Pattern geometry optimization on superbiphilic aluminum surfaces for enhanced pool boiling heat transfer

In this study, the optimal surface pattern of low and high wettability regions for enhanced boiling heat transfer is investigated using aluminum superbiphilic surfaces. Samples are fabricated by combining chemical vapor deposition of a ﬂuorinated silane to turn them superhydrophobic and nanosecond laser texturing to render selected areas superhydrophilic. Triangular lattice pattern of superhydrophobic circular spots is utilized with spot diameters between 0.25 mm and 1.0 mm and pitch values of 0.5–2.5 mm. Pool boiling heat transfer performance of superbiphilic surfaces is evaluated using saturated water at atmospheric pressure. A strong wettability contrast is shown to be important in ensuring high heat trans- fer performance of wettability-patterned surfaces. Highest heat transfer performance is achieved using 0.5 mm diameter spots with a spot pitch of 1 mm and a corresponding superhydrophobic area frac- tion of approx. 23%. The optimal pitch value will provide a high density of potentially active nucleation sites but still allow for the development of the thermal boundary layer thus not inhibiting the activation of neighboring spots. The size of (super)hydrophobic spots appears not to have a major inﬂuence on the boiling performance when using the optimal spot pitch. The developed superbiphilic surfaces increase the CHF and provide greatly enhanced heat transfer coeﬃcients especially at medium and high heat ﬂuxes, making them suitable especially for high-heat-ﬂux applications.


Introduction
Progress in research and development of electronic devices, aerospace and space flight systems, nuclear power systems and refrigeration applications brings along increased cooling requirements as the size of the systems and their components decreases while their power dissipation requirement often increases, outlining the need for new cooling solutions [1] . Utilization of boiling heat transfer is long recognized as a viable method for advanced thermal management [2] . Phase-change heat transfer enables low temperature differences between the cooled surface and the cooling medium (i.e., low surface superheat in boiling) and the invariable saturation temperatures at the given operating pressure allow Abbreviations: AC, alternating current; CA, water contact angle; CHF, critical heat flux (also used a symbol); CLT, completely laser-textured sample; CVD, chemical vapor deposition; HPO, homogeneously hydrophobic sample; HTMS, (heptadecafluoro-1,1,2,2-tetrahydrodecyl)trimethoxysilane; ONB, onset of nucleate boiling; PEEK, polyether ether ketone; PTFE, polytetrafluoroethylene; REF, untreated reference sample; ROA, roll-off angle; SEM, scanning electron microscope; SHPO, homogeneously superhydrophobic sample; sXXpYY, biphilic sample with XX spot diameter and YY spot pitch. * Corresponding author.
for predictable cooling temperature levels. Heat transfer coefficient of several dozen kW per square meter Kelvin are obtainable in boiling combined with an upper heat flux limit (i.e., the critical heat flux (CHF) incipience, where nucleate boiling transitions towards much less efficient film boiling) above 1 MW per square meter with no intensification. However, enhancement methods have the potential to further boost the heat transfer performance of boiling by decreasing the surface superheat through increased heat transfer coefficients and increasing the safety margin through increased CHF values. Numerous methods for surface and fluid modification to achieve boiling enhancement have been presented in the last two decades [3][4][5][6][7][8][9] . Boiling surface modification methods are mostly based on changing the topography (and morphology) of the surface and its wetting behavior, which have been identified as the main factors affecting the overall nucleate boiling process including bubble nucleation, growth, departure and coalescence. Especially the wettability of the boiling surface can significantly influence the onset of nucleate boiling, heat transfer intensity and CHF incipience [10][11][12][13] . Specifically, surfaces with high wettability (i.e., hydrophilic and superhydrophilic surfaces with a static contact angle (CA) below 90 °) typically delay the onset of nucleate boiling due to a higher energy barrier with higher overall sur-

Nomenclature
Latin symbols A % percent share of area (%) C sf liquid/surface combination parameter in Rohsenows' correlation h heat transfer coefficient (W m -2 K -1 ) k thermal conductivity (W m -1 K -1 ) M 2 beam quality factor n exponent in Rohsenow [14][15][16] . However, such surfaces also provide increased liquid supply (and wicking) towards dry spots during bubble departures, which almost universally increases the critical heat flux by delaying dryout on well wettable surfaces [17,18] . Conversely, poorly wettable surfaces (i.e., hydrophobic and superhydrophobic with a static CA above 90 °) tend to provide much lower temperatures of transition into the high-heat-transfer-coefficient nucleate boiling regime [14,19] , but typically fail to prevent bubble coalescence and transition into film boiling at much lower heat flux values [20][21][22][23] , although recent studies show that efficient boiling on superhydrophobic surfaces is possible if it is induced from the Wenzel wetting regime [24,25] . As each of the extreme wettabilities has both important advantages and nonnegligible drawbacks in regard to boiling performance, surfaces with mixed regions of high and low wettability have been proposed and researched in the last decade. Such surfaces consist of poorly wettable areas, where bubble nucleation is supposed to take place, and a highly wettable surrounding area, which prevents bubble coalescence and provides liquid supply towards the poorly wettable regions. Heterogenous wettability of the surface could possibly ensure both an early transition into nucleate boiling on (super)hydrophobic spots and increase the CHF by delaying the dryout due to enhanced liquid supply by the (super)hydrophilic area surrounding the aforementioned spots.
