Experimental investigation on water repellency and anisotropic wettability of microgrooved polymer surfaces

Abstract

Simple patterns on a surface can enhance water repellency and simultaneously impose directional wettability. Surfaces exhibiting periodic microscale grooves are examples of such surfaces. Here, we design microgrooved surfaces with three different groove widths and experimentally investigate their impact behaviors on the surfaces. In terms of wetting state, the robustness of water repellency against an impinging droplet is evaluated. Contact angle of a surface alone cannot represent the water repellency against impinging droplets. Surfaces with large contact angles are found to be less water repellent. However, water repellency of a surface depends on its capillary pressure, which resists the wetting state transition. The anisotropic pattern of grooves naturally affects the contact line motion of a droplet, particularly during the spreading and receding phases. Therefore, directional behaviors of the spreading and receding diameter and temporal characteristics were also experimentally examined. Temporal characteristics of smooth surfaces are nearly identical to those in the direction parallel to the grooved surface, while distinctive characteristics were observed in the perpendicular direction. This discrepancy probably originated from the discontinuity of the contact line experienced in the perpendicular direction.

Graphic abstract

1 Introduction

Bio-inspired surfaces such as those of plant leaves exhibiting complex topologies have been widely studied owing to their unique wetting characteristics (Koch et al. 2008). A unique characteristic is superhydrophobicity, which is fundamentally attributed to surface roughness where liquids exhibit two different wetting states. One is the Cassie–Baxter (Cassie or fakir) state (Cassie and Baxter 1944) and the other is the Wenzel state (Wenzel 1936). In the Cassie state, the liquid rests on top of the roughness features, whereas the liquid flows on the roughness features in the Wenzel state. The Cassie state has been considered to be favorable for superhydrophobic surfaces because of its higher contact angle (CA) and lower CA hysteresis compared to those of the Wenzel state (He et al. 2004). Therefore, robustness of water repellency depends on the stability of the Cassie state.

From the surface topology and intrinsic wettability of the material that forms it, an energetically stable state can be analytically determined (Lafuma and Quéré 2003). However, in numerous experimental reports, the Cassie state was observed even in the regime where the Wenzel state was stable (Öner and McCarthy 2000; Yoshimitsu et al. 2002). The transition from this Cassie state to the Wenzel state is hindered by an energy barrier (Patankar 2004). The system has to pass through a higher intermediate energy state. Hence, the system requires an additional energy source. Furthermore, even in the Cassie regime, irreversible transition to the Wenzel state can occur if a sufficient amount of energy is supplied to the system. This metastable character of the Cassie state was previously reported (Reyssat et al. 2008).

A type of additional energy, which can trigger impalement transition, arises from the drop impact. At the point of initial contact between an impinging droplet and a surface, the contact induces water hammer pressure P_WH (Field et al. 2012). After the contact phase, the pressure of the droplet is decreased to dynamic pressure P_D (Engel 1955; Field 1999). These two pressures are called wetting pressure P_wet. On the rough surface, however, there is a pressure, which resists the impalement transition. This anti-wetting pressure is called capillary pressure P_C. This is because the origin of the anti-wetting pressure is the capillary force along the contact line of the liquid and the roughness features (Jung and Bhushan 2008). Thus, the wetting state of an impinging drop depends on the balance between P_wet and P_C. Given that numerous solid–liquid interactions accompany the impact process, the wetting state of an impinging droplet is noteworthy.

Apart from water repellency, directional wettability is another primary wetting character of bio-surfaces, which is frequently simulated and investigated (Bixler and Bhushan 2012; Lee et al. 2013). This directionality originates from the anisotropic arrangement of surface roughness (Koch et al. 2008). Simple geometries such as periodic grooves induce directional wettability and water repellency (Vaikuntanathan and Sivakumar 2016; Guo et al. 2018). For an impinging droplet, anisotropy has been mainly observed in the spreading phase. Differences exist in the spreading characteristics of the drop measured at two primary orientations, i.e., perpendicular and parallel to the groove direction.

