Dynamic behavior of micrometric single water droplets impacting onto heated surfaces with TiO2 hydrophilic coating

International Journal of Thermal Sciences 79 (2014) 1e17

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Dynamic behavior of micrometric single water droplets impacting onto heated surfaces with TiO2 hydrophilic coating El-Sayed R. Negeed a, b, *, M. Albeirutty a, Y. Takata c a

Center of Excellence in Desalination Technology, King Abdulaziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia Reactors Department, Nuclear Research Center, Atomic Energy Authority, P.O. Box 13759, Cairo, Egypt c International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Department of Mechanical Engineering, Kyushu University, 744 Motooka, NishiKu, Fukuoka 819-0395, Japan b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 24 January 2013 Received in revised form 16 December 2013 Accepted 16 December 2013 Available online 1 February 2014

Dynamic behavior of micrometric single water droplets impacting onto heated surfaces with and without superhydrophilic coating is investigated using a high-speed video camera in this research study. Superhydrophilic surface coating, SHS, is achieved by coating the surface with Titanium dioxide, TiO2, and by exposing the surface to ultraviolet, UV. Mirror heat transfer surfaces of different metals have been considered. The experimental runs are carried out by spraying single water droplets onto heated surfaces where, the droplet diameter and velocity were independently controlled. The droplet behavior during the collision with the hot surface has been observed with the high-speed video camera. By analyzing the experimental results and comparison between the present results and the results due to other investigators, the effects of surface wettability, thermal properties of the heat transfer surface, droplet velocity, droplet size and surface superheat on the dynamic behavior of micrometric single water droplets impacting onto the heated surfaces were investigated. Empirical correlations are presented describing the hydrodynamic characteristics of an individual droplet impinging onto the heated surfaces, and concealing the affecting parameters in such process. Ó 2013 Elsevier Masson SAS. All rights reserved.

Keywords: Droplet impact Superhydrophilic surface Surface wettability Hot surface-liquid droplet contact

1. Introduction Collision between liquid droplets and a hot surface is of great interest in metal industry and many of the industrial applications. Such applications cover treatment of heat from electronic equipments, desalination, petroleum refining, chemical combustion, gas turbine, diesel engine, spray painting, nuclear reactors, medicine and metallurgical processes. Spraying a hot surface with liquid droplets gives much higher heat fluxes than can be obtained by forced convective cooling. High heat transfer rate is beneficial because it allow the size, cost, and complexity of heat exchanger equipment to be reduced. Under practical conditions, the dispersion of the liquid results in the generation of numerous droplets that can be difficult to study systematically. The study of single droplet impingement upon heated surfaces can be used to understand the transient heat transfer characteristics which are required in order to predict the global heat transfer characteristics of an entire spray, Bernardin et al. [1]. * Corresponding author. Reactors Department, Nuclear Research Center, Atomic Energy Authority, P.O. Box 13759, Cairo, Egypt. E-mail addresses: [email protected], [email protected] (E.-S.R. Negeed). 1290-0729/$ e see front matter Ó 2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ijthermalsci.2013.12.011

Heat transfer rate depends not only on the physical properties of the liquid, but also on the conditions of the solid surface. To the best of the author’s knowledge, the effect of wetting angle on the evaporation of water droplet on a heated solid surface has received inadequate attention. One reason may be the difficulty in controlling the static contact angle as only the exclusive parameter with the other parameter being unchanged. This renders a general understanding of impinging sprays extremely complex. In the current cooling technique, the required cooling ability is achieved mainly by changing the sprayed water conditions such as type of nozzle, water mass velocity, temperature, impinging velocity and droplet diameter of water, etc. In addition to these, the conditions of cooled surface; roughness, wettability and thermal properties of cooled material such as thermal conductivity and heat capacity, and oxidation layer on the hot surface are also important. In the future, these surface conditions must also be considered to enhance cooling ability ensuring the uniformity of cooling rate, Rein [2]. In order to obtain insights into some of the important mechanisms governing the interaction of sprays with the hot surfaces, it is fundamentally beneficial in studying the phenomena occurring during the interaction between the single water droplets and hot surfaces.

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Nomenclature Cp dmax dd L.H h NS SHS

T Tsi vd

Specific heat at constant pressure, J/kg K Maximum spread diameter of the impact droplet on the hot surface, m Droplet diameter, m Latent heat of vaporization, J/kg Height of droplet during impact with surface, m Normal surface Superhydrophilic surface by coating the surface with Titanium dioxide (TiO2) and by exposing it to ultraviolet (UV) Temperature, K Initial surface temperature, K Droplet velocity, m/s

Greek letters Density, kg/m3 Thermal conductivity, W/m K Dynamic viscosity, N s/m2 Superheat (the difference between the hot surface temperature and the formed saturation temperature) ¼ Ts  Tsat, K DTsub Subcooling (the difference between the formed vapor saturation temperature and the sprayed water droplet temperature) ¼ TsatT1, K q Droplet-solid surface contact angle, degree s Surface tension, N/m