To this effect, Betz et al. [26] fabricated smooth and flat surfaces combining hydrophobic (CA of 7-25 °) and hydrophilic regions (CA of 110 °) with a pitch of 50-200 μm and a spot size of 40-60% of the pitch value. The highest recorded CHF of 1900 kW m -2 and heat transfer coefficient of 85 kW m -2 K -1 were achieved on a surface with a pitch of 100 μm between hydrophobic spots, representing 65% and 100% enhancement over a plain hydrophilic surface. In another study, Betz et al. [13] combined a PTFE coating and reactive ion etching to produce superbiphilic surfaces, i.e., surfaces with superhydrophobic spots and a superhydrophilic surrounding area. They achieved heat transfer coefficients of over 150 kW m -2 K -1 and enhanced CHF values on superbiphilic surfaces with a pitch of 100 μm and a spot size of 50 μm (2:1 ratio), while the shape of the spot (circular/hexagonal) proved to be of little significance. Their results prove that the hydrophobic spots facilitate nucleation, while the hydrophilic surrounding area delays CHF incipience. Furthermore, the authors argue that (super)biphilicity should be considered an additional tool for phase-change enhancement and not as a direct competitor of other micro-and nanofabrication methods, which can be combined in many ways to produce surfaces with heterogeneous wettability. Coyle et al. [27] set out to elucidate how the shape of the hydrophobic spots (rings/hexagons/stars or their mix) on biphilic surfaces influences their performance and found that the highest CHF values were achieved for near-circular spot shapes. However, there was significant deviation between heaters with the same pattern and both the CHF and the heat transfer coefficient were not enhanced compared to the values for a homogeneously hydrophilic surface. Jo et al. [14] produced biphilic surfaces using PTFE-coated areas and areas of SiO 2 oxide on silicon heaters with a CA of 123 °a nd 54 °, respectively. Dot size and pitch were found to be important especially at low heat fluxes, while the number and the size of dots were dominant at high heat fluxes. Larger dots resulted in the onset of nucleate boiling at a lower superheat, while lower pitch caused more frequent bubble coalescence and shorter growth times. Lim and Bang [28] experimented with biphilic silicon surfaces using a combination of spray-coated square hydrophobic areas (CA of 151 °) and SiO 2 hydrophilic areas (CA of 42 °) with spot sizes of 2-3 mm and pitch values of 4-8 mm. All biphilic surfaces but one exhibited enhanced boiling performance with the surface with highest percentage of hydrophobic areas (2 mm spots, 4 mm pitch; 25% hydrophobic fraction) performing the best (15% and 34% increase in the CHF and the heat transfer coefficient, respectively). Nucleation was primarily observed on the edges of hydrophobic spots, while bubble departure diameter decreased with smaller spot size and pitch values, resulting in higher CHF values. Rahman and McCarthy [29] selectively hydrophobized biotemplated nickel-coated nanostructures with PTFE to produce a superbiphilic surface with 45 μm diameter spots and 90 μm spot pitch.
While approx. 25% lower CHF in comparison with purely superhydrophilic surfaces was recorded on the superbiphilic sample, a significant enhancement of the heat transfer coefficient was achieved (149 kW m -2 K -1 in comparison to 69 kW m -2 K -1 for a purely superhydrophilic sample) with the onset of nucleate boiling occurring at less than 3 K of superheat. Shen et al. [30] reported that bubble generation at extremely low temperatures (sometimes even below saturation) on hydrophobized areas of biphilic surfaces is induced by a significant presence of incondensable (and stable) gas retained by the hydrophobic surface and that "gassy" boiling causes unique bubble behavior. In additional studies, Shen et al. [31,32] and Yamada et al. [33] describe how inefficient intermittent bubble generation at subatmospheric pressures can be partially mitigated by the use of biphilic surfaces. The contact line mobility during bubble growth was investigated and the authors found that the strong pinning effect of the edge of the hydrophobic spots will likely be overcome below a certain threshold pressure, resulting in deactivation of the nucleation site. Hydrophobic spot sizes of 0.5 mm and 1 mm were tested in combination with pitch values of 1.5 mm and 3 mm at atmospheric and subatmospheric pressure. While large hydrophobic spots exhibited better performance at low heat fluxes and atmospheric pressure, their performance severely deteriorated with both increasing heat flux and decreasing pressure, and the sample with small spots and small pitch was identified as a superior surface. Furthermore, Shen et at. [34] have also demonstrated that application of biphilic surfaces to boiling of fluids with significantly lower surface tension (specifically, ethanol) is also possible. The highest heat transfer coefficients were obtained for a pitch-to-spot size ratio of 2.75:1 (2 mm spots with 5 mm pitch) with a ratio of 3:1 also exhibiting similar behavior. Zupan či č et al. [20] produced biphilic surfaces using a hydrophobic PDMS coating (CA of 138 °) on stainless-steel surfaces, which were locally turned superhydrophilic by nanosecond laser texturing of the coating. Square spots with sizes for 0.25-2 mm were produced using pitch values between 1.5 mm and 4 mm. The 0.25 mm spot size performed the best with a twofold thin-foilburnout heat flux enhancement and a maximum heat transfer coefficient of 51.2 kW m -2 K -1 , but an even higher CHF enhancement (250%) was achieved using a homogenous superhydrophilic surface. The authors report that smaller hydrophobic spots reduce bubble diameters and increase nucleation frequency, which was also confirmed through an analysis of wall-temperature distributions [35] . On the other hand, larger hydrophobic spots promote an earlier transition into nucleate boiling and exhibit higher heat transfer coefficients at low heat fluxes, but become covered with vapor at higher heat fluxes, creating local dry-outs and reducing the heat transfer intensity.
