Water-Droplet Impact and Sliding Behaviors on Slippery Surfaces with Various Weber Numbers and Surface Inclinations

Abstract

The dynamic behaviors of water droplets on a slippery surface are significant to practical anti-icing applications. Herein, the impact and sliding behavior of water droplets on lubricant-infused surfaces (LISs) were investigated with a high-speed camera. LISs were prepared by infusing perfluoropolyether oils into anodized porous surfaces. The results show that the maximum spreading diameter and retraction velocity of the impact droplet increased with the We number. For LIS-100, the spreading factor at 2.5 ms increased from 2.00 to 3.88 with We increasing from 30 to 267. Low-viscosity lubricant facilitated the retraction speed and rebound of droplet impact on the surface, while high-viscosity lubricant contributed to the lubricant stability of the LIS. Additionally, high inclination angle (θ) facilitated the rapid shedding of water droplets on the surface. The velocity increased rapidly from 1.04 to 4.66 mm/s with θ increasing from 15° to 45°. The LIS prepared with low-viscosity lubricant had a high sliding velocity, and the sliding velocity of water droplets on LIS-100 was about seven times faster than that on LIS-104. This work reveals the impacting law of water droplets on LISs and provides useful information for the design of LISs under drop impact conditions.

1. Introduction

Self-cleaning coatings are mainly divided into hydrophilic and hydrophobic [1,2], which are widely used in anti-icing, anti-fouling, and other fields [3,4,5]. Inspired by Nepenthes, a lubricant-infused surface (LIS) is a typical self-cleaning surface, and it is prepared by infusing a lubricant into porous surfaces [6]. Notably, an LIS has potential applications in the field of anti-icing because the presence of lubricant can delay the freezing time of water droplets [7,8] and reduce the adhesion strength of ice [9,10,11,12]. Similar to other anti-/de-icing technologies including superhydrophobic [13,14,15] and self-de-icing pavements [16,17], anti-icing LISs have the potential to be used on outdoor equipment such as transmission lines, wind turbines, and aircraft [18,19,20,21]. It is a common phenomenon that the LIS is impacted by dews, rain, or other fluids. The dynamic water repellency of the LISs determines whether the droplets bounce or slide off the surface in time, which greatly affects the anti-icing performance of LISs. Therefore, it is of significance to understand the impact and sliding behavior of water droplet on the LISs.

Droplet dynamic behaviors on the LISs have been widely studied [22,23,24]. The impact of the water droplet on the horizontal LIS is divided into three stages: spreading, retraction, partial bounce, or complete bounce [25]. The lubricant film prevents direct contact between the water droplet and the solid substrate, forming a stable liquid/liquid interface between the droplet and the LIS. Although the liquid/liquid interface has a large contact area, droplets can still easily bounce or slide off the surface and can, thus, be used to repel impinging liquids. This is different from the bounce mechanism of a water droplet on a superhydrophobic surface where the droplet bounces easily because the presence of the trapped air layer reduces the contact area between the droplet and the underlying substrate [26,27]. Therefore, LISs demonstrate excellent dynamic water repellency.

The impact behavior of water droplets on LIS is related to surface characteristics and droplet state. Surface characteristics include the underlying substrate structure [28], surface wettability [29], lubricant film thickness [30], lubricant viscosity [31], etc. Among them, the viscosity of the lubricant has a significant impact on the dynamic behavior of water droplets, which has attracted more and more attention from researchers. For example, variation in the viscosity of silicone oil can lead to changes in spreading speed, retraction kinetics, and lubricant-film stability [31]. The water-droplet state includes drop size, impact velocity, impact angle, etc. It is reported that the impact velocity of water droplets, which is determined by the Weber (We) number, influences the initial kinetic energy of the droplet, thereby affecting the impact behavior such as the maximum spreading diameter of the droplet [32]. In short, most studies have focused on the water-droplet-impact dynamics of an LIS prepared with different silicone-oil viscosities at typical We numbers. In addition to silicone oil, perfluoropolyether oil is commonly used as lubricant for LISs [33,34,35]. Although, perfluoropolyether oil, which is a fluorinated compound, has some impact on the environment [19]; however, it has received widespread attention because of its low surface tension [36], low evaporation loss [37], insolubility with most repellent liquids [38,39], good water-droplet mobility [33], and anti-icing properties [40]. The water droplet impact and sliding behavior of these LISs at different We numbers have not been systematically reported. In addition, LIS may be in an inclined state in practical applications. The dynamic behavior of water droplets on an inclined slippery surface is affected by the inclination angle, which has not been researched as well.

