Unexpected Suppression of Leidenfrost Phenomenon on Superhydrophobic Surfaces

The Leidenfrost phenomenon entails the levitation of a liquid droplet over a superheated surface, cushioned by its vapor layer. For water, superhydrophobic surfaces are believed to suppress the Leidenfrost point ($\it{T}$$_{\rm L}$)-the temperature at which this phenomenon occurs. The vapor film obstructs boiling heat transfer in heat exchangers, thereby compromising energy efficiency and safety. Thus, it is desirable to realize superhydrophobicity without suppressing $\it{T}$$_{\rm L}$. Here we demonstrate that the $\it{T}$$_{\rm L}$ of water on microtextured superhydrophobic surfaces comprising doubly reentrant pillars (DRPs) can exceed those on hydrophilic and even superhydrophilic surfaces. We disentangle the contributions of microtexture, heat transfer, and surface chemistry on $\it{T}$$_{\rm L}$ and reveal how superhydrophobicity can be realized without suppressing $\it{T}$$_{\rm L}$. For instance, silica surfaces with DRPs facilitate ~300% greater heat transfer to water droplets at 200$^{\circ}$C in comparison with silica surfaces coated with perfluorinated-nanoparticles. Thus, superhydrophobic surfaces could be harnessed for energy efficient thermal machinery.


Introduction
Known for over two centuries, the Leidenfrost phenomenon entails the levitation of an evaporating liquid droplet on a hot surface such that the droplet's weight is counterbalanced by the pressure of the vapor film formed underneath 1 . This phenomenon has attracted interest across many disciplines 2,3,4,5,6,7,8,9,10,11,12 , and it has been applied to engineering applications, such as directional droplet propulsion 7,9 , electricity generation 13 , and green chemistry 14 , among others 3 . For liquids with strong intermolecular forces 15 and a high boiling point such as water, the Leidenfrost phenomenon occurs-the Leidenfrost point (TL)-at temperatures significantly higher than at normal temperature and pressure (NTP: 293 K and 1 atm). For example, for a smooth and flat silica surface, the TL of water is in the range 270°C-300°C 16,17 . As a corollary, the Leidenfrost phenomenon can be realized at NTP with liquids that have ultralow boiling points, such as liquid nitrogen and 1,1,1,2-tetrafluoroethane with boiling points of −196°C 18 and −26.1°C 9 , respectively. In either scenario, a vapor film with a thickness of ~100 µm levitates the droplet above the surface, after which the droplet slowly evaporates, akin to film boiling 3,9,18 . Roughening of surfaces can have profound consequences on TL: for example, hierarchical micro/nano-texturing furthers the wettability of a silica surface with water, increasing the temperature needed for the water droplet to achieve the Leidenfrost state (e.g., TL > 400°C) 16,17,19,20 . Conversely, when hydrophobic coatings are applied to micro/nanotextured surfaces, they can give