Non-wettable hierarchical structure effect on droplet impact and

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Non-wettable hierarchical structure effect on droplet impact and spreading dynamics Hyungmo Kim, and SeolHa Kim Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00707 • Publication Date (Web): 30 Apr 2018 Downloaded from http://pubs.acs.org on May 2, 2018

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Non-wettable hierarchical structure effect on droplet impact and spreading dynamics Hyungmo Kim1 and Seol Ha Kim2,* 1

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SFR NSSS Design Division, KAERI, Daejeon, 34057, Republic of Korea

Center of Heat and Mass Transfer, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, 100190, China

Corresponding Author *

Researcher, Seol Ha Kim

Heat and Mass Transfer Research Center CAS, IET (Chinese Academy of Science, Institute of Engineering Thermophysics) Beijing, China Tel: +86-15811563567 E-mail: [email protected]

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ABSTRACT

In this study, the nano/micro hierarchical structure effect of a non-wettable surface on droplet impact was investigated by high-speed visualization. A dual-scale structure of a superhydrophobic surface was designed for manipulating a wide range of capillary pressures (103–106 Pa), and it was supposed to trigger a hierarchical effect on the droplet dynamics. Distilled water droplet of various size and initial velocity were subjected to the prepared samples, and the impact behavior, the spreading diameter and contacted time, were quantitatively measured. The apparent maximum spreading and contact time of the low Weber number (We#) condition was less dependent on the microscaled design factor of the multiscale-fabricated surface. However, in the high We# condition, the wavy formation shape and the fragmented criteria of the droplet impact were affected by the configuration of the surface morphology. The hierarchical effect from the dual-scale structure on droplet spreading dynamics has been discussed through a balance between capillary pressure induced by the structure and the dynamic pressure of droplet impact.

KEYWORDS Droplet Impact, Hierarchical Structure, Spreading Factor, Wavy Behavior


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INTRODUCTION Superhydrophobic characteristics have been widely investigated owing to their potential in various engineering applications: self-cleaning, drag reduction, anti-icing, anti-dust, fog-resistant coating, etc.1–10. Nano/micro-scale surface modification technique advances in quick, numerous functional surfaces of superhydrophobic conditions have been introduced during the last few decades. This non-wettable condition could be established by the chemical makeup and physical geometry, and it generally results in a contact angle of the water droplet of approximately 160–170°. Furthermore, inspired by examples of extreme non-wettability in nature, such as lotus leaves or aphids, hierarchical double-scale nano/micro structures have been developed through several methods: electrodeposition, nanotube growth, lithography, etc.11–14. Because the hierarchical-structured surface provides an amplified performance of the above engineering practices15–20, its detailed physical mechanism on the interaction with a droplet has been investigated. Since many applications and experiments involve an impinging droplet rather than stationary droplets, the study of transient droplet impact on the superhydrophobic surface is important. The dynamics of the droplet impact on the surface is an evaluation approach based on the stability or repellency. As a water droplet impacts the superhydrophobic solid surface, it reacts in different ways, such as rebounding, fragmentation, etc., depending on the collision condition, fluid properties, droplet kinematics, and surface characteristics21–23. Recently, several experimental and numerical studies of droplet impact have been conducted to characterize the detailed behavior of the droplet, such as the maximum spreading, splashing, and rebounding, using a high-resolution visualization technique. A few relevant studies were reviewed for the motivation of this study. First, for the characteristics of the impacting droplet, the spreading ability after impact was measured24–27. The maximum deformation of the falling droplet on the non-wettable surface could be determined by balancing the Laplace pressure at the deformed curvature and the kinetic-induced hydrostatic momentum. In addition, the spreading factor ( 𝐷"#$ ⁄𝐷% ) was correlated experimentally with the We# (𝜌𝑣 ) 𝐷% ⁄𝜎)28. Second, sufficient kinetics of the falling droplet broke the spreading perimeter and produced numerous small flying droplets, called splash. For the last few decades, the threshold of the splashing event has been evaluated by the droplet kinetics (We# and Re#) and surface parameters22,29–31. Since the surface roughness could perturb the spreading perimeter of the droplet, the influence of the surface roughness on splash behavior was analyzed with numerous empirical observations and correlations. Recently, Kim et al. explained the physical role of the surface morphology in the splashing determinant by ACS Paragon Plus Environment