Due to the extreme complexity of phase-change heat transfer, which is still not completely understood and no definitive model of it exists, most studies of heat transfer enhancement methods rely on a trial-and-error approach to find the combination of parameters, which give the highest performance [9,36] . Conversely, a systematic approach to optimization of the biphilic pattern geometry to maximize the boiling enhancement was utilized in a few studies. A study of the effect of the hydrophobic spot pattern was performed by Jo et al. [37,38] , who report better low heat flux behavior with a small pitch value and a large spot size, while increasing the number of spots and decreasing their diameter results in higher heat transfer coefficients at high heat fluxes independent of the pitch value. Interestingly, the authors report that the fraction of the hydrophobic area is not a significant factor, although only fractions of up to 19.6% were used in the study. The opposite was shown by Motezakker et al. [39] , who used a constant pitch of 1 mm with hydrophobic spots (CA of 165 °) in a rectangular grid (surrounded by a hydrophilic area with a CA of 20 °), while the spot diameter was varied to achieve hydrophobic surface fractions between 0.2% and 100%. The study yielded convincing evidence that the percentage of the area covered by hydrophobic spots plays a very important role in bubble dynamics and boiling performance enhancement. Specifically, a coverage fraction of approx. 38% (spot diameter of 700 μm and edge-to-edge distance of 300 μm at a constant pitch value of 1 mm) was found to be optimal for boiling enhancement and corresponded perfectly with the highest overall nucleation frequency and smallest bubble diameters. Furthermore, the onset of nucleate boiling was achieved at the lowest superheat within the study using this pattern geometry. Larger hydrophobic spots (also resulting in larger hydrophobic surface fraction) exhibited worse boiling performance due extensive horizontal bubble coalescence, causing the appearance of a vapor blanket at lower heat fluxes. Recently, Pontes et al. [36] published a systematic analysis of the effect of the geometry of biphilic patterns on bubble dynamics and boiling performance. The biphilic surfaces consisted of hydrophobic spots (CA of 163 °) and hydrophilic surrounding area (CA of 64 °) on stainless steel with hydrophobic spot diameters between 1.5 mm and 5.2 mm, while the pitch was varied as a fraction or a multiple of the spot diameter (0.5, 1 or 2). Surfaces were prepared with either one, two or three hydrophobic spots to evaluate the bubble dynamics and spot interaction. Single-spot experiments showed that the bubble diameter is constrained by the size of the hydrophobic area and necking is promoted on smaller spots, slightly increasing departure frequency. Results of measurements using two adjacent hydrophobic spots indicate that moderate horizontal bubble coalescence promotes additional liquid flow between the spots and increases the amount of removed heat, although too small pitch values can result in vapor blanketing of the surface. Optimal hydrophobic spot size and pitch can therefore aid in providing ancillary liquid flow to further enhance boiling heat transfer in a similar fashion as was for example reported by Rahman et al. [40] or Jaikumar et al. [41] using different approaches to boiling performance enhancement. While the findings of the described studies provide some information about the influence of biphilic pattern's geometry on boiling heat transfer (enhancement), many questions are still not answered.
The present study investigates various combinations of superhydrophobic spot diameter and pitch values to determine the significant biphilic surface design factors to optimize enhancement in pool boiling of water. Superbiphilic aluminum surfaces are fabricated by combining hot water treatment with chemical vapor deposition (CVD) of a fluorinated silane to render the entire surface superhydrophobic (CA of ~165 °and roll-off angle (ROA) below 5 °), while laser texturing is used to modify the morphology and wettability of selected areas of the surface by removing the coating and causing superhydrophilic oxide growth with a resulting CA < 1 °S pot diameters of 0.25-1.0 mm are used in combination with a triangular lattice pattern and pitch (i.e., side length) values between 0.5 mm and 2.5 mm. Boiling heat transfer performance is evaluated using pool boiling tests performed under saturated conditions at atmospheric pressure. The effects of spot size, spot pitch, (super)hydrophobic area fraction, pattern's size scale and wettability contrast are elucidated through the comparison of boiling curves, heat transfer coefficients and high-speed video analysis.

Sample fabrication
All samples were prepared on 6082 aluminum alloy discs with a diameter of 18 mm and thickness of 4 mm with the planar face of the disk serving as the heat transfer area. Aluminum has a lower price and much lower density than copper, which is commonly used in heat transfer engineering, while its thermal conductivity is adequately high, making the research of aluminum surface functionalization for enhanced phase-change heat transfer warranted. All samples were embedded with a type K thermocouple glued into a 9 mm deep hole with a diameter of 0.8 mm, which was used to record sample's temperature 2 mm below the boiling surface to allow for surface temperature extrapolation. Samples were first sanded by hand using P1200 and P2000 grit sandpaper to produce a smooth surface with a roughness of approx. S a = 0.15 μm.
To prepare the samples for hydrophobization, they were ultrasonically cleaned for 5 min in acetone, ethanol, 2-propanol and water, respectively, with drying in between. Afterwards, the samples were submerged in hot water at roughly 90 °C for 60 min to induce the growth of pseudoboehmite ( and bayerite (Al(OH) 3 ) on the exposed aluminum [42][43][44] . This hot water treatment turns the surface hydrophilic and changes the nanomorphology through the growth of nanoneedles, since nanoroughness is important for achieving superhydrophobicity [45,46] . The cleaning process and hot water treatment were performed with the sample already mounted in the sample holder as described later.