In this study, the water droplet impact and sliding behaviors on the LISs with different We numbers and surface inclinations were investigated. Perfluoropolyether oils (GPL 100 and GPL 104) were used as the lubricant. The LISs were prepared by infusing lubricant into anodized porous surfaces. The droplet impact behavior, including spreading, retraction and bouncing process, maximum spreading diameter, and spreading factor of the prepared LISs, was studied. Furthermore, the sliding velocity of droplets on the inclined LISs under different conditions was compared. Understanding the effects of We number and tilt angle on the droplet impact and sliding behavior on LISs with different lubricant viscosities may help us to explore the application of LISs under water droplet impact.

2. Materials and Methods

Perfluoropolyether oils (DuPont Krytox GPL 100, GPL 104) were purchased from Changsha Zhixuan Chemical Products Co., Ltd., Changsha, China. n-octadecyltrimethoxysilane (98%) was purchased from Aladdin Reagent Co., Ltd., Shanghai, China. Aluminum plates (1061) were supplied by Dongguan Chaomei Aluminum Products Co., Ltd., Dongguan, China. Phosphoric acid (H₃PO₄, ≥85%) and anhydrous ethanol were obtained from Chuandong Chemical Co., Ltd., Chongqing, China. Sodium hydroxide (NaOH, ≥98.0%) was supplied by Chengdu Kelong Chemical Co., Ltd., Chengdu, China.

The porous surfaces were prepared via anodic oxidation. Specifically, aluminum plates of size 25 × 20 × 1 mm³ were ultrasonically cleaned with alcohol for 3 min, and then soaked in NaOH solution (1 mol/L) for 2 min to remove the surface grease. Then, the plates were washed with deionized water. The cleaned sample was used as the anode and the stainless-steel plate was used as the cathode for anodic oxidation. The current density was 0.12 A/cm², and the oxidation time was 10 min. The anodized aluminum oxide (AAO) samples were cleaned with alcohol to remove the residual electrolyte and then dried in an oven at 70 °C. To increase the hydrophobicity of the porous surface, the prepared samples were modified in a silane solution (2 wt%, 1 g of silane and 50 g of alcohol) for 30 min and placed in a drying oven at 90 °C for 1 h. Finally, the lubricant was infused into the modified porous surface by vacuum method. In detail, the sample immersed in the lubricant was placed in a vacuum vessel and subsequently evacuated to remove the air from the nanopores for complete infusion. Capillary forces also play an important role in the migration of lubricant into the pores during this process. Finally, the LISs were successfully prepared. GPL100 and GPL 104 infusing slippery surfaces were denoted as LIS-100 and LIS-104, respectively. The fabrication process is shown in Scheme 1. The bare aluminum plate (the untreated sample) was used as the control sample.

The morphology of the sample was characterized using field emission scanning electron microscopy (SEM, Zeiss Auriga, Oberkochen, Germany). The wettability of samples [41] was evaluated by water contact angle (CA) and sliding angle (SA), which were measured with a contact-angle-measuring instrument (SINDIN, SDC-350, Dongguan, China). For CA, the water droplet size was 3 μL, and the average value was obtained by measuring five areas of the sample surface. For SA, the droplet size was 5 μL, and its value was measured by tilting the sample stage until the water droplet slid off. To measure the lubricant CA, the lubricant was added to the syringe. The contact-angle-measuring instrument was also adopted to measure the surface tension of the lubricant and interfacial tension between the lubricant and the water.