rise to superhydrophobicity, characterized by water contact angles, qr ≥ 150°, and an empirical constraint on contact angle hysteresis, e.g., Dq ≤ 20°2 1,22,23 . Superhydrophobicity lowers the TL of water by facilitating (i) low adhesion energy per unit area at the solid-liquid-vapor (SLV) interface given by the Young-Dupré equation, !" = #$ × (1 + cos % ), where gLV is the surface tension, and % > 90° is the actual (or intrinsic) contact angle of the liquid (water) 24 , and (ii) reduced liquid-solid contact area (hence adhesion) due to the interfacial entrapment of air 4,25,26,27,28 . For instance, after a flat metallic surface was rendered superhydrophobic by coating it with the Glaco Mirror Coat Zero TM coating (hereafter referred to as Glaco), the TL of water reduced from 210°C to 130°C; similarly, Glaco-coated superhydrophobic steel balls 4 and rotors 26 exhibited TL approaching 100°C and also afforded significant reduction in frictional drag 4 . Taken together, these findings give credence to conventional wisdom that superhydrophobicity lowers the TL of water 25,27,28,29 .
Superhydrophobic surfaces have been exploited to enhance pool boiling 30 ; however, their applications in thermal machinery operating at high temperatures remain limited as superhydrophobicity generally lowers the TL of water. Specifically, the vapor film prevents the interfacial heat transfer because of its lower thermal conductivity than that of the liquid 31 , for example, in boiler pipes, heat exchangers, and turbines. This situation, known as boiling crisis or burnout 32 , can severely impact energy efficiency, damage machinery, and cause accidents 33 .
Hence, it is of practical interest to investigate whether the lowering of the TL of water is a universal attribute of superhydrophobicity, similarly to the water contact angle, qr > 150°, the contact angle hysteresis, Dq < 20°, and the robust entrapment of air under water on superhydrophobic surfaces, because superhydrophobicity without suppressing the TL of water could reduce frictional drag 34 while facilitating interfacial heat transfer.
Here, contrary to conventional wisdom, we demonstrate that superhydrophobic surfaces do not always lower the TL of water. We utilize silica surfaces adorned with a specialized biomimetic microtexture comprising doubly reentrant pillars (DRPs) that exhibit superhydrophobicity despite their hydrophilic surface chemistry. 22,23,35,36 Counterintuitively, water's TL on these superhydrophobic silica surfaces is significantly higher than that on flat hydrophilic silica surfaces and even higher than that on superhydrophilic microtextured silica surfaces (see Table 1 for the apparent contact angles of water droplets). We combine experiment and theory to pinpoint the contributions of microtexture, interfacial heat transfer, and surface chemistry to the onset of the Leidenfrost phenomenon on these surfaces.