r l m DTsup

While the amount of heat transfer during the droplet spreading period may, itself, be relatively small in comparison to the heat transfer during the evaporation process, the temperature rise in the fluid during spreading may cause changes in properties that lead to a significant increase in the spreading ratio. In addition to the changes in spreading ratio, temperature gradients develop in the liquid film as spreading process. Hot spots in the film could cause regions of boiling and evaporation, while other parts of the liquid have not yet reached this condition, Healy et al. [3]. A most comprehensive review on drop impact on hot surface modeling can be found in Yarin [4], Rein [5] and Moreira et al. [6]. Most of the existing models estimate the typical thickness of the lamella as a function of the impact parameters; contact angle, impact Reynolds number and Weber number. During a droplet impact on the hot surface, many different flow phenomena such as spreading, splashing, depositing and rebounding may occurred. Processes occurring during spray impingement on hot surfaces and the shape of the lamella generated at early time of drop impact for various impact conditions are determined by Reynolds, Weber numbers, surface roughness, shape elasticity, porosity and local wettability, Roisman et al. [7]. Liu [8] showed that, the dynamic behavior of droplet impacting onto heated surface may be affected by many parameters, such as droplet size, contact angle, impact velocity, liquid temperature, initial substrate surface temperature, surface roughness, and thermophysical properties, as well as surfactant and gravity effects. Pasandideh et al. [9] and George et al. [10] showed that, the impact velocity, i.e. the impact Reynolds and Weber numbers, has a remarkable influence in the dynamic behavior of droplet impacting onto heated surfaces. Bhardwaj and Attinger [11] numerically investigated the influence of wetting on the spreading and the transient drop shape

s sc

Time, s Contact time between the droplet and the hot surface for the first collision, s

Subscripts 1 Initial c Contact between the droplet and the heat transfer surface d Sprayed droplet L Water m hot surface metal s Hot surface wall v Vapor Dimensionless numbers Kd Dimensionless number indicating Weber and Reynolds numbers, ¼ We0.5Re0.25 Ksup Dimensionless number indicates surface superheat and impact droplet subcooling, ¼ (CpvDtsup)/ (L.HþCpLDtsub) Kth Dimensionless number compares the thermal properties of the hot surface metal to the thermal properties of the sprayed liquid, ¼(lmrmCpm)/(lLrLCpL) Re Reynolds number compares inertia force to viscous force, ¼(vdddrL/mL) We Weber number compares inertia force to surface tension force, ¼ðv2d dd rL =sL Þ

during the impact of drops on a smooth solid surface for isothermal and non-isothermal conditions. Roisman [12] showed that, drop impacting onto a dry smooth substrate creates a radially expanding film flow, and if the impact parameters; Reynolds and Weber numbers, are high enough this film is relatively thin and is bounded by a rim formed by capillary forces. The flow in the lamella and propagation of the rim determine the evaluation of the drop spreading diameter. Srikar et al. [13] and Lembach et al. [14] showed that, the efficiency of drop cooling was enhanced in the presence of covering the heat transfer surfaces with electrospun non-woven polymer nonfiber mats. That is because elimination of receding and bouncing of the drops was observed, and the drops evaporated completely. As the droplet impacts upon the hot solid surface, heat is transferred from the solid to the liquid phase. This energy transfer to the droplet increases its mean temperature, while liquid vaporizes from the bottom of the droplet. If the heat transfer rate is large enough during the impact, liquid vaporized from the droplet forms a vapor layer between the solid and the liquid phase, which repels the droplet from the solid surface. In this case, the heat transfer reaches a local minimum and the evaporation life time of the droplet becomes maximum. This phenomenon was known as the Leidenfrost phenomenon. Based on the evaporation life time of a droplet, mainly four different evaporation regimes can be identified depending on the wall temperature; film evaporation, nucleate boiling, transition boiling and film boiling, Nikolopoulos et al. [15]. The present work contributes to the study of film boiling impact regime only. Ukiwe and Kwok [16], and Fard et al. [17] predicted correlations for the drop maximum spreading diameter as a function of droplet Reynolds, Weber numbers and contact angle. Sikalo et al. [18] showed that the average contact angle (qc) during spreading can