One difference between the two primary directions can be found in spreading factor β and ratio of the spreading diameter D to the initial value D₀, which reflects the ability of deformation during impact. This factor is important for understanding the dynamic aspect of the solid–liquid interface. The maximum spreading diameter D_m is a direct measure of the maximum solid–liquid contact area. It is examined in the normalized form called the maximum spreading factor $\beta_{\text{m}} = D_{\text{m}} /D_{0}$. On the surfaces with grooves, the value of β_m parallel to the groove is larger than that of β_m perpendicular to the groove (Vaikuntanathan and Sivakumar 2016; Guo et al. 2018). In addition, the spreading ends sooner in the perpendicular direction (Pearson et al. 2012). These anisotropic features have the potential to overcome the axisymmetric limitation of the drop impact in a surface-tension-dominated regime.

As mentioned earlier, superhydrophobic and directional properties can be obtained simultaneously by simply forming grooves on a surface when its intrinsic wettability is hydrophobic (i.e., CA > 90°) (Lafuma and Quéré 2003). Until now, few experimental examinations have been performed on the anisotropic behaviors of grooved surfaces. Considering the numerous surface materials available and the geometric variation of the groove, directional behaviors should be inspected in detail. Especially, dynamic behaviors with respect to time should be investigated quantitatively for a better understanding of the impact process on anisotropic surfaces. However, the temporal variation of diameter with respect to anisotropic characteristic has been reported in a few studies only and is limited to several impact cases with a relatively low precision of measurements (Kannan and Sivakumar 2008). Furthermore, the wetting state based on P_wet and P_C of anisotropic surfaces with periodic grooves has not been experimentally investigated along with the anisotropic behaviors. Therefore, in this study, the wetting state and anisotropic behaviors of impacting droplets on microgrooved polymer surfaces were experimentally investigated simultaneously. In addition, the precise measurement techniques used in this study reveal the anisotropy on the temporal characteristics with a high spatiotemporal resolution.

2 Materials and methods

Surfaces made of polydimethylsiloxane (PDMS) and with unidirectional microscale grooves were prepared for this study. We used a replica molding technique for repeated production (see "Appendix" for the detailed procedure). Surfaces were designed to have identical ridge dimensions with different groove widths of 20, 40, and 80 μm and denoted them as G₂₀, G₄₀, and G₈₀, respectively. The dimensions of the prepared surfaces were measured using a three-dimensional (3D) laser microscope (VK-9700, KEYENCE Corporation). The reconstructed 3D and optical images of the PDMS microgrooved surfaces are shown in Fig. 1a–f. The values of the breadth of the ridge b, width w, and depth h of the grooves (Fig. 1g) for each surface are listed in Table 1.

Fig. 1

Reconstructed three-dimensional schematic images of a G₂₀, b G₄₀, and c G₈₀; top view optical images of d G₂₀, e G₄₀, and f G₈₀; g diagram of geometric parameters

Table 1 Geometric parameters of the microgrooved surfaces and the water contact angle (CA) values estimated and measured on the microgrooved surfaces

The liquid used in all our impact experiments was filtrated de-ionized (DI) water of density ρ = 995 kg m⁻³, surface tension σ = 72.0 mN m⁻¹, and viscosity μ = 1 mPa s. Droplets were generated from a flat needle of gauge number 32 and an outer diameter of approximately 0.23 mm. The terminal impact speed was regulated by varying the drop release height. The sizes and terminal velocities were measured for each single droplet (totally 208 drop impacts were recorded and analyzed). Size D₀ of the impinging droplets was 2.06 ± 0.02 mm. The impact speed V ranged from 0.16 to 1.19 ms⁻¹.

The entire impact process was recorded by a simple imaging system consisting of a high-speed camera (Phantom VEO710L, Vision Research Inc.), an objective lens (Plan Achromat 4X, Nikon Corporation), an optical adapter (InfiniTube™ Ultima, Infinity Photo-Optical Company), and a light-emitting diode backlight. The frame rate and exposure time were 7020 frames per second (0.14 ms for each frame) and 5 μs, respectively. To identify the anisotropic wetting behavior, recording was conducted along two primary directions. The quantities along (across) the groove direction are denoted by the subscript ‖ (⊥) and are called the parallel (perpendicular) quantities as shown Fig. 2b, c. The temperature and relative humidity were maintained at 24 °C and 34%, respectively, throughout the experiments. Subsequently, the recorded images were manipulated systematically using a user-designed image-processing algorithm (MATLAB Image Processing Toolbox, The MathWorks, Inc.). The diffraction limit of the optical system (~ 2.5 μm) is smaller than the physical dimension of the imaging plane corresponding to a pixel (~ 6.2 μm). Since the image-processing algorithm is based on the grayscale of pixels, the uncertainties in the length measurement are estimated to be two pixels. Considering the imaging conditions including the frame rate, the uncertainties of time, diameter, and ratio of diameters are approximately ± 0.14 ms, ± 0.012 mm, and ± 0.017, respectively.

