Wetting characteristics

Taro leaf

Figure 1a,b show photographs of leaves of the taro plant before and after plucking, respectively. Additional images of the leaves before plucking are provided in supplementary information. Figure 1c shows sessile water droplets on the leaf, qualitatively exhibiting the the superhydrophobicity of the leaf. To quantify the wetting characteristics of the leaf, we measured the static contact angle, advancing angle, and receding angle of a water droplet on the leaf. We repeated the experiments around seven times at different locations of the same leaf and on different leaves for different volumes of droplets in the range of [2.1–3.9] μL. These measurements are listed in Table 1. The average value of the static contact angle, advancing angle and receding angle are around 150 °, 153 ° and 144 °, respectively, implying contact angle hysteresis of around 9 °. The maximum uncertainty in these measurements is around ± 2 °. Therefore, the leaf shows excellent superhydrophobic characteristics. The rear side of the leaf also shows similar wetting characteristics and these measurements are provided in the supplementary﻿ information.

Figure 1 (a) A photograph of Colocasia esculenta (taro) plants in garden of our campus. Some leaves of an other plant (bottom left corner) can be seen as wet as compared to the leaves of the taro. (b) A plucked leaf of taro (c) Deionized water droplets on the leaf. Full size image

Table 1 Measured values of static,advancing and receding contact angle on the taro leaf. Full size table

Figure 2 shows SEM images of the surface of the leaf at four different increasing zoom levels from (a) to (d). Additional SEM and optical microscopic images are provided in the supplementary information. In Fig. 2a,b we note pentagon as well as hexagon structures creating honeycomb-like structures on the surface of the leaf. In Fig. 2c,d we see a second tier flakes-like nanoscale structures on top of the primary pentagon and hexagon structure. Therefore, the leaf exhibits a two-tier structure, honeycomb structure as the primary structure and flakes-like structure as the secondary structure. The average side of the polygon is around 50 μm, and the thickness of the wall of the hexagon is around 3 μm.

Figure 2 SEM image of the surface of the taro leaf. Zoomed-in view of the SEM image with systematic increase in magnification (a) 150X (b) 750X (c) 10000X (d) 30000X. Full size image

Bioinspired surface

Measurement of static contact angle: Figure 3 shows SEM images of bioinspired surfaces manufactured in the cleanroom, with different thicknesses and sides of the hexagon. The top and 25 ° tilted view, are shown. Additional microscopic images are provided in the supplementary﻿ information. The measured static contact angle for a water droplet is indicated on each top-view frame. Figure 3 shows that on increasing the side of the hexagon while keeping the thickness constant, the static contact angle increases. However, if the thickness is increased, keeping the side constant, the contact angle decreases. By varying the side or thickness of the hexagon, fractional area of contact between the droplet and surface changes for a droplet in Cassie-Baxter state. As the fractional area decreases, the contact angle increases and vice-versa. The maximum static contact angle (θ) achieved on the bioinspired surface is around 148 ° for the hexagon thickness of 10 μm and side 200 μm.

Figure 3 SEM images of the bioinspired surface taken from top and 25 ° tilt. The first and third row show the surfaces manufactured with different lengths of the side of the hexagonal cavity with 5 μ and 10 μ thickness of the wall of the cavity, respectively. The length of the side is shown on the top of each frame in first and third rows. Full size image

We collapse the data by defining a geometrical parameter b/a that is the ratio of inner to the outer radius of the circumscribed circle to the hexagonal cavity (Fig. 4a,b). In other words, b/a represents the relative thickness of hexagonal wall with respect to length of the side of a hexagonal unit. A larger value of b/a denotes a smaller thickness of the hexagonal wall and vice-versa. b∕a = 1 for a hypothetical case of zero thickness wall. Table 2 summarizes the surfaces tested with different geometries and the corresponding values of b∕a and θ and shows that θ monotonically increases with b∕a.

