Manipulating the degree of droplet contact with a surface significantly impacts applications involving drag reduction, corrosion inhibition, droplet transportation, and thermal management. Extensive studies have been conducted to study droplet wetting behavior on plain and micro/nanostructured surfaces, with a particular focus in the recent literature on heated surfaces, where evaporation beneath the droplet impacts the apparent wettability. In previous literature, the peak droplet lifetime and minimum heat transfer on heated surfaces were observed at the Leidenfrost point. In this study, however, we report the existence of two distinct peaks for droplet lifetime on heated surfaces structured with silicon micropillar arrays. Initially, droplets exhibit complete wetting at low surface temperatures, but as surface temperature increases, the wetting state transitions first to a contact non-wetting state (i.e., a Cassie–Baxter-like state) and then to the non-contact Leidenfrost state; two distinct local maxima in droplet lifetime are observed, one corresponding to each transition. The contact non-wetting transition temperature and Leidenfrost point increase with larger micropillar pitch and taller height, which we attribute primarily to the resulting lower effective thermal conductivity of the micropillar array beneath the droplets, in agreement with the analytical force-balance-based modeling. This study provides a comprehensive investigation of the effect of surface structuring on contact non-wetting and Leidenfrost phenomena and will serve as design guidelines in controlling the contact non-wetting and Leidenfrost temperatures for specific applications.

A liquid droplet evaporates or boils when it encounters a hot surface with a temperature higher than its saturation temperature. At a sufficiently high surface temperature, the droplet is levitated by a layer of rapidly evaporating vapor and hovers over the hot surface. This phenomenon, termed as the “Leidenfrost effect” in 1756,1 has been studied extensively due to its unique thermofluidic nature and its potential in heat transfer and drag reduction applications. A Leidenfrost droplet evaporates slowly due to the poor conductive and radiative heat transfer through the vapor layer. The temperature at which the heat transfer rate is minimal and the droplet lifetime is maximal is referred to as the Leidenfrost point (LFP). A higher LFP is desired in many applications that demand high heat transfer rates. This includes spray cooling for microprocessors,2 nuclear reactors,2,3 satellites,2,3 quenching in metallurgical process,4 micro-chemical reactors,5 and fuel injection in combustion engines.6,7 On the contrary, a lower LFP is preferred to facilitate droplet motion,8 control ice/frost formation,9 and realize a drag reduction of up to 85%10,11 due to the presence of the vapor layer.

Consequently, methods that can tune LFP have drawn much attention. Surface properties (wettability, topographic characteristics, and chemical properties), droplet properties12–15 (droplet size, deposition method, and thermophysical properties), and external stimuli16,17 (electric fields) were found to influence the LFP. Among these methods, chemical and mechanical surface engineering have a wider degree of control over the LFP. An up to 100 °C LFP reduction10,18–20 for water droplets was demonstrated by increasing the surface hydrophobicity with Teflon/graphene/Glaco coatings17,19,20 or by silanization,10 which promotes a stable vapor layer formation. On the other hand, a ≈ 70–270 °C increase in the LFP of water/FC-72 droplets was achieved by creating hydrophilic nanoporosity or fabricating nanostructures.5,6,12,15,21–23 With the hydrophilicity enhancement, more bubble nucleation sites and cooling of nanowires disturb the vapor layer and collectively enhanced the LFP. Laser machining6,24 or microfabrication,3,4,7,14,15,17–21,23,25 which creates microstructures or micropillars on flat substrates, is another commonly used method to tailor LFP. The increased wettability and capillary pressure with microstructures can lead to ≈ 36–200 °C increase in LFP.6,7,17,21,24,25 Moreover, Saneie et al.26 reported an increase in LFP with a larger silicon micropillar pitch l for l >10 μm and a higher LFP with a smaller pitch for l <10 μm due to vapor jet ejections. On the other hand, an LFP reduction of ≈ 10–80 °C on micro-engineered surfaces was also observed by some researchers, which was attributed to the enhanced heat transfer area and impeding of the vapor escape by the micropillars.3,4,27 Meanwhile, a recent work by Adera et al.27 observed that non-wetting droplets resided on superhydrophilic micropillar surfaces at low superheats and the droplets were in contact with the tips of the micropillars, which were distinct from Leidenfrost.