After the hot water treatment, the surfaces were hydrophobized using the CVD process. The coating mixture was prepared by mixing 0.95 mL of toluene ( ≥99.7%, Honeywell International Inc.) with 0.05 mL of (heptadecafluoro-1,1,2,2-tetrahydrodecyl)trimethoxysilane (abbreviated to HTMS; Gelest Inc.). Multiple samples at a time were placed in a plastic container together with an open vial containing the coating mixture. The container was covered with aluminum foil and placed in a preheated oven for 90 min at 85 °C. Afterwards, the container was left to cool down before it was opened and the now homogeneously superhydrophobic samples were removed. The used hot water treatment and hydrophobization process was adapted after Yang et al. [47] and Chavan et al. [48] . The static contact angle on such surfaces is ~165 °, the ROA is < 5 °and the contact angle hysteresis is approximately 5 °, which qualifies the surfaces as superhydrophobic.
To produce the superhydrophilic regions of the superbiphilic surfaces, laser texturing was utilized to remove the fluorinated silane coating and induce oxide growth through ablation and melting of the material. As the produced metallic oxides have high surface energy [49] , the laser textured areas exhibit superhydrophilicity with a CA < 1 °immediately after laser texturing [49,50] . While laser texturing has been successfully employed to produce enhanced boiling surfaces without additional treatments [51][52][53][54][55][56][57] , its flexibility and precision makes it perfect for manufacturing biphilic surfaces with different hydrophobic spot patterns. Laser texturing was performed using a pulsed fiber laser (SPI Lasers, G4, SP-020PA) with a wavelength of λ = 1060 nm, full width at half maximum pulse duration of 45 ns and beam quality of M 2 = 1.3. The laser beam was guided across the surface with the scanning head (Raylase, SS-IIE-10) combined with the F-Theta lens with a focal distance of 163 mm. The laser texturing was performed in open air atmosphere using a set of parameters obtained through preliminary testing, which were chosen so that superhydrophilicity was achieved alongside minimal damage to the surface and minimal roughness increase making the superhydrophobic spots welldefined. Laser texturing was performed using an average power of 7.4 W, scanning velocity of 300 mm s -1 , pulse frequency of 90 kHz and average pulse fluence of 7.19 J cm −2 . The samples were textured in the focus of the F-theta lens (beam spot diameter: 38 μm) with parallel laser beam passes across the surface in only one direction with a lateral separation of 30 μm. Wettability of the superhydrophobic spots after laser texturing of the surrounding area was evaluated through a separate experiment and no change in their wetting behavior was detected.
Wettability of the samples was evaluated using sessile drop measurements on a custom goniometer setup. Measurements were performed with a droplet volume of 15-20 μL and were repeated on at least five locations on each evaluated sample. The apparent contact angles were determined by analyzing the captured images of individual droplets on the surface of the sample using a custom MathWorks MATLAB script. Accuracy of contact angle measurements is estimated to be approx. 2 °based on several rounds of repeated tests and calculated standard deviation of the measurements.
All samples used in this study are listed in Table 1 alongside the values of the spot diameter and the spot pitch. Several samples were prepared as the baseline of the experiment to enable an objective evaluation of enhancement obtained with superbiphilic surfaces. An untreated reference sample REF was prepared without undergoing the hot water treatment and was first exposed to water only after several hours of exposure to air, which causes a protective oxide film to grow on the surface and possibly reduces the extent of the surface chemistry changes when the latter is exposed to hot water during the boiling measurements. To determine how a completely laser-textured sample influences boiling performance, sample CLT was prepared by directly laser texturing the sanded surface with the same parameters that were used in preparing superhydrophilic regions of the superbiphilic surfaces. Similarly, sample SHPO was treated in hot water and hydropho- bized without subsequent laser texturing. Finally, sample HPO was prepared by direct hydrophobization after sanding without the hot water treatment, consequently exhibiting hydrophobicity with a contact angle of approx. 124 °and no ROA due to the absence of appropriate micro-and nanostructure required for superhydrophobicity. Superbiphilic samples were named so that their individual names denote the spot diameter and the pitch value (e.g., the sample s05p1 has s = 0.5 mm circular spots and the pitch of the triangular lattice is p = 1.0 mm). Sample s05p1 was fabricated and tested twice to evaluate the repeatability of the surface functionalization process (the second sample is denoted with the suffix "r" for repeatability), while two additional samples were treated in hot water and then directly laser textured without hydrophobization (denoted with suffix "nc" for "no coating") to investigate the importance of the wettability contrast. The percentage of the surface covered by superhydrophobic areas (i.e., the superhydrophobic fraction A SHPO ) is also listed in Table 1 for every surface. Fig. 1 (a) shows the schematic depiction of the triangular lattice pattern geometry and Fig. 1 (b) shows a scanning electron microscope (SEM) image of the pattern produced on the sample s025p05.

Experimental setup
Individual samples were mounted into a PEEK holder using a silicone O-ring, while flexible epoxy resin (Duralco 4538) was used to seal the gap and prevent boiling on the side of the sample. The holder with the sample was then mounted onto the bottom flange of the boiling chamber so that the boiling surface was horizontal and facing upwards. The boiling experimental setup is shown schematically in Fig. 2 (a) and consists of a glass cylinder with an internal diameter of 100 mm between two stainless-steel flanges.  Heat is supplied to the sample through conduction using a copper heating stem with three 400 W AC cartridge heaters. A cross section of the heating part of the setup including the heating stem and the sample in the sample holder is shown in Fig. 2 (b). There are four type K thermocouples imbedded in the axis of the heating stem 5 mm apart from one another with the top thermocouple located 4 mm below the contact surface with the sample. The entire heating stem is pressed against the sample using springs and thermal paste (Arctic MX-4) is used to ensure low contact resistance, which was calculated to be below 0.15 K W -1 . The produced vapor is led into an external water-cooled glass condenser mounted above the upper flange and returned to the boiling chamber as condensate. The upper part of the condenser is open to the atmosphere to avoid pressure buildup and ensure atmospheric conditions. An immersion heater is used to preheat approx. 500 mL of twice-distilled water prior to the measurements and degas it through vigorous boiling for at least 60 minutes.
