Investigation of the Enhancement of Boiling Heat Transfer Performance Utilizing a Hybrid Wetting Surface with a Macroscopic Millimeter-Scale Pillar Array

Abstract

The heat transfer process is an important part of energy utilization and conversion, and boiling heat transfer is one of the most significant and effective heat transfer modes in use. Enhancing boiling heat transfer can directly improve energy use efficiency and promote the sustainable development of the energy industry. Surfaces with mixed wetting topologies have been proven to possess the potential to enhance boiling heat transfer. However, the heat transfer promoting mechanism of these types of surfaces requires further clarification on actual heat exchanger surfaces with macroscale heat transfer enhancement structures, such as millimeter-scale pillars. In this study, the boiling heat transfer enhancement mechanism and the performance of the hybrid wetting surfaces with an array of macropillars were explored using both experimentation and numerical simulation. In the experiment, the single bubble growth dynamics at the onset sites of nucleation of these hybrid wetting surfaces in the initial boiling stage were recorded using a CCD camera with a top view. The boiling heat transfer coefficient was also measured at the stable boiling stage. Within the entire tested range of heat flux (3.75–18 W/cm²), the hybrid wetting surfaces significantly enhanced the boiling heat transfer, and the HPo(bottom)–HPi(top) surface (surf-2) exhibited the best heat transfer performance. At the representative heat flux 12.5 W/cm², the boiling heat transfer coefficient of the HPo (bottom)–HPi (top) surface (surf-2) and the HPi (bottom)–HPo (top) surface (surf-3) were more than 33% and 18% higher than the pure copper flat surface, and more than 16% and 3% higher than the uniform HPi surface (surf-4), respectively. On the one hand, due to the view field of camera being blocked by the fiercely growing bubbles in the stable boiling stage, it was difficult to record bubble numbers and gather statistics at the onset sites of nucleation in order to correlate the bubble dynamics with the mechanism of boiling heat transfer enhancement. On the other hand, the single bubble growth dynamics recorded during the initial boiling stage lacked information about the hybrid wetting surfaces in the vertical cross-sectional plane. Therefore, a two-dimensional VOF-based numerical simulation was adopted to supplement the contribution of hybrid wetting surfaces in the vertical plane. The simulation results indicated that the hybrid wetting surfaces with macropillars can inhibit bubble overgrowth and accelerate bubble departure compared with spatially uniform hydrophobic surface. The bubble radius and departure time on surf-2 were smaller than those on surf-3. These are believed to be the reasons why the surf-2 surface exhibited the best heat transfer performance in the experiment. Both the experiment and numerical analysis proved that the hybrid wetting surfaces with macroscale pillars can promote the boiling heat transfer, thus demonstrating potential applications in actual horizontal or vertical tube boiling heat exchangers.

1. Introduction

The efficiency of energy power equipment is related to the sustainable development of the entire energy industry and the living environment. Due to the large number of heat exchangers in the energy power equipment, enhancing the heat transfer performance in the heat exchangers plays an important role in promoting the efficiency of the energy industry and maintaining the sustainable development of our living environment.

Boiling is an important heat transfer mode in actual heat exchangers. Among various factors, surface wettability has a significant influence on the intensity of boiling heat transfer [1,2]. At low heat flux, a hydrophobic (HPo)/superhydrophobic (sHPo) surface is able to promote nucleation and increase the heat transfer coefficient, while at a high heat flux, the number of active nucleation sites would be limited by the hydrophobic properties of the surface due to the large contact diameter of the bubbles. Conversely, a hydrophilic (HPi)/superhydrophilic (sHPi) surface can create bubbles with smaller sizes and fewer numbers, leaving ample open spaces for nucleation bubbles to independently grow. Therefore, increasing the surface wettability at high heat flux can prevent coalescence of bubbles and the formation of a gas film, thereby augmenting both the HTC (heat transfer coefficient) and CHF (critical heat flux) [3,4]. An ideal boiling heat transfer surface should possess the ability to promote nucleation in the regime of isolated bubbles and suppress the excessive growth of individual bubbles simultaneously. However, a surface with spatially uniform wettability does not satisfy this requirement. Hybrid wetting surfaces have been focused on since the seminal work of Betz et al. [5,6]. It has been proven that superhydrophilic surfaces with isolated super-hydrophobic islands show excellent performance in pool boiling. The largest CHF and HTC in the experiment are over 100 W/cm² and more than 100 kW/(m²K), respectively.