Figure 4 (a) Schematic of honeycomb geometry of the bioinspired surface, biomimicking first-tier structure found on the taro leaf (b) A unit cell of the honeycomb structure showing geometrical parameters a and b. AUTOCAD–R24.0 (www.autodesk.com) was used to create the CAD model. Full size image

Table 2 Comparison between measurements and predictions of a free-energy based model, proposed by Patankar22, assuming that the droplet is in Cassie-Baxter state. Full size table

Comparison of measurements with a theoretical model: Figure 5 shows the comparison of the measured static contact angles (θ) of a water droplet with the predictions of the model for Cassie-Baxter state, described in ‘Methods’. The measurements as well as the model predictions are plotted against b∕a. Figure 5 shows that θ increases with b/a in measurement as well as in the model. The data is in reasonably good agreement, with the model capturing the trend of the measurements. The maximum error in the values predicted by the model with respect to measurement is around 10%. This also implies that a gently placed droplet on the bioinspired surfaces assumes Cassie-Baxter state.

Figure 5 Comparison between measured static contact angles at different values of b/a on the bioinspired surfaces and the predictions of a free-energy based model for a droplet in Cassie-Baxter state. The model was proposed by Patankar22 and here we employ it for the surfaces with hexagonal-cavities. b/a is the ratio of inner to the outer radius of the circumscribed circle to the hexagonal cavity. Full size image

Contact angle hysteresis: We used sliding droplet method to measure advancing and receding contact angle on the bioinspired surfaces. In these measurements, the droplet did not slide on any bioinspired surface at any tilt angle, and it got stuck to the surface. Figure 6 shows this behavior on two surfaces, with a smaller and larger b/a considered (b/a = 0.65 and 0.97). In case of tilt at 90 °, the droplet loses its symmetry due to gravity and the contact angle at the leading edge of the contact line is larger than at the trailing edge (Fig. 6, first row). In case of tilt at 180°, the droplet retains its spherical cap shape and does not fall off the surfaces i.e., it becomes a pendant droplet (Fig. 6, second row).

Figure 6 Test of droplet sliding on the bioinspired surfaces with b/a = 0.65 (left) and b/a = 0.97 (right). Images for the tilt at 90° and 180° are shown in top and bottom row, respectively. The droplet does not slide and sticks to the surface even for the tilt at 180°. Full size image

In order to explain this behavior, we hypothesize that the continuous contact line is responsible for the sticking of the droplet on the surface, By contrast, the contact line is discontinuous on a micropillared surface, as shown in Fig. 7b. We estimate the order of magnitude of surface tension force (F γ ) and gravitational force (F g i.e., droplet weight) of a pendant droplet (tilt at 180 °) on honeycomb and micropillared surfaces, as shown schematically in Fig. 7c. Since the pendant droplet represents the case in which it is most likely to fall off the surface, as compared to the surfaces titled at lesser than 180 °, we present the analysis for the pendant droplet. The order of F g of a typical 2.57 μL droplet is given by:

$${F}_{g}=\rho Vg=2.52\times 1{0}^{-5}N \sim 1{0}^{-5}$$ (1)

where ρ is the density of water (998 kgm−3), V is the droplet volume, and g is the gravitational acceleration (9.81 ms−2).

Figure 7 (a) The contact line (shown as red) on the bioinspired surface with hexagonal cavities. The contact line can be approximated as a circle, as shown in the figure (black circle). (b) The contact line on a surface with micropillars. (c) Free body diagram of a pendant droplet with possible forces shown on the droplet. The droplet sticks to the bioinspired surface if the vertical component of the surface tension force acting on the contact line exceeds the droplet weight. Full size image

In order to estimate F γ , we approximate zig-zag contact line on the bioinspired surface, shown in red as circle in Fig. 7a. The perimeter of the circle is slightly shorter than the actual length of the contact line. The expression and order of magnitude F γ for a bioinspired surface (b/a = 0.98) is given as follows:

$${F}_{\gamma }=\pi d\gamma sin\theta =1.44\times 1{0}^{-4}N \sim 1{0}^{-4}$$ (2)

where γ is surface tension (7.2 × 10−2 Nm−1), d is the wetted diameter and θ is the contact angle (θ = 139 ° for a pendant droplet on the surface with b∕a = 0.98). Assuming droplet shape as a spherical cap, we estimate d with the given droplet volume (2.57 μL) and contact angle and obtain d ≈ 1 × 10−3 mm. Therefore, in the case of the bioinspired surface (continuous contact line surface), the order of magnitude of supporting surface tension force (F γ ) is one order of magnitude larger than the weight of the droplet (F g ). Therefore, the surface tension force arrests the contact line motion on these surfaces, explaining the sticking behavior of the droplet and consequently, it results in the largest possible contact angle hysteresis.