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analyzing an airflow superposed by a designed-structure surface31. The expelled airflow during droplet spreading amplified the perturbation of the liquid-vapor interface supported by the Kelvin-Helmholtz instability model; then, the mechanisms of promoting the splashing characteristics were discussed quantitatively. The promoted splashing or break up of the impacting droplet effectively reduced the contact time, which affects the above engineering applications32-37. For example, high-speed supercooled (-50 ℃) water droplets contact an aircraft in anti-icing. The contact time should be minimal to cause the droplet to rebound from the surface before icing5. The Varanasi group reported a minimum contact time (approximately 7–8 ms) by designing a single minusshaped ridge macrostructure on the non-wettable surface to cause a non-axisymmetric retraction force of droplet spreading33. Thus, several advanced designs of a multi-complex ridge of a microstructure (three-forked, crossshaped, five-forked, etc.) on a superhydrophobic surface have been introduced to manipulate the water droplet hydrodynamics, obtaining a reduced contact time of approximately 5 ms. These multi-scaled non-wettable surfaces can control the momentum distribution of the droplet spreading and recoiling process, resulting in various hydrodynamics of the droplet impact scenario28,35-37. To optimize the droplet behavior on the impacting process for each practical application, an understanding of the multi-scaled hierarchical structure effect on the droplet impacting process is required. This is a relatively simple problem on a flat non-wettable or macro-textured (submillimeter) surface, dual-scale hierarchical structures between nanometers (10–100 nm) and micrometers (approximately 10 µm) create more complex hydrodynamics of the droplet. In this study, the detailed physical mechanisms of the dual-scale hierarchical structures on the droplet impact were investigated by a systematical surface design and high-speed visualization technique. Several non-wettable samples were fabricated that consisted of micro-scale holes on a nanoscale (approximately 10-100 nm) hydrophobic surface. Analyzing the pressure range involved in the impacting droplet, which had a wide range of the We# (approximately 200), the hierarchical structure effect was discussed. As a motivation of this work, all the prepared samples showed similar contact angle of droplet in equilibrium condition, but it would produce different behavior in transient impacting condition owing to the interaction between liquid and designed hierarchical structures. Although the spreading factor and contact time were less dependent on the dual-scale surface morphology, the spreading perimeter shape and its event criteria were affected by the hierarchical design. The additional airflow by the structure, which was investigated in a previous study, and the collision between the spreading perimeter (precursor) and micro-scale hole were discussed as the major mechanisms of the hierarchical effect. This study ACS Paragon Plus Environment

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provided a detailed understanding of the dual-scale structure on the droplet impact, and the results were relevant for various engineering applications.

EXPERIMENTS Sample Preparation Superhydrophobic surfaces were fabricated that supported a chemical treatment and geometrical modification using a micro-electro mechanical system (MEMS) technique38. Fig. 1 shows a schematic of the sample fabrication process and the representative detailed image (scanning electron microscopy). First, as a control group, a flat superhydrophobic surface was manufactured by a reactive ion etching (RIE) process and a self-assembly monolayer (SAM) coating. By switching between etching and passivation of the RIE process, the nanowire or nano-needle shape of the textured surface was formed. This was referred to as the black silicon formation method32. Second, for the hierarchical structure surface, an additional micro-scaled etching process was performed before the black silicon process. A wet etching with a tetramethyl ammonium hydroxide solution on a micro-scaled patterned silicon substrate was carried out. The depth of the cavity was controlled by the etching conditions: time (approximately 12 min) and temperature (approximately 90 ℃). After the geometric modification, all samples were subjected to the hydrophobic coating process (HDFS, heptadecafluoro-1,1,2,2-tetrahydrodecyl trichlorosilane, in n-hexane), as the chemical makeup process. Finally, Table 1 lists a detailed configuration of the fabricated surface and the contact angle test. By fixing the distance (60 µm) between the cavities, the gap and space were controlled. Regardless of the configuration, all surfaces produced a superhydrophobic contact angle (160–165°) and minimal contact angle hysteresis features. Droplet impact test and data reduction By controlling the droplet size (2–5 µL) and falling height (0–50 cm) under atmospheric conditions, a wide range of the We# (5–250) and Re# (700–6000) of the droplet impact was tested. To analyze the quantitative and qualitative shape of the droplet, a side-view high-speed camera (approximately 20000 fps) was used with several optical accessories: a diffusor, light source, etc. The captured images were processed to obtain the transient droplet spreading diameter, which provided the maximum spreading and contact time, and the droplet shape determinants: rebound off, wavy perimeter, fragmented (splashed), etc. ACS Paragon Plus Environment

