Controlled bubble departure diameter on biphilic surfaces for enhanced pool boiling heat transfer performance

International Journal of Heat and Mass Transfer 150 (2020) 119360

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt

Controlled bubble departure diameter on biphilic surfaces for enhanced pool boiling heat transfer performance Do Yeong Lim, In Cheol Bang∗ Department of Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea

a r t i c l e

i n f o

Article history: Received 23 September 2019 Revised 8 January 2020 Accepted 10 January 2020

Keywords: Pool boiling Wettability Bubble departure diameter Critical heat flux Heat transfer coefficient

a b s t r a c t To elucidate the boiling heat transfer on a biphilic surface, the bubble departure diameter and the bubble location were controlled through the variation of the size and pitch of hydrophobic patterns on the biphilic surface. We postulated that if the average bubble departure diameter can be reduced, both the critical heat flux (CHF) and heat transfer coefficient (HTC) can be enhanced owing to the reduced dry spot area and increased active bubble cycle. The bubble dynamics and boiling performance were evaluated by adjusting the hydrophobic pattern size and the pitch of the biphilic surface using a porous superhydrophobic material with high adhesion to vapor, 14.5% of CHF and 34.1% of HTC in S2P4N64 biphilic surface were enhanced over the bare surface. The bubble departure diameter decreased as the pattern size and pitch decreased, and the CHF was enhanced in inverse proportion to bubble departure diameter. This study indicates that the bubble departure diameter on biphilic surfaces can be controlled according to the intentions of the designer. © 2020 Elsevier Ltd. All rights reserved.

1. Introduction After Nukiyama [1] remarked firstly the different boiling regimes by the pool boiling curve, the pool boiling heat transfer has received intensive attention over the past several decades. Boiling enables very efficient heat transfer due to the high latent heat by the phase change from a liquid to a vapor. The efficiency of the boiling heat transfer (BHT) is more than one order of magnitude higher than that of the single phase heat transfer [2], and is a topic of an ongoing study in the field of high-power density system for cooling such as electric devices [3] and nuclear power plants [4]. The BHT performance is evaluated by heat transfer coefficient (HTC) meaning the effectiveness of heat transfer, particularly in the nucleate boiling regime, and the critical heat flux (CHF) meaning the limit point of boiling heat transfer caused by a vapor film forming on the heating region resulted in a very small HTC and a sudden temperature increment. Because enhancing HTC and CHF is important to the safety and efficiency of the high-power density system utilizing BHT, theoretical and experimental studies to understand the phenomena and mechanism of HTC and CHF are essential. However, BHT is a very complex phenomenon involving various interrelated factors and difficult to observe and solve phys-

∗

Corresponding author. E-mail address: [email protected] (I.C. Bang).

https://doi.org/10.1016/j.ijheatmasstransfer.2020.119360 0017-9310/© 2020 Elsevier Ltd. All rights reserved.

ically and qualitatively such that it is still difficult to reach a conclusion. To understand and improve the pool boiling heat transfer performance, various studies were conducted not only by the surface modification [5–9] and heterogeneous surfaces [10–12], but also by the studies on modified working fluid such as the nanofluid study [13–16] and the mixed fluids with different surface tension [17]. Although it still needs to be further investigated, previous studies have revealed that a wettability is the most effective parameter for enhancing and understanding the BHT because it is related to the bubble dynamics, the three-phase contact line, and the wicking ability. Wettability, i.e., the contact angle, depends on the force balance of the surface tension of each solid–fluid–vapor phase. The contact angle of the fluid formed on the solid surface is a quantitative parameter that indicates how well the fluid contacts the solid [18]. Until recently, several studies have been conducted to figure out the effect of the characteristics of wettability on BHT [19–24]. Phan et al. [19] investigated the effect of the wettability on the bubble dynamics and reported that as the wettability increases, the bubble departure diameter increases, and the bubble departure frequency decreases. A low superheat was sufficient for the nucleation of bubbles on a hydrophobic surface; however, at high heat fluxes, the bubble spreads over the surface, creating a vapor film. Nam et al. [20] reported that owing to the remaining bubble on the hydrophobic surface, a rapid bubble departure cycle was generated. O’Hanley et al. [21] reported that the change in the wetta-