In case of a discontinuous contact line, i.e., on a micropillared surface (Fig. 7b), we consider a surface with pitch (p) of 76 μm and cross-section area of the pillar as square with a = 20 μm side, considered by Patil et al.13. The measured static contact angle on this surface is around 150°13. We consider the same droplet volume (2.57 μL) on this surface, as done earlier on the honeycomb surface. Approximate number of pillars (n) on the contact line is given by πd/p i.e., around 41. Thus, the approximate length of the contact line is, l c ≈ na = 0.82 mm. The expression and order of magnitude F γ on the micropillared surface is given as follows:

$${F}_{\gamma }={l}_{c}\gamma sin\theta =3.04\times 1{0}^{-5}N \sim 1{0}^{-5}$$ (3)

Therefore, from Eqs. 1 and 3, F γ ~ F g on the micropillared surface,. This implies that the droplet slides on the micropillared surface, consistent with the measurements of Patil et al.13.

Cassie-Baxter to Wenzel state wetting transition: We estimate impact velocity or Weber number (We) for Cassie-Baxter to partial or full Wenzel state wetting transition on the bioinspired surfaces. We carried out measurements at several impact velocities or We, as given in ‘Methods’. The droplet becomes sessile shortly after the impact, and we measured the static contact angle of the sessile droplet (θ) using Eq. 4. Figure 8 shows the variation of θ with b/a, for different cases of We. We ≈ 0 corresponds to a gently placed droplet on the surface.

Figure 8 Static contact angle of the droplet (θ) on the bioinspired surface measured after it impacts on the surface with a given Weber number (We) and becomes sessile. The angle is plotted as a function of b/a i.e., the ratio of inner to the outer radius of the circumscribed circle to the hexagonal cavity. Different cases of We are considered and We ≈ 0 corresponds to a gently deposited droplet. Predictions of θ obtained by a free-energy based model are also plotted in which droplet is assumed to be in full Wenzel state. Left and right insets represent sessile droplet shapes for We ≈ 0, We = 4.5 and We = 15.9, marked by color coded arrows. Full size image

In Fig. 8, θ increases with b/a for all cases of We. The largest increase is for We ≈ 0, explained by an increase in the hydrophobicity of the surface with b/a while the droplet assumes Cassie-Baxter state, as discussed earlier. However, θ decreases with an increase in We at a given b/a. We attribute this behavior by postulating that the droplet assumes partial or full Wenzel state during the impact. Note that if the droplet were in Cassie-Baxter state, θ would not have changed with We. To verify this hypothesis, we plot the dimensionless wetted diameter (d/d o ) in the sessile state as function of We in Fig. 9. Figure 9 illustrates that at a given We, d/d o is larger for b/a = 0.65 as compared to b/a = 0.98, explained by a larger hydrophobicity of the former case. We note that as We increases at a given b/a, d/d o increases. If the droplet were in Cassie-Baxter state, d/d o would not have changed with We. Therefore, the droplet spreads more due to a larger kinetic energy available at larger We. However, the contact line motion gets arrested since the droplet assumes a partial or full Wenzel state. This implies a larger d/d o in the sessile state at larger We (Fig. 9) and consequently, it reduces the corresponding θ (Fig. 8). A larger We (or impact velocity) corresponds to a larger break-in pressure12,14, which helps to break the liquid-gas interface in the microcavities and consequently, the droplet fills those cavities to assume a partial or full Wenzel state. The height of the wall of the cavity is large enough (29 ± 1 μm) to avoid the wetting transition by sagging of the liquid-gas interface above the cavity14.