Fig. 2

Two orthogonal measurement directions with respect to the groove length direction. a Top view; b parallel quantities measured along the groove direction; c perpendicular quantities measured across the groove direction

To verify the fundamental wettability of the prepared surfaces with DI water, we measured the water CA on the microgrooved surface prior to the impact test. For reference, we also prepared a flat and smooth surface without grooves. This flat PDMS surface and the flat portion of the microgrooved surface have a roughness value (arithmetic mean deviation, Ra) of 46 nm. The equilibrium CA θ_e on the flat and smooth surface was approximately 96 ± 1°. This corresponds to the intrinsic CA of the PDMS material used in this study. Compared to the CA measured on the microgrooved surfaces (Table 1), the apparent water repellency increased by the formation of microscale grooves. In addition, higher values of CA across the grooves, θ_e⊥, than those along the grooves, θ_e‖, were observed (Fig. 3). This anisotropic characteristic was reported experimentally (Guo et al. 2018).

Fig. 3

Sessile drop on the G₈₀ for the contact angle measurements a parallel, θ_e‖ and b perpendicular, θ_e⊥ to the groove direction. The drop volume is 5.0 μL. The base line for the measurement is indicated in blue solid line

The noteworthy aspect of θ_e is that both the CAs (θ_e⊥ and θ_e‖) increase as the groove width w increases. From the geometric information of the rough or structured surfaces, we can estimate the apparent CA corresponding to the wetting state of the liquid on those surfaces. The apparent CA in the Wenzel state, θ_W, is expressed as follows (Wenzel 1936):

$$ \cos \theta_{\text{W}} = r\cos \theta_{\text{e}} , $$

(1)

where r is the roughness factor, which is the ratio of the actual surface area to the nominal projected area. For a Cassie drop, the apparent CA θ_C is expressed as follows (Cassie and Baxter 1944):

$$ \cos \theta_{\text{C}} = \phi \cos \theta_{\text{e}} + \phi - 1, $$

(2)

where ϕ is the texture area fraction, which is defined as the proportion of the projected wet area underneath the droplet. In this study, $r = 1 + 2h/\left( {w + b} \right)$ and $\phi = b/\left( {w + b} \right)$. The values of θ_C evidently increase as w increases due to reduced ϕ (Table 1). In addition, θ_C lies between θ_e⊥ and θ_e‖. From the large gap between the values of θ_W and the measured CA, and the contrary trend with increasing w, the wetting state of the sessile droplets used for the CA measurements would be in the Cassie state.

As mentioned earlier, the energetically stable state can be analytically determined. Threshold CA θ_e,c, which decides the lower energy state for a specified roughness, is given by equating Eqs. (1) and (2) (Bico et al. 2002):

$$ \cos \theta_{\text{e,c}} = \frac{\phi - 1}{r - \phi }. $$

(3)

From the analytical perspective, the Cassie state is feasible when θ_e is larger than θ_e,c. Thus, the energetically stable state of the microgrooved surfaces in this study is the Wenzel state, although the gently deposited sessile droplets are in the Cassie state.

3 Results and discussion

3.1 Wetting states of impinging droplets

The Cassie state maintained for the sessile droplets is metastable because the microstructured surfaces in this study are more stable in the Wenzel state. To determine the stability of the Cassie state (or the water repellency), the impact behaviors of impinging droplets with additional energy in the form of P_wet were investigated. Since the scale of the phenomena is smaller than the capillary length $l_{\text{C}} = \sqrt {\sigma /\rho g}$, where g is the gravitational acceleration, gravity can be neglected (de Gennes et al. 2004). The impact regime is generally introduced by the Weber number $We = \rho V^{2} D_{0} /\sigma$ of the droplets, which scales the importance of the inertia compared to the capillary force. The viscous effect in a free surface situation can be assessed by the Ohnesorge number $Oh = \mu /\sqrt {\rho \sigma D_{0} }$. The We regime of the present study ranges from 0.8 to 40, as shown in Fig. 4. In most of the previous studies, We ranges are broader than that in this study. A few of these We ranges are 20–200 (Lv et al. 2016), 5–280 (Guo et al. 2018), and 1–100 (Vaikuntanathan and Sivakumar 2016). Although the impact regime is relatively narrow in this study, we provide an approximately 50% denser interval between the impact cases than that provided in previous studies.