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Nomenclature A Cp Dd e g hfg Lheater Pr P q Rstd S T V

area [mm2 ] specific heat at constant pressure [kJ/kg K] bubble departure diameter [mm] thermal effusivity [J/m2 K s0.5 ] gravity acceleration [m/s2 ] latent heat of vaporization [kJ/kg] heater length [mm] Prandtl number pitch of hydrophobic pattern [mm] heat flux [kW/m2 ] resistance standard [] size of hydrophobic pattern [mm] wall superheat temperature [K] voltage [V]

Greek symbols β receding contact angle [°] μ viscosity [kg/m•s] σ surface tension [N/m] ρ density [kg/m3 ] Subscripts g vapor phase h heater l liquid

bility of a plain surface without a structure had little effect on the CHF, and a porous structure must be introduced to affect the CHF. Kandlikar [22] developed a CHF model that describes the effect of receding contact angle on CHF using the force balance equation acting on the departure bubble with Zuber’s assumption [25], and he theoretically explained that the CHF decreases as the receding contact angle changes from zero to 180°. As a similar work, Allred et al. [23] confirmed that the CHF of plain surface was determined by the receding contact angle, even though the static contact angle showed hydrophobicity. To capitalize on both advantage of hydrophilicity and hydrophobicity on BHT, Zhang et al. [24] utilized the smart wettability surface that passively changed the wettability from hydrophobicity to hydrophilicity according to surface temperature and showed enhanced HTC and CHF over the hydrophilic surface. BHT studies with wettability heterogeneous surface have been performed to utilize the wettability gradient effect by a mixture of hydrophilic and hydrophobic properties [12,26–34]. Betz et al. [26,27] studied the boiling phenomenon of a wettability mixed surface by patterning a hydrophobic material on the hydrophilic surface, called a biphilic surface. The hydrophobic pattern on the biphilic surface enhanced the HTC by increasing the nucleationsite density. Jo et al. [12,28] reported that HTC enhancement on smooth the biphilic surfaces without any structure was due to the fast onset of boiling (ONB) occurring on hydrophobic patterns and the absence of waiting time due to the bubble remaining on the hydrophobic patterns after bubble departure. Additionally, the biphilic surfaces are characterized by bubble dynamics controlled by the hydrophobic pattern vapor pinning adhesion and wettability gradient. Several researchers reported that the hydrophobic pattern on the biphilic surface had an optimized size and pitch. Although Shen et al. [29] and Motezakker et al. [30] figured out the optimized pattern size and pitch which maximized CHF and HTC in the biphilic surface, they provided an insufficient explanation of enhancement mechanism about the hydrophobic pattern. Zupancic et al. [32] observed the temperature distribution of the biphilic surface, and the temperature was low in hydrophobic pat-