The impact and sliding behavior of the water droplet on the slippery surface was observed with a high-speed camera (Revealer, M220, Hefei, China) with a macro lens. The maximum frame rate was 2000 fps, which captured the dynamic behaviors of the water droplet upon impact. The water droplets were generated with a syringe connected to a peristaltic pump (Rongbai, BT100-2J, Baoding, China), and the diameter of the water droplets was about 2.2 mm. A high-power LED lamp was used to ensure sufficient light. The experimental apparatus is shown in Scheme 2. The height (H) between the sample and the syringe was in the range of 5–45 cm. The We number was controlled by the falling height (i.e., H) of the water droplet. Here, $We=\rho v^{2}r/\gamma$ [30,42], where r is the droplet radius, ρ is the droplet density (1000 kg/m³), γ is the water surface tension (72 mN/m), and v is the droplet impact speed. The impact velocities and We numbers corresponding to water droplets of different falling heights are shown in

Table 1. The impact velocities and We numbers corresponding to water droplets of different falling heights.

Falling Height (cm)	Droplet Radius (mm)	Impact Velocity (m/s)	We
5	1.10	0.98	30
15	1.10	2.94	89
25	1.10	4.90	148
35	1.10	6.86	207
45	1.10	8.82	267

. The surrounding temperature was maintained at 25 °C. The camera was placed above the sample to observe the maximum spreading diameter and this measurement did not consider the size of the wavy-shaped fingers.

3. Results and Discussion

3.1. Morphology and Wettability

The morphologies of the flat and AAO surfaces are shown in Figure 1a,b. The bare surface was relatively smooth, while the AAO surface was distributed with many nanopores with an average pore size of 230 ± 24 nm. From the cross-sectional morphology of the porous surface (Figure 1c), the depth of the nanopores was 11.33 μm, which provides space for the storage of lubricant.

Surface modification facilitates the formation of a stable lubricant layer on the porous surface [19], which is a key standard for LIS preparation. Here, silane was chosen to modify the porous surface and the surface micrograph is shown in Figure 1d. There was no significant difference in the surface morphology of AAO before and after the modification [43]. Nevertheless, modification can make sure the surface is preferentially wetted by the lubricant rather than by water droplets that need to be repelled [44]. The formation of a stable layer satisfies the following criteria [6]:

$$∆E_1=R\left({\gamma }_o\cos {\theta }_o-{\gamma }_w\cos {\theta }_w\right)-{\gamma }_{ow}>0$$

(1)

$$∆E_2=R\left({\gamma }_o\cos {\theta }_o-{\gamma }_w\cos {\theta }_w\right)+{\gamma }_w-{\gamma }_o>0$$

(2)

where γ_w and γ_o represent the surface tensions for the water and the lubricant, and γ_wo represents the interfacial tension at the water–oil interface. θ_w and θ_o are the CA of the water and oil on the modified flat surface. R is the roughness factor. Here, R was calculated using the equation $R=\cos {\theta }_r/\cos \theta$ [45], where θ_r is the water CA on the unmodified AAO surface (28.2°) and θ is the water CA on the unmodified flat surface (79.7°). The measurement of the relevant parameters is shown in

Table 2. Parameters for Equations (1) and (2).

Parameters	R	γw (mN/m)	γo (mN/m)	γwo (mN/m)	θw (°)	θo (°)	∆E1 (mN/m)	∆E2 (mN/m)
GPL 100	4.9	72	17	27	102.5	10.0	132.3	214.3
GPL 104	4.9	72	19	56	102.5	17.1	110.3	219.3

The measurement of surface and interfacial tension was conducted using the pendant drop method. Notably, when measuring the γ_w and γ_o, the droplet was suspended in air. When measuring the γ_wo, the oil droplet was suspended in water because the density of perfluoropolyether oil is higher than that of water.

. Both GPL 100 and GPL 104 satisfy ∆E₁ > 0 and ∆E₂ > 0. This indicates that the lubricant can form a stable layer on the modified porous surface; that is, the water droplet can remain atop the lubricant layer instead of entering the nanopore through the layer.