Fig. 4

Impact regime of this study represented by We and Oh of impinging droplets

On the smooth PDMS surface without grooves, liquid lamella of the impinging drop gently spreads and then recedes. Subsequently, the contact line is pinned followed by damped oscillations of the top interface. The typical impact process is depicted in Fig. 5. Bouncing does not occur on the smooth surface regardless of We. However, on G₂₀, the droplet starts to rebound from the smallest We. Two bouncing droplets with nearly same We were observed at different primary directions, as shown in Fig. 6. Each pair of images (one in each direction) is captured at identical instants from the initial contact. The contact lines do not get pinned in the receding phase and finally bounce off without remnant liquid on the surface. This is strong evidence for the enhanced water repellency of G₂₀ compared to that of the smooth surface in addition to the increased θ_e discussed earlier.

Fig. 5

Impact sequences of the water drop with We = 34.4 on the smooth polydimethylsiloxane (PDMS) surface. Elapsed time from the initial contact is indicated at the top right corner (in ms)

Fig. 6

Drop impact sequences on the G₂₀. a The droplet with We = 3.94 is imaged at the parallel direction; b the droplet with We = 3.96 is imaged at the perpendicular direction. At each pair of images for two directions, elapsed time from the initial contact is indicated at the top right corner (in ms)

The droplets with We higher than 15 exhibit sticky behaviors on G₂₀. In the receding phase, the contact line is pinned, and a part of the drop sticks to the surface as shown in Fig. 7. The pinned contact line and the remnant liquid on the surface are evidence of the impalement transition to the Wenzel state (Lafuma and Quéré 2003). To validate the wetting state transition with respect to the balance between P_wet and P_C, we first evaluate P_C for the surfaces used in this study. By virtue of periodic grooves, the balance between the force from the internal drop pressure and the capillary force along the contact line can be examined through the groove length as follows:

$$ wP_{\text{C}} = 2\sigma \left| {\cos \theta } \right|, $$

(4)

where $wP_{\text{C}}$ is the force applied on unit area of the free surface and $2\sigma \left| {\cos \theta } \right|$ is the capillary force, which resists the transition.

Fig. 7

Impact sequences of the droplets having the same We = 15.2 on the G₂₀. Images recorded at the a parallel and b perpendicular direction, respectively. At each pair of images for two directions, elapsed time from the initial contact is indicated at the top right corner (in ms)

In addition, there are two distinctive mechanisms responsible for impalement transition: sag and de-pinning mechanism (refer Fig. 8) (Patankar 2004). In the sag mechanism, the liquid–air interface pinned on top of the roughness features touches the basal surface. The increased pressure inside a drop deforms the interface. Simultaneously, local CA θ (depicted in Fig. 8a) between the interface and roughness feature increases. However, this contact angle has an upper limit called the advancing contact angle θ_A. If the local contact angle exceeds the advancing angle, the pinning fails and the contact line slides downward to touch the basal surface (Fig. 8b). This is the de-pinning mechanism.

Fig. 8

Schematic diagrams (side view) of the impalement transition corresponding to a sag mechanism and b de-pinning mechanisms. The solid (dotted) line indicates the interface of the drop in the Cassie state (in transition)

Based on the de-pinning mechanism, P_C can be conveniently evaluated by replacing θ with θ_A (110° in this study) in Eq. (4). Subsequently, P_C for de-pinning, P_C,depin, can be expressed as:

$$ P_{\text{C,depin}} = 2\sigma \left| {\cos \theta_{\text{A}} } \right|/w. $$

(5)

To calculate P_C accurately based on the sag mechanism, P_C,sag, we require complete information of the drop. We can estimate the sag geometry by adopting a marginal-deformation approximation as adopted in previous studies (Jung and Bhushan 2007). Since groove width is significantly smaller than drop size, the curvature along the groove length direction would be negligible when compared to that in the direction perpendicular to the groove. Hence, P_C,sag is expressed in a simple form as:

$$ P_{\text{C,sag}} = \sigma /R, $$

(6)

where R is the radius of curvature of the interface at the touch-down moment. In addition to the values of P_C, we present the critical local CA θ_sag, at which the sag transition occurs, in Table 2. Since the θ_sag values for G₂₀ and G₄₀ are larger than θ_A in this study, impalement transitions on G₂₀ and G₄₀ will occur through the de-pinning mechanism.