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be roughly estimated as qc z 130 if Weber and Reynolds numbers are high. Myers and Charpin [19] developed a mathematical model of the Leidenfrost effect on an axisymmetric droplet. Negeed et al. [20] experimentally investigated the effects of surface roughness, and droplet characteristics on the impact behavior of a mono-dispersed water droplet onto Sus304 surfaces using high-speed camera. Negeed et al. [21] investigated the effects of the thermal properties of the hot surface, and droplet characteristics on the impact behavior of a mono-dispersed water droplet onto heated surfaces using high-speed camera. Negeed et al. [22] investigated the influence of the oxide layer over the hot surfaces on the impact behavior of single droplets onto oxidized high temperature surfaces using a high-speed camera. Negeed et al. [23] investigated the effect of surface roughness on the impact behavior of water droplet at elevated surface temperatures using high-speed camera. They presented the effects of the surface roughness degree, initial temperature of hot surface, droplet Weber number, surface superheat on the hot solideliquid contact time, and on the maximum droplet spread diameter. Through the years many efforts have also been made on probing the phenomenon of a droplet impact onto superheated surfaces. Kumar et al. [24] numerically indicated that the impact process of the hollow droplet on the substrate is distinctly different from an analogous continuous droplet. The hollow droplet results in a large central splash, a smaller final splat diameter, a thicker and more uniform splat as compared to the analogous continuous droplet. The solidification time for the splat formed with hollow droplet is also relatively large. Kumar et al. [25], and Kumar and Gu [26] simulated the hydrodynamic behavior of the impact of a hollow droplet on a flat surface using the volume of fluid surface tracking method (VOF) coupled with a solidification model within a onedomain continuum formulation. Kamnis et al. [27] numerically simulated the dynamics of transient flow during the impingement process, including spreading, break-up, air entrapment and solidification. The simulation is able to accurately give a demonstration of dynamic flow patterns such as the generation of fingers and satellite droplets during impingement. Phan et al. [28] developed a new model to describe the effect of the contact angle on the process of bubble growth. Based on the concept of macro- and micro-contact angles, an explicit theoretical relation between the bubble departure diameter and the contact angle was deduced. For wetted surfaces (0
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first time, a full simulation of the impact and subsequent evaporation of a drop on a heated surface is performed. The influence of wetting on the heat transfer during evaporation was investigated. Several numerical models have been developed to describe the hydrodynamics of droplet impact on a surface. Tabbara and Gu [32], and Kamnis and Gu [33] developed numerical models which simulated the detailed transient of a molten metal droplet impacting, deforming, and solidifying on a flat, solid substrate. Tabbara and Gu [34] developed a novel numerical modeling and simulation of a semi-molten droplet impingement, the simulation provides an insight to the heat transfer process during the impact. Qiao and Chandra [35] measured the temperature drop of a stainless steel surface during the impact of the subcooled liquid in low gravity. Inada et al. [36] studied the effect of initial droplet temperature or the degree of subcooling on the film boiling impact. Ge and Fan [37] developed a three dimensional model and numerical simulation to describe the collision mechanics of a subcooled droplet with a superheated surface. Nikolopoulos et al. [15], and Chandra and Avedisian [38] investigated the collision dynamics of a liquid droplet impinging on a hot surface. Strotos et al. [39] parametrically studied the effects of Weber number, droplet size, wall temperature and liquid thermal properties on the cooling process of the heated plate during the impaction period. 1.1. Surface wettability Surface wettability is a one of the important parameters that influence the liquidevapor phase change phenomena. Wetting is a phenomenon where a solid surface is covered with a liquid, and the related interfaces of three related phases of solid, liquid, and vapor. Generally, a droplet-surface contact angle, qc, is used as a measurement standard by which the level of wettability is quantitatively shown, Phan et al. [28], Moita and Moreira [40], and VignesAdler [41]. A surface with a contact angle below 10 is called a superhydrophilic surface (SHS), Takata et al. [42]. Superhydrophilic coating is a one of the most categories of enhancement of the surface wettability. In a superhydrophilic coating, the water is made to spread over the surfaces (sheeting of water), which carries away dirt and other impurities. TiO2 is a one of the photocatalysts, has an amazing trait, Fujishima et al. [43] called photo-induced superhydrophilicity. In the meantime, TiO2 has received much recent attention as a photocatalyst with exciting potential for many energy and environmental applications crossing traditional disciplinary boundaries, Zorba et al. [44]. Since the discovery of ultraviolet (UV) light induced photocatalytic activity that can enhance its surface wettability, TiO2 has been extensively used in self-cleaning and related applications. Takeuchi et al. [45] summarized the self-cleaning effect of hydrophilic TiO2 film as follows. There is a formation of a chemisorbed H2O layer on the TiO2 film due to its hydrophilic property. This chemisorbed H2O layer attracts water molecules by van der Waals forces and the hydrogen bonds that obstruct the contact between surface and adsorbed contaminants. As a result, the impurities adsorbed on the coated surface are removed by the spreading action of water and the coated TiO2 surface exhibits a self-cleaning effect. Ganesh et al. [46] experimentally investigated that, the hydrophilicity of the TiO2 coated films increases with an increase in the thickness of the TiO2 and a state of superhydrophilicity was attained when the thickness of TiO2 reaches 220 nm. In recent years, advanced coating has been developed and it has become possible to control surface wettability to some extent. When the TiO2 surface is exposed to UV, the contact angle gradually decreases and ultimately reaches zero. Using this feature, one could control the surface wettability by switching on and off the UV illumination, consequently enabling the control of heat transfer, Takata et al. [42].

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There are many experimental studies that proposed the use of TiO2 coating as the heat transfer surface [47e51]. Some important results obtained throughout these studies are that falling film evaporation is considerably enhanced by very thin stable film on the heat transfer surface, that the critical heat flux (CHF) increases by approximately two times as the normal surface in pool boiling, that the minimum heat flux (MHF) point shifts to higher surface superheat, and that in the water drop evaporation on hot surface the wetting limit temperature increases drastically by the decrease in contact angle. From the previous experimental results, there is no doubt that the surface with superhydrophilic coating, SHS, has a big advantage in phase change heat transfer such as boiling and condensation. An alternative method to make a hydrophilic heat transfer surface is through plasma irradiation. By exposing the surface to plasma for a short time, the surface wettability is increased considerably. Although the heat transfer between a droplet and hightemperature solid surface has been widely studied by a number of researchers, the influence of wettability during this heat transfer process has not yet been made clear. Its influence is, however, actually large and cannot be neglected. The present study aims to disclose the effect of surface wettability, and the thermal properties of heat transfer surface on the impact behavior of a mono-despised water droplet onto superheated surfaces using a high-speed video camera. To realize this aim, the heating surfaces of Stainless steelgrade 304 (Sus304), Brass- grade C3604 (Brass C3604) and Aluminum were considered as normal surfaces (NS), and superhydrophilic surfaces (SHS). The SHS is achieved by coating the surfaces with Titanium dioxide, TiO2, and by exposing them to ultraviolet, UV. The experimental runs are carried out by spraying single water droplets onto the NS and SHS. By analyzing the photographs of the experimental runs taken by the high-speed camera, the effects of the surface wettability, thermal properties of heat transfer surface, surface superheat, droplet impinging velocity and droplet size on the solideliquid contact time, and the maximum spread of droplet will be experimentally investigated. In the present study, the water droplets diameter of size 300, 500 and 700 mm were considered, which is comparable with the actual size used in the spray cooling system and in multi-effect unit used in seawater desalination plant. The main dimensionless groups governing drop impact and employed in the present review are: We ¼ ðv2d dd rL =sL Þ, Re ¼ (vdddrL/mL), Kth ¼ (lmrmCpm)/(lLrLCp), and Ksup ¼ (CpvDTsup/L.HþCpLDTsub), Yarin [4], Negeed et al. [21] and Negeed et al. [22]. A dimensionless group Kd as a function of hydrodynamic Weber and Reynolds numbers, Kd ¼ We0.5Re0.25, plays an important role in description of different transitions and mechanisms, as in drop impact literature (Yarin [4], Mundo et al. [52], Stow and Hadfield [53], Roisman [12], Marmanis and Thoroddsen [54], Scheller and Bousfield [55] and Negeed et al. [21]). The droplet-surface contact angle, qc, is used as a measurement standard by which the level of wettability is quantitatively shown, Phan et al. [28], Moita and Moreira [40]. Therefore in the present work, the main dimensionless groups governing drop impact are: We, Re; Kd, Kth; Kd, Ksup and qc. 2. Experimental work In the present work, experiments of single water droplets impacting onto heated surfaces made of Sus304, Brass and Aluminum are carried out. Two experimental runs were carried out to manifest the effect of surface wettability on the behavior of an individual droplet impacting. The heating surface in the first run is adapted as a normal surface (NS), where the heating surface in the second run is adapted as a superhydrophilic surface (SHS), by