GPL100 and GPL104 were, respectively, injected into the modified AAO to prepare LIS-100 and LIS-104. The wettability of the slippery surface is shown in Figure 2. The CA of the hydrophilic bare surface was very low, only 79.7°, and the water droplets could not slide on the surface (SA > 90°). The CA of LIS-100 and LIS-104 were 114.7° and 115.3°, respectively, exhibiting hydrophobicity (CA > 90° [46]). It is worth noting that the hydrophobicity of the LIS was much lower than that of superhydrophobic surfaces (CA > 150° [2,47]). However, the SA of the LIS was very low (about 2°) and demonstrates excellent slippery properties. Equations (1) and (2) prove that the lubricant film can exist stably under water droplets, which lays a foundation for LISs to have good water-droplet mobility.

3.2. Effect of We Numbers on the Water-Droplet-Impact Behaviors

The effect of We numbers on the droplet-impact behaviors on the LISs were studied, and the results are shown in Figure 3. The dynamic behaviors of the impact droplet included spreading, retraction and bounding [48]. In general, the gravitational potential energy of a free-falling water droplet was completely converted into kinetic energy before impact. In the spreading stage, the droplet gradually spread in the radial direction. The kinetic energy of the water droplet was partially converted into surface energy and partially dissipated. The energy dissipation mainly came from viscous dissipation and three-phase contact line (TPCL) pinning. After the water droplet reached the maximum diameter, the surface energy overcame the adhesion of the surface and converted into kinetic energy, and the droplet began to retract. The droplet-spreading diameter gradually decreased, the droplet height increased, and the droplet gradually presented a columnar shape. Secondary droplets may be generated at the top of the droplets and separated from the initial water droplets. The spreading and retraction were asymmetric. The spreading of the droplet on the surface (2.5 ms) was much faster than its shrinking (about 18 ms). In the rebound stage, the inertial force in the vertical direction was greater than the droplet gravity and surface adhesion, and the droplet partially rebounded on the surface. The kinetic energy and surface energy of the droplet were gradually converted into gravity energy. At different We numbers, the water droplets deformed into pancakes on the bare, LIS-100 and LIS-104 surfaces and reached the maximum diameter at 2.5 ms. However, at a lager We, the drop become flatter during spreading because of the high impact velocity. This led to a larger maximum diameter and faster spreading speed. Thus, droplets with different We numbers exhibited some different spreading behaviors.

The retraction and bounding of the droplet depend largely on the characteristics of the surface, and this bounding behavior is called “substate dependent bouncing” [49]. When We = 30, the water droplet did not bounce on the bare surface and adhered to the surface at the end of the retraction stage. This is because the hydrophilic surface increases the dissipation of the initial kinetic energy of the droplet. When the We number increased to 267, the energy dissipation caused by the TCPL pinning increased, and the water-droplet retraction ability decreased significantly, showing a larger contact diameter. The water droplet impacting LISs retracted faster and could partially bounce in contrast to what was observed on the bare surface, especially for LIS-100 at a lower We number. The presence of the lubricant film suppressed the direct water–solid contact, thus significantly reducing the energy dissipation caused by the contact line pinning (from the SA in Figure 2). Therefore, the dissipation caused by the deformation of the droplet during the spreading and retreating process was weak, so it had more energy for rebounding at the end of the retraction phase. It is worth noting that the bounce behavior of an LIS is different from that of a superhydrophobic surface where water droplets can achieve complete rebound [27,50]. This is because an LIS has a high adhesion to water droplets in the direction perpendicular to the surface. To sum up, compared with bare surfaces, LISs have more excellent dynamic water repellency.