In recent years, there has been growing interest in heterogeneous surfaces, including bi-conductive surfaces [7,8] and biphilic (hybrid wetting) surfaces [1,2], which can suppress bubble overgrowth. Many practical hybrid wetting surface methods for manufacturing biphilic surfaces that are easy to implement have been developed. Hou et al. [9] used a simple one-step laser ablation technique to produce superhydrophilic/superhydrophobic hybrid surfaces with a SHPi triangular pattern in the SHPo background, and found that condensed droplets have rapid nucleation and growth in the SHPi mode. Egab et al. [10] used the film-wrapping approach to prepare actual round tubes with hybrid wetting outer surfaces. They found that the macroscopic flat mixed wetting surfaces with a diamond pattern had the highest heat circulation and heat transfer coefficients. Shen et al. [11] prepared polished copper surfaces with a biphilic pattern (mixed wetting pattern), by depositing an array of macro-scale circular spots of fluoropolymer coating. These biphilic surfaces were proven to significantly increase heat transfer rates. Motezakker et al. [12] fabricated biphilic spot array surfaces with different macro or micro spot sizes and pitch distances by adopting deep reactive ion etching (DRIE) technology. They demonstrated that biphilic surfaces can directly increase both the critical heat flux (CHF) and boiling heat transfer coefficient. In the above studies, the macro millimeter-scale hydrophobic and hydrophilic parts are contained within hybrid wetting surfaces, but they are still macroscopically flat or smooth.

In general, the overall boiling heat transfer coefficient of the wetting surface can be obtained through experimental tests. However, due to the blockage of the camera view by the fiercely growing bubbles, the specific characteristics of bubble growth cannot be acquired in direct experiments, especially during the stable boiling stage. Instead, numerical approaches have been used to clearly predict the bubble growth process and further reveal the mechanism of boiling heat transfer enhancement in hybrid wetting surfaces from the viewpoint of bubble dynamics. Liao et al. [13] studied how a mixed wetting surface with micro-nanostructures can effectively reduce the starting temperature of explosive boiling by the molecular dynamics (MD) simulations. Guo et al. [14] analyzed the evaporation behavior of the mixed wetting surfaces using molecular dynamics (MD) simulations with LAMMPS software. Li et al. [15] and Yu et al. [16] used the lattice Boltzmann method (LBM) to predict the single bubble growing process on a single pillar or a pillar array surface, respectively. However, the dimensions of their computational domains were represented by the lattice unit and not using the actual physical size.

Most studies on the enhancement of boiling heat transfer using hybrid wetting surfaces have focused on microscale mixing patterns or macroscopically flat/smooth surfaces. However, for practical heat exchangers, surfaces with macroscale raised pillars are generally adopted to promote performance instead of a pure flat surface. Generally, these heat transfer surfaces with macroscale raised pillars feature uniform wetting properties. Shen et al. [17] designed a chemical deposition approach to process the hybrid wetting pattern on the millimeter-scale pillar array surface. It was proved that these hybrid wetting surfaces could augment boiling heat transfer in the nucleate boiling regime from the viewpoint of the HTC value. However, the differences in the bubble growing process among different wetting surfaces were not clearly presented, nor was the key factor leading to the enhancement of boiling heat transfer elucidated. In this study, single bubble growth dynamics at the onset site of nucleation of hybrid wetting surfaces in the initial stages of boiling were recorded using a CCD camera with a top view, and the heat transfer coefficient that calibrated the boiling heat transfer performance was measured at the stable boiling stage. Then, a numerical method that can precisely reproduce the bubble growing process on the hybrid wetting surfaces was established. By comparing the single bubble growth dynamics on the different hybrid wetting surfaces, the effect of wetting properties at different parts of the pillars on the bubble dynamics was analyzed, and the promoting mechanism of boiling heat transfer on different wetting surfaces was elucidated.