tern due to the large number of nucleation site and fast departure frequency. Gong and Cheng [33] and Ma et al. [34] numerically revealed the enhanced HTC and CHF on the biphilic surface due to the contact line pining and low onset of boiling temperature on hydrophobic region and they also suggested that there existed the optimum hydrophobic pattern size and pitch. In this study, using the characteristics that biphilic surfaces can control bubble dynamics, the bubble size and the bubble location are artificially adjusted to elucidate CHF and HTC phenomena. we hypothesize that porous superhydrophobic materials with very high vapor pinning adhesion can control the bubble departure diameter and that a smaller bubble diameter yields a smaller dry/hot spot, resulting in an improved CHF. To confirm our hypothesis, the boiling performance of biphilic surfaces with hydrophobic patterns having different square pattern sizes and pitches was compared and analyzed using high-speed video (HSV) and infrared (IR) thermometry. Additionally, a CHF model for a biphilic surface was proposed using the force-balance model, and accordingly, a new direction for boiling studies involving a biphilic surface was proposed. 2. Experiment 2.1. Heater fabrication As shown in Fig. 1(a), the bare heater was composed of a Si surface comprising 200 nm of SiO2 deposited via thermal oxidation for electrical insulation, 700 nm of indium tin oxide (ITO) deposited via radiofrequency sputtering, and 100 nm of Au deposited via electron-beam evaporation on the backside of the Si. Because ITO is opaque and electrically conductive in the mid IR range (wavelength of 3–5 μm), it has been used to observe temperature distributions of heater using direct electrical heating and IR thermometry [35,36]. The heater surface size was 50 × 50 mm2 for the SiO2 /Si substrates, 50 × 32 mm2 for the ITO heaters, and 9 × 32 mm2 for the Au electrodes, resulting in a heating area of 32 × 32 mm2 . In this study, the SiO2 surface was used as the hydrophilic surface. Biphilic surfaces were fabricated by coating porous superhydrophobic materials on an SiO2 /Si bare heater. The square hydrophobic pattern was coated via a spray-coating method using a commercial hydrophobic spray made of self-assembling alkanethiol (a hydrophobic alkyl chain with a thiol group) molecules (Hydrobead standard, Hydrobead Corp.). For the spray coating, masking tape was attached, and then the hydrophobic material was adhered to the masked surface via spraying and cured by heating on the hotplate at 200 °C for 2 h. One uniform hydrophilic SiO2 surface, one uniform hydrophobic surface, and five biphilic surfaces were prepared. As presented in Fig. 1(b) and Table 1, five biphilic surfaces had square hydrophobic patterns with different pattern sizes and pitches, and the size and pitch were determined according to the bubble departure diameter (in this paper, S refers to the size of hydrophobic patterns, P refers to the pitch between hydrophobic patterns, and N refers to the total number of hydrophobic patterns). After the hydrophobic coating procedure, the surface characterization was conducted. A scanning electron microscopy (SEM) image of the fabricated heater indicated that the hydrophobic coating material had a porous structure as depicted in Fig. 1, and the coating thickness of hydrophobic pattern was measured by surface profiler as 17.0 ± 5.1 μm. Before boiling experiment, the static contact angles of the bare SiO2 surface and hydrophobic surfaces were measured as 41.8° and 150.5°, respectively, and the receding contact angles were 29.0° and 149°, respectively. To confirm the robustness of coating material adhesion on the biphilic surface for withstanding vigorous boiling phenomenon, standard test for measuring adhesion by tape test on fully coated hydrophobic surface

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Fig. 1. (a) schematic design of the SiO2 /ITO heater surface and (b) the image of S3P8N16 biphilic surface. (c) SEM images (magnification ratio: upper, × 100 k; lower, × 500), and (d) static and receding contact angles of the SiO2 surface and the hydrophobic surface, which the hydrophobic surface exhibited a porous superhydrophobic characteristic. Table 1 Test matrix of biphilic surfaces in the pool boiling experiments. Index

Pattern size (mm)

Pattern pitch (mm)

Pattern number

Area ratio (Apattern /Ah )

Bare S2P4N64∗ S2P5N36 S2P6N25 S3P6N25 S3P8N16 Phobic

0 2 2 2 3 3 –

0 4 5 6 6 8 –

0 64 36 25 25 16 –

0.0 0.25 0.14 0.10 0.22 0.14 1.0

∗

S: size, P: pitch, N: number of hydrophobic patterns.