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RESULTS & DISCUSSION Droplet impact on the non-wettable surface In general, since a superhydrophobic surface minimizes the liquid-solid wetting and viscous dissipation of the droplet impact, which reduces the bouncing momentum, a small inertia of the water droplet can rebound off of the surface. Fig. 2 shows the general rebounding shape of the droplet on the superhydrophobic surface. The droplet deformed with impact until maximum spreading. Then, the droplet recoiled to bounce up on the solid surface. The maximum spreading diameter became larger in the high We# condition. In addition, the droplet with enough kinetic energy (see S0, 4 µL, and We# of approximately 220) produced a wavy shape of the spreading perimeter. An impacting droplet, which had a sufficient kinetic momentum, formed a disk-shape on the solid surface during spreading, and the edge of the disk had a rim structure that was thicker than the disk28. This thick rim contained a wavy shape at the spreading perimeter by a local retraction force, which was induced by the surface tension. The dual-scale hierarchical structure surface promoted the wavy shape and fragmented behavior of the droplets (see S2 and We# of 120 and 220) by triggering an instability of the liquid-vapor interface at the disk edge. Although all the samples provided the same superhydrophobic condition on a stationary water droplet, the transient dynamics of the droplet were different for each dual-scale structure condition. The early splashing behavior on the hierarchical structured surface was discussed in a previous study28. This study provided a general description of the droplet impact affected by the hierarchical structured surface and a detailed mechanism of the wavy shape. Fig. 3 shows the transient spreading diameter, which was normalized by the initial size of the impacting droplet (𝐷% ), for a range of the We# (5–150) and surface conditions (S0, S2, and S4). (For detail dynamics, see the supplementary videos of the droplet impacts on the samples39) In addition, to normalize the impact time, an oscillation period (𝜏% ), which was regarded as the Rayleigh time, was applied and defined, as shown below. 12 5

/0 4 𝜏% = . 63

(1)

First, regardless of the samples, the transient behaviors of the droplet expansion and retraction overlapped in the low We# condition (be1ow 100). The hierarchical surface morphology did not affect the droplet spreading behavior, except the splashing event at the high We# condition (over 150). Furthermore, the normalized contact time showed no dependency on the We# and surface morphology. This normalization of the contact time and the low dependency on the droplet impact condition implied that 1) an inertia effect dominated the viscous effect for the water droplet ACS Paragon Plus Environment