The viscosity of the lubricant has a great influence on the impact behavior of water droplets on an LIS. When We = 30, the contact diameter of the water droplet on the LIS-100 at 8.0 ms was smaller than that of the droplet on the LIS-104 surface, indicating that the lower the viscosity of the lubricant, the faster the retraction velocity. The drop on the LIS-100 partially rebounded with a tiny water residual remaining on the surface at 18.0 ms. For LIS-104, the secondary droplet was separated from the primary droplets under the action of inertial force. However, due to the large adhesion of the surface to the water droplets in the vertical direction, the primary droplet struggled to bounce off the surface. The retraction of water droplets after spreading is driven by capillary force, which is balanced by viscous force [51]. The viscous force at the contact line increases with the lubricant viscosity during the retraction phase. The low viscosity of lubricant reduces the shear stress between water droplets and oil layer, thus reducing the energy dissipation of water droplets in the retraction process. When the We number increased, the water droplet still bounced on the LIS-100. Obviously, the bounce height decreased when We = 267. For the water droplet on LIS-104, the bouncing energy was further weakened at larger We numbers, and no secondary droplets were even produced. This is because the high-velocity impact water droplet has a larger spreading diameter and retraction distance, thereby increasing the energy dissipation in the retraction phase. Although the water droplets on the LIS-104 could not bounce off like on the bare surface, the impact droplet eventually reverted to a hemispherical shape on the surface due to hydrophobicity. When the surface is tilted, LIS-104 still has water-shedding ability, which is discussed in the next section. To sum up, compared with LIS-104, LIS-100 had better rebound ability.

The time evolution of the spreading factor (D/D₀, the diameter of the impacting droplet normalized by the initial droplet diameter) on the sample surfaces at different We numbers was measured according to high-speed images, and the results are shown in Figure 4. For LIS-100, the D/D₀ at 2.5 ms increased from 2.00 to 3.88 with We increasing from 30 to 267. Additionally, the larger the We number, the greater the slope of the D/D₀-t curve during the retraction process (this represents the contraction velocity [48]). This demonstrates that an impact droplet with a large We number can increase the spreading factor and retraction velocity. At the same We number, the D/D₀ of the droplet on all surfaces changed similarly during the spreading stage, because the droplet spreading is mainly determined by the balance between capillary force and inertia [30], which is similar to superhydrophobic surfaces [52]. By contrast, the retraction process is substrate-dependent due to the non-negligible viscous dissipation, and this is consistent with the previous result. For all We numbers, the D/D₀ of the water droplets on LIS-100 and LIS-104 decreased rapidly compared with the bare surface. This indicates that the water droplets are easy to retract on the slippery surface due to low energy dissipation. The dynamic behavior of the retraction phase of the LIS is determined by lubricant viscosity; the retraction velocity (the slope of the D/D₀-t curve) decreased with the increase in the viscosity. For example, at We = 148, the D/D₀ of LIS-100 and LIS-104 decreased to 0.79 and 1.55 at 12.0 ms from about 3.50 at 2.5 ms, respectively. Therefore, the results confirm that the droplet-impact dynamic behaviors are related to the We number and the lubricant viscosity, and a large We number and low viscosity enhance the retraction velocity of the impact droplet.

The high-speed images of the maximum spreading diameter of water droplets on bare, LIS-100, and LIS-104 surfaces at different We numbers are shown in Figure 5. When the We number was low (i.e., 30 and 89), the spreading of the water droplet on all surfaces was relatively gentle. The film thickness of the spreading lamella was not uniform, a liquid ring formed at the edge, and the film at the center was thinner. With the increase in the We number, the edge of the spreading water droplet appeared as wavy-shaped fingers. On the bare surface, this wavy front occurred after We = 148, while it was not obvious on the LISs at the same We number. For bare surfaces, high-speed water droplets directly contact the solid substrate after impacting, which easily causes water-droplet instability. On the contrary, the lubricant layer of an LIS encapsulates water droplets at the three-phase contact line (called the wetting ridge) [53], which can delay the instability of water droplets. Additionally, when We = 207, wavy fingers were clearly observed on LIS-100. However, the edge of the water droplets was relatively stable after spreading on LIS-104, and only a small number of ripples appeared at We = 267. This may be because the lubricant with low viscosity was easily replaced by water when the high-speed water droplets impacted the slippery surface. Exposure of the surface morphology of the underlaying substrate causes instability in water droplets [32]. Therefore, the lubricant with high viscosity is beneficial to the lubricant stability of the LIS under high-speed water-droplet impact.