In this study, we show that two peaks of droplet lifetime exist on silicon micropillar surfaces. The first peak is associated with the contact non-wetting stages at lower temperatures (164–194 °C) and the second peak is associated with the Leidenfrost point (312–356 °C). Experiments show that the transition temperature and LFP increase with micropillar pitch l and height h. This study provides deeper insights on modifying the LFP with micropillar surfaces to suit the intended applications.

Cylindrical silicon micropillar surfaces were fabricated by photolithography and deep reactive ion etching with various diameters d, heights h, and center-to-center distances, pitch l, as listed in Table I. The micropillar surfaces were rinsed with acetone, isopropanol, and de-ionized water and subsequently cleaned with oxygen plasma (PDC-001, Harrick Plasma) prior to the tests. The droplet lifetime evaporation method28 was adapted to determine the LFP and transition temperature. The micropillar surfaces were placed on top of a thick copper block (10.3 cm × 4.8 cm × 2 cm) that served as a constant temperature source due to its high thermal mass. The copper block and micropillar surfaces were heated up by a hotplate (HP88854100, Thermo Scientific) with incremental hotplate temperatures from 100 to 540 °C. Surface temperatures of the copper block were measured by three K-type thermocouples (L-0044T, Omega) and captured using a data acquisition system (34972a, Keysight). At each steady-state temperature, a 10 μl water (Sigma-Aldrich) droplet with a radius of ≈ 1.3 mm was dispensed by a micro-pipette (YE6A820078, Shcheer) from a height of 5 mm, which corresponds to a constant Weber number of ∼3.5 and a “gentle landing” for the droplet. Under this experimental condition with Weber number < 4, droplet dynamics can be neglected, as discussed in the previous work.29 Droplet dynamics and evaporation time were observed with a high-speed camera (V7.1, Phantom), and the experiment was repeated 10 times. To prevent the levitated droplets from escaping out of the high-speed camera viewing range, a superhydrophobic square cage made of four 50 μm diameter functionalized stainless-steel wires (1/16, Malin Co) was used. Hydrophobic functionalization was performed by immersing the wires in 1 mmol TFTS (Trichloro [1H, 1H, 2H, and 2H-perfluorooctyl] silane, MKBV0653V, Aldrich) in hexane (SHBH1930V, Sigma-Aldrich) solution and heated to 60 °C for 1 hour. The lifetime of 10 droplets was measured, averaged, and plotted against the temperature of the surface.

TABLE I.

List of micropillar samples with different geometries, transition temperature T1, and LFP.

Sample numberd (μm)h (μm)l (μm)T1 (°C)LFP (°C)
Plain silicon … … … … LFP 
A1 36.4 38.3 80 171 312 
A2 36.4 38.3 110 182 343 
A3 36.4 38.3 120 183 356 
A4 36.1 27.4 120 175 328 
B1 21.3 20 164 322 
B2 21.3 30 185 331 
B3 21.3 50 194 349 
Sample numberd (μm)h (μm)l (μm)T1 (°C)LFP (°C)
Plain silicon … … … … LFP 
A1 36.4 38.3 80 171 312 
A2 36.4 38.3 110 182 343 
A3 36.4 38.3 120 183 356 
A4 36.1 27.4 120 175 328 
B1 21.3 20 164 322 
B2 21.3 30 185 331 
B3 21.3 50 194 349 

Experimental results and droplet behaviors at different stages are shown in Fig. 1. For water droplets impinging a flat silicon surface, three distinct stages of impact behaviors can be observed, as shown in Fig. 1(a). The stages are the nucleate boiling stage, transition stage, and Leidenfrost stage. Droplets first experience liquid spreading and gentle boiling for surface temperature T ≈ 100 °C with bubble growth inside the liquid droplets. As T was elevated up to 254 °C, nucleate boiling became more vigorous with higher temperatures, which was accompanied by bubble bursts and tiny droplet ejections, as shown in the image of stage 1 in Fig. 1(a). As a result, droplet lifetime decreased as temperature increased at the nucleate boiling stage. For T =264–286 °C, the bubble growth and burst disturbed the liquid surface and caused the breakage of the droplets into smaller droplets, as shown by the right image of stage 2 in Fig. 1(a). Since smaller droplets need less vapor to be levitated, a lower surface temperature was required to achieve the Leidenfrost state.12–15 This stage is termed the transition stage, where both nucleate boiling and the Leidenfrost phenomenon occur. A sharp increase in droplet lifetime was observed when the droplet behavior transitioned from pure nucleate boiling to the transition stage. Beyond 286 °C, the Leidenfrost effect dominated and the droplets were suspended above the surface upon impact, where a supporting vapor layer formed in between the droplet and surface. The vapor layer was identified through the light transmitted from the droplet bottom using the imaging, e.g., stage 3 of Fig. 1(a). The vapor layer thickness e can be estimated by30 