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under a given experimental condition, and 2) the corresponding oscillation period was balanced between the inertia and capillarity. The scaling diagram of Fig. 3 showed the two regimes of the retraction velocity, divided by 𝐷⁄𝐷% = 1. While the early retraction regime produced a high retraction velocity and dependence on the We#, the slower retraction showed an overlaid trend of all cases. According to the Taylor-Culick incorporated model, the initial retraction velocity was determined by the surface tension force and the disk thickness of the droplet, which relied on the initial impact condition (We#). Then, the droplet retracted to approximately its initial diameter (𝐷⁄𝐷% = 1). The retracting behavior became slow28. At the high kinetic energy condition (We# of 120–150), the droplet on the flat non-wettable surface (S0) had a rebounding behavior; however, the hierarchical structures (S2 and S4) produced splashing events. Furthermore, the hierarchical surface morphology also had an influence on the splashing behavior. The morphology dependency on the fragmenting process was analyzed based on an induced air-flow by the cavities31. Maximum spreading and contact time evaluation The maximum spreading ability, which was characterized by the spreading factor (𝐷"#$ ⁄𝐷%), and the contact time (𝜏"#$ ⁄𝜏% ) of the test droplets are plotted by We# in Fig. 4. Since the surface morphology did not affect the maximum spreading and contact time, as observed above, the spreading factors were plotted without noting the test samples. First, the trend of the spreading factor was proportional to the 𝑊𝑒#;/= , which was higher than the Clanet study or Leidenfrost condition data (𝑊𝑒#;/> )25. Based on a previous analytical solution of the spreading shape, the maximum deformation of the impacting droplet is controlled by balancing the initial driven hydrostatic pressure and the Laplace pressure from the deformed curvature. The analytical derivation assumes a uniform deceleration of droplet spreading over time (𝐷% ⁄𝑣%) and no viscous dissipation during the impact and cylindrical droplet shape of the maximum deformed state. The discrepancy is related to the limitations associated with the assumptions, and other studies have shown a range of We# dependency (𝑊𝑒#%.)@A%.=> )24,25. For the contact time, there was no dependency on the We# until the droplet splashing events in this study. Generally, around 2.3 of the normalized contact time, which was shown in the literature28, was observed before the splashing events. When the We# was over 100, the falling droplet started to fragment on the surface; therefore, its contact time decreased sharply. For a larger droplet, more splashing behavior occurred. Lastly, Fig. 5 shows the spreading factors of all experimental data compared to the relevant studies25–27,40. Table 2 summarized the models and related parameters which were ACS Paragon Plus Environment

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compared in this study. The comparison studies suggested the spreading factor was based on a classic energy balance approach (Chandra and Avedisian work)41. Lee et al. suggested a theoretical model for the structured surfaces27. As shown in Fig. 5, the experimental data of this study showed good agreement with the previous prediction. There was a difference at only the low We# condition. In summary, the maximum spreading and contact time did not reflect on the dual-scale hierarchical structures before the splashing event. Because of the non-wettable condition of the flat and hierarchical surface, the liquid-solid contacts of the droplet impact were minimized, regardless of the dual-scale surface morphology. Therefore, the dual-scaled effect was not realized by modulating the liquid-solid wetting mechanism. Hierarchical structure effect on droplet instability As explained above, the non-wettable surface condition did not show a hierarchical structure effect on the general droplet impact dynamics (maximum spreading diameter and contact time) owing to no liquid-solid wetting events. Instead of modulating the liquid-solid contact, the hierarchical structure may have a different effect The effect of the dual-scale structure on the droplet impact dynamics of a non-wettable condition was investigated, as shown in Fig. 6.To analyze the detailed momentums associated with droplet impact, the liquid-vapor interface permeability inside the gaps between the micro-scale structures were discussed. Deng et al. reported that the final droplet wetting state after impact was determined by balancing the hydrodynamic momentums: the water hammer pressure, dynamic pressure, and capillary pressure23. The former two pressures acted as a wetting momentum; the later pressure contributed to the anti-wetting mechanism. The initial impact of the droplet on a flat surface generated a compression effect on the inner pressure of the droplet, referred to as the water hammer pressure. Deng et al. evaluated the effective water hammer pressure under a spherical shape of the droplet and a low impinging speed, as follows23. 𝑃DEF ≈ 0.2𝜌𝐶𝑣

(2)

The parameter 𝐶 was the speed of sound in water (approximately 1490 m/s). Because of the large scale of the speed of sound, the effective water hammer pressure was larger than the dynamic pressure in the practical water droplet test with a velocity range of 0.1–10 m/s. Balancing the wetting momentums with the anti-wetting pressure, which was a capillary pressure induced by the surface structure, the permeability of the liquid-vapor interface into the gap between the structure was determined. As shown in Fig. 6, if the effective water hammer pressure was greater than


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the other pressures (dynamic and capillary pressures), the compressed pressure of the droplet supported the penetration of the liquid-vapor interface into the gap between the structures. This liquid penetration expelled the air, which was occupied in the gaps, and the expelled air flowed around the droplet during the spreading process. The influence of the expelled airflow on the liquid-vapor interface instability and splashing threshold under the superhydrophobic condition was discussed, as a hierarchical structure effect28. Instead of the liquid penetration assisted by the effective water hammer pressure, the other hierarchical structure effect was evaluated. As shown in Fig. 6, the spreading area, which was larger than the initial droplet size, was dependent on the balance between the dynamic pressure (𝑃K ) and capillary pressure (𝑃L ), as defined below. 𝑃K = 0.5𝜌𝑣 )