The variation in the maximum spreading factor (D_max/D₀) with We number for bare, LIS-100 and LIS-104 is shown in Figure 6. The D_max/D₀ increased with the We number. For example, in LIS-100, the D_max/D₀ increased from 1.84 to 3.37 with We increasing from 30 to 267. This is because D_max is determined by the balance between the capillary force and acceleration after impact. The larger the We number, the larger the initial kinetic energy of the water droplet and the larger the spreading diameter of the water droplet. The D_max/D₀ of the bare surface was slightly larger than that of the LISs, because the hydrophilic surface has a large adhesion to water and tends to increase the spreading diameter of the droplet during the spreading process. Additionally, Figure 6 shows that the viscosity of the lubricant had no obvious effect on the maximum spreading diameter of the water droplets. This is because the viscous dissipation in the lubricant layer during the spreading stage is very small. The ratio of the viscous dissipation inside the lubricant layer to the viscous dissipation inside the water droplet is expressed as [32]

$$\frac{{\eta }_{w}h}{{\eta }_{o}t}\ll 1$$

(3)

where η_w and η_o are the viscosity of water and lubricant oil, respectively; t and h are the thickness of the water droplet and lubricant layer, respectively. Therefore, the viscous dissipation inside the lubricant layer during the spreading stage can be ignored compared with that inside the water droplet. To sum up, D_max/D₀ is related to We and not to the viscosity of the lubricant.

3.3. Effect of Surface Inclinations on the Water-Droplet Impact and Sliding Behaviors

To explore the influence of surface inclination on the dynamic behavior of water droplets on the different sample surfaces, the We number was maintained at 148. Figure 7 shows the time evolution of a water droplet sliding on the bare, LIS-100 and LIS-104 surfaces with inclinations (θ) of 15°, 30° and 45°. The maximum spreading factor of the water droplet and bouncing height is shown in Figure 8. During spreading, the inclination angle had no obvious effect on the droplet outline along the tangential surface (Figure 7). At 0~2.5 ms, the water droplets spread on the inclined surfaces. Unlike horizontal surfaces, the diameter of the water droplets continued to increase along the surface under tangential acceleration and reached a maximum at about 3.5 ms (Figure 8a). At this time, the maximum spreading diameter is related to the substrate surface. LIS-100 had the lowest D_max/D₀. When t > 2.5 ms, the lower end of the droplet-spreading lamella expanded along the surface and the upper end retracted. When the viscosity of the lubricant is low, the retraction resistance at the upper end of the water droplet lamella is small, so the maximum spreading diameter is smaller than other surfaces. This phenomenon is more obvious for larger inclination angles. When θ = 15°, the bouncing heights of the water droplets on LIS-100 and LIS-104 were 2.89 mm and 2.07 mm, respectively (Figure 8b). This demonstrates the greater the viscosity of the lubricant, the smaller the bouncing height of water droplets. Additionally, the water droplet on the bare surface was directly spread on the surface after impact. Therefore, the viscosity of the lubricant still affects the impact behavior of water droplets on the surface.

The impact behavior of water droplets on the surface is affected by the inclination angle of the surface. For LIS-100, the D_max/D₀ increased from 3.00 to 3.35 with θ increasing from 15° to 45° (Figure 8a). Notably, when θ = 45°, a secondary water droplet was generated along the surface tangential direction. Moreover, the bouncing height at 15.5 ms decreased from 2.89 mm to 1.29 mm with the increase in surface inclination. When the water droplet impacted the inclined surface at the velocity of v₀, the velocity along the normal direction to the surface was v_n = v₀ cosθ, and the velocity along the tangential direction to the surface wsa v_t = v₀ sinθ. The v_n decreased with the increase in θ, which was not conducive to the bouncing of droplet. On the contrary, v_t increased with the increase in θ. This facilitates the tangential deformation of water droplets along the surface, so the spreading diameter of water droplets increases, and even a secondary water droplet appears. To sum up, surface inclination can aggravate the deformation of the droplet along the tangential direction of the surface and reduce the rebound ability.