A Keysight data logger (34972A) was used together with a 16channel multiplexer module (Keysight 34902A) to record the temperatures during the experiments with a sampling rate of 1 Hz. A moving average filter was applied to calculated heat flux and surface superheat values in data processing to reduce the effect thermocouple noise. At several selected heat fluxes, high-speed video camera (Photron FASTCAM Mini UX100) was used to evaluate the bubble departure diameter and departure frequency on selected surfaces.

Measurement procedure
Laser texturing of each sample was preformed immediately before the pool boiling measurements to avoid possible contamination of the surface with airborne hydrophobic contaminants and the consequent loss of superhydrophilicity [50,[58][59][60][61]. After mounting the sample into the boiling chamber, the latter was filled with twice-distilled water and the immersion heater was turned on to bring the temperature of the water to saturation. After vigorous boiling with the aim of degassing the surface and the water, the heater was turned off and the system was left to cool to a temperature below 90 °C ensuring that all vapor entrapped on the surface and inside the surface structures would be eliminated to avoiding premature onset of nucleate boiling [30] , skewing the results of pool boiling performance evaluation. To start each experimental run, the temperature of the water was brought back to saturation and the voltage on cartridge heaters in the heating stem was simultaneously increased. A dynamic measurement approach was used throughout the entire measurement by constantly increasing the power of the cartridge heaters, achieving a slow heat flux increase at a rate of less than 0.2 kW m -2 s -1 in the natural convection regime and less than 2 kW m -2 s -1 in the nucleate boiling regime. This was evaluated and justified in a previous study (see the Supporting Information of [53] ) and no deviations from the results recorded through steady-state measurements are expected. The heat flux was continuously increased until CHF incipience was reached, after which the surface was allowed to cool down for the vapor film to disappear. The CHF incipience was detected as a sudden substantial rise in surface temperature indicating the formation of a vapor film and transition towards film boiling; the last set of temperature measurements before this temperature increase is taken as the CHF point and corresponds to the uppermost point of each boiling curve. At least two boiling experimental runs were performed on every surface with comparable boiling behavior exhibited in both; only the results of the first run on each surface are shown to improve the clarity of data presentation.

Data reduction and measurement uncertainty
Heat flux was calculated through the spatial temperature gradient measured in the heating stem in accordance with the suggestions in [62] . The gradient was evaluated through linear interpolation of four temperatures recorded in the heating stem: where T i are individual temperatures and x is the distance between adjacent thermocouples (5 mm). Since the thermal conductivity of copper is temperature-dependent and its value decreases with temperature in the range of temperatures recorded within this study, an equation was defined based on thermal diffusivity measurements performed on copper and aluminum samples corresponding to the material of the heating stem and the samples: into which the temperature is inserted in degrees Celsius and thermal conductivity is calculated in W m -1 K -1 . Using the temperature-dependent thermal conductivity of copper evaluated at the mean temperature of the stem (arithmetic average of all four thermocouples), the heat flux was calculated through the following equation: The calculated heat flux is then used to extrapolate the surface temperature of the aluminum samples, the thermal conductivity of which is calculated at the measured sample temperature using the following equation: which is also based on temperatures in degrees Celsius. The extrapolation of the surface temperature is performed in accordance with: where x 2 is the distance from the thermocouple in the sample to the surface (2 mm). Finally, the surface superheat is evaluated based on the average temperature of the water as recorded by two type K thermocouples immersed into the boiling chamber and the surface temperature of the sample: The heat transfer coefficient as a measure of the heat transfer intensity is calculated from the surface superheat and the heat flux: The measurement uncertainty was evaluated based on the methodology proposed in [62] using During the nanosecond laser texturing of aluminum surfaces under atmospheric conditions, Al 2 O 3 is formed as the primary type of oxide and typically appears as a porous layer [63] . In our previous study [25] , where aluminum surfaces were laser-textured with comparable parameters, we have found that a porous, approximately 410 nm thick layer of aluminum oxide covers the entire laser-textured region. Based on the estimated range of effective thermal conductivity it was shown that the maximal temperature drop across the porous layer is less than 0.2 K at 1.5 MW m -2 . As this is significantly less than the measurement uncertainty of the surface superheat, we do not account for this effect when extrapolating the surface temperature. In addition to the surface oxides, thermal resistance of HTMS coating with thermal conductivity of 0.2 W m -1 K -1 [48] can also safely be neglected. The thickness of the coating deposited by the CVD method is only ~1 nm [48] , so its contribution to the uncertainty of the surface superheat is insignificant.