was conducted before and after the experiment, and coating material adhesion was confirmed according to ASTM D3359. 2.2. Pool boiling apparatus As shown in Fig. 2, the pool boiling experimental apparatus used deionized (DI) water as a working fluid and evaluated the boiling performance of heater applied by the direct joule heating method in a boiling chamber. The experimental apparatus consisted of a boiling chamber, cartridge heaters, a copper electrode, a reflux condenser, T-type thermocouples, and an IR reflecting mirror. The dimensions of the boiling chamber were 150 × 150 × 400 mm3 , and it was made of 10-mm-thick a transparent polycarbonate material for visualization of boiling phenomenon. The working fluid in the boiling chamber was maintained under saturation conditions using four cartridge heaters, a T-type thermocouple, and a proportional–integral–derivative (PID) control system. The Au electrode of fabricated heater was attached to the copper electrode on the bottom of the boiling chamber using conductive epoxy (CW2400), and silicon epoxy (Permatex

Fig. 2. Schematic of the test section of the experimental apparatus.

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Corp.) was used to insulate and fix the heater. The power was applied to Au electrode and the ITO of the heater using a directcurrent power supply having a maximum voltage of 150 V and a maximum current of 35 A (5.25 kW, KJP-50 0 0PL) for voltage control. The voltage applied to the heater was measured using a dataacquisition system (Agilent, 34980A). The applied current of system was calculated using the voltage applied to an additional resistance standard (0.001  with accuracy 0.01% at 20 °C, CROPICO RS3), and the heat flux of the heater was calculated as follows:

q =

Vh · Vstd Ah · Rstd

(1)

where Vh , Vstd , Rstd , Ah represent the voltages applied on the heater and resistance standard, the resistance standard (0.001 ), and the actual heating area, respectively. The temperature of the heater was measured via IR thermometry. The IR intensity, which varied with respect to the temperature of the ITO of the SiO2 /ITO heater, was measured using an IR camera through an IR reflecting mirror under the chamber. Fig. 3. Comparison of boiling curves of bare heater surface with the results of other studies.

2.3. Experimental procedure and uncertainty analysis In this study, the boiling chamber was degassed for 2 h under the atmospheric-pressure saturation condition with four cartridge heaters to remove the remaining gas in the working fluid and heater surface before starting the experiment. Subsequently, a heat flux was applied to the heater by controlling the voltage. The heat flux was increased by 20 kW/m2 per step until it reached 100 kW/m2 , and thereafter, the heat flux was increased by 100 kW/m2 per step. The heat flux was applied for 5 min to achieve the steady state at each heat-flux step. For each experimental case, two nominally identical heaters were tested, and the CHF criterion was determined at the moment when the IR intensity from heater rapidly increased, which indicated a rapid increase in the temperature. In the experiment, the phenomena were observed using HSV and IR thermometry. HSV was used to observe the boiling phenomenon, with a spatial resolution of 640 × 480 pixels and an frame rate of 10 0 0 frames per second. IR thermometry was used to observe the IR intensity of the heater, with a spatial resolution of 320 × 256 pixels at the frame rate of 172 frames per second. After the boiling experiment, the heater temperature was calculated by calibrating the IR intensity with the directly measured temperature data of the SiO2 surface using the thermocouple. IR intensity calibration process was conducted by matching the IR intensity with heater temperature and conducting the regression, and it had 0.9% of the matching error. Since the actual boiling region size (32 × 32 mm2 ) and the heater surface size (50 × 50 mm2 ) were different, the lateral heat loss from boiling region to the non-boiling region due to the conduction and natural convection should be analyzed. Using the commercial computational fluid dynamic code, ANSYS CFX, and experimentally measured temperature data of heater, an iterative calculation was conducted while changing the HTC value of boiling region until the heater temperature from CFD simulation was matched with experimentally measured temperature data. as the simulation results, the lateral heat loss ratios were 5.1% and 1.0% at the heat flux of 100 kW/m2 and 800 kW/m2 , respectively. The maximum uncertainty of the measured voltage at the heater and the additional resistance standard applied by power supply (5.25 kW, KJP-50 0 0PL) was ± 1%. Then, the uncertainty of applied heat flux by power supply was analyzed using Eq. (2), as follows:



Uq = q

UV2

h

Vh2

+

UV2

std

2 Vstd

+

UR2

std

R2std

(2)