Fig. 1|
Representative scanning electron micrographs of surfaces investigated in this study and their wettability with water at NTP. a) Flat silica; b) Glaco-coated silica that exhibits superhydrophobicity; c) tilted view (45°) of cylindrical pillars with a diameter (D) of 10 µm, height (H) of 50 µm, and pitch (L) of 50 µm; d) tilted view (45°) of doubly reentrant pillars with D = 10 µm, H = 50 µm, and L = 50 µm; e, f) magnified views of DRPs with the vertical length and width of the double reentrant edge, respectively, Sv = 2 µm and Sh = 0.5 µm. g-j) Representative images of water droplets (15 µL) on the surfaces outlined in panels (a-d) and their apparent contact angles (CAs).
Silica surfaces with DRPs exhibited superhydrophobicity with qr = 150° ± 1° and Dq =19° ± 2° (Fig. 1j), similarly to Glaco-coated silica. The sliding angles of water droplets (10 µL) on Glaco-coated silica and silica with DRPs were 7° ± 3° and 13° ± 2°, respectively ( Table 1 and Methods). To confirm this result, we ascertained TL on these surfaces by tracking the lifetime of sessile water droplets on them as a function of surface temperature to determine how long it took for the water droplets to evaporate on these surfaces. As the surface temperature (Ts (°C)) increases, the droplet lifetime decreases due to faster evaporation. In the vicinity of TL, the droplet lifetime starts increasing monotonically due to the formation of an insulating vapor layer underneath the droplet that diminishes the interfacial heat transfer. By gradually increasing the temperature in the range 70°C-440°C, the TL values for hydrophilic silica surfaces-flat and those adorned with cylindrical pillars-were pinpointed to be ~286°C and ~314°C, respectively, (Fig. 2e). For superhydrophobic surfaces-DRPs and Glaco-coated silica-there were no distinct peaks in the droplet lifetime curves (Fig. 2f). Therefore, we utilized high-speed imaging to monitor vapor film formation at the droplet-solid interface to pinpoint the onset of Leidenfrost  Next, we observed the behavior of water droplets (15 µL) on silica with DRPs at T = 347°C via high-speed imaging complemented with high-magnification optics (Fig. 3). We found that a typical droplet exhibited an up-and-down vibratory motion under the influence of its vapor force built underneath, weight, and adhesion at the SLV interface (Figs. 3a-3c, and Supplementary Materials, Video S5). As the droplet moved upward, the number of DRPs in contact with the droplet decreased and vice versa, and the air-water interface assumed concave and convex curvatures, respectively (Figs. 3d and 3e). After the initial contact, when the center of mass of the droplet was at the highest point, it was still pinned to ~3-10 DRPs, which preempted the onset of the Leidenfrost phenomenon ( Figs. 3b and 3c). We considered that as a liquid droplet is placed on a hot substrate, its vapor flow is obstructed by the surface microtexture, which builds up an upward vapor force, Fv (N). If Fv is greater than the droplet's weight, G (N), it tends to lift it, whereas the liquid-solid adhesive force, FAd (N), impedes this motion (Fig. 3d). Conversely, if Fv < G, the droplet tends to sink into the microtexture, which the adhesive force, FAd, also counters (Fig. 3e). In the concave configuration, the vapor has adequate space to escape; thus, Fv drops ( Figs. 3f and 3h). Subsequently, the droplet advances and silicon (50 µm), respectively. When the water droplet lands onto DRPs, it only touches the pillars for a depth of ~2 µm (Fig. 4a), after which the air-water interface assumes a convex shape and any further liquid movement does not increase the liquid-solid contact (Fig. 4b).
Particularly, the liquid-solid contact on the DRPs is sensitive only to the dimensions of the pillars' caps and not to the penetration depth (Lp); this peculiarity would cease to exist at ultrahigh Weber numbers, where the drops would penetrate the microtexture, and those cases are beyond the scope of this study. In stark contrast to DRPs, when a water droplet rests on superhydrophilic cylindrical pillars (Supplementary Materials, Fig. S6, and Video S7), it tends to penetrate them (Fig. 4c), thus increasing the liquid-solid contact area and deepening the liquid penetration depth (Fig. 4d). The enhanced penetration depth remarkably impacts heat transfer, which we next investigate computationally by simulating the temperature distributions in DRPs and cylindrical pillars, followed by presenting an analytical model to derive expressions for Fv to gain mechanistic insights into the onset of the Leidenfrost phenomenon.

