19.0 °C with an accuracy of ±0.1 °C, the relative humidity (u) was 45% with an accuracy of ±1%, respectively. An uncertainty analysis has been carried out and the results are summarized in Table 1.
2.2. Preparation of the surface with different contact angles The fabrication of super-hydrophobic surface is composed of two steps: creating the desired roughness on the metal surface and modifying the as-prepared rough surface with fluoroalkylsilane coating. Firstly, the copper foils (20 mm 10 mm 0.2 mm) which have been cleaned in HCl aqueous solution for 10 min and ultrasonically rinsed in de-ionized water, were immersed into a sealed vessel (total volume: 80 ml) containing an aqueous solution of 1.0 mol/l NaOH and 0.05 mol/lK2S2O8 at 60 °C. After 10–60 min, the copper foils were taken out from the solution and rinsed with distilled water, and then they were put into an oven and kept at 160 °C for 1 h. Thus, a dark film that covered uniformly on the copper foil was obtained. Secondly, the copper foils were modified by immersing into a pre-hydrolyzed ethanol–fluoroalkylsilane solution at room temperature for 1 h, followed by drying in the oven at 120 °C for another 1 h. Finally, the copper foil surfaces became super-hydrophobic by means of chemical etching and fluorination modification. The water contact angles of the surfaces were measured with the contact angle system (DCA, DSA100, KRUSS, Germany) at room temperature. The droplet volume was set using a burette with a 10 ll scale division; the average contact angle value was obtained by measuring five different positions of the same sample. The overall uncertainty for measured contact angle was ±5°. Fig. 2 shows copper surfaces with different contact angles. The plain copper surface has a contact angle of 76° as shown in Fig. 2a. The controlling factor that determines the value of the contact angle is the chemical etching time. The contact angles of 97.2°, 108.8° and 123.9° of the treated copper surfaces are obtained as the chemical etching time were set at 10 min, 20 min and 30 min respectively. After etching for 30 min and 60 min and modifying with the fluoroalkylsilane coating, the contact angles of the surfaces increase to 140.5° and 154.9°. Fig. 3 shows SEM images of the plain copper surfaces and surfaces treated with different time. The results showed that as the reaction time increased from 10 min to 30 min, thicker and longer CuO ribbons formed on the substrate, and the contact angles increased at the same time. However, when the reaction
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9
52
1 8
40
7
13 70
11
10 4 5
40
12
2
26
13 3
Unit:mm Thermocouples locations
6
cooling water source; 2. power source for thermoelectric cooler; 3. thermoelectric cooler; 4. cold plate; 5. T-type thermocouples; 6. HP data acquisition system; 7. microscope; 8. camera lens; 9. CCD; 10. computer; 11. power supply cable; 12. water inlet; 13. water outlet Fig. 1. Experimental system and apparatus.
Table 1 Uncertainty analysis for measured variables. Variable
Typical value
Uncertainty
Relative uncertainty (%)
Tw T1
26 to 0 °C 19.0 °C 45% 0–5.0 mm 0–180°
0.1 °C 0.1 °C 1% 0.001 mm 0.1°
3.8 – – 0.02 0.05
u d h
time increased from 30 min to 60 min, there was no significant change on the microstructure and the contact angles did not increase more. Hence one can infer that 30 min is an optimal reaction time under the present conditions. The water droplets show different shapes on these surfaces. The larger the contact angle is, the more spherical the water droplet presents on the surface. The water droplet presents a nearly perfect spherical shape on the super-hydrophobic surface, as shown in Fig. 2f. A stable cold plate surface temperature is needed to start an experiment. Therefore the cooling water system was turned on firstly to reduce the cold surface temperature and maintain at 12 °C. A 6 ll micro-syringe was used to place a droplet of distilled water on the testing cold surface. The microscope focus and image recording system were adjusted to work properly for observing the water droplet. After that the thermoelectric cooler was turned on and thus a gradual cooling process of the test surface was started
(time zero). During the test, the water droplet freezing process and crystal growth on its surface at different time were observed and recorded by the microscopic image system, the magnification was set 10. The cold plate temperature was set to be 8.5 °C which controlled by the power source. 3. Experimental results and discussion In our previous work [10], droplets freezing process on two different surfaces with contact angle of 72° (plain copper surface) and 162° (super-hydrophobic surface) were observed. It was found that the frost crystal growth on the frozen droplets that were dripped onto the super-hydrophobic surface and the copper surface shows a significant different pattern. The frost crystals grow on much larger portion of the frozen water droplet surface on the super-hydrophobic surface than that on the plain copper surface. And the frost crystal growth on the super-hydrophobic surface presents of much more dendritic growth. In this paper, close observations were made of the water droplet freezing process on a set of copper surfaces with contact angles varying from 97.2° to 154.9°. The freezing time and crystals growth velocity on the frozen droplet surface were also compared. The images of the droplet freezing process on five different samples were recorded per 5 min. Fig. 4 shows a group of typical pictures of droplet freezing process on the plain copper surface (h = 76.0°), hydrophobic surface (h = 123.9°) and super-hydrophobic
L. Huang et al. / Experimental Thermal and Fluid Science 40 (2012) 74–80
(a) CA=76.0° (Plain copper surface)
(b) CA=97.2°
(c) CA=108.8°
(d) CA=123.9°
(e) CA=140.5°
(f) CA=154.9°
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Fig. 2. Copper surfaces with different contact angles.