Where the maximum uncertainties of Vh , Vstd , and Rstd were ± 1.0%, ± 1.0%, and ± 0.01%, respectively, and the calculated uncertainty of the heat flux was ± 1.4%. Also, as the similar analysis, the uncertainty of the heat transfer coefficient was analyzed by adding the uncertainty of the heater temperature, and it was calculated as ± 1.7% 3. Results and discussion Through pool boiling experiments, the characteristics of both CHF and HTC were analyzed for seven cases of heater surfaces. To prevent damage in the heater due to the sudden temperature rise when the CHF was reached, the experiments were conducted until the CHF was nearly reached, and the power supply was turned off at reaching the CHF. The boiling curve for the bare SiO2 heater in Fig. 3 had initially natural convection regime until isolated nucleate boiling started at the wall superheat 11 K. The CHF of bare heater surface was reached at the heat flux of 803 ± 2 kW/m2 . To confirm the validity of the experimental data, the boiling curve data for the bare case were compared with the result of other pool boiling studies [12,37,38] since they used silicon based heater as the bare surface. Although the trend of each boiling curves had slightly different, Fig. 3 showed that the CHF values were agreed well with each other. For uniformly hydrophobic surfaces, the onset of nucleate boiling (ONB) superheat temperature was 3 K, and the CHF was 41 ± 5 kW/m2 which was 94.9% lower than that of the bare heater. For biphilic surfaces, the ONB temperatures were same to uniformly hydrophobic surfaces as 3 K, which 8 K lower than that of the bare heater. The CHF was 920 ± 122 kW/m2 on the S2P4N64 surface and 842 ± 21 kW/m2 on the S2P5N25 surface with enhancement ratio of 14.5% and 4.8%, respectively, compared with the CHF of the bare heater. The other three biphilic surfaces exhibited CHF values similar to that of the bare heater. The largest HTC of the bare surface was 22 kW/m2 K at a heat flux of 800 kW/m2 , and the largest enhancement in the HTC compared with the bare heater was 34.1% on the S2P4N64 surface. Except for the S3P8N16 surface, all the biphilic surfaces exhibited HTC enhancements. The CHF and HTC for each heater are presented in Table 2. The enhancements of the CHF and HTC, which are indicative of the boiling performance, differed for each biphilic heater, suggesting that the influence of the hydrophobic pattern on the boiling phenomena varied with respect to the pattern geometry. To analyze the

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Table 2 Results for the pool boiling CHF and maximum HTC enhancement. Index

CHF (kW/m2 )

Enhancement (%)

HTC (kW/m2 K)

Enhancement (%)

Bare S2P4N64 S2P5N36 S2P6N25 S3P6N25 S3P8N16 Phobic

803 ± 2 920 ± 122 842 ± 21 802 ± 2 787 ± 42 800 ± 7 41 ± 5

Ref. 14.5 4.8 0.0 −2.1 0.0 −94.9

22 30 225 24 23.0 23 4

Ref. 34.1 11.2 5.8 3.1 2.2 −83.4

Fig. 4. (a) Boiling curves of each surface and (b) HTC of each surface. S represents the size of the hydrophobic pattern, P represents the pitch of the pattern, and N represents the number of the pattern. The largest CHF and HTC enhancements were observed on the S2P4N64 biphilic surface.