2. Hybrid Wetting Surface Preparation and Boiling Experiment Measurement

2.1. Hybrid Wetting Surface Preparation

Four types of macropillar surfaces were prepared, two with spatially uniform wetting properties and the other two with hybrid wetting properties (

Table 1. The tested surfaces (HPi—hydrophilic, HPo—hydrophobic, surf—surface) in the experiment.

Surface Name	Surf-1	Surf-2	Surf-3	Surf-4
Apparent contact angle θ (º)	115	115-60	60-115	60
Wettability Abbreviation for surface samples	HPo	HPo-HPi	HPi-HPo	HPi
Wettability on top face of pillar	HPo	HPi	HPo	HPi
Wettability on bottom face of pillar	HPo	HPo	HPi	HPi
Groove width (mm) between pillars Wg	1.0	1.0	1.0	1.0
Pillar width (mm) Wr	1.0	1.0	1.0	1.0
Groove depth (mm) Dg	1.5	1.5	1.5	1.5

). The two spatially uniform wetting surfaces were hydrophilic (HPi) and hydrophobic (HPo), respectively. The hybrid wetting surf-2 in Table 1 had a hydrophilic (HPi) top and a hydrophobic (HPo) bottom, and surf-3 had a hydrophobic (HPo) top and a hydrophilic (HPi) bottom. Photos of real test surface samples are presented in the Supplementary Material. The detailed fabrication process is provided in Ref. [17]

The copper block base had dimensions of 40 mm × 40 mm × 10 mm (length × width × height). In order to ensure the total number of macro-scale pillars, square pillars with dimensions in millimeters were used. The groove width (W_g), pillar width (W_r), and groove depth (D_g) were 1 mm, 1 mm, and 1.5 mm, respectively, as shown in Figure 1.

2.2. Boiling Heat Transfer Measurements

The visualization saturated pool boiling experiments were implemented to obtain the single bubble growth dynamics in the initial boiling state by the CCD camera from the top view and to measure the heat transfer coefficients of the hybrid wetting surfaces in the stable boiling stage. Schematics and actual pictures of the test devices are presented in the Supplementary Material. The experimental data processing and verification are presented in Ref. [17].

3. Numerical Method for Bubble Growing

The evolution history of the single bubble growth dynamics can effectively reveal the essence of the boiling heat transfer [18,19,20]. However, during the boiling experiment, the high-speed camera view was blocked by the violently generated bubbles in the stable boiling process, and the bubble growing process could not be clearly observed. Therefore, a numerical method that can precisely predict the bubble growth dynamics was implemented to further reveal the mechanism of boiling heat transfer enhancement using hybrid wetting surfaces.

In this paper, the VOF (volume of fluid) method for the multiphase fluid, which uses the surface compression scheme [21,22], was adopted. The details of the numerical method were introduced in Ref. [23], including the contact angle model and the smooth function to reduce the non-physical parasitic currents at the phase interface, among others. In order to predict the mass transfer between the liquid and vapor phases of water in the phase change process, the condensation and evaporation model was added in the VOF method. The accuracy and reliability of current numerical method was validated using experimental data on single bubble growth reported in Ref. [18].

3.1. Condensation and Evaporation Model

According to the kinetic gas theory and Hertz Knudsen formula [24,25],

$$F=C\sqrt{M/\left(2\pi R{T}_{\mathrm{activate}}\right)}\left(p-p_{\mathrm{sat}}\right)$$

(1)

where F is the mass transfer rate (Kg/s/m²), M is the molecular mass, T_activate is the activation temperature (corresponding to a saturated boiling point or a condensation temperature), C is the accommodation coefficient, R is the universal gas constant, p_sat is the saturation temperature, and p is the steam fractional pressure.