Computational and analytical modeling
Temperature distributions in silica surfaces adorned with DRPs and cylindrical pillars as a function of water penetration depth were simulated using COMSOL ® (COMSOL Multiphysics, version 5.4 44 ). In this approach, we assumed that (i) a quasi-steady state, (ii) the water temperature was 99°C 3 , (iii) the convective heat transfer coefficient for the vapor inside microtextures was 20 W/(m 2 ×K) 31 (Fig. S7), and (iv) the evaporation at the air-water interface was considered as an outflow of heat flux. The experimentally observed penetration depths of water droplets into the microtextures comprising DRPs and cylindrical pillars were 2 and 20 µm, respectively (Figs. 4a and 4c). Consequently, the top region of the DRPs (Fig. 4f) were significantly hotter than that of the cylindrical pillars (Fig. 4h), which explains why the heat transfer in the case of the DRPs was significantly lower than that in the case of cylindrical pillars ( Fig. 4e and 4g). The higher heat transfer in the case of cylindrical pillars generated higher vapor fluxes and hence the upward vapor force, thereby lifting the droplet at lower temperatures than that in the case of DRPs. 4b and 4d). This heat transfer rate, Q1, is also equal to the heat transfer rate absorbed from the substrate underneath Q2 (W) (Region 2 in Figs. 4b and 4d). Therefore, where , = 4 % , where 4 (W/m 2 ) is the heat flux from the hot surface. A0 = L 2 (m 2 ) is the projected area of the periodic unit (Fig. 5a), me (kg) is the mass of evaporated water in a periodic cell, t (s) is time, and hfg (J/kg) is the latent heat of the evaporation of water.
Accounting for heat conduction across the vertical direction, Eq. (1) yields  Note that keff (W/(m×K)) is the effective heat transfer coefficient determined by the area average of air and the solid fractions 17 : where kv (W/(m×K)) and ks (W/(m×K)) are the thermal conductivities of the vapor and the solid, respectively, and e is the ratio of the vapor area to the projected area, ε = ( , − π( /2) , )/ , .
Since the radius of the droplet's base (Rb (m), ~0.7 mm from experimental observation) is dramatically larger than the height of the pillars, i.e., Rb >> H, the lubrication analysis can be applied 46 . As the vapor is produced from the bottom of the droplet and released from the spaces between pillars, the continuity equation can be written as where ur (m/s) is the radial vapor velocity. Considering an approximately linear temperature distribution along the pillars 12 , we can obtain the vapor velocity along the z-axis: After applying lubrication analysis, the momentum equation for flow in the porous media can be reduced to classical Brinkman Equation 47 : where Pr (Pa) is the pressure distribution at the r-direction, µv (Pa×s) is the dynamic viscosity where = S / . Next, we substitute Eq. (6) into Eq. (8), and applying the boundary conditions, we obtain the radial pressure profile as Thus, the vapor force, Fv (N), exerted by this vapor film onto the droplet can be estimated by Furthermore, the meniscus adhesive force on each DRP, Fadi (N), is estimated as overcomes the adhesive force (Fad) and gravitation force (G), which allows the droplet to be levitated by a continuous vapor layer: where G = mg is the gravitation force, m (kg) is the mass of the droplet, g (m/s 2 ) is the gravitation acceleration, and n is the number of DRPs in contact with the water droplet and can be estimated as = YP , * # * . At the onset of the Leidenfrost phenomenon, Ts is equal to TL.
Substituting Eqs. (10) and (11) into Eq. (12), the temperature corresponding to TL is Equation (13) captures the dependence of the TL on the thermal, structural, chemical, and inertial characteristics of the system, especially the heat conduction at the water-substrate interface that scales with the penetration length (Lp), microtexture dimensions, liquid-solid adhesion, and the vapor flow through the microtexture. As the penetration depth, Lp, increases, TL drops for both microtextures (Fig. 5b). To disentangle the effects of geometry and surface chemistry, we utilized the model to predict the variation in the TL of water with pillar height and surface chemistry. We found that TL in both cases increased with increased pillar height (Fig. 5c) because the taller the pillars are for a given pitch, the larger is the space to escape for the vapor, lowering Fv. The model also pinpointed that as the surface hydrophobicity increases, TL drops (Fig. 5d). Therefore, the onset of the Leidenfrost phenomenon depends on a delicate balance among Fv, G, and FAd, which cannot be satisfied by all superhydrophobic surfaces.
Thus, these forces could be balanced to engineer superhydrophobic surfaces that can prevent the onset of the Leidenfrost phenomenon even better than hydrophilic and superhydrophilic surfaces.