effects of the size and pitch of the hydrophobic pattern, the bubble dynamics for each heater were analyzed using HSV images and IR thermometry (Fig. 4). The enhancement of the HTC on the biphilic surface was attributed to active nucleation sites due to the differences in the wetting state and thermal conductivity between the hydrophilic and hydrophobic regions. As shown in Fig. 1, the hydrophobic region had a porous structure with a Cassie–Baxter state [39], a low surface energy and a low thermal conductivity (~1 W/mK, characteristics of hydrophobic alkanethiol material). When the surface was heated, the heat from the ITO heater to Si/SiO2 surfaces was easy to be transferred than did the hydrophobic region owing to their higher thermal conductivity (thermal conductivity of Si ~110 W/mK at 100 °C). Since heat transfer to Si/SiO2 surfaces by conduction was faster than hydrophobic patterns and the vapor film existed on the hydrophobic pattern due to the Cassie–Baxter state, the nucleation occurred easily at the hydrophobic pattern boundary site despite of the low wall superheat. HSV image depicted in Fig. 5 shows that a small nucleation bubble created at the boundary of the pattern and moved to the center of the hydrophobic pattern. then, the bubble base was pinned on the pattern until it departed from the surface. The most distinctive feature of the bubble departure process on hydrophobic patterns was that there was a remaining bubble on the hydrophobic pattern even if bubbles escaped owing to necking phenomena [12]. The remaining bubbles acted as new nucleation bubbles, resulting in no waiting time in the bubble ebullition cycle. Therefore, the mechanism involving easy nucleation ability without a waiting time for nucleation and additional nucleation site at the boundary of hydrophobic patterns was the main reason for the HTC enhancement of the biphilic surface. In the Table 2, results of HTC enhancement showed that the HTC enhancement was proportional to the num-

ber of hydrophobic patterns. This means that the HTC enhancement was mainly attributed to the additional nucleation site with easy nucleation ability. Fig. 6 shows the nucleated bubbles on each heater. The bubble arrangement on the biphilic heaters at a low heat flux of 40 kW/m2 depended on the initial designed pitch and size of the hydrophobic pattern. The hydrophobic region acted as a bubble emitting area, and the hydrophilic region acted as a liquid supply area, resulting in the separation of the vapor and liquid pathways. This pathway separation appeared up to a heat flux of 200 kW/m2 ; however, it was not observed over a heat flux of 300 kW/m2 , owing to the massive merging of bubbles. The bubble departure diameter was determined by the force balance model acting on the bubble such as the buoyancy force, surface tension, liquid inertia force. Using the buoyancy force (FBuoyancy ), surface tension (Fσ ) on the hydrophobic pattern as depicted in Fig. 7, the bubble departure diameter was derived as a similar work of Shen et al. [40]. If the bubble is pinned to the hydrophobic pattern until bubble departure occurs, the theoretical bubble departure diameter is derived from the equilibrium equation of the two forces, Fbuoyancy = π D3d g(ρl − ρg )/6 and Fsur f ace tension = 4Sσ , and the derived equation is as follows:

 Dd =

24σ S π ( ρ l − ρg )

1 / 3 (3)

where Dd , σ , and S represent the bubble departure diameter, the size of the hydrophobic pattern, and the surface tension of the liquid–vapor phase, respectively. Compared with the theoretical value and the measured departure diameter (manually measured up to 100 kW/m2 ), a smaller pattern size yielded a smaller departure diameter. However, overall measured bubble departure diameter value was ~ 0.6 mm smaller than the calculated value in

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Fig. 5. (a) a schematic of the nucleation mechanism on the hydrophobic pattern, (b) HSV images of the process of bubble nucleation and merging to a single bubble, and (c) HSV images of the bubble growth and departure of a single bubble on the hydrophobic pattern, with a size of 3 mm.

Fig. 6. HSV images of artificially arranged nucleate bubbles on each surface at a heat flux of 40 kW/m2 .

Fig. 8 because there would be the not considered forces acting on the bubble. A smaller pattern pitch yielded a smaller departure diameter, which indirectly confirms that the bubble behavior was affected by the pattern pitch as well as the pattern size. This was

Fig. 7. Forces acting on the bubble on the biphilic surface.

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Fig. 8. Measured bubble departure diameter on each surface, with calculated results for heat fluxes ranging from 10 to 100 kW/m2 .