Table 2 The critical local contact angle θ_sag at which the sag transition occurs and the capillary pressure P_C corresponding to the sag P_C,sag and de-pinning mechanisms P_C,depin

As mentioned earlier, the wetting pressures of an impinging droplet comprise of $P_{\text{D}} = 0.5\rho V^{2}$ and $P_{\text{WH}} = k\rho CV,$ where k is a constant, which depends on the impact conditions, and C is the sound speed of the droplet (Engel 1955; Field 1999). Since P_WH is applied to a very confined area (Field 1991) and is released in the early stage of contact, P_WH and P_D were evaluated separately at the contact and spreading stages, respectively (Deng et al. 2009). In this study, this two-stage approach was applied and coefficient k was determined to ensure that wetting pressures for the drops leaving the remnant liquid after bouncing exceed P_C. Since remnant liquid is the evidence of impalement transition, one of the wetting pressures must be larger than P_C. The possible range of k, which makes P_WH satisfy the condition for impalement transition, can be determined for the droplet whose P_D is smaller than P_C. The range of k narrowed down to a specific value as the examination proceeded toward the impact cases with three different values of P_C. It is noteworthy that coefficient k has been usually determined empirically for textured surfaces (Kwon et al. 2013; Maitra et al. 2014). These empirical values are usually two orders of magnitude smaller than the values based on the analytic processes on flat surfaces (k = 0.2) (Engel 1955). In this study, k is 0.0025, which is two orders of magnitude smaller than 0.2. It is interesting to note that some researchers treated P_D and P_WH together (Maitra et al. 2014). In this one-stage approach, P_C is balanced with P_D + P_WH. In addition, the dependency of k on P_C has been reported in other experimental studies (Dash et al. 2012). Clear differences exist among the experimental studies on P_WH and k. Hence, it is necessary to study them in the near future.

The resultant pressure map from k = 0.0025 is presented in Fig. 9. For all the impact cases on G₂₀, P_D is lower than P_C. However, P_WH exceeds P_C for the droplets with We higher than 15. When P_WH solely exceeds P_C, a narrow portion around the initial contact point of the area underneath the drop wets the roughness. This partial impalement occurs because P_WH acts on the initial contact point for a very short period (Hyväluoma and Timonen 2008). As We or P_WH is further increased, the amount of remnant liquid stuck to the surface increases because the liquid volume that penetrates the grooves increases (Fig. 10). All the microgrooved surfaces in this study display an identical trend.

Fig. 9

Wetting pressure P_wet of impinging droplets are presented with their We on a G₂₀ having the P_C of 2.53 kPa, b G₄₀ having the P_C of 1.26 kPa, and c G₈₀ having the P_C of 0.46 kPa. The data points corresponding to impact sequence figures are denoted. The inset images display the receding phase of the impacting drop with We = 28.8 recorded at the parallel direction

Fig. 10

The remnant liquids stick to the surface G₂₀ imaged at the a parallel and b perpendicular directions. Images are captured right after the detachment of the main drop. We corresponding to each impact case is denoted below

On the microgrooved surface G₄₀, P_WH starts to exceed P_C when We is approximately five (Fig. 9). The sticky behaviors from the partial impalement of the impinging droplets with We of approximately seven are depicted in Fig. 11. The decreased water repellency is directly identifiable from the lower value of P_C for G₄₀ than that for G₂₀. On G₈₀ with the lowest value of P_C, all the impact cases undergo impalement transition. Furthermore, both the P_wet values exceed P_C as We of the impacting droplets reach approximately 28. However, no special difference is observed, as depicted in the inset of Fig. 9c. It should be noted that the apparent CA measured on G₈₀ is the highest among the three microgrooved surfaces, whereas P_C and the resulting water repellency are the lowest. Therefore, we consider that the degree of hydrophobicity cannot be evaluated by CA alone, at least for these types of one-tier roughness surfaces.