Discussion
These experimental and theoretical findings might aid the rational design of superhydrophobic surfaces in thermal power engineering, for instance, for reducing frictional drag without compromising interfacial heat transfer. We illustrate this by comparing the time it takes to evaporate a drop of water placed on silica with DRPs with that on Glaco-coated silica, both maintained at 200°C. Although both surfaces were superhydrophobic, the water evaporated much faster on silica with DRPs than that on Glaco-coated silica (Fig. 6). Silica with DRPs facilitated a 300% higher heat transfer than Glaco-coated silica because the former suppressed the Leidenfrost phenomenon to well above 200°C, whereas the latter experienced film boiling at TL ≈ 130°C. In conclusion, we have demonstrated that it is possible to realize superhydrophobic surfaces that do not suppress the TL of water via a judicious choice of surface microtexture and chemistry. This design can yield superhydrophobic surfaces or coatings for simultaneously reducing frictional drag and preempting boiling crisis in thermal machinery, such as heat exchangers, boiler pipes, and turbine blades. The coating-free aspect of the bioinspired DRP architecture is also enticing for its robustness against harsh conditions and organic fouling.

Sample preparation
Silicon wafers (p-doped, 4-inch diameter, and 500 µm thickness with a 2.4-µm-thick thermally grown silica layer) were used as substrates (Fig. 1a). To fabricate DRPs (Fig. 1d), we applied photolithography, dry etching, and thermal oxide growth, followed by the protocols reported in the previous studies. 23,37 Besides DRPs, we microfabricated silica surface adorned with arrays of cylindrical pillars, which were rendered superhydrophilic (Fig. 1c), manufactured by the same materials above, and the pitch, height, and top diameter of cylindrical pillars were the same as those of the DRPs. After surface fabrications and before droplet experiments, all samples were cleaned with Piranha solution (H2SO4: H2O2 = 3:1) for 15 min at 110°C and stored in the vacuum oven for 24 h at 50°C and ~0.03 bar. Consequently, the actual (or intrinsic) contact angle ( % ) of water on the silica surface was stabilized at ~40°.
For comparison, Glaco coating was used to coat flat silica (same materials in the DRPs) as the common superhydrophobic surface (Fig. 1b). The effect of surface chemistry was studied by coating perfluorodecyltrichlorosilane (FDTS) on DRPs using a molecular vapor deposition system (ASMT 100E), as described previously 53 . All the surface structures were examined by a scanning electron microscope (Helios Nanolab SEM).

Contact angle measurements
We characterized the wettability of these surfaces with water by measuring apparent CAs of water droplets (6 µL) and advancing and receding angles at a rate of 0.2 µL/s. The water CAs on the surfaces of different samples were measured using a drop shape analyzer (Kruss: DSA100) interfaced with the Advance software. The sliding angles of water droplets (10 µL) on these surfaces were measured by an automatic tilting stage, where a camera was used to record the movement of droplets. All experiments were repeated at least three times.

Droplet generation for Leidenfrost experiments
To generate water droplets, we used a Harvard Apparatus syringe pump (PHD ULTRA: 703007INT) and a 60-mL plastic syringe connected by a plastic syringe extension tube. A stainless-steel capillary (diameter: ~0.51 mm) was used to dispense water perpendicular to heated test surfaces. The flow speed was set as 100 µL/s, and the syringe system continuously generated 15-µL droplets (radius: ~1.5 mm, which is smaller than the capillary length of water ~2.7 mm at NTP).

Confocal experiments
A Zeiss upright laser confocal microscope (Model number: LSM710) was used to detect the meniscus at the interface between a droplet and pillars. A ~100-µL water droplet with Rhodamine B (Acros) was gently placed on samples using a manual syringe, and a 20X microobjective lens was immersed into the droplet before acquisition. The 520-nm laser at the Zstack mode was used to scan the droplet-surface interface. Subsequently, using Imaris v.8.1 by Bitplane, we obtained cross-sectional images to visualize the meniscus shape ( Supplementary  Materials, Fig. S5b-c).

High-speed imaging
A high-speed camera (model number: Phantom V1212) with a zoomed lens was applied to record images at a high frame rate. To ensure that all the images have the same configuration, the imaging parameters of the camera such as frame per second (FPS), image pixels, and exposure time in all experiments were set to 1000 FPS, 512 ´ 512 pixels, and 200 µs, respectively. A triaxial stage was used to adjust the position of the samples with respect to the high-speed camera. The hot plate was leveled using a bubble leveler, and the images were calibrated by the stainless-steel capillary. For image processing, Phantom Camera Control 2.8 software was used.