(3)

𝑃L = −2𝜎𝑐𝑜𝑠𝜃⁄𝑔

(4)

If the dynamic momentum of the droplet was larger than or comparable to the anti-wetting pressure (capillary pressure), the edge of the spreading perimeter could permeate through the gap and collide with the micro-scale structures (as shown in Fig. 6). This mechanism could also affect the liquid-vapor interface instability of the spreading perimeters. Fig. 7 shows a theoretical comparison of the above pressures along the capillary characteristic length, which was regarded as a structure gap (g) in this study. The capillary pressure showed an anti-proportional trend with the characteristic length (Eq. 4). The dual-scaled length of the prepared surfaces produced two ranges of capillary pressure. First, the nano-scale structures (10–100 nm) generate a high range of anti-wetting capillary pressure, and the capillary pressure was larger than the effective water hammer pressure of the water droplet test. Thus, the liquidvapor interface could not percolate to the gap between the nano-scale structures during impact. Therefore, all test surfaces showed non-wettable features in this study, regardless of the micro-scale surface morphology. Second, the capillary pressure was induced by the microscale structure (10–50 µm), and it was lower than the effective water hammer pressure. Therefore, the liquid could penetrate into the gap between the micro-scaled structures during the impact process. This comparison result implied that a dual-scale effect on the liquid penetration may influence the droplet dynamics during impact. Finally, the dynamic pressure range of this study (approximately 1000 Pa) had a similar scale to the capillary pressure range produced by the micro-scale structure. If the dynamic pressure was lower than the capillary pressure (see 2 µL and We# of approximately 30), the spreading perimeter was not able to permeate the gap and collide with the structures. This permeability and collision would be supported by a ACS Paragon Plus Environment

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comparable level of pressure range between the dynamic one and the anti-wetting capillary pressure, and this would contribute to destabilization of the liquid-vapor interface of the spreading perimeter. As an unstable behavior of the droplet interface, the wavy shape event was evaluated in this study. In general, the wavy shape is a precursor to the splashing behavior. In this study, it was assumed that the wavy behavior was established by the interaction between the spreading droplet and the hierarchical structures. Regarding the penetration or collision event between liquid droplet and microscale holes, unfortunately, it is hard to provide a direct proof in experimental observation. It requires higher resolution of visualization work or mesoscale of numerical simulation support, which are beyond of this study. Recently, after the rough modelling work by Deng et al.23, several numerical simulation indirectly explained the liquid-air interfacial dynamics between microstructures through LBM (Lattice Boltzmann Method), etc7,42. Not only the numerical works but also recent liquid penetration test on hydrophobic mesh-type samples43 also took into account the detail liquid-air interface motion at the structures, analyzing the pressure balance introduced above. Fig. 8 shows the shape of the spreading perimeter in this study. In general, for a We# of 50–100, the wavy events occurred on all samples, and the hierarchical structure surfaces (S1–S4) created wavy events earlier than those of the flat surface (S0). If a droplet with sufficient kinetics contacted the flat non-wettable surface, the edge rim structure of the thin liquid disk produced a wavy structure. However, the hierarchical structure was able to promote the wavy shape by triggering instability of the liquid-vapor interface of the droplet impact. As explained above, the dynamic pressure momentum, which was higher than or comparable to the capillary pressure induced by the microscale structures, triggered instability of the spreading perimeter. Furthermore, since the gap of the micro-scale morphology manipulated the capillary pressure, the wavy events were dependent on the structure morphology. As the gap of the structure increased, the We# criteria of the wavy shape event decreased owing to a weakened capillary pressure against to the dynamic pressure. In the quantitative analysis, the pressure ratio of 𝑃K ⁄𝑃L ~0.5 showed good agreement with the criteria of the wavy events in this study.