Surface morphology
Scanning electron microscopy (SEM) imaging was performed using JEOL JSM-6500F SEM at an accelerating voltage of 15 kV utilizing a secondary electron detector to analyze the morphology of modified surfaces. Fig. 3 (a) shows the surface of the untreated reference sample after exposure to water with clearly evident pseudoboehmite needle structure. An analysis of the surface s075p1 is shown in Fig. 3 (b) with the upper row dedicated to the morphology of the laser-textured area surrounding the superhydrophobic spots, the analysis of which is shown in the bottom row of the said figure. Laser texturing induced roughness through ablation and solidification of the molten material. No distinct (micro)cavities, capable of serving as active nucleation sites [52,53] , are observable. The hot-water-treated circular spot exhibits similar micromorphology as the untreated surface with the only difference stemming from  the contrast and brightness of individual figures with overall similar nanoneedle size and density. The CVD-applied HTMS coating is not visible in the figure since its thickness is ~1 nm [48] , which makes it hard to detect using SEM imaging.

Reference boiling experiments
The evaluation of boiling performance of the set of reference surfaces is shown in Fig. 4 (a) in the form of a boiling curve com-parison. The CHF value on the untreated aluminum surface is approx. 1090 kW m -2 at a surface superheat of 32 K. Rohsenow's correlation [64] was fitted onto the experimental data for the reference surface using n = 1 with R 2 of 0.967; a C sf value of 0.0187 was obtained. A slightly higher value of the C sf coefficient could be explained by the growth of pseudoboehmite and bayerite on the aluminum surface when it is exposed to water [42][43][44] , which causes slight hydrophilicity and shifts the boiling curve towards higher superheats.
Hydrophobization of the surface without the hot water pretreatment (sample HPO) will shift the boiling curve towards lower superheats while the CHF will remain comparable since the wettability modification is not extreme. Conversely, the superhydrophobic sample SHPO, which underwent the hot-water pretreatment before CVD hydrophobization, exhibits even better boiling performance with the boiling curve shifted over 5 K towards lower surface superheats. However, a slightly lower CHF compared to the reference surface was recorded on the superhydrophobic sample and is attributed to weaker rewetting due to the low-surfaceenergy nature of the coating and the preference to remain in contact with vapor rather than with the liquid. Finally, the completely laser-textured sample (CLT) exhibits the highest CHF in this comparison but also the highest superheat values in the nucleate boiling regime, which is due to the high surface energy of the oxides formed during the laser texturing process. While the oxide layer aids in liquid replenishment and delays dryout (thus enhancing the CHF value), the higher energy barrier for nucleation results in higher surface superheat recorded in our experiments. A boiling curve "hook back" was also observed on the CLT sample and is attributed to secondary boiling effects as discussed by Kruse et al. [65] . This change in boiling behavior is attributed to the appearance of additional nucleation events on top of laser-induced surface structures at high heat fluxes, which only appear at high heat fluxes, when the temperature of top parts of the microstructures is sufficiently high for nucleation to occur. No observable permanent damage was detected on any of the surfaces following CHF incipience.
Heat transfer coefficient values for all four surfaces are compared in Fig. 4 (b) at four selected heat flux values matching early (150 kW m -2 ), moderate (500 kW m -2 ) and high heat flux nucleate boiling (10 0 0 kW m -2 ) as well as CHF incipience on every surface. The same heat flux values are also used in other comparisons of boiling performance. It is clearly evident from the aforementioned figure that the heat transfer performance of the SHPO surface out- matches all other surfaces in this comparison at all heat flux values. Especially during nucleate boiling at low heat fluxes, the heat transfer coefficient of the SHPO surface is approximately twice that of the other surfaces in this comparison due to the incipience of nucleate boiling at a surface superheat below 5 K. This also agrees with the observation by Allred et al. [24] , who report that highly efficient boiling is possible on poorly wettable surface, if they are properly degassed so that boiling is initiated from the Wenzel wetting regime and not from the Cassie-Baxter regime. Lastly, the heat transfer performance of the superhydrophilic CLT surface is actually slightly lower than that of the reference sample until the high heat flux nucleate boiling region is reached, where the surface superheat starts to decrease with increasing heat flux (i.e., the secondary pool boiling effects appear) and a significant increase in the heat transfer coefficient is observed.

The effect of spot hydrophobicity
To verify that the magnitude of the contrast in wettability of the circular spots and surrounding area is important for significant boiling performance enhancements using (super)biphilic surfaces, a comparison shown in Fig. 5 (a) was made. Two surfaces with superhydrophobic spots were tested alongside their counterparts with uncoated (hydrophilic) spots (suffix "nc"). The wettability contrast on the latter surfaces is therefore much smaller than on the two superbiphilic surfaces since the hydrophilic spots provide a much lower contrast magnitude against the superhydrophilic surrounding area compared to the superhydrophobic spots. This is reflected in higher boiling performance of the surfaces with hydrophobized spots (solid lines) compared to those with uncoated spots (dashed lines). High-speed video analysis of the nucleate boiling process on the s05p1 and s05p1nc samples (shown in Fig. 6 for the heat flux of 40 kW m -2 ) revealed that superhydrophobic spots provide slightly lower bubble departure diameters (~1.1 mm) compared to hydrophilic spots (~1.3 mm), while the nucleation frequency on hydrophobic spots is significantly higher. At 80 kW m -2 the average nucleation frequency on s05p1 sample equaled 133 Hz, but only 87 Hz on the s05p1nc sample. It should be noted that not all available spots were active at that time. Differences in nucleation frequencies confirm that significantly lower surface superheat is needed to initiate boiling on superhydrophobic spots, which results in an overall enhancement of the heat transfer coefficient. Both "nc" surfaces exhibit similar boiling curves as the reference surface, but with a notably higher CHF due to the superhydrophilic nature of the majority (~77%) of the surface. A similar but more subtle hook back phenomenon is also observed on all biphilic surfaces within this comparison, which suggests that nucleation also takes place on superhydrophilic surrounding areas at high heat fluxes, when their temperature is high enough to overcome the increased nucleation energy barrier caused by their high surface energy.