The Clapeyron–Clausius equation relating pressure to temperature for the saturation condition is as follows:

$$\frac{dp}{dT}=-\frac{L}{T\left(v_{\mathrm{v}}-v_{\mathrm{l}}\right)}$$

(2)

where L is the latent heat, v_v is the vapor phase specific volume, and v_l is the liquid phase specific volume. The two formulas above are combined and simplified to obtain the following equation:

$$F=\frac{2C}{2-C}\sqrt{M/\left(2\pi R{T}_{\mathrm{activate}}\right)}L\frac{{\rho }_{\mathrm{v}}{\rho }_{\mathrm{l}}}{\left({\rho }_{\mathrm{v}}-{\rho }_{\mathrm{l}}\right)}\frac{\left(T-T_{\mathrm{activate}}\right)}{T_{\mathrm{activate}}}$$

(3)

where C > 0 is on behalf of evaporation, C < 0 is on behalf of condensation, and ${\rho }_{\mathrm{v}}$ and ${\rho }_{\mathrm{l}}$ are the density of the vapor and liquid, respectively. For small pressure changes, Equation (3) can predict high mass transfer rates and large heat generation/absorption rates [26]. It should be noted that the accommodation coefficient is variable, and in this study, it was confirmed using the experimental data of the single bubble growth in Ref. [18] in the following section.

3.2. Validation of the Numerical Method Using Bubble Growth Dynamics on a Flat Surface

The numerical method described above was implemented using the OpenFOAM open-source CFD platform and validated using experimental data on single boiling bubble growth on the flat plate [18].

The boiling saturation temperature was 373.15 K and the wall superheat was 7 K, which was linearly distributed within a distance of 0.00075 m from the wall. The contact angle at the wall was 50°. The initial radius of the bubble was 0.0002 m, and the adjustment coefficient of the mass diffusion formula at the gas–liquid interface was C = 0.5. A two-dimensional (2D) axisymmetric computational domain was used with a grid size of 20 μm, as shown in Figure 2. The width and height of the computational domain were 4 mm and 6 mm, respectively.

According to the experimental data in Ref. [18], the bubble detachment time was approximately 53 ms, while the corresponding time from the numerical prediction was approximately 52.5 ms in Figure 3. A comparison of the variation histories of the bubble diameter between the numerical simulation and the experiment [18] is plotted in Figure 4 below.

According to the curves in Figure 4, the vertical diameter of the bubble in the simulation was consistent with the experiment, but the overall mean bubble diameter (area-weighted integral) was slightly smaller than the vertical direction diameter. The experimental data and the simulation results differed slightly with each other at each moment, which can be attributed to differences in the overheating temperature layer thickness and the linear distribution of overheat temperatures between the experimental and numerical setups. Overall, the numerical results were consistent with the experimental results.

3.3. Geometric Model and Grid Independence Study

It should be emphasized that the numerical simulation was designed to provide clear evidence demonstrating the effect of hybrid wetting on the dynamics of single bubble growth, rather than reproducing the entire bubble growth process in the boiling heat transfer experiment. In order to reduce computational consumption and consider the contribution of hybrid wetting surfaces in the vertical cross-sectional plane to the bubble growth dynamics, a two-dimensional computational domain with the geometric model of the macro-pillar surface illustrated in Figure 5 was adopted. The radius of the initial bubble was 0.2 mm, and the radius of the rounded corner was 0.1 mm, as shown in Figure 5.

The original grid size in the computational domain was 40 μm in Figure 6. A two-dimensional adaptive mesh refinement (AMR) technique was employed to promote computational precision [27]. A grid independence verification was conducted, and the corresponding results are shown in Figure 7. The AMR-1 dictated the one-level AMR, which means that the basic grid was dynamically refined once, i.e., the minimal grid size after refinement was 20 μm. The AMR-2 and AMR-3 indicate that the basic grid was refined twice and three times, respectively, resulting in the finest grid sizes of 10 μm and 5 μm, respectively. Figure 7a shows the variations in the bubble equivalent radius r ($\sqrt{S_{bubble}/\pi }$) with dimensionless time (the ratio of the physical time to the departure time of the AMR-1 case, t/t_amr-1,depart). The dimensionless departure time for the AMR-1 case was significantly smaller than those for the AMR-2 and AMR-3 cases. There was a small difference between the values of the dimensionless departure time for the AMR-2 and AMR-3 cases; however, the curves of equivalent radius for the two cases nearly coincided with each other. Additionally, the computational time (using Intel Xeon CPU E5-2676 v3, 12 cores parallel computation) showed an exponential growth trend with increasing AMR levels, as shown in Figure 7b. Therefore, considering the trade-off between computational accuracy and efficiency, the two-level AMR, which was accurate enough for the bubble profile prediction while maintaining high computational efficiency, was adopted for the following analysis. According to Figure 7b, the representative CPU time for predicting the bubble dynamics was approximately 30,000 s.