surface (h = 154.9°). It was found that the droplet presents different shape on different surfaces before the experiment starts. The water droplet spreading on the plain copper surface is of spherical crown shape due to the small contact angle and good wettability of the surface, while the water droplet presents hemispherical and nearly perfect spherical shape on the hydrophobic and super-hydrophobic surfaces, respectively. Some typical Parameters of the water droplet on different surface are showed in Table 2. The water droplet height is 1.23 mm, 1.73 mm and 2.08 mm, respectively on these three different surfaces measured by the image processing software, the contact area on the cold surface is 7.74 mm2, 2.66 mm2 and 0.67 mm2, respectively. The water droplets are transparent before freezing takes place. As the cold surface temperature was reduced from 12 °C to 8.5 °C, the droplets lose their transparency gradually and remain supercooled for a period of time. After the test started about 196 s, 310 s and 458 s respectively, the water droplets begin to freeze on these three different surfaces. The freezing of the water droplets starts from the bottom surface of the droplet that contacts with the cold surface, and propagates upwards and finally reaches to the top of the droplet. The whole processes last 10 s, 16 s and 27 s on the three different surfaces respectively. At the end of the freezing process the droplet becomes fully opaque and a small sharp-pointed protrusion appears on the top of the droplet. It is postulated that the effects of surface tension and volume dilatation
resulted from liquid-to-solid phase change caused the shape change and protrusions formation [11]. The water density decreases during freezing process, and the conservation of mass requires that its volume expands. This may at least partially explain the appearance of the protrusion of water droplet freezing. The numerical modeling results by Wang et al. [11] supported this postulation. Another possible reason is resulted from Hindmarsh’s experimental observation [13]. They videoed the freezing process of a suspended water droplet in the cold air stream, and observed many gas bubbles during the freezing process and a bulge appears at the top of the droplet after it completely frozen. Therefore, it may be well presumed that the droplet generally nucleated from the outward surface and formed a solid shell around the droplet. The bulging observed at the surface was due to the shell being pushed out by a pressure build up inside the droplet from the formation of gas bubbles and the density change of water to ice. The exterior surface of the droplet is very smooth except for a protrusion on the top after it freezes into ice solid. It is observed that columnar frost crystals appear at the protrusion first and some smaller frost crystals form around these columnar frost crystals subsequently. This phenomenon may be attributed to the small surface energy of the protrusion, it acts just like a mini particle with small nucleation potential barrier, and therefore the nucleation and condensation of air vapor may occur at the protrusion
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(a) Plain copper surface
(b) Etching for 10 min
(c) Etching for 20 min
(d) Etching for 30 min
Fig. 3. SEM images of different surfaces.
of the frozen droplet surface easier. During this period, droplet freezing and the frost crystals appearance on the three surfaces are very similar. However, after 20 min the phenomena happening on the three frozen droplet surfaces are quite different. On the plain copper surface the frost crystals grow mainly on the top of the ice droplet and along the vertical direction, the frost crystals are short and thick. On the hydrophobic and super-hydrophobic surfaces the frost crystals grow on almost every position of the droplet surface, they flourish on the frozen droplets surface and are thinner and more slender than that of the plain copper surface. At about 60 min some of frost crystals on the upper position of the droplet thaw and fall down onto the crystals of the lower part of the droplet on the super-hydrophobic surface. This phenomenon was not observed on the copper surface and would certainly enhance the growth of the frost crystals in the horizontal direction. Based on the recorded images, the average height of the frost crystals grow on the frozen droplets was measured at different times. Fig. 5 compares the frost crystals height on five different surfaces. From this figure, it can be seen that the frost crystals height increases from 1.08 mm, 1.11 mm, 1.17 mm to 1.19 mm only on the frozen droplets as the contact angle increases from 97.2°, 123.9°, 140.5° to 154.9° of the cold surfaces. However, it should be pointed out that the frost crystals height on the frozen droplet that grow on the plain copper surface is only 0.86 mm. This indicates that the frost crystals growth velocity on the hydrophobic surface is larger than that on the plain copper surface. The present results well explain the observation of Liu et al. [7] that the influence of surface hydrophobicity is limited to the very initial period of the frost deposition process. After a continuous frost layer formed on the surface, the frost formation behavior on both the hydrophobic and the hydrophilic surface shows no significant differences. Therefore a hydrophobic surface does not actually restrain frost deposition as effectively as it is expected and it has
no recognizable influence on the frost thickness growth for long test runs. From the above experimental observation and measurements, it is found that the water droplet freezing process and the frost crystals formed on the frozen ice droplets were completely different on the hydrophobic and the plain copper surfaces. The freezing time of the water droplet is defined as the time from the turning on of the thermoelectric cooler to the completion of the droplet freezing. Fig. 6 depicts the variation of droplet freezing time with the contact angle under the same environmental conditions. One can see clearly from the figure, the droplet freezing time increases with the contact angle very quickly. For example, on the plain copper surface with contact angle of 76.0°, the freezing time is only 206 s. As the surface contact angle increases from 76.0° to 154.9°, i.e. the cold surface changes from the plain copper to the super-hydrophobic surface, the freezing time increased to 485 s which is more than doubled the time of the plain copper surface. As mentioned above, the contact angle has an obvious effect on the water droplet shape on the surface. The larger the contact angle is, the smaller the contact area with the cold surface. The smaller contact area weakens the heat transfer from the cold surface to the water droplet, and therefore slows the cooling and freezing process of the water droplet on the hydrophobic surface. From the observation of the freezing process of the water droplets, it was found that the frost crystals appeared at the protrusion of the frozen droplet surface both on the plain copper surface and the hydrophobic surfaces. However, the frost crystals growth on the water droplets that frozen on the hydrophobic surface and the copper surface shows a significant difference. The frost crystals present much more dendritic growth of the frozen water droplet surface on the super-hydrophobic surface than that on the plain copper surface.