The comparison of heat transfer coefficients at selected heat fluxes shown in Fig. 5 (b) substantiates previous findings. The performance of surfaces with superhydrophobic spots is higher than that of the reference surface at all heat fluxes, whereas the surfaces with uncoated spots only enhance boiling performance at very high heat fluxes, which perfectly matches the behavior of the CLT surface. Both superbiphilic surfaces enhance the boiling performance with notable increases of the heat transfer coefficient especially at higher heat fluxes.

Effect of size scale
Even though heat transfer enhancement was provided by both superbiphilic surfaces shown in Fig. 5 , the enhancement magnitude differed between the two samples despite the same pitch-todiameter ratio of 2 and the same superhydrophobic surface fraction of 23%. As the surface with smaller spots (and corresponding smaller pitch) exhibited superior performance, the effect of the size scale of the (super)biphilic pattern was investigated with the results shown in Fig. 7 . Two additional surfaces were fabricated using the same pitch-to-diameter ratio with the spot pitch value being twice that of the circular spot diameter and the recorded boiling curves are shown in Fig. 7 (a). While a comparable CHF was achieved on all four superbiphilic surfaces (between 1400 kW m 2 and 1480 kW m 2 ), slightly different heat transfer coefficients were recorded depending on the spot diameter/pitch. The fraction of superhydrophobic areas on all four surfaces included in this comparison is the same (23%). The early nucleate boiling performance of all four surfaces is comparable, but the surfaces with 0.5 mm and 0.75 mm diameter spots exhibited superior performance at medium and high heat fluxes. Increasing the spot size to 1 mm or decreasing it to 0.25 mm had a negative effect on the boiling performance. High-speed video analysis showed that the bubble departure diameter increases slightly with the hydrophobic spot size (on average from ~1.0 mm for 0.25 mm spot size up to ~1.3 mm for the 1.0 mm spot size with a standard deviation of the bubble diameter of ± 0.2 mm), which is in agreement with our previous observations on biphilic surfaces [20] . These values were measured up to about 200 kW m -2 where individual bubbles were still identifiable. However, the bubble departure diameters are very comparable between different hydrophobic spots [39] , implying that an optimal distribution of active nucleation sites cannot be achieved at a certain pitch-to-diameter ratio with many different spot sizes. When the size of the hydrophobic spots increases and pitch-to-diameter ratio is kept constant, the allowable nucleation site density (e.g., the number of hydrophobic spots per unit of surface area) is decreased. This will create larger temperature gradients across the surface and decrease the heat transfer coefficient as observed on sample s1p2. On the other hand, when the pitch between hydrophobic spots is decreased significantly below the bubble departure diameter (sample s025p05 with the highest theoretical nucleation site density), individual active nucleation sites will locally cool down the sample and also limit the development of thermal boundary layer above the neighboring hydrophobic spots, thus decreasing the probability for simultaneous nucleation from multiple potential nucleation sites. As a result, such surface will also not provide the optimal heat transfer coefficient. That said, the highest heat transfer coefficient will be obtained on samples with the hydrophobic spot pitch close to the expected bubble departure diameter. Samples s05p1 and s075p15 best match this criterion and also show the best overall heat transfer performance.
Nevertheless, the heat transfer coefficient comparison shown in Fig. 7 (b) reveals that the heat transfer coefficient is enhanced for 16-38% over the reference surface (up to approx. 500 kW m -2 ) and an even greater enhancement of 45-83% is observed at the CHF.

Effect of spot pitch
To clarify the effect of spot pitch on the boiling performance of wettability-patterned surfaces, multiple variants of the previously best-performing surface s05p1 were fabricated with a constant spot diameter of 0.5 mm and pitch values between 0.75 mm and 2.5 mm (the latter corresponding to the capillary length for saturated water under atmospheric pressure and terrestrial gravity). Furthermore, another s05p1 sample (denoted with the suffix "r") was fabricated to evaluate the repeatability of the surface manufacturing process and the boiling experiments.
A comparison of boiling curves for samples with different pitch values at a constant spot diameter of 0.5 mm is shown in Fig. 8 (a).
The sample with 2.5 mm capillary-length spacing (superhydrophobic surface fraction of 4%) exhibited virtually no enhancement over the reference surface with nearly the same CHF value. Similarly, the sample with half-capillary-length spacing of 1.25 mm (superhydrophobic surface fraction of 15%) exhibited similar surface superheats as the untreated surface, albeit the CHF was enhanced to approx. 1360 kW m -2 . Reducing the pitch value down to 0.75 mm (superhydrophobic surface fraction of 40%) also did not provide superior performance compared to the s05p1 sample, since superheat values similar to the reference surface and the s05p125 sample were recorded although the CHF was increased to the highest value within this comparison (1460 kW m -2 ). While this could at first glance point to mistakes in the surface fabrication process, another sample (s05p1r) exhibited nearly identical performance as the s05p1 sample (i.e., within the measurement uncertainty), indicating that the significant boiling enhancement must be a consequence of sample geometry and not faulty fabrication, testing methods or randomness of the boiling process.