4. Results and Discussion

4.1. Analysis of the Experimental Data

The heat transfer coefficients obtained from the experiment over the entire range of heat flux, 3.75–18 W/cm², are presented in Figure 8. The HTC curves for surf-1 (HPo) (uniform hydrophobic surface) and the hydrophilic flat surface (HPi) (represented by the green asterisk symbols and dotted line) intersect each other at approximately 4 W/cm². For heat fluxes greater than 4 W/cm², the HTCs of the flat surface (HPi) were larger than those of surf-1 (HPo). Thus, the spatially uniform hydrophobic surf-1 with macropillars didn’t demonstrate capability in enhancing boiling heat transfer. Except for surf-1 (HPo), the other three surfaces enhance boiling heat transfer in comparison with the flat surface (HPi). Additionally, the HTCs of the hybrid wetting surfaces with macropillars, i.e., the surf-2 (HPo–HPi) and the surf-3 (HPi–HPo), were both larger than those of the uniformly hydrophilic surface with macropillars, i.e., surf-4 (HPi). Therefore, the hybrid wetting surfaces with macropillars can augment the boiling heat transfer within the range of heat flux reported in this study. Furthermore, surf-3 (HPi–HPo), was superior to surf-2 (HPo–HPi) in enhancing the boiling heat transfer.

In this section, the effect of the hybrid wetting surfaces on the enhancement of boiling heat transfer at a fixed heat flux of 12.5 W/cm² imposed on the test surface is primarily discussed.

Table 2. Heat transfer coefficients in the stable nucleate boiling stage under a heat flux of 12.5 W/cm².

Surface Name	Surf-1	Surf-2	Surf-3	Surf-4	Flat Surface
Representative abbreviated name	HPo	HPo-HPi	HPi-HPo	HPi	HPi
Heat transfer coefficient h (W/(cm2 K))	0.86	1.35	1.20	1.16	1.01

shows the HTCs at a heat flux of 12.5 W/cm² for all the test surfaces reported in Figure 9, Figure 10, Figure 11 and Figure 12, which exhibit the bubble growth dynamics recorded using a CCD camera at the onset sites of nucleation for surf-1 to surf-4, under a heating power of 200 W (12.5 W/cm²) in the initial boiling stage. The bubble growth dynamics could not be clearly recorded in the stable boiling stage due to the violent generation of bubble groups which blocked the camera view.

Figure 9 shows the growth of bubbles at the onset sites of nucleation for surf-1 (HPo): the spatially uniform hydrophobic surface with macropillars. Two effective observation zones, which correspond to Figure 9a–d, were selected. At zone 1, the initial bubble arised in the groove between pillars (Figure 9a), followed by another bubble in the groove at the lower right of the initial bubble, which then coalesced with the initial bubble (Figure 9b). Subsequently, a third bubble occurred at the intersection of grooves to the left of the initial bubble, which also coalesced with the initial bubble (Figure 9c). Finally, the coalesced bubble at the initial onset site of nucleation continued rising (Figure 9d). At zone 2, as shown in Figure 9e–h, the bubble arose on the top surface of the pillar and then grew gradually and stably.

Figure 10 shows the growth of bubbles at surf-2 (bottom HPo–top HPi): the onset site of nucleation for the hybrid wetting surface with macropillars. Two observed zones were also selected. At zone 1 (Figure 10a–d), the initial bubble arose at the intersection of grooves, i.e., at the center region of the four pillars. Then the initial bubble expanded (Figure 10b). Its upper part rose and moved toward another bubble that arose at another intersection of grooves to the right (Figure 10c). Finally, the coalesced bubble moved towards the grooves between the pillars to the right (Figure 10d). At zone 2 (Figure 10e,f), a bubble occurred at the root of one pillar (Figure 10e). Then, it gradually transferred to the top surface of the pillar and stably expanded (Figure 10f–h).