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CONCLUSION In this study, dual-scale hierarchical structures of superhydrophobic surfaces were designed for manipulating a wide range of the capillary pressures (103–106 Pa). Distilled water droplets of various sizes (2–5 µL) and initial velocities (0.4–3.1 m/s) were subjected to the test samples, and the impact behavior (spreading diameter and contact time) were quantitatively measured. All the prepared samples showed superhydrophobic characteristics in equilibrium condition, but it would produce different behavior in transient impacting condition owing to the interaction between liquid and designed hierarchical structures. The major findings of this study are listed below. -

The transient droplet spreading and contact time were less dependent on the hierarchical structures of the non-wettable condition before the splashing event. Because of the minimized liquid-solid contact condition of the nanostructured superhydrophobic surface, the hierarchical structure effect through the liquid-solid contact did not affect the transient droplet dynamics.

-

To determine the dual-scaled structure effect, the liquid penetration was analyzed, which was supported by the hammer pressure (𝑃DEF ) and dynamic momentum (𝑃K ), inside the dual-scale structure gaps, balancing the corresponding anti-wetting pressure (capillary pressure, 𝑃L ).

-

While the capillary pressure of the nano-scale structure was larger than the effective water hammer pressure, the capillary pressure of micro-scaled structure is lower than that the effective water hammer pressure. Therefore, the dual-scale structure effect on liquid penetration could be established, and an influence on the liquid-vapor interface instability (splashing and wavy shape) during spreading was shown.

-

For the wavy shape of the droplet impact test, the criteria for the wavy events showed a dependency on the micro-scale structure morphology. For the quantitative analysis, the pressure ratio of 𝑃K ⁄𝑃L ~0.5 showed good agreement with the criteria of the wavy events in this study.

-

(Recommendation) The direct observation of the liquid-air interfacial dynamics at the microscale holes is helpful to give a more detail analysis of the droplet dynamics and above results about the pressure ratio. However, it requires sensitive design of experimental setup to observe fast transient physics of droplet in micrometer’s resolution. ACS Paragon Plus Environment

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ACKNOWLEDGMENT This research was supported by the Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1A6A3A03008942).

CONFLICT OF INTEREST The authors declare no competing financial interest.

SUPPORTING INFORMATION Representative videos of the droplet impact and rebounding are included.

NOMENCLATURE D

size of the droplet

[m]

v

velocity

[m/s]

P

pressure

[Pa]

C

speed of sound

[m/s]

g

gap

[m]

ρ

density

[kg/m3]

σ

surface tension

[N/m]

τ

time scale

[s]

Greek symbols

Subscripts max

maximum

0

initial

EWH

effective water hammer

C

capillary

D

dynamics ACS Paragon Plus Environment

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Kwon, Y.; Patankar, N.; Choi, J.; Lee, J. Design of Surface Hierarchy for Extreme Hydrophobicity. Langmuir 2009, 21 (8), 6129–6136.

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Page 16 of 23

See a Supporting Information for more detail droplet behaviors. It includes 5 videos of droplet bouncing dynamics on S0 and S2 with various We# range (60-220). Wavy shape of spreading perimeters can be observed in Video#3-5, and fragmenting shape of droplet also can be recognized in Video #4 (weak fragmenting) and Video #5 (prompt fragmenting).

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Chandra, S.; Avedisian, C. T. On the Collision of a Droplet with a Solid Surface. Proc. R. Soc. A-Math. Phys. Eng. Sci. 1991, 432 (1884), 13−41.

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Quan, Y.Y.; Zhang, L.Z. Numerical and Analytical Study of the Impinging and Bouncing Phenomena of Droplets on Superhydrophobic Surfaces with Microtextured Structures. Langmuir 2014, 4 (30), 1164011649.

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Ryu, S.; Sen, P.; Nam, Y.; Lee, C. Water Penetration through a Superhydrophobic Mesh During a Drop Impact. Phys. Rev. Lett. 2017, 118, 014501.