The heat transfer coefficient recorded on surfaces with the same spot diameter are compared at four heat flux values in Fig. 8 (b,c). Similar to the previously observed behavior, some superbiphilic surfaces only enhance the boiling performance at high heat fluxes due to the increased CHF value with no significant enhancement below 10 0 0 kW m -2 . The comparison of heat transfer coefficients versus the superhydrophobic fraction of the surface [ Fig. 8 (c)] reveals that the boiling performance enhancement seems to increase with increasing fraction of the superhydrophobic area up to 23% [sample s05p1(r)] and then decreases again when the fraction is increased further. This behavior matches the observations by Motezakker et al. [39] , who reported the trend of boiling performance first increasing up to an optimal value with increasing share of superhydrophobic areas and then decreasing again. Their results, however, indicate that the optimal fraction of surface hydrophobicity is approx. 38% (0.7 mm dimeter spots and pitch value of 1 mm), although samples with a hydrophilic area with a CA of 20 °surrounding superhydrophobic spots were used in their study.
Results in Fig. 8 further prove our observations from the previous section. The best overall performance was achieved on the sample s05p1 with the pitch distance (1.0 mm) very close to the average bubble departure diameter (~1.1 mm). Samples s05p125 and s05p25 with the pitch higher than the bubble departure diameter will provide lower nucleation site density and thus lower heat transfer coefficient, while sample s05p075 will not allow simultaneous activation of all nucleation sites, which will again result in reduced boiling performance. It is shown that optimization of the spot-to-diameter ratio on biphilic or textured surfaces should be performed based on the actual bubble diameter, which depends not only on fluid type and boiling conditions (e.g., pressure, subcooling, gravity etc.), but also on surface properties [66,67] . We believe this is the main reason why several authors have reported different optimal distributions of active nucleation sites. One of the breakthrough studies in this field was published by Rahman et al. [40] , who showed that nucleation site (or active nucleation area) spacing should be based on the capillary length criterion for a given fluid (and operating conditions). The study in question only involved one-dimensional separation of active nucleation areas and the bubble departure diameters during saturated pool boiling of water on plain copper reached the capillary length of water (~2.5 mm), which was also found to be the optimal pitch of nucleation area separation. Later, Zakšek et al. [68] found that optimal pitch between active boiling areas distributed in a single dimension is slightly larger as predicted by the capillary length criterion. They concluded that the capillary length criterion can be used as a starting point in the optimization procedure, but the actual optimum should be based on the maximization of active nucleation site density, which is also supported by the results of this study. Furthermore, we show that the optimal two-dimensional distribution of active nucleation sites on biphilic surfaces can be achieved by varying the hydrophobic spot pitch around the optimal value determined by the bubble departure diameter. As the bubble departure diameter can change with surface topography and wettability (and partially also with hydrophobic spot size), the optimal distances are not universal for each fabrication type. This can possibly explain different observations in the literature.

Effect of spot diameter
To further explore the effect of surface pattern geometry, two additional surfaces were prepared using the identified optimal spot pitch of 1.0 mm and spot diameter values of 0.25 mm and 0.75 mm. The results of boiling performance evaluation on these surfaces with a constant pitch are shown in Fig. 9 . The performance deviations using a constant spot pitch of 1.0 mm are much smaller than those shown for the analysis of different pitch values ( Fig. 8 ). This is again in agreement with the previous discussion since all surfaces have the same pitch close to the optimal value for the given fabrication type and operating conditions. Consequently, all three superbiphilic samples exhibit relatively comparable performance as the bubble diameter varies only slightly with the spot diameter and does not have a major influence on the heat transfer performance. In this essence, the spot pitch or rather its value relative to the bubble departure diameter can be singled out as the most important influencing the boiling heat transfer performance. A higher CHF value recorded on the sample with 0.25 mm diameter spots is caused by a larger fraction of superhydrophilic surface area, resulting in a boiling curve more similar to the completely laser-textured sample (CLT). However, the s025p1 sample still exhibits superior performance in comparison with the CLT surface as there are preferential nucleation sites (i.e., superhydrophobic spots) present on the superbiphilic sample. The sample with 0.75 mm diameter spots exhibits a comparable CHF to the s05p1 sample. The surface with 0.5 mm spot diameter still exhibits the highest overall heat transfer coefficient value at CHF, but the boiling performance of the other two surfaces is largely comparable up to 10 0 0 kW m -2 . The analysis of heat transfer coefficient versus the fraction of the superhydrophobic areas present on each surface again confirms that the spot diameter does not have a significant effect on the boiling performance when the optimal pitch value is used [ Fig. 9 (c)].

Conclusion
The results indicate that a strong wettability contrast is important in increasing the boiling heat transfer performance of wettability-patterned surfaces. To achieve the optimal enhancement, (super)hydrophobic spot pitch value should be approximately matched with the value of the bubble departure diameter, which needs to be identified for the given surface functionalization method and set of operating conditions. The optimal pitch value will provide a high density of potentially active nucleation sites but still allow for the growth of the thermal boundary layer thus not inhibiting the activation of neighboring spots. The size of (super)hydrophobic spots is shown not to have a major influence on the boiling performance when optimal spot pitch is used. Although the surface with the smallest spots exhibited slightly increased CHF, this is attributed to a higher fraction of superhydrophilic area. The optimal fraction of (super)hydrophobic areas also depends on the surface functionalization approach and spot pattern, which results in different reports found in literature. While a higher heat transfer coefficient at low and medium heat fluxes can be achieved with properly degassed homogeneously superhydrophobic surface, the developed superbiphilic surfaces increase the CHF and provide greatly enhanced heat transfer coefficients at high heat fluxes.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Supplementary materials
Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijheatmasstransfer. 2020.120265 .