Fig. 11

Drop impact sequences on the G₄₀. a The droplet with We = 6.83 is imaged at the parallel direction; b the droplet with We = 6.89 is imaged at the perpendicular direction. At each pair of images for two directions, elapsed time from the initial contact is indicated at the top right corner (in ms)

3.2 Directional wetting characteristics

As is apparent from the impact sequences (Figs. 5, 6, 10), the shape of a drop, particularly the length of contact line and CA, is distinguishable between the parallel and perpendicular directions. To assess directional wettability, we precisely measure temporal variations of the spreading and receding diameters. As shown in Fig. 12, the diameters D over time on G₈₀ are compared to those on the smooth surface. For better visibility, we present only the diameters of the selected droplets with relatively high We. On the smooth surface, the spreading diameters increase with time until they reach D_m as shown in Fig. 12a. The diameter of the drop with higher We is greater than that with lower We throughout the spreading and receding phases. The gap between the values of the diameters with respect to We reaches its maximum at the time of D_m and gradually decreases in the receding phase. A similar tendency with respect to time and the value itself can be found from the D measured along the groove direction on G₈₀ (Fig. 12b).

Fig. 12

Temporal variations of the drop diameters after impact on the a smooth surface, and G₈₀ measured in the b parallel and c perpendicular directions. The values of We for each impact case are denoted. Scaling law analyses for the spreading factors are presented in the inset

Dynamic behavior of the D measured perpendicular to the groove (Fig. 12c) is distinguished from others especially in the receding phase. Although the decreasing rate temporarily falls off about 1 ms after the beginning of the receding phase, it is insignificant to the overall receding rate. However, as shown in Fig. 12a, b, receding begins with a relatively slow rate, which decreases rapidly about 3 ms later. In this study, the log–log plots of the spreading factor β are given in the inset images to reveal the quantitative difference in the dynamic receding of diameters. On the smooth and G₈₀ surfaces measured in the parallel direction, there are two distinct regions with two different scaling exponents in the receding phase. Regardless of the existence of microgrooves, the values of scaling power of each region coincide (− 0.1 and − 0.7). In contrast, the spreading factor measured perpendicular to the groove on G₈₀ is scaled as $\beta \sim t^{ - 1.6}$ throughout the receding phase. Previously, the relationship between the dynamic receding diameter and time was scaled as $\beta \sim t^{ - 1}$ on microtextured surfaces (Lv et al. 2016). The power of scaling was fixed to − 1. The surfaces were covered with an isotropic array of microscale posts. Previous studies on the receding dynamics of smooth surfaces differ from the present study without anisotropy. However, they are similar for microgrooved surfaces measured across the grooves. We consider that this similarity comes from the discontinuity experienced by the contact line across the groove direction because this discontinuity would be experienced on the isotropic pillar array in any direction.

Among the studies on the spreading and receding dynamics on grooved surfaces, Kannan and Sivakumar (2008) reported that D_‖ followed a tendency similar to that observed for smooth surfaces such as the surface used in this study. D_⊥ showed two different receding rates, and the first rate was significantly slower than the second. Interestingly, this was observed on the smooth surface and the G₈₀ measured parallel to the grooves (D_‖) in the present study. Certain differences in the experimental conditions between both the studies exist. However, such differences are not significant enough to affect the trend, and the clear cause for the opposing trend of the receding phase according to the measurement direction requires further study. The groove scale considered in the study by Kannan and Sivakumar (2008) was an order of magnitude higher than that in the present study. In addition, only three values of We were given in the previous study (48, 82, and 169). Moreover, the receding diameter on the smooth surface for We = 42 showed an opposing behavior to the arguments of the previous study. It actually showed two distinctive regions with several milliseconds of relatively insignificant changes.