Figure 11 shows the growth of a bubble at an onset site of nucleation for the hybrid wetting surface with macropillars, surf-3 (HPi–HPo), where the top surface was hydrophobic and the bottom surface was hydrophilic. Due to the intense boiling process, only one effective zone was observed using the CCD camera, even at the beginning stage of boiling. The initial bubble formed in the grooves between two pillars as shown in Figure 11a. The initial bubble did not remain at the center of the groove, and its upper part stretched out from the groove between the pillars and into the upper intersection of the grooves. Then as shown in Figure 11b, the bubble moved into the groove located at the upper side of the pillar, which was close to the onset site of bubble shown in Figure 11a. Finally, this bubble settled there and continued to stably grow, as shown in Figure 11c,d.

Figure 12 shows the growth of bubbles at the onset sites of nucleation for surf-4 (HPi): the uniformly hydrophilic surface with macropillars. Only one effective zone was observed using the CCD camera. One bubble arose in the groove between the pillars (Figure 12a). It continued to grow at the original site (Figure 12b,c) until it departed from the surface (Figure 12d). Meanwhile, another bubble arose in the groove below the first bubble (Figure 12b), but it quickly departed from the surface (Figure 12c).

As shown in Table 2, the spatially uniform hydrophilic surf-4 (HPi) promoted boiling heat transfer compared with the pure copper flat hydrophilic surface. This was attributed to the larger heat transfer area of surf-4, which included the extra four side surfaces surrounding the macro square pillars. However, the spatially uniform hydrophobic surf-1 (HPo) could not promote the boiling heat transfer. This is due to its spatially uniform hydrophobic feature. As mentioned by Betz et al. [5,6], at a low heat flux, the hydrophobic surface can promote nucleation, and in such cases, the hydrophobic surface can provide a higher heat transfer coefficient than the hydrophilic surface. However, once the heat flux exceeds a certain value, the large contact diameter of the bubbles limits the maximum total number of active nucleation sites. Based on the theory that HTC depends linearly on the nucleation site density [5,6], the HTC of the hydrophobic surface cannot be enhanced any further. In contrast, in this scenario, the hydrophilic surface, due to the small contact diameter of the bubbles, activates many more nucleation sites, leading to a larger HTC than the hydrophobic surface.

In Figure 9a–d, three bubbles arose at three adjacent sites on the uniformly hydrophobic surf-1 (HPo). For the other three surfaces with macropillars, no bubbles arose close to the initial onset site of nucleation. This indicates that the hydrophobic zone of surf-1 could indeed promote the initial nucleation. However, these bubbles coalesced quickly into a larger bubble instead of growing and departing in isolation. The coalesced bubble may have prevented subsequent nucleation. Therefore, the effective number of nucleation sites for surf-1 (HPo) was not as much as the other four test surfaces, which may result in the lowest HTC for surf-1 (HPo) among the five test surfaces, as shown in Table 2.

As shown in Figure 10 and Figure 11, some bubbles on the hybrid wetting surfaces could not stably grow in the original onset sites of nucleation and move drastically, especially for surf-2 (HPo–HPi), where the top was hydrophilic and the bottom was hydrophobic. Similar phenomena, where boiling droplets move spontaneously, were reported for the hydrophobic network (a hydrophobic surface with isolated hydrophilic islands) in Ref. [5]. To the authors’ knowledge, these phenomena are attributed to the asymmetric surface tension force arising from the gradient wetting surface, which can automatically drive the liquid or vapor to flow [28,29,30]. Ultimately, the hybrid wetting bumpy surfaces consisting of hydrophilic and hydrophobic patterns represent a distinct form of gradient wetting surface. When the bubbles span the hydrophilic and hydrophobic regions simultaneously, the surface tension forces in the two wetting regions align, resulting in the movement of the bubbles.

4.2. Analysis of Numerical Results

In Section 4.1, the performance of the boiling heat transfer of the five test surfaces were compared based on experimental data. To analyze the bubble growth phenomena, a sufficient number of isolated onset sites of nucleation should be recorded and statistical analysis should be conducted during the stable boiling stage. However, due to the limitations of the CCD camera technique used in this study, only a limited number of onset sites of nucleation were clearly observed in the initial boiling stage. In this section, numerical simulation was implemented to analyze the bubble growth dynamics and its effect on the boiling phase-change heat transfer.