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Langmuir

Table of Contents Graphical Abstract

Figure 1. Test sample fabrication process and contact angle. Table 1. Test sample configuration and the contact Angle Figure 2. Representative pictures of droplet impact on the samples (see supplementary videos [39]) Figure 3. Normalized droplet parameters (diameter-time) change with impact event (hallowed: stable rebounding, filled: fragmenting) Figure 4. Maximum spreading factor and the contact time trend Figure 5. Maximum spreading comparison with the previous models [25-27, 40] Table 2. Relations of maximum spreading models [25-27, 40] Figure 6. Mechanism of droplet interaction with the hierarchical structures. 1) At the impact moment (contact stage), liquid-air interface of the droplet can be penetrated into microscale holes but not into nanoscale needles, 2) At spreading stage, spreading edge of liquid can be collided with the microscale structure depending on the pressure balance (𝑃K ⁄𝑃L ). Figure 7. Pressure comparison on the hierarchical structures. Figure 8. Wavy perimeter occurrence evaluation (Pressure ratio (𝑃K ⁄𝑃L ) indicates the force balance between wetting and anti-wetting at the spreading stage)


17

Langmuir 7

10

𝑷𝑪_𝑵𝒂𝒏𝒐

𝟏𝟎 − 𝟏𝟎𝟎𝒏𝒎

6

10

𝑷𝑬𝑾𝑯 (𝑾𝒆# 𝟑𝟎 − 𝟏𝟓𝟎) Dual-scaled Hierarchical Structure

Pressure [Pa]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 23

5

10

PC PD PEWH

4

10

𝑷𝑪_𝑴𝒊𝒄𝒓𝒐 𝟏𝟎 − 𝟓𝟎𝝁𝒎

𝑷𝑫 (𝑾𝒆# 𝟑𝟎 − 𝟏𝟓𝟎)

3

10

2

10

-8

10

-7

10

-6

10

-5

10

-4

10

-3

10

Capillary Chracteristic Length [m] Graphical Abstract


18

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Langmuir

Silicon Wafer Sample (Smooth)

Black Silicon & HDFS Coating Wet-Etching Process

(Non-wettable Feature)

Example : S2 (S30G30)

2 µm

165°

30 µm

20 µm

Figure 1. Test sample fabrication process and contact angle.

Table 1. Test sample configuration and the contact angle

Test Sample

Gap [µm]

Space [µm]

Depth [µm]

S0

-

-

-

S1

20

40

10

S2

30

30

10

S3

40

20

10

S4

50

10

10

Contact Angle [°]

164 – 166 θhyst ~ 3 - 5


19

Langmuir S0 (2µl, We# : ~ 60) Initial Condition

0 ms

S0 (2µl, We# : ~ 120) Deformation w/ Impact

0.7 ms

Wavy

S2 (2µl, We# : ~ 120) We# Increase We# Increase

Maximum Spreading

1.2 ms

Wavy Recoil/ Receding

3.2 ms

S0 (4µl, We# : ~ 220) Splashing

Rebounding

5.7 ms

S2 (4µl, We# : ~ 220)

Figure 2. Representative pictures of droplet impact on the samples (see supplementary videos [39])

4.0

4.0

4.0

3.0 2.5

3.0 3.5 2.5

3.0 3.5

3.0

3.0 2.0

2.5

2.5 1.5

2.0

2.0 1.0

1.5

1.5 0.5

1.0

1.0 0.0

0.5

0.5

D/D0 [-]

3.5

3.5 4.0

D/D0 [-]D/D0 [-]

3.5

3.5 4.0

2.0 1.5

0.5

2.5 3.0 2.0 2.5 1.5 2.0 1.0 1.5 0.5 1.0

0.0 0.5 0.0 0.0

1.0

0.0

Droplet Fragmented

D/D0 [-] D/D0 [-]

4.0

D/D0 [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 23

0.0 0.0

0.4 0.0

𝑫𝒎𝒂𝒙

0.4 0.0

0.8 0.4

B B D D F F 𝑾𝒆# S0 S2 H H 𝟓 B J 𝟒𝟓 D L 𝟏𝟐𝟎 F N H P 𝟏𝟓𝟎 J R L T N V P X R T V 0.81.2 1.2 1.6 1.6 2.02.0X 2.4 2.4 𝝉𝒄𝒕

B B D F H J L N P R T V X

B D F H S4 J L N P R T V X

2.8

t0 [-] t/t0t/[-]

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 0.8 1.2 1.6 2.0 2.4 2.8 0.4 0.8 1.2 t/t 1.6 [-] 2.0 2.4 2.8 0

t/t0t/[-] t [-] 0

Figure 3. Normalized droplet parameters (diameter-time) change with impact event (hallowed: stable rebounding, 0.0 filled: fragmenting) 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 ACS Paragon Plus Environment t/t0 [-]

20

Page 21 of 23

4

Spreading Factor [-]

3

3 2

2µL (S.F.) 4µL (S.F.) 2µL (C.T.) 4µL (C.T.)