e(kvΔTμvρ1ghfgρvσ2)1/3R4/3,
(1)

where kv,μv,g,hfg,ρv, and R are the vapor thermal conductivity, vapor dynamic viscosity, gravity of Earth, latent heat, vapor density, and droplet radius, respectively. ΔT represents the superheat, which is the difference between the surface temperature and the saturation temperature. Using this calculation, the vapor layer thickness was ≈ 10–50 μm in our case, which is in agreement with the previous literatures.21,25,27,30 The LFP of flat silicon surface was found to be 290 °C and agrees with the previously reported range of 269–365 °C.3,5,14,19,24 Beyond the LFP, the droplet lifetime decreased because of the higher surface temperature.

FIG. 1.

Droplet lifetime vs surface temperature, and the corresponding dynamics of water droplets as captured by high-speed camera/schematic drawings on (a) flat silicon surface and (b) micropillar surface with d =6 μm, l =20 μm, and h =21.3 μm (sample B1). Error bars for droplet lifetime and surface temperature represent the standard deviations for the measurements of 10 droplets and temperature readings of three thermocouples.

FIG. 1.

Droplet lifetime vs surface temperature, and the corresponding dynamics of water droplets as captured by high-speed camera/schematic drawings on (a) flat silicon surface and (b) micropillar surface with d =6 μm, l =20 μm, and h =21.3 μm (sample B1). Error bars for droplet lifetime and surface temperature represent the standard deviations for the measurements of 10 droplets and temperature readings of three thermocouples.

Close modal

Similar to droplet behavior on a flat silicon surface, on a micropillar silicon surface, the droplet boiled, and its lifetime decreased with the surface temperature when deposited at 100–144 °C. However, once the surface temperature rose to only 164 °C, a sharp lifetime increase was observed. The deposited droplet boiled and separated into smaller droplets. Unlike in the Leidenfrost regimes/“cold Leidenfrost regime”20 where liquid droplets were suspended by a vapor patch and not in contact with the substrate surface, the droplets with smaller sizes resided on top of the micropillar surface in a non-wetting state, as shown in the stage 2 (i.e., first transition stage) of Fig. 1(b) at 164 °C on the micropillar silicon surface. This transition temperature T1 was much lower than that on the flat silicon surface, which was 264 °C. This result can be explained by the high effective thermal conductivity of the porous micropillar gap under the droplet, which was composed of silicon micropillars with a thermal conductivity kSi of 100 W/m·K and water vapor with kv equaling 0.025 W/m·K at 100 °C. The effective thermal conductivity of the micropillar surface underneath the droplet was much higher than that of the vapor layer under a Leidenfrost droplet.27 Accordingly, there was a higher evaporation rate of the liquid droplet at a lower surface temperature and, thus, more vapor generation. Moreover, the existence of the micropillars can hinder the flow of the generated vapor by the viscous loss from the micropillar sidewalls.14,27 Due to the aforementioned reasons, non-wetting droplets were observed at a much lower surface temperature.