Leidenfrost experiments
A hot plate (temperature: 20°C-540°C) was placed on a triaxial stage and balanced by a bubble level. Considering the nonequilibrium nature of the hot plate, the actual temperatures of the hot plate surface were measured by a K-type thermocouple and recorded by a temperature data logger (Omega: RDXL6SD).
We moved the capillary tip with a droplet as close to the surfaces as possible to gently release droplets from the capillary onto the surfaces to minimize the droplet impact. Thus, all the droplets keep the same low Weber number (We » 1.7) to minimize its effect on the Leidenfrost point. Water droplets (15 µL) were generated by a syringe pump and released from the needle tip to the heated sample surface. A high-speed camera was used to record the impact, bounce, and vibration of droplets and observe liquid-vapor-solid interactions at the interface between droplets and surfaces. All the experiments were repeated at least three times.
To measure Leidenfrost points on different surfaces, the classical lifetime method 10 was used to measure TL on these surfaces. The first peak in the curve between the lifetime and surface temperatures yields TL 10,25 . To measure the lifetimes of droplets, the temperature of the hot plate increased by 10°C at each step, and the droplet evaporation times were recorded by a timer. All experiments were repeated at least five times. Since there is usually no clear lifetime peak when the Leidenfrost transition occurs on superhydrophobic surfaces, we used the highspeed camera to detect TL on Glaco-coated flat silica and silica with DRPs by observing the moments of vapor film formation and droplet bouncing while gradually increasing the temperature.

Calculations
Simulation results were obtained by utilizing the heat transfer module in COMSOL (5.4) (the detailed boundary conditions are shown in Supplementary Materials). Equations 1-13 were solved using the commercial software Wolfram Mathematica (11.0). The thermal properties of water were taken at 99°C, and other materials' properties were taken at 225°C, which is an average temperature between the water and the hot substrate.

Figure S1
Droplets' behaviors on flat silica surfaces maintained at different temperatures: the Leidenfrost phenomenon appeared at TL ≈ 286°C. Representative snapshots of droplet behavior when the surface temperature was below TL (76°C, 158°C, and 245°C) and above TL (347°C and 441°C). Although the droplets bounced after initially contacting the hot surface at 245°C, we observed transition boiling at the bottom of the droplet after several bounces. Therefore, the droplet is in transition boiling at 245°C, which can also be seen from the lifetime curve (Figure 2e).

Figure S2
Droplets' behaviors on silica with cylindrical pillars maintained at different temperatures: the Leidenfrost phenomenon appeared at TL ≈ 314°C. Representative snapshots of droplet behavior when the surface temperature was below TL (76°C, 158°C, and 245°C) and above TL (347°C and 441°C). Although droplets bounced when initially contacting the hot surface at 245°C, we observed transition boiling at the bottom of the droplet after several bounces. Hence, the droplet is in transition boiling at 245°C, which can also be deduced from lifetime curve (Figure 2e).

Figure S3
Droplets' behaviors on Glaco-coated flat silica maintained at different temperatures: the Leidenfrost phenomenon appeared at TL ≈ 130°C. Representative snapshots of droplet behavior when the surface temperature was below TL (76°C) and above TL (158°C, 245°C, 347°C, and 441°C).

Figure S4 Droplets' behaviors on silica with DRPs maintained at different temperatures:
the Leidenfrost phenomenon appeared at TL ≈ 363°C. Representative snapshots of droplet behavior when the surface temperature was below TL (76°C, 158°C, 245°C, and 347°C) and above TL (441°C).
We performed droplet experiments on the FDTS-coated DRPs at the same temperature as those performed on other surfaces (i.e., ~347°C) and found that the water droplet was levitated by a vapor film and started bouncing on the FDTS-coated DRPs (Figure S5a).
Through confocal experiments, we obtained water droplet meniscus curvatures at the interfaces of FDTS-coated and untreated DRPs. On the untreated DRPs, a water droplet meniscus goes down to the doubly reentrant edges (Figure S5b). After FDTS coating, a water droplet can stay only on the top of the DRPs and cannot wet the edges (Figure S5c).
Thus, the adhesion is significantly reduced by not only increasing the actual (intrinsic) contact angle qo to 112° but also changing the contact length slightly. Thus, the local pinning effect is eliminated from the surface of the FDTS-coated DRPs.

Figure S6
Droplet detachment from cylindrical pillars at 347°C. Once a water droplet touches the surface of the heated pillars, it deforms and penetrates the spaces between the pillars. Then, the water will absorb heat from the pillars and evaporate rapidly. The generated vapor will push the water upward. After the water detaches from the tops of all the simple pillars, the droplet will be levitated by the generated vapor.