The purpose of the numerical simulation was to demonstrate the effect of hybrid wetting on single bubble growth dynamics, and not to precisely reproduce the experimental results. Nonetheless, the bubble growth dynamics reported in Section 4.1 provided insight into the effect of hybrid wetting from a top view. Therefore, the VOF method was adopted to simulate the bubble growth dynamics by considering the contribution of the hybrid wetting surface in the vertical cross-sectional plane. The initial superheat at the wall was 10 K, and the saturation temperature was 373.15 K. The uniform temperature field at 373.15 K was heated by the superheated wall for 0.1 s, then this temperature field was taken as the initial temperature field in the simulation. The apparent contact angles of the hydrophobic surface and the hydrophilic surface were set to be 120° and 60°, respectively. Figure 13 presents the evolution histories of the bubble growth dynamics over time on the four types of wetting surfaces with macro pillar array, as reported in Table 1.

The profiles of the bubbles produced on the four types of wetting surfaces with macropillars in Figure 13 differ from each other. When the top surfaces were hydrophobic (θ_top = 120°), i.e., surf-1 (HPo) and surf-3 (HPi–HPo), the triple contact lines easily spread over the top surface wall, eventually staying at the top corner vertex of the square pillar. Conversely, when the top surface of the pillar was hydrophilic (θ_top = 60°), i.e., surf-2 (HPo–HPi) and surf-4 (HPi), the contact lines could not pass over the top corner vertex to spread on the top surface. This is attributed to the direction difference between the surface tensions in the triple contact line zone on the HPo and HPi surfaces. The horizontal component of the surface tension on the HPo surface could promote the bubble extending in the direction of x-axis, while the surface tension on the HPi surface prevented the bubble from spreading in the x-axis direction.

From Table 2, it is shown that the boiling heat transfer coefficients for surf-1 (HPo) and surf-2 (HPo–HPi) were the lowest and highest of all the five surfaces, respectively. The difference between the two surfaces was that the top surface was HPo for surf-1 and HPi for surf-2. Therefore, it is reasonable to speculate that the suppression effect of the hydrophilic parts in surf-2 on bubble growth led to the higher HTC of surf-2. In other words, in comparison with the spatially uniform hydrophobic surf-1, the hydrophilic parts of the hybrid wetting surf-2 (HPo–HPi) limited the increase in bubble diameter and further increased the number of the nucleation sites.

The radii of the departing bubbles corresponding to surf-3(HPi–HPo) and surf-4 (HPi) were nearly the same (2.07 mm and 1.99 mm, shown in

Table 3. Bubble departure time and radius for the wetting surfaces according to numerical results.

Surface Name	Surf-1	Surf-2	Surf-3	Surf-4	Flat-1	Flat-2
Contact angle θ (º)	120	120-60	60-120	60	120	60
Departure time (ms)	80	50	60	40	120	120
Area (mm2)	17.5	8.32	13.5	12.4	26.0	5.51
Radius (mm)	2.36	1.63	2.07	1.99	2.88	1.32

). However, the bubbles on the uniformly hydrophilic surf-4 (HPi) departed the surface nearly 33% faster than on the hybrid wetting surf-3 (HPi–HPo). In other words, the departure frequency of the bubbles on surf-4 was distinctly higher than the bubbles with almost the same size on surf-3. The boiling heat transfer performance of surf-4 could be benefit from the high frequency of bubble departure. However, as shown in Table 2, the boiling heat transfer coefficient for the hybrid wetting surf-3 (HPi–HPo) was larger than that for the uniformly hydrophilic surf-4 (HPi). It is speculated that the promotion of boiling heat transfer on surf-3 (HPi–HPo) comes from the increased nucleation site density on its hydrophobic part compared with surf-4.

From Figure 13 and Table 3, it can be observed that the hybrid wetting of surf-2 and surf-3 could reduce the bubble radius and departure time compared to the spatially uniform HPo surf-1. This indicates that the HPi part of the hybrid wetting surface could suppress the overgrowth of the bubble on the HPo part and accelerate the departure. Additionally, the results showed that surf-2 with the HPi top had a smaller bubble radius and a shorter departure time than surf-3 with the HPo top. This difference is believed to be the primary reason for surf-2 having better boiling heat transfer performance than surf-3 at approximately the same nucleation rate.