~𝑾𝒆#𝟎.𝟑𝟑

2 1

1

0

Splashed Droplets

10

We# number

Contact Time Factor [-]

100

Figure 4. Maximum spreading factor and the contact time trend

4.0

Spreading factor (Model) [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

3.5

Clanet et al. [25] Ukiwe et al. [26] Lee et al. [27] Pasandideh et al. [40]

3.0

2.5

2.0

1.5

1.0 1.0

1.5

2.0

2.5

3.0

Spreading factor (Exp.) [-]

3.5

4.0

Figure 5. Maximum spreading comparison with the previous models [25-27, 40]


21

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Page 22 of 23

Table 2. Relations of maximum spreading models [25-27, 40] Reference

Relations ∗ 𝐷"#$ =' A ' 𝑊𝑒 +

Clanet [25]

(𝐴: 0.9, 𝐵: 0.25)

Ukiwe & Kwok [26]

Lee [27]

∗ ∗ 𝑊𝑒 + 12 𝐷"#$ = 8 + 𝐷"#$

8

3 1 − 𝑐𝑜𝑠𝜃 + 4

∗ ∗ 𝑊𝑒 + 12 𝐷"#$ = 8 + 𝐷"#$

8

4

@A BA

@A − 3Ψ BA

where Ψ = 𝑐𝑜𝑠𝜃 1 − 𝜙F + 𝜙F 1 − 𝜔F + 𝜔F 𝑟F 𝜃 − 1 (𝜔F : 0 𝑛𝑜𝑛𝑤𝑒𝑡𝑡𝑎𝑏𝑙𝑒 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛 , 𝜙F : 0.2 fitted value)

Pasandideh-Fard [40]

∗ 𝐷"#$ =

Initial Droplet

@ARST 8 SUVWFX RY @A ⁄ BA

Spreading Area

𝑫𝟎 ⁄𝟐

(𝑷𝑬𝑾𝑯 )

Spreading Droplet

Water Hammer Pressure

Spreading Perimeter

𝑷𝑪 1) Penetration : 𝑷𝑬𝑾𝑯 > 𝑷𝑫 , 𝑷𝑪

2) Collision : 𝑷𝑫 > 𝑷𝑪

Figure 6. Mechanism of droplet interaction with the hierarchical structures. 1) At the impact moment (contact stage), liquid-air interface of the droplet can be penetrated into microscale holes but not into nanoscale needles, 2) At spreading stage, spreading edge of liquid can be collided with the microscale structure depending on the pressure balance (𝑃K ⁄𝑃L ).


22

Page 23 of 23 7

10

𝑷𝑪_𝑵𝒂𝒏𝒐 6

Pressure [Pa]

10

5

10

PC PD

(2µL, We#:30)

PD

(2µL, We#:150)

𝑷𝑪_𝑴𝒊𝒄𝒓𝒐

PEWH (2µL, We#:30)

4

10

PEWH (2µL, We#:150)

3

10

2

10

-8

10

-7

10

-6

-5

10

-4

10

-3

10

10

Capillary Chracteristic Length [m] Figure 7. Pressure comparison on the hierarchical structures.

250

w/ Wavy w/o Wavy 200

𝑷𝑫 ⁄𝑷𝑪 ~𝟎. 𝟓

150

We#

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

100

50

0

No10 Str.

20

30

40

50

Gap [µm] Figure 8. Wavy perimeter occurrence evaluation (Pressure ratio (𝑃K ⁄𝑃L ) indicates the force balance between wetting and anti-wetting at the spreading stage)

.


23

Non-wettable hierarchical structure effect on droplet impact and

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