coating the surface with Titanium dioxide (TiO2) and then by exposing it to ultraviolet (UV). A schematic diagram of the experimental apparatus is illustrated in Fig. 1. It consists of a microjet dispenser (Model MJ-020) manufactured by MECT Co., [56], a digital high-speed video camera (phantom v43 serial 2309) provide 8-bit per color components, at 15,037 fps at a full resolutions of 256  128 pixels, a data logger and a hot metallic sample. The most effecting lighting for viewing the droplets was found from a collimated light source reflecting off the surface. A flashlight was found to produce clear images when mounted opposite the camera at the same elevation. The images captured were found to be at low levels of brightness, most pixels being at gray level of 38. The sample software provided with the frame grabber was capable of capturing a sequence of images to the PC storage unit. The microjet dispenser can control the diameter and the velocity of the ejected droplet by changing the open duration of the magnetic valve, the ejection pressure and the inner diameter of the nozzle (0.1, 0.15, 0.20 and 0.25 mm). Three metals types of the hot surface (Stainless Steel (Sus 304), Brass (C3604) and Aluminum) are used. Each hot metallic cylindrical shape sample has the same dimension of 30 mm in diameter and 90 mm in length. The TiO2 was coated on the surfaces by sputtering process. We formed titanium, Ti, layer first and then TiO2 layer. The Titanium coating layer thickness is 0.5 mm upward the hot samples, the TiO2 coating layer thickness is 11.9 mm over the Ti coating layer. The surface becomes superhydrophilic when it is exposed by UV light for more than 12 h. A chromel-alumel K type thermocouple of 0.3 mm diameter was used in measuring temperature range up to 1640 K C. A 1.2 mm small groove was engraved from the edge of the top surface to the center. Within the groove, a 0.3 mm diameter chromelealumel K type thermocouple was embedded in solder in the hot surface at the axial center and at 2.0 mm in depth from the hot surface. The surface was then polished with chrome oxide to a mirror finish and cleaned with benzene. The thermocouple is connected to a data logger and the temperatures measured are stored in a PC. This setup provides a temperature closed to the surface with fair response times to transient temperature fluctuations. For each experiment, three cylindrical blocks made of Stainless Steel (Sus304), Brass (C3604) and Aluminum with NS and SHS were used as shown in Fig. 2. Fig. 2 shows that, TiO2 superhydrophilic coating on the surfaces results in making the surfaces to become very clear. That because TiO2 superhydrophilic coating on the surfaces removes the impurities and dirt on the surfaces, also the surfaces become totally free from any asperities on them. Fig. 4 shows the droplet-solid contact angle (qc). 2.1. Experimental procedure First, each sample is heated in an electric furnace up to initial surface temperature (Tsi) 613 K, and then placed on a sample holder made of insulation material. The experiment begins when the sample temperature (Ts) has reached 573 K and then, it was cooled by an impingement of water droplet to 373 K. A single water drop is ejected from a needle of the microjet dispenser and the behavior of the water drop during the collision with the hot surface is recorded on the memory of a digital high-speed camera. By analyzing the collected pictures, the liquidesolid contact time and the maximum spread diameter of droplet on the hot surface are deduced for NS and SHS. In typical case, an impinging water drop jumps up immediately after the first collision with a hot surface (sputtering effect). The liquidesolid contact time is defined as the duration of the water drop contacts with the hot surface during the first collision. The water drop once spreads and forms a liquid film on

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Fig. 1. Schematic diagram of layout of experimental apparatus.

the hot surface and then shrinks its diameter before its takeoff. The maximum spread diameter of droplet is defined as the maximumextended diameter of the film. These photographic observations are carried out at temperature intervals of 20 K from 573 K to 373 K. The sample is lighted up only when taking pictures because the intensity of the light is too strong. Prior to photographic observations the ejection conditions of water drops were determined. By a

0.5mm/div.

number of trials, the diameter and the impinging velocity of the drop can be independently adjusted to desired values. The sprayed droplet conditions; droplet velocity, droplet size and its corresponding Weber number and Kd are summarized in Table 1. The diameters listed in Table 1 are the nominal values as the actual diameter changes slightly with ejection conditions. The initial conditions and properties of impinging droplet and hot surface

0.5mm/div.