In addition, as the vapor layer thickness scales with ΔT1/3R4/3, the vapor layer is not thick enough to suspend the droplet for small droplets at a temperature lower than the Leidenfrost temperature. Thus, the droplet resides on the micropillar surface with its bottom touching the micropillar tops. With increased surface temperatures, the droplet can remain in the non-wetting stage 3 upon deposition. The longest droplet lifetime and minimal heat transfer rate were observed at this stage, which is represented by the first peak on the plot of Fig. 1(b). After that, the second transition stage with non-wetting stage was followed by the Leidenfrost stage. The non-wetting droplet evaporated until its size was small enough to be lifted by the vapor layer. As the droplet behavior transitioned from the second transition stage to the Leidenfrost stage with increasing temperature, the droplet lifetime began to increase as the Leidenfrost stage became more dominant due to the low thermal conductivity of the vapor layer. A second peak was observed at 322 °C, which was the LFP, and the droplet lifetime continued to decrease after the LFP. In brief, the wetting state of droplets on micro-structured surfaces transitioned from stages of complete wetting to partial contact, non-wetting, and then to Leidenfrost regimes with an elevated surface temperature. The dual-peak of droplet lifetime on the micropillar surfaces corresponded to the non-wetting and Leidenfrost stage as expected. This result contrasts with the single peak of droplet lifetime observed at the LFP of 290 °C for a flat surface.

We explored the geometric effects of micropillars on the droplet evaporation with samples of various pitches l and heights h. Figure 2 shows the results of the transition temperatures T1, at which non-wetting droplets and the LFPs were observed, as indicated by the solid and dashed arrows, respectively. As shown in Fig. 2, droplets deposited on micropillar surfaces possess a dual-peak in their lifetime, where the maximum evaporation time and minimal heat transfer rate occur at the first peak in non-wetting stage. Both T1 and LFP increased as the pitch and height of the pillar increased, while T1 ranged from 164 to 194 °C and LFP ranged from 312 to 356 °C. We attribute this behavior to the reduced effective thermal conductivity since the solid silicon with higher thermal conductivity was replaced by gas with low thermal conductivity as the pitch increased. Moreover, the total heat transfer area also became smaller with larger l. The thermal resistance of micropillars Rpillar can be expressed as Rpillar=h/[(1ε)kSi], where ε stands for the porosity. With the same porosity, the micropillar thermal resistance increased with taller h. Therefore, the higher thermal resistance associated with larger l and h resulted in higher T1 and LFP. As discussed in the literature,20 hydrophilicity/hydrophobicity of the surfaces affected the Leidenfrost point by either preventing/favoring the vapor spreading to form vapor patches that suspend the droplets in the Leidenfrost regime. The higher LFP on the micropillar silicon surface (312–356 °C) compared to that on a flat silicon surface (290 °C) can be attributed to the intrinsic superhydrophilic characteristic of micropillar structures. The enhanced capillary effect led to a higher downward force and prevented the formation of a stable vapor layer. This result is consistent with the conclusions of Duursma et al.4 and Tran et al.25 

FIG. 2.

Effect of micropillar geometries on the transition temperature T1 (indicated by the solid arrows) of non-wetting droplets and the Leidenfrost point LFP (indicated by dashed arrows): (a) effect of pitch l: tests were conducted on micropillar samples A1–A3. The insets above the plots are the SEM images of the micropillars of A1–A3. (b) Effect of height h: samples B1, A3, and A4 with the same porosity of 0.93 were tested and compared. Geometries, T1, and LFP of the tested samples are listed in Table I.

FIG. 2.

Effect of micropillar geometries on the transition temperature T1 (indicated by the solid arrows) of non-wetting droplets and the Leidenfrost point LFP (indicated by dashed arrows): (a) effect of pitch l: tests were conducted on micropillar samples A1–A3. The insets above the plots are the SEM images of the micropillars of A1–A3. (b) Effect of height h: samples B1, A3, and A4 with the same porosity of 0.93 were tested and compared. Geometries, T1, and LFP of the tested samples are listed in Table I.