7

Fig. 10. Comparison of the measured CHF with the bubble departure diameter at 100 kW/m2 of each surface.

ered one pattern area. From this phenomenon, it is noted that the size of nucleated bubble at pattern boundary can be estimated as 1~1.5 mm which is half of the influence region between 2 mm and 3 mm. From CHF enhancement by biphilic surface point of view, the measured bubble departure diameter was analyzed with CHF enhancement. Fig. 10 shows the relationship between the measured CHF and the bubble departure diameter, this revealed that the CHF increased as the bubble departure diameter decreased as an inversely manner.

4. Conclusions

Fig. 9. Temperature distributions on bare, S2P4N64, and S3P6N25 heaters measured via IR thermometry at heat fluxes of 100, 600, and 800 kW/m2 .

because the fluid at the bubble interface was pushed out in the radial direction at the time of bubble growth, and pushed fluid was acted as the liquid inertia to the bubbles on neighboring patterns. Thus, an additional liquid inertia force occurred in the equilibrium of the forces acting on the bubble given by Eq. (4), resulting in a smaller bubble departure diameter over the theoretical values. In Fig. 9, the temperature distribution of the surface indicates that temperature in the pattern and the surrounding temperature were separated. Interestingly, the biphilic heater with a hydrophobic pattern size of 2 mm had a lower temperature than its surroundings, while the biphilic heater with a hydrophobic pattern size of 3 mm had a higher temperature than its surroundings. This was because the effect of the influence region on the temperature profile was different. Small nucleation bubbles generated at the pattern boundary absorbed the heat by the phase change. Then, the influence region of the hydrophobic pattern size of 2 mm covered overall one pattern area and this lead to lower temperature over the surroundings. On the other hand, the influence region by small nucleation in the pattern size of 3 mm did not cov-

To control the departure diameter of bubbles, biphilic surfaces were fabricated using a porous superhydrophobic material that formed a strong pinning force with the bubbles. The bubble departure diameter was controlled by varying the size and pitch of the hydrophobic pattern on the biphilic surface. The boiling phenomena were analyzed using the observation from the HSV and IR Thermometry. Findings of this study are as follows: i) The biphilic surface of S2P4N64 enhanced the both CHF and HTC as 14.5% and 34.1% over the bare heater surface, respectively. ii) The enhanced HTC on biphilic surfaces is due to the easy nucleation on the hydrophobic pattern, which is in a Cassie–Baxter state, and the rapid bubble cycle by the remaining bubble after bubble departure. With Cassie–Baxter state and the thermal conductivity difference of hydrophilic and hydrophobic, nucleation initially occurred at the boundary of hydrophobic patterns, and this was acting as additional nucleation site. iii) The theoretical bubble departure diameter is derived based on pattern size. However, bubble departure diameter was affected by both the pattern size and pitch. A smaller size and pitch of the pattern yielded a smaller bubble departure diameter and a higher CHF. In future study, the experiments and hypotheses of the present study will be verified for a wider variety of pattern geometries, and a biphilic CHF prediction model that considers the pattern pitch will be developed.

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D.Y. Lim and I.C. Bang / International Journal of Heat and Mass Transfer 150 (2020) 119360