0.5mm/div.

(a) Sus304 normal surface (NS). (b) Brass normal surface (NS). (c) AL normal surface (NS). (A) Normal surfaces made of : (a) Sus304, (b) Brass and (c) AL.

0.5mm/div.

0.5mm/div.

0.5mm/div.

(a) Sus304 surface with TiO2 (c) AL surface with TiO2 (b) Brass surface with TiO2 superhydrophilic coating (SHS). superhydrophilic coating (SHS). superhydrophilic coating (SHS). (B) Surfaces with TiO2 superhydrophilic coating made of : (a) Sus304, (b) Brass and (c) AL. Fig. 2. Photographs of surfaces made of Sus304, brass and aluminum, and for (A): Normal surfaces (NS), and (B): Surfaces with TiO2 superhydrophilic coating (SHS) and by exposing them to UV.

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E.-S.R. Negeed et al. / International Journal of Thermal Sciences 79 (2014) 1e17 Table 2 Initial conditions and properties of the impinging droplet and heat transfer surfaces.

Fig. 3. Experimental apparatus for measuring droplet-solid contact angle.

Impinging droplet

Water

Initial droplet temperature, T1 Saturation pressure, psat Saturation temperature, Tsat Initial droplet velocity, vd Initial droplet diameter, dd Droplet density, rL Droplet specific heat, CpL Droplet thermal conductivity, lL Droplet viscosity, mL Droplet surface tension, sL Latent heat of vaporization, LH Initial surface temperature (outside from electrical furnace) Surface temperature at beginning experimental measurement Hot surface (normal and coated with TiO2) Sus304 density, rs Sus304 specific heat, Cps Sus304 thermal conductivity, ls Brass (C3604) density, rs Brass (C3604) specific heat, Cps Brass (C3604) thermal conductivity, ls AL density, rs AL specific heat, Cps AL thermal conductivity, ls

20  C 1.0 Bar 100  C 1.0, 2.5 and 4.0 m/s 300, 500 and 700 mm 1000 kg/m3 4.186 kJ/kg K 0.58 W/m K 0.00085 kg/m s 0.0717 kg/s2 2257 kJ/kg 340  C 300  C Sus304, Brass (C3604), AL 7640 kg/m3 0.644 kJ/kg K 25.7 W/m K 8530 kg/m3 0.396 kJ/kg K 121 W/m K 2595 kg/m3 1.14 kJ/kg K 220 W/m K

estimates are given in Negeed et al. [21]. The error in contact angle measurement is approximately 0.001, the error in TiO2 layer thickness is approximately 0.001 mm. 3. Results and discussion 3.1. Effects of coating the surfaces with TiO2 superhydrophilic on the behavior of droplet impacting onto heated surfaces Fig. 4. Droplet-solid contact angle.

used in the present experimental work are listed in Table 2. The value of the droplet-solid contact angle (qc) for different finished surfaces are listed in Table 3. It was found that, the qc dramatically decreases with coating the surface with TiO2 superhydrophilic and then it irradiated using UV. 2.2. Uncertainty analysis The uncertainty in the surface temperature is caused by errors in the measured temperature as well as uncertainties in the thermocouple location. The thermocouple measuring the temperature gradient is inserted into hole with a diameter of 0.12 cm. The thermocouple junction snugly fit into the hole; the error in location is estimated to be less than one tenth the diameter, or 0.012 cm. The error in surface temperature is approximately 0.6 K, the error in droplet velocity is approximately 0.01 m/s, the error in droplet diameter is approximately 5.72 mm, and the error in time measurement is approximately 0.77 ms. Details of these error Table 1 Conditions of the impact droplet onto heat transfer surfaces. dd vd (m/s) (mm) 1.00

2.50

4.00

300 We ¼ 4.18, Kd ¼ 8.87 We ¼ 26.15, Kd ¼ 27.87 We ¼ 66.95, Kd ¼ 50.15 500 We ¼ 6.97, Kd ¼ 13.01 We ¼ 43.58, Kd ¼ 40.88 We ¼ 111.58, Kd ¼ 73.57 700 We ¼ 9.76, Kd ¼ 16.74 We ¼ 61.02, Kd ¼ 52.62 We ¼ 156.21, Kd ¼ 94.69

Figs. 5e7 show snapshots taken of the water droplets impinging onto heated normal surfaces (NS), and surfaces with TiO2 superhydrophilic coating (SHS) for 200 K surface superheat. Fig. 5 compares three different surface metals (Sus304, Brass and AL) for NS and SHS respectively. From the figure, differences are obvious among three surface metals. First, the duration from collision to takeoff, sc, becomes smaller as the thermal properties increases. For instance, the duration from collision to takeoff for a normal surface and for 1.0 m/s droplet velocity and 300 mm droplet diameter is 0.6 ms for Sus304 metal (Fig. 3A a), and that is 0.533 ms for Brass metal (Fig. 3A b), and that is 0.467 ms for AL metal (Fig. 3A c). Comparing Fig. 5A with B it can be shown that, the sc becomes smaller as surface with TiO2 superhydrophilic coating. For instance for 1.0 m/s droplet velocity and 300 mm droplet diameter, the sc is 0.6 ms for a normal Sus304 surface (Fig. 5A a), and that is 0.467 ms for Sus304 surfaces with TiO2 superhydrophilic coating (Fig. 5B a). The behavior of droplet with impacting velocity of 1.0 m/s onto