Additionally, some noise points can be seen around the main bubble in Figure 13. These noise points were considered to be caused by gas micelles that escaped from the main bubble when the bubble triple line crossed the corner vortex of the rib. However, the influence of these gas micelles on the main bubble growth dynamics was considered insignificant.

Figure 14 shows the evolution histories of bubble growth dynamics for the uniformly hydrophobic and hydrophilic flat surfaces, specifically, the flat-1 (HPo) and the flat-2 (HPi) in Table 3, respectively. The bubble radius on the flat-1 was larger than the uniformly hydrophobic surf-1 (2.88 mm for the flat-1 and 2.36 mm for the surf-1, as shown in Table 3). The departure time on the flat-1 was also longer than that that of surf-1 (150 ms for flat-1 and 80 ms for surf-1, as shown in Table 3). The difference in the bubble radius and departure time between flat-1 and surf-1 was attributed to the limitation effect of the macropillar on the horizontal spreading of the bubble size. The bubble radius on the hydrophilic surface of flat-2 was smaller than that of the hydrophilic surface of surf-4 (HPi) with macro pillars (1.32 mm for flat-2 and 1.99 mm for surf-4), but the bubble departure time was much longer than that of surf-4, as presented in Table 3. The higher bubble departure efficiency of surf-4 was believed to result from the larger heat transfer area of the pillars. This is also one of the reasons why the heat transfer coefficient of surf-4 was higher than flat-2, as shown in Table 2.

5. Conclusions

Wetting surfaces with a macroscopic millimeter-scale pillar array were fabricated, and their heat transfer performances in the nucleate boiling regime were investigated using numerical simulations and experiments. Under the geometrical conditions of the fabricated surfaces, it was found that the heat transfer coefficient for the spatially uniform hydrophobic macropillar surface was the lowest. The hybrid wetting surfaces with macropillars were found to effectively augment the boiling heat transfer, especially for the hybrid surface with a hydrophilic top surface and hydrophobic bottom surface.

Over the whole range of heat flux, 3.75–18 W/cm², the HTCs of the hybrid wetting surfaces were greater than those of the spatially uniform wetting surfaces. In other words, the hybrid wetting surfaces could significantly promote the boiling heat transfer. Additionally, the hybrid HPo (bottom)–HPi (top) surface exhibited the best boiling heat transfer performance. At the representative heat flux of 12.5 W/cm², the boiling heat transfer coefficient of the HPo (bottom)–HPi (top) (surf-2) and the HPi (bottom)–HPo (top) (surf-3) surfaces were more than 33% and 18% higher than the pure copper flat surface, respectively, and more than 16% and 3% higher than the uniform HPi surface (surf-4), respectively. Observations of the onset sites of nucleation in the experiment also prove that the initial bubble tended to locate at the intersections of the grooves or at the grooves between the pillars.

The growth dynamics of a single bubble located at the groove between the square pillars were reproduced using a two-dimensional VOF numerical simulation. It was found that the hydrophilic part of the hybrid wetting surfaces effectively prevented the spreading of the triple line, suppressed the bubble size, and eventually accelerated the bubble’s departure away from the wall. Additionally, both the bubble radius and departure time on the hybrid HPo (bottom)–HPi (top) surface were smaller than those on the hybrid HPi (bottom)–HPo (top) surface. These factors are considered critical in achieving the best boiling heat transfer performance on surf-2.

In summary, from the perspectives of experimental measurements and numerical simulations, it was proven that the boiling heat transfer performance of the wetting surfaces with macroscopic millimeter pillars can be improved using the hybrid wetting mode. In comparison with microstructures on the order of tens of microns, it is more convenient to fabricate macroscopic millimeter-scale pillars on the actual heat exchanger surface. Therefore, hybrid wetting surfaces with macro-scale pillars have greater potential to directly promote energy transfer efficiency and further support sustainable development of the energy industry. In the future, actual heat transfer surfaces, such as the inner and outer walls of straight tubes and screw tube in boiling heat exchangers, can be fabricated using the hybrid wetting surface with macro-scale pillars to further test their heat transfer performance in the realistic application scenarios.