Figure 9 Variation of dimensionless wetted diameter of the droplet (d/d 0 ) in the sessile state with respect to Weber number (We) for two cases of b/a = 0.65 and 0.98. Full size image

To further corroborate our measurements, we plot θ in Wenzel state predicted by a free-energy based model22, described in ‘Methods’. The values estimated using Eq. 13 are plotted together with measurements at several We as function of b/a in Fig. 8. At We ≈ 0, the droplet is in Cassie state and therefore, the predicted values of Wenzel state do not agree with measurements at We ≈ 0. The model predictions are much closer to We = 9.1 and We = 15.9, with a maximum error of around ±16%. The errors are larger for We = 1.1 and We = 4.5. This is explained by the fact that droplet could assume partial Wenzel state at intermediate We. However, the model considers a full Wenzel state. Overall, the Cassie-Baxter to Wenzel state wetting transition depends on the We (or impact velocity) and b/a (shape of the cavity).

Droplet impact dynamics

Taro leaf

To understand water repellency characteristics of the leaf, we recorded the impact dynamics of a water droplet on it at several impact velocities. These velocities and corresponding Weber numbers (We) are provided in ‘Methods’. Figure 10 shows the impact dynamics on the leaf at different We. High-speed visualization movies of these cases are provided with the supplementary﻿ information. Each column in Fig. 10 shows time-sequenced frames of the impacting droplet for different cases of We, just before the impact (0 ms) and after the impact till 12 ms. For all cases of We except the lowest (We = 0.1), the impact dynamics is nearly similar. First, the droplet spreads and wets the surface with the maximum spreading. Second, the droplet rebounds with a receding contact line and simultaneously stretches in the vertical direction. Finally, the droplet detaches from the surface.

Figure 10 Impact dynamics of a microliter water droplet on the taro leaf at different Weber numbers (We) or impact velocities. The time instances of each row is indicated on the left. High-speed visualization movies are provided with the supplementary information. Supplementary information 9, 10, 11 and 12 correspond to cases of We = 1.1, 4.5, 9.1 and 15.9, respectively. Full size image

As We increases, the droplet spreading is faster (scales as d o /v) and the instantaneous maximum wetted diameter of the droplet increases. This is evident in the second row of Fig. 10 at 2 ms. The vertical stretching before the detachment of the droplet from the surface increases with an increase in We. During the impact, the kinetic energy of the droplet converts to surface energy and vice-versa during the recoiling. The droplet bounces if during the rebound the sum of kinetic and surface energy exceeds the initial surface energy23,24. Since the taro leaf exhibits superhydrophobicity, a larger kinetic energy is available during the recoiling, which is responsible for the bouncing.

Out of the five cases of We, the droplet bounces for each We except at We = 0.1. Theoretical minimum velocity at which bouncing starts to occur is expressed as follows24,25, \({v}_{c} \sim \sqrt{\gamma | cos{\theta }_{a}-cos{\theta }_{r}| /(\rho {d}_{o})}\). Substituting measured values of θ a and θ r (Table 1) in this expression, we obtain v c = 0.062 m/s. In present measurements, the droplets start to bounce at 0.22 m/s, consistent with the theoretical model. Overall, the leaf exhibits excellent water repellency characteristics.

Bioinspired surface

Figure 11 shows the impact dynamics of the droplet at different values of b/a keeping We constant at 15.9. High-speed visualization movies of these cases are provided with the supplementary information. The droplet does not bounce in all cases of We, however, it breaks up at larger b/a. As b/a increases, the droplet fate changes from no-breakup (b/a = 0.65, 0.78) to breakup (b/a = 0.85, 0.98). In the latter, the droplet rebounds, necking of the droplet occurs (as seen in row corresponding to 6 ms in Fig. 11) and it does not bounce. A secondary smaller size droplet (4-8% volume of the primary droplet) detaches from the primary droplet in cases of breakup. Comparing frames in row corresponding to 8 ms in Fig. 11, we note that a transition from no-breakup to breakup occurs as b/a increases. The last row of the Fig. 11 shows that the droplet becomes sessile at around 300 ms after the impact.