Table 3 Droplet-solid contact angle (qc) for different finishing of the hot surfaces. Finishing of the hot surface

Droplet-solid contact angle (qc), degree

Sus304, normal Brass (C3604), normal AL, normal Sus304, coated with TiO2 superhydrophilic Brass (C3604), coated with TiO2 superhydrophilic AL, coated with TiO2 superhydrophilic

88 84 81 8 5 3

     

1 1 1 1 1 1

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normal surfaces has the same behavior of that on surfaces with TiO2 superhydrophilic coating. Where the impact droplet spreads to form maximum radius and then shrinks and bounces off from the surface. Therefore, the contact time consists of two components; spreading period and shrinking period. According to the photographic observations, the spreading and shrinking periods tend to decrease as surfaces with TiO2 superhydrophilic coating. That is

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because the surfaces with TiO2 superhydrophilic coating are very clean and totally free from any asperities on the surfaces. Inaddition, since a droplet tends to spread as the contact angle becomes small (for surfaces with TiO2 superhydrophilic coating), the contact area between the droplet and the heating surface increases. Therefore, a wide range of the heating surface is cooled quickly during the first collision of the droplet, therefore the droplet-solid

Fig. 5. Behavior of an impact droplet on hot surface; effect of thermal properties of heat transfer surface for droplet size 300 mm, 1.0 m/s impinging velocity, 200 K surface superheat and for: (A) normal surfaces (NS), and (B) surfaces with TiO2 superhydrophilic coating (SHS).

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contact time decreases. On the contrary, when the contact angle is large (for normal surfaces) the solideliquid contact area becomes small, and hence the heat transfer rate from the hot surface to the droplet becomes smaller compared with the case of lower contact angle, therefore the droplet-solid contact time increases. The interfacial temperature and the wetting limit temperature are influenced by the contact angle and also by the thermal properties of the heat transfer surfaces, as a result, the sc becomes

smaller as the thermal properties of the heat transfer surface increases. For instance for 1.0 m/s droplet velocity and 300 mm droplet diameter, the sc is 0.467 ms for Sus304 surface with TiO2 superhydrophilic coating (Fig. 5B a), and that is 0.333 ms for AL surface with TiO2 superhydrophilic coating (Fig. 5B c). This seems due to the difference in the thermal diffusivity of the materials. Figs. 5 and 6 show snapshots taken of the water droplets impinging onto heated normal surfaces, NS, and surfaces with TiO2

Fig. 6. Behavior of impact droplet on hot surface; effect of thermal properties of heat transfer surface for droplet size 500 mm, 1.0 m/s impinging velocity, 200 K surface superheat and for: (A) normal surfaces (NS), and (B) surfaces with TiO2 superhydrophilic coating (SHS).

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superhydrophilic coating, SHS, for two different diameters (300 and 500 mm), respectively. From the figures it is depicted that, the sc increases with increasing droplet diameter since for a normal Sus304 at 200 K superheated, 1.0 m/s droplet velocity and for 300 mm droplet diameter the sc is 0.6 ms (Fig. 5A a), and that is 1.6 ms for 500 mm droplet diameter and that is 1.33 ms for 500 mm droplet diameter (Fig. 6A a). Also, the sc becomes smaller as the surface thermal properties increases.

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Figs. 6 and 7 show snapshots taken of the water droplets impinging onto normal surfaces and surfaces with TiO2 superhydrophilic coating, and for 1.0 and 2.5 m/s droplet impact velocity respectively. From the figures, differences are obvious among two velocities. First, the sc becomes smaller as the impinging velocity increases. For instance, for 1.0 m/s and 500 mm droplet diameter and a normal Sus304 surface the sc is 1.33 ms (Fig. 6A a), and that is 1.133 ms for 2.5 m/s (Fig. 7A a). Moreover, the droplet with

Fig. 7. Behavior of impact droplet on hot surface; effect of thermal properties of heat transfer surface for droplet size 500 mm, 2.5 m/s impinging velocity, 200 K surface superheat and for: (A) normal surfaces (NS), and (B) surfaces with TiO2 superhydrophilic coating (SHS).

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impinging velocity of 2.5 m/s and droplet diameter of 500 mm spreads to form maximum radius and then shrinks and bounces off from the surface when impacting onto normal surfaces, while it fragments into small pieces when impacting onto surfaces with TiO2 superhydrophilic coating. The corresponding Weber number for 2.5 m/s is 43.58, i.e. Andreani and Yadigaraoglu [57] indicated that for a normal surface if the impact Weber number is smaller than 30, practically no break-up occurs; if the impact Weber number is larger than a critical value of about 50e80, a droplet will form a thin liquid film on the impact surface, as soon as disintegrate into a smaller droplets. Chen and Hsu [58] stated that, for normal surfaces the subcooled droplet tends to disintegrate during the impact at We equals 55. Mundo et al. [52] stated that break-up occurs when Kd > 57.7. In the present study for normal surfaces the corresponding values of We and Kd at which the break-up occurs are 66.95 and 50.15, respectively, while they are 43.58, Kd ¼ 40.88, respectively, for surfaces with TiO2 superhydrophilic coating. Also from Figs. 6 and 7 it can be seen that, the sc becomes smaller as the thermal properties increases for both NS and SHS.