The abovementioned anisotropic characters are prevalent among the microgrooved surfaces in this study observed from the maximum spreading factor β_m of all the surfaces, as shown in Fig. 13. For all the microgrooved surfaces, β_m measured perpendicular to the groove direction, β_m⊥, is smaller than that measured parallel to the groove, β_m‖. The difference between them is visible when We increases. For a given We, the values of β_m‖ on grooved surfaces are similar to that on the smooth surface. This property is consistent with that mentioned in previous studies addressing surfaces with grooved patterns (Kannan and Sivakumar 2008; Vaikuntanathan and Sivakumar 2016; Guo et al. 2018). Furthermore, the authors of the previous studies concluded that pinning of a drop on the pillar top and impalement transition hinder the spreading of the drop liquid perpendicular to the groove. In this study, the values of β_m⊥ are closely gathered for a given We, whereas the values of β_m‖ are relatively dispersed. This is probably due to limited contact line motion across the groove. However, this type of discontinuous motion of the contact line requires an analysis of the flow inside the drop (Liu and Chen 2017). Thus, a study on the underlying mechanism of this phenomenon would be an effective topic for future study if suitable techniques to measure the flow inside a drop were available.

Fig. 13

The maximum spreading factors β_m on the smooth surface and the microgrooved surfaces. The filled (hollow) symbols indicate the β_m measured perpendicular (parallel) to the groove direction

Another aspect of anisotropy is apparent in the spreading time, t_s, of the impinging droplet. In Fig. 14, t_s on the smooth surface, G₄₀, and G₈₀ are presented. In this study, the t_s measured perpendicular to the groove is shorter than that measured parallel to the groove regardless of the groove width. This implies that spreading along the groove direction continues after the end of spreading in the perpendicular direction. This indicates the highly complex and asymmetric flow inside the droplet during the spreading phase. Except for this directional property, the overall trends are reasonably consistent with those of the previous reports. t_s has been revealed to be independent of the impact velocity (Okumura et al. 2003; Clanet et al. 2004). Moreover, it has been reported that t_s increases as the impact velocity decreases only when the impact velocity is significantly low (Okumura et al. 2003). In this study, t_s is almost invariant as We exceeds approximately 10.

Fig. 14

The spreading time t_s of the droplets impact on a G₄₀ and b G₈₀. The filled (hollow) symbols indicate the t_s measured perpendicular (parallel) to the groove direction

4 Conclusions

In this study, we experimentally examine the wetting state and directional behaviors of microgrooved PDMS surfaces. The application of microscale texture dramatically changes the wettability of the surfaces. For impinging droplets, water repellency of the surfaces is greatly increased. Drop impact experiments show that the ability to resist liquid impalement is determined by the P_C of the surface. Therefore, G₂₀ with the shortest groove width and largest P_C exhibits the best water-repellent performance. It is noteworthy that CA is no more a relevant parameter for assessing water repellency, although it has been conventionally regarded as a measure of superhydrophobicity. This corresponds to the experimental result that all the impact cases on G₈₀ leave remnant liquid on the surface, while the measured and estimated CA on G₈₀ is the greatest. Another wetting characteristic arising from the groove pattern is the anisotropic variation of spreading and receding during impact. The D measured on the smooth surface and D_‖ behave alike, showing two steps of receding. It should be noted that the receding diameter was scaled with a single decaying exponent (Lv et al. 2016). However, we believe that elaborate data acquisition with a fine resolution in this study reveals the actual characteristic of the receding phase. In fact, D_┴ decreases faster with a single decaying exponent. This directional wettability is supported by consistent and vast experimental data. Thus, we consider that this study resolves ambiguous directional properties found in a previous study (Kannan and Sivakumar 2008).

Appendix: Replica molding procedure

The Si mold master was fabricated via a conventional photolithography method. The master was coated with a self-assembled monolayer (SAM) for repeated use and a smooth mold surface. The SAM coating procedure is as follows:

• 1. Reduce the humidity in the desiccator chamber to below 30% by desiccants (moisture absorbing particles).

• 2. Load the Si master in the desiccator chamber.

• 3. Load a 0.7-μL solution of heptadecafluoro-1,1,2,2-tetrahydrodecyl-trichlorosilane (HDFS, Gelest) on the Teflon plate.

• 4. Incubate for 48 h.

• 5. Unload the Si master and immediately clean it with n-hexane.

• 6. Rinse the Si master with DI water and blow with N₂ gas.

After coating SAM on the master surface, the following replica molding procedure is followed:

• 1. Mix the polymer base with the curing agent (10:1 weight to weight).

• 2. Pour PDMS onto the Si master.

• 3. Degas the poured PDMS under 0.9 bar for 30 min.

• 4. Thermally cure the degassed PDMS for 20 min at 100 °C.

• 5. Peel off the cured PDMS from the Si master.