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Time (min)
θ =76.0°
θ =123.9°
θ =154.9°
0
Frozen
20
60
Fig. 4. Water droplet freezing process and crystal growth on different surfaces.
Table 2 Parameters of the water droplet on different surface. Variable of the water Height Surface area in contact with air (A1) Surface area in contact with the cold surface (A2) Volume (V) Surface/Volume (A1/V) Surface/Volume (A2/V) Time for starting freeze Time for freezing
h = 76.0° 1.23 mm 1.62 mm2 7.74 mm2 6 ll 0.27 m1 1.29 196 s 10 s
For dendritic growth from a subcooled solution, the dendrite growth velocity and morphology are dependent largely upon the behavior of the tip region. Karma [14] considered for simplicity the solidification of a pure melt, in which case the rate of crystallization is governed by the transport of heat away from the growing solid. According to the Gibbs–Thomson theory, the translational speed of liquid–solid phase transition is closely related to the super-cooling degree of the medium and the curvature of the phase interface. For liquid–solid phase transition, the growth velocity of a
h = 123.9° 1.73 mm 4.53 mm2 2.66 mm2 6 ll 0.75 m1 0.38 310 s 16 s
h = 154.9° 2.08 mm 21.54 mm2 0.67 mm2 6 ll 3.59 m1 0.11 458 s 27 s
solid–liquid interface increases with the increasing super-cooling degree and the curvature of the phase interface. The experimental observation shows that a water droplet on a superhydrophobic surface is more close to a perfect sphere, that is, its sphericity is large. Therefore, the curvature of the frozen ice droplet surface that is formed on the superhydrophobic surface from the same amount of water is large. The water droplet on the plain copper surface is more closer to a spherical crown, the droplet surface is flat and with a smaller curvature after freezing.
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to the smaller contact area between the droplet and the cold surface. It is observed that a small sharp-pointed protrusion appears on the top of the droplet at the end of the freezing process, the frost crystals appear at this protrusion first. The reason for the protrusion formation might be closely related to the density change of water freezing and the dissolved air discharge in water. The measured frost crystal growth velocity on the hydrophobic surfaces is larger than that on the plain copper surface. Moreover, the frost crystal growth velocity slightly increases with the contact angle of the hydrophobic surfaces. This revealed although the hydrophobic surface can effectively retard the water droplet freezing time and thus crystal nucleation, it will lose anti-frosting performance as the frost formation. Therefore, the hydrophobicity of a surface has a very weak influence on the frost deposition process, especially during the late stage of the process. Fig. 5. Variations of crystal height with different contact angles.
Acknowledgements This work is supported by the Beijing Natural Science Foundation Project (No. 3073014), Beijing Outstanding Scholar Program (No. 20061D0501500186) and Beijing Science and Technology Plan Project of Beijing Science and Technology Commission (No. Z07020600290793). References
Fig. 6. Variations of water droplet freezing time with different contact angles.
Therefore, we may conclude that the frost crystals growth on the water droplet that freezes on a hydrophobic surface is faster than that on the plain copper surface. 4. Conclusions In summary, a set of hydrophobic surfaces with different contact angles were successfully fabricated on the copper foil substrate by chemical etching and fluorination modification method. The largest contact angle obtained is 156.2° and water droplets on the superhydrophobic surfaces present a nearly perfect spherical shape. A series of micro-observations of the water droplet freezing processes and the frost crystals formation on the frozen water droplets were carried out on both the hydrophobic surfaces and the plain copper surface. The experimental results showed that the contact angle has a direct influence on the water droplet freezing time and frost crystal growth velocity. For a water droplet of 6 ll, the larger the contact angle of the copper surface is, the larger the sphericity of the water droplet. The freezing process of the water droplet on the large contact angle surfaces begins later due
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