3.2. Effects of coating the surfaces with TiO2 superhydrophilic on the maximum diameter of spread droplet on heated surfaces Fig. 8aec illustrates the effect of the coating the surfaces with TiO2 superhydrophilic, and droplet velocity on the maximum diameter ratio of spread droplet on the hot surface (dmax/dd) for 300 mm droplet diameter and for Sus304, Brass and AL surface metal, respectively. From the figure it was shown that, the (dmax/dd) increases with increasing droplet velocity or increasing Kd. That is due to the fact that the larger impacting inertia force causes a strong impact with heat transfer surface. The (dmax/dd) increases with decreasing surface superheat. Also, the (dmax/dd) is higher as the higher thermal properties of the hot surface. In-addition it can be seen that, TiO2 superhydrophilic coating on the surfaces results in remarkably increasing the (dmax/dd). That is due to the increase of the surface wettability for the surfaces with TiO2 superhydrophilic coating; where the droplet-solid contact angle (qc) dramatically decreases.

Fig. 8. Effects of coating the heat transfer surfaces with TiO2 superhydrophilic and impacting droplet velocity on the maximum diameter of spreading droplet for 300 mm droplet diameter and for surfaces made of: (A) Sus304, (B) Brass and (C) AL.

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Figs. 8 and 9 illustrate the effects of the TiO2 superhydrophilic coating on the surfaces, thermal properties of the hot surface and droplet velocity on the (dmax/dd) for 300 mm and 700 mm droplet diameter, respectively. From these figures it can be seen that, the (dmax/dd) increases with increasing the droplet diameter or increasing the Kd. Coating the surface with TiO2 superhydrophilic results in remarkably increasing the (dmax/dd), also the (dmax/dd) is higher as the higher thermal properties of the heating surface for all values of impacting droplet diameters. 3.3. Effects of coating the surface with TiO2 superhydrophilic on the solideliquid contact time Fig. 10aec illustrates the effects of the coating the surface with TiO2 superhydrophilic, and droplet velocity on the non-dimensional solideliquid contact time, sc(Vd/dd), for 300 mm droplet diameter and for Sus304, Brass and AL surface metal respectively.

11

From the figure it was shown that, the contact time sc decreases with increasing droplet velocity. This result is due to the fact that the larger impact velocity causes a strong impact with heat transfer surface which result in violent evaporation. The sc(Vd/dd) increases at lower surface superheat (DTsup). The sc(Vd/dd) is longer as the lower thermal properties of the hot surface metal. Also it can be seen that, coating the surfaces with TiO2 superhydrophilic results in dramatically decreasing the sc. That is due to the increase of the surface wettability; where the droplet-solid contact angle (qc) dramatically decreases, also since a droplet tends to spread as the contact angle becomes small, the contact area between the droplet and the heating surface increases. Figs. 10 and 11 illustrate the effects of the surface wettability, hot surface thermal properties and droplet velocity on the sc(Vd/dd) for 300 mm, 500 mm and 700 mm droplet diameter, respectively. From these figures it can be seen that, the droplet-solid contact time, sc, increases with increasing the droplet diameter. Also it can be seen

Fig. 9. Effects of coating the heat transfer surfaces with TiO2 superhydrophilic and impacting droplet velocity on the maximum diameter of spreading droplet for 700 mm droplet diameter and for surfaces made of: (A) Sus304, (B) Brass and (C) AL.

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that, coating the surfaces with TiO2 superhydrophilic on the surfaces results in dramatically decreasing the sc. 3.4. Dimensionless correlations for the droplet hydrodynamic characteristics of single water droplets impinging onto heated surfaces with TiO2 superhydrophilic coating From the experimental results scientific correlations can be deduced to represent the relationships between the droplet hydrodynamic characteristics of an individual droplet impinging onto a heated normal surface (NS), and a surface with TiO2 superhydrophilic coating (SHS), and the affecting physical parameters; Reynolds number, Weber number, non-dimensional indicating surface superheat and non-dimensional indicating the hot surface thermal properties where, the affecting physical parameters as:  The range of droplet diameter is from 300 to 700 mm, and the range of droplet velocity is from 1.0 to 4.0 m/s.  The range of Reynolds number is from 352.64 to 3265.12

    

The range of Weber number is from 4.16 to 156.21 The range of Kd is from 8.87 to 94.69 The range of KSup is from 0.04 to 0.36 The range of Kth is from 50 to 260 The range of qc is from 82 to 88 for a normal surface, and that from 3 to 8 for a surface with TiO2 superhydrophilic coating.

From the analysis of the experimental results, the final forms for the maximum ratio of the diameter of spread droplet and for the droplet-hot surface contact time can be presented as: For a normal surfaces (NS)


0:115 dmax ¼ 0:238ðKd Þ0:475 Ksup ðKth Þ0:098 dd

sc



Vd dd

 ¼ 0:383ðKd Þ0:447 Ksup


0:669

ðKth Þ0:129

(1)

(2)

For a surface with TiO2 superhydrophilic coating (SHS)

Fig. 10. Effects of coating the heat transfer surfaces with TiO2 superhydrophilic and impacting droplet velocity on the droplet-hot surface contact time for 300 mm droplet diameter and for surfaces made of: (A) Sus304, (B) Brass and (C) AL.