Figure 11 Impact dynamics of a microliter water droplet on bioinspired surfaces with different values of b/a, keeping Weber number as constant (We = 15.9, i.e., v = 0.82 m/s). High-speed visualization movies are provided with the supplementary information. Supplementary information 1, 2, 3 and 8 correspond to cases of b/a = 0.65, 0.78, 0.85 and 0.98, respectively. Full size image

These trends can be explained as follows. As the droplet spreads, the available kinetic energy converts into the surface energy and at the instance of maximum spreading, most of the kinetic energy converts into the surface energy. After the maximum spreading, the droplet contact line pins at the edge of the wall of the hexagonal cavity. Similar behavior of the pinning of the contact line was reported on a corrugated surface and surface with protruded sharp edges, by Wang and co-workers15,26. While the droplet rebounds, the surface energy converts into the kinetic energy. As b/a increases, the hydrophobicity of the surface increases (Table 2), that helps in reducing the maximum spreading. This is due to the fact that the increase in the surface energy at the expense of the kinetic energy at the instance of the maximum spreading is smaller on a surface with larger hydrophobicity24. In Fig. 11, the dimensionless wetted diameter at the instance of maximum spreading (d∕d o ) for b/a = 0.98 is around 10% lesser than at b/a = 0.65 (Fig. 9). Therefore, lesser kinetic energy lost into surface energy and larger kinetic energy is available during the recoil at larger b∕a. During recoiling, the available kinetic energy squeezes the droplet upwards due to the pinned contact line and consequently, a liquid column rises upward around axis of impact. Since the kinetic energy dominates surface energy, the droplet undergoes breakup at larger b/a.

Similarly, Fig. 12 shows the effect of We on the impact dynamics keeping b/a constant (= 0.97). High-speed visualization movies of these cases are provided with the supplementary information. As We increases, the droplet fate changes from no-breakup (We = 1.1 to 9.1) to breakup (We = 15.9). As We increases, the available kinetic energy during the recoiling increases and it helps in neck formation and the subsequent breakup. A regime map is plotted on b/a-We plane in Fig. 13 and summarizes the droplet fate. The map shows that the breakup occurs at We = 15.9 and b/a > 0.85.

Figure 12 Impact dynamics of a microliter water droplet on a bioinspired surface with b/a = 0.97, at different Weber numbers (We) or impact velocities. High-speed visualization movies are provided with the supplementary information. Supplementary information 4, 5, 6 and 7 correspond to cases of We = 1.1, 4.5, 9.1 and 15.9, respectively. Full size image

Figure 13 Regime map of the droplet fate on the bioinspired surfaces, namely, no-breakup and breakup, on Weber number (We) - b/a plane. A dashed line is shown as guide to the eye. The break-up is defined if the volume of the secondary droplet is more than 4% of the initial volume. Full size image

The impact dynamics is further quantified by plotting the time-variation of the dimensionless height (h/d o ) of the droplet until droplet becomes sessile. Figure 14(a,b) shows h/d o on the surfaces with the smallest and the largest b/a (=0.65 and 0.98), respectively at different We. The oscillatory response of h/d o is similar to response of an underdamped spring-mass system, in which the oscillation amplitude decays exponentially. Here, the surface tension and viscosity manifest as stiffness force and damping force, respectively. The estimated oscillation frequency (using FFT algorithm) is in the range of 0.12–0.18 mHz and agrees with the prediction of a model27,28 (\(f \sim \sqrt{\gamma /\rho {d}_{o}^{3}}=0.12\) mHz). The oscillation amplitudes of h/d o , plotted in Fig. 14, are larger in case of b/a = 0.98 as compared to b/a = 0.65 at respective We. In addition, the time taken to reach the sessile state is larger in the former than the latter, at respective We. As mentioned earlier, this is due to larger kinetic energy available during the recoil in case of b/a = 0.98, due to larger hydrophobicity of this surface.