Declaration of Competing Interest None. CRediT authorship contribution statement Do Yeong Lim: Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing review & editing, Visualization, Resources. In Cheol Bang: Conceptualization, Supervision, Project administration. Acknowledgment This research was supported by the Nuclear Energy Research Program and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (Nos. 2017R1A2B2008031, 2018M2B2A9066012). References [1] N. Shiro, The maximum and minimum values of the heat q transmitted from metal to boiling water under atmospheric pressure, Int. J. Heat Mass Transf. 27 (1984) 959–970, doi:10.1016/0017-9310(84)90112-1. [2] S.M. Ghiaasiaan, Two-Phase Flow, Boiling, and Condensation, Cambridge University Press, 2017, doi:10.1017/9781316597392. [3] D. Il Shim, G. Choi, N. Lee, T. Kim, B.S. Kim, H.H. Cho, Enhancement of pool boiling heat transfer using aligned silicon nanowire arrays, ACS Appl. Mater. Interfaces 9 (2017) 17595–17602, doi:10.1021/acsami.7b01929. [4] M.H. Lee, H. Heo, I.C. Bang, Effect of thermal activity on critical heat flux enhancement in downward-hemispherical surface using graphene oxide coating, Int. J. Heat Mass Transf. 127 (2018) 1102–1111, doi:10.1016/j.ijheatmasstransfer. 2018.07.151. [5] R. Chen, M.-.C. Lu, V. Srinivasan, Z. Wang, H.H. Cho, A. Majumdar, Nanowires for enhanced boiling heat transfer, (2009). doi:10.1021/nl8026857. [6] S. Shin, G. Choi, B. Rallabandi, D. Lee, D. Il Shim, B.S. Kim, K.M. Kim, H.H. Cho, Enhanced boiling heat transfer using self-actuated nanobimorphs, (2018). doi:10.1021/acs.nanolett.8b02747. [7] A. Sitar, M. Može, M. Crivellari, J. Schille, I. Golobicˇ , Nucleate pool boiling heat transfer on etched and laser structured silicon surfaces, Int. J. Heat Mass Transf. (2020) 147, doi:10.1016/j.ijheatmasstransfer.2019.118956. [8] R.K. Gouda, M. Pathak, M.K. Khan, Pool boiling heat transfer enhancement with segmented finned microchannels structured surface, Int. J. Heat Mass Transf. 127 (2018) 39–50, doi:10.1016/j.ijheatmasstransfer.2018.06.115. [9] A. Jaikumar, S.G. Kandlikar, Pool boiling inversion through bubble induced macroconvection, Appl. Phys. Lett. (2017) 110, doi:10.1063/1.4977557. [10] M.M. Rahman, M. McCarthy, Boiling enhancement on nanostructured surfaces with engineered variations in wettability and thermal conductivity, Heat Transf. Eng. 38 (2017) 1285–1295, doi:10.1080/01457632.2016.1242961. [11] A.R. Betz, J. Xu, H. Qiu, D. Attinger, Do surfaces with mixed hydrophilic and hydrophobic areas enhance pool boiling? Appl. Phys. Lett. 97 (2010) 1–4, doi:10.1063/1.3485057. [12] H. Jo, H.S. Ahn, S. Kang, M.H. Kim, A study of nucleate boiling heat transfer on hydrophilic, hydrophobic and heterogeneous wetting surfaces, Int. J. Heat Mass Transf. 54 (2011) 5643–5652, doi:10.1016/j.ijheatmasstransfer.2011.06.001. [13] S.M. You, J.H. Kim, K.H. Kim, Effect of nanoparticles on critical heat flux of water in pool boiling heat transfer, Appl. Phys. Lett. 83 (2003) 3374–3376, doi:10.1063/1.1619206. [14] I.C. Bang, S. Heung Chang, Boiling heat transfer performance and phenomena of Al2 O3 -water nano-fluids from a plain surface in a pool, Int. J. Heat Mass Transf. 48 (2005) 2407–2419, doi:10.1016/j.ijheatmasstransfer.2004.12.047. [15] S.J. Kim, I.C. Bang, J. Buongiorno, L.W. Hu, Surface wettability change during pool boiling of nanofluids and its effect on critical heat flux, Int. J. Heat Mass Transf. 50 (2007) 4105–4116, doi:10.1016/j.ijheatmasstransfer.20 07.02.0 02. [16] J.Y. Kim, I.C. Bang, CHF enhancement partitioning based on surface wettability and porosity on CeO2 nanoparticle coated surface, AIP Adv. 9 (2019), doi:10. 1063/1.5121918. [17] N. Zhang, D.F. Chao, Models for enhanced boiling heat transfer by unusual Marangoni effects under microgravity conditions, Int. Commun. Heat Mass Transf. 26 (1999) 1081–1090, doi:10.1016/S0735-1933(99)0 0 099-8.

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