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0:165 dmax ¼ 0:318ðKd Þ0:467 Ksup ðKth Þ0:098 dd

sc



Vd dd

 ¼ 0:228ðKd Þ0:459 Ksup


0:647

ðKth Þ0:132

(3)

dmax 1:653 ¼ 0:426ðKd Þ0:475 ð1:0  cosðqc ÞÞ dd

(4)

sc

Fig. 12A and B determines, respectively, the degree of agreement of developed correlations (equations from (1) to (4)) with the experimental results for NS and SHS. The figure shows that, the deviations between the predicted values and the experimental ones for the (dmax/dd) and for the sc(Vd/dd) are in the range of 20e 20% and 20e35%, respectively. If neglecting the effects of Ksup and Kth on the maximum diameter of spread droplet and considering the affecting parameters are Kd and qc and from the analysis of the experimental results, the simplified final form for the (dmax/dd) and sc(Vd/dd) can be presented as: For a normal surface (NS)

  Vd 2:147 ¼ 1:143ðKd Þ0:447 ð1:0  cosðqc ÞÞ dd

13

(5)

(6)

For a surface with TiO2 superhydrophilic coating (SHS)

dmax 0:110 ¼ 0:397ðKd Þ0:467 ð1:0  cosðqc ÞÞ dd

sc

  Vd 0:145 ¼ 1:197ðKd Þ0:459 ð1:0  cosðqc ÞÞ dd

(7)

(8)

Fig. 12C and D determines, respectively, the degree of agreement of developed correlations (equations from (5) to (8)) with the experimental results for NS and SHS. The figure shows that, the deviations between the predicted values and the experimental

Fig. 11. Effects of coating the heat transfer surfaces with TiO2 superhydrophilic and impacting droplet velocity on the droplet-hot surface contact time for 700 mm droplet diameter and for surfaces made of: (A) Sus304, (B) Brass and (C) AL.

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Fig. 12. Relationship between the experimental and the predicted results obtained from equations for the maximum spreading diameter and the droplet-hot surface contact time.

ones for the (dmax/dd) and for the sc(Vd/dd) are in the range of 20e 20% and 25e40%, respectively.

3.5. Comparison between the present results and results obtained by other researchers Roisman [12] has proposed a new scaling relation for the drop maximum spreading diameter as a function of droplet Reynolds and Weber numbers as:

dmax ¼ 0:87Re0:2  0:40Re0:4 We0:5 dd

(9)

Senda et al. [59] have experimentally proposed an empirical correlation for the drop maximum spreading diameter as a function of Weber numbers as:

dmax ¼ 1:0 þ 0:463We0:345 dd

(10)

Fig. 13a and b illustrates the comparison between the present experimental results and the results obtained by other researchers for the effect of coating the surface with TiO2 superhydrophilic on the surfaces (SHS), and the dimensionless number Kd on the (dmax/ dd), and sc(Vd/dd), respectively.

From Fig. 13a it can be seen that, the (dmax/dd) increases with increasing Kd. This is due to that the increase in Kd results in higher inertia force that in turn counteracts the surface tension force leading to a more expansion of the spreading droplet over the hot surfaces. Also it can be seen that, coating the surface with TiO2 superhydrophilic results in increasing the (dmax/dd) from 30 to 40% of that of the normal surfaces. That is due to the increase of the surface wettability with the use of TiO2 superhydrophilic coating on the surfaces; where the droplet-solid contact angle (qc) dramatically decreases (see Table 3). From Fig. 13 b it can be seen that, the sc(Vd/dd) increases with increasing Kd. Also it can be seen that, coating the surface with TiO2 superhydrophilic results in decreasing the sc(Vd/dd) from 35 to 45% of that of normal surface. That is due to the increase of the surface wettability with the use of TiO2 superhydrophilic coating on the surfaces; where the droplet-solid contact angle (qc) dramatically decreases (see Table 3). 4. Conclusions Effects of the use of TiO2 superhydrophilic coating on the surfaces, and the thermal properties of the heat transfer surfaces on the impact behavior of a mono-despised micrometric water droplet onto heated surfaces were experimentally investigated in this research study. From this study, the following conclusions can be drawn:

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15

Fig. 12. (continued).

Fig. 13. Comparison between the present results and results obtained by other researchers for the effects of Kd and coating the surfaces with TiO2 superhydrophilic on: (a) the maximum spreading diameter and (b) the droplet-hot surface contact time.

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1. The use of TiO2 superhydrophilic coating on the heat transfer surface results in remarkably increasing the surface wettability; where the droplet-solid contact angle dramatically decreases. 2. Increasing the surface wettability results in remarkably increasing the maximum spreading diameter of the impact droplet over the hot surface, and also results in dramatically decreasing the liquidesolid contact time. 3. The droplet-hot surface contact time increases with decreasing surface superheat, decreasing impinging velocity and increasing droplet size. Also, the contact time increases as the lower thermal properties of the heat transfer surface. 4. The maximum spread of an impacting droplet on the hot surfaces increases with decreasing surface superheat, increasing impinging velocity and increasing droplet size. Also, the maximum spread of droplet on the hot surface increases as the higher hot surface thermal properties. 5. New empirical correlations have been deduced describing the relation between the droplet hydrodynamic characteristics of an individual droplet impinging onto heated normal surfaces and surfaces with TiO2 superhydrophilic coating, and the affecting parameters. 6. The comparison between the obtained results and the published results shows that, increasing the surface wettability, with the use of TiO2 superhydrophilic coating on the heat transfer surfaces, results in increasing the maximum spreading diameter from 30 to 40% of that of normal surfaces, while it results in decreasing the liquidesolid contact time from 35 to 45% of that of normal surfaces. 7. The surface coated with TiO2 superhydrophilic can be an ideal heat transfer surface and will be applicable to various heat transfer phenomena that are affected by surface wettability.

Acknowledgments The authors wish to express their sincere deep gratitude and appreciate to Masamichi KOHNO, Sumitomo HIDAKA, Nobuya ISHIHARA and Keisuke TAGASHIRA (Department of Mechanical Engineering Science, Faculty of Engineering, Kyushu University, Fukuoka, Japan for their great efforts and continuous help.

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