To study the water-droplet-shedding ability of the slippery surfaces after impact, the sliding time of the droplet on the surface with an inclination angle of 30° was recorded with a high-speed camera. The time-lapsed images of the water droplet are shown in Figure 9. Since the SA of the bare surface was greater than 90°, the water droplets could be pinned to the inclined surface and could not slide, so we do not consider it in Figure 9. The droplet kept in close contact with the lubricant of the LIS. The droplet shed from the LIS-100 and LIS-100 surfaces within tens of seconds, showing excellent slippery performance. Notably, the droplet slid to the lower end of the LIS-100 surface in 2.48 s, which was faster than that on the LIS-104 (18.56 s). Therefore, the LIS-100 had better water-droplet-shedding ability than the LIS-104.

The sliding velocity is calculated according to the sliding time of water droplets on the LIS-100 and LIS-104 surfaces with different inclination angles, and the results are shown in Figure 10. When the θ was 30°, the average sliding velocity of water droplets on the LIS-100 surface was 4.19 mm/s, which was about seven times faster than that on the LIS-104 (0.56 mm/s). The acceleration and gravity (mg sinθ) of the water droplet after impact are the driving forces that promote the droplet to slide, which is balanced with the surface dissipation force (F_d). The F_d depends on the viscous stress η_oU/h and $F_{\mathrm{d}}\propto {\eta }_{o}U/h$ [54], where η_o is the lubricant viscosity, U is the droplet velocity, and h is the thickness of lubricant film. Thus, the larger the lubricant viscosity, the greater the F_d. This indicates that the sliding resistance of water droplets on LIS-104 was larger than of LIS-100, resulting in a lower sliding velocity. The surface inclination also had a great effect on the sliding velocity of water droplets. For LIS-100, the velocity increased rapidly from 1.04 to 4.19 mm/s with θ increasing from 15° to 30°. When θ continued to increase to 45°, the sliding velocity only increased to 4.66 mm/s. This is because the generation of secondary water droplets reduced the quality of the original water droplet. To sum up, low lubricant viscosity and high inclination angle are conducive to the rapid shedding of water droplets on the surface. It is worth noting that, although the previous results showed that the high inclination angle did not facilitate the bounce of the water droplets on the lubricated surface, the droplets could only partially bounce, even at a horizontal LIS. Therefore, it is more important to improve the water-droplet-shedding ability of an LIS through surface inclination in practical application.

4. Conclusions

The effect of We number and surface inclination on the water-droplet impact and sliding behaviors on slippery surfaces with different lubricant viscosities was studied. LISs were prepared by infusing GPL100 and GPL 104 into modified porous surfaces, which showed excellent slippery performance. Droplets with different We numbers exhibited distinct impact behaviors on the slippery surfaces. A large We led to a larger maximum diameter and faster spreading and retraction velocity of the impact droplet. At different We numbers, LISs had more excellent dynamic water repellency than the bare surface. Furthermore, the low-viscosity lubricant (GPL 100) was beneficial to the rebound ability and retraction velocity of the water-droplet impact on the surface. By contrast, the lubricant with high viscosity facilitated the lubricant stability of the LIS under high-speed water-droplet impact (GPL 104). The spreading factor (D_max/D₀) strongly depended on We number rather than the surface characteristics. Additionally, the surface inclination was another factor affecting the dynamic behaviors of the LISs. Low inclination was able to enhance the rebound ability and high inclination was conducive to the rapid shedding of water droplets on the surface. Notably, the droplets could only partially bounce even at on a horizontal LIS. Thus, it is more important to improve the water-droplet-shedding ability of an LIS through surface inclination. At different surface inclinations, the LIS prepared with low-viscosity lubricant had high sliding velocity; therefore, it had better water-shedding ability. This study demonstrates the dynamic behavior of slippery surfaces and provides some guidance for the design of LISs under droplet-impact conditions.