Close modal

T1 can be theoretically estimated by a 1D force balance model proposed by Adera et al.,27 where the surface tension was included as the wetting force and the pressure caused by evaporation was the non-wetting force. A porous micropillar media below the droplet was considered at the non-wetting stage, compared to the homogeneous vapor layer at the Leidenfrost stage. T1 can be determined as a function of the micropillar geometry (d, h, and l)27 

T1=Tsat+8π(ρvhfgσcosθμv)(dhK(Rs+Revap)εRbase2)(1tanh(hβ/2)hβ/2),
(2)

where Tsat,θ,K,Rs,Revap,Rbase, and β are the saturation temperature (100 °C), the intrinsic contact angle of silicon with a value of 38–42°,31,32 the permeability of micropillar structures,33,34 spreading resistance,27 evaporation resistance calculated by Schrage's equation,35 droplet base radius and geometric factor β=ε/K,27 respectively. The LFP for cylindrical micropillar surfaces can be determined by extending the model on square micropillars developed by Kwon et al.14 Accordingly, the LFP was estimated with the following equation:

LFP=Tsat+ρvhfgh2KPcapμvkeffλ2,
(3)

where Pcap,keff, and λ are the capillary pressure of the cylindrical micropillars that can be calculated by the force-balance model of Adera et al.,36 the effective thermal conductivity of the micropillars,14,37 and the droplet-surface contact patch length captured by the high-speed camera images at the LFP, respectively. The model estimations (hollow dots) of Eqs. (2) and (3) were compared with the experimental measurements (solid dots) in Fig. 3. The two analytical models captured the trends with reasonable agreement and can be adopted to predict the transition temperature and LFP on micropillar surfaces. We attribute the discrepancies between model prediction and experimental results to the deviations in evaluating the approximated contact patch length,14 permeability K,33,34 and capillary pressure Pcap based on the literature.36 A slightly higher deviation between model prediction and experimental measurement was observed for sample B1, which had a larger h/l ratio (1.07) compared to other samples with a h/l <1. We attributed this larger discrepancy to the convective loss from sidewalls of micropillars, which were neglected in the model used.27 The discrepency was larger and underpredicted the transition temperature for micropillars with higher aspect ratios. We attribute this difference to the assumption of flat liquid meniscus in the LFP model of Kwon et al.14 In the actual case, especially for higher h/l, there was a higher evaporation rate due to the curved meniscus. The vapor generated beneath the droplet drove an outward flow that lifted the droplet up and led to a lower measured LFP compared to the modeling results.

FIG. 3.

Experimental results compared to model predictions of transition temperature T1 and LFP for samples A1–A4 and B1–B3. The solid and hollow dots represent the experimental measurements and model results, respectively. The square symbols and circular symbols represent the stand for T1 and LFP values, respectively. Calculations were performed based on the transition temperature model of Adera et al.27 for T1 and an extended LFP model of Kwon et al.14 

FIG. 3.

Experimental results compared to model predictions of transition temperature T1 and LFP for samples A1–A4 and B1–B3. The solid and hollow dots represent the experimental measurements and model results, respectively. The square symbols and circular symbols represent the stand for T1 and LFP values, respectively. Calculations were performed based on the transition temperature model of Adera et al.27 for T1 and an extended LFP model of Kwon et al.14 

Close modal

In summary, we showed that a dual-peak droplet lifetime behavior exists for water droplets' impact on a heated micropillar-based silicon surface. In comparison to the Leidenfrost behavior on a flat surface, which exhibits only three distinct stages of behavior, the behavior on a micropillar surface exhibits five stages where droplets transition from complete wetting to partial contact non-wetting and then to the Leidenfrost state. The longest droplet lifetime and minimal heat transfer rates were observed at the non-wetting stage on a micropillar surface, as opposed to that at the Leidenfrost stage on a flat surface. We also found that the transition temperature T1 and LFP increased with the larger micropillar pitch and height. We fitted T1 values with the force-balance model of Adera et al.27 and the LFP values with the extended model of Kwon et al.14 The experiments and modeling show reasonably good agreement. The insights obtained from this work suggest that the micropillar surfaces can be tailored to accommodate applications where specific T1 and LFP are desired.

We gratefully acknowledge the funding support from the National Research Foundation (NRF) Singapore through the Singapore-MIT Alliance for Research and Technology (SMART) Center, Low Energy Electronic Systems (LEES) Interdisciplinary Research Group (IRG). We also gratefully acknowledge the funding support from the Office of Naval Research (ONR), with Dr. Mark Spector as the program manager under Award No. N00014-15-1-296 2483. D. J. Preston acknowledges funding received by the National Science Foundation Graduate Research Fellowship under Grant No. 1122374. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation.

The data that support the findings of this study are available within this article.

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