3D Micropatterned Functional Surface Inspired by Salvinia Molesta via Direct Laser Lithography for Air Retention and Drag Reduction

Bioinspired functional surfaces are attracting increasing interest in surface engineering, mostly in the field of wettability. The Salvinia‐effect is a remarkable example of superficial air retention and drag force reduction caused by selective chemical coating (super‐hydrophobic wax and hydrophilic dead cells) and peculiar 3D hierarchical morphological structures. The replication of Salvinia‐like patterns at the microscale has always been prevented by limitations in microfabrication techniques, thus hindering relevant technological applications at this dimensional scale. Integrating 3D laser lithography and traditional microfabrication techniques, dimensionally downscaled, 3D micropatterned surfaces inspired for the first time by both morphology and chemical coating of the hairs present on the Salvinia Molesta leaves are reproduced. The effect of design and different surface energies (bare hydrophilic, hydrophobic, selective hydrophilic/hydrophobic coating) on the wettability are modeled and investigated. Bioinspired surfaces demonstrated to be super‐hydrophobic in terms of apparent static contact angle (up to 170°) and provide tunable adhesion with roll‐off angle from less than 10° to 90°. They successfully proved remarkable underwater air retention capability, sustained by stable Cassie‐Baxter state under external hydrostatic pressure up to 4 atm. The proposed surfaces are tested in hydrodynamic conditions: drag force reduction is successfully demonstrated with up to 40% of energy saved.


Introduction
In surface and material engineering, the control of wettability of a solid material has always been a key factor for the implementation of desired interactions with the environment in wet conditions. [1]The fabrication of smart functional surfaces represents an enormous innovation in several fields related to surface engineering, where the controlled manipulation of the liquid phase is required, such as tunable wettability, efficient We investigated the effect of the design and the chemical functionalization on the wettability properties of the artificial surfaces.We characterized the surfaces in terms of apparent static contact angle and roll-off angle and successfully verified their remarkable air retention capability.This property represents a necessary starting condition for applications in hydrodynamic conditions, such as drag force reduction, whose performance was investigated considering different types of chemical coatings on the micro-hairs.
Salvinia Molesta is a floating plant that lives in still waterways: it can retain an air layer, as oxygen reservoir, when submerged in water.The surface of the leaf is covered with many millimetric hairs with the peculiar shape of an egg-beater, that is a stalk with a crown-like head. [11,15]These hairs are coated with wax nanocrystals, but on the top of the crown-like heads there are hydrophilic patches made of dead cells (Figure S1).These cells ensure an anchoring point for the water droplet so that they can stabilize the air layer by means of pinning effects (Figure 1a). [11]The overall behavior is thus affected not only by the morphology but also by the surface chemistry.The Salviniaeffect describes a sort of alternative state, still relatively little studied, compared to Wenzel and Cassie-Baxter states. [16]In Wenzel state a droplet placed on a micropatterned surface fills all the microcavities until it finds its equilibrium configuration: the pinning effect at the liquid-solid interface is particularly strong and roughness enhances wettability (hydrophobic substrate can become super-hydrophobic, while hydrophilic substrate can become super-hydrophilic).In Cassie-Baxter configuration air remains trapped below the liquid phase, so that even a hydrophilic solid can act as hydrophobic, providing reduced adhesion and water repellency. [7,12]he stability of this state is granted as soon as the energetic cost associated with all the liquid-air interfaces remains smaller than the energy gained not to perfectly conform to the roughness of the surface. [16,17]Nevertheless, a metastable Cassie-Baxter state is still possible when it represents a local minimum of the energy associated to solid-liquid-air interfaces, in spite of a smaller Wenzel state energy. [17]Any perturbation (mechanical, thermal, air diffusion, and bubble nucleation) of a metastable Cassie-Baxter state can provoke its irreversible transition to Wenzel state, in which the liquid phase is firmly bound to the surface.Combinations of hydrophilic regions superimposed onto super-hydrophobic microstructures (chemical discontinuity and hierarchical morphology) can prevent the failure of the Cassie-Baxter state under perturbation: they stabilize the air-liquid interface at a defined level at the top of the structures since any displacement of this interface would require energy.More in general, the stability of the pinning effect depends on a series of characteristics: selective hydrophobicity; the presence of microscale, or millimeter scale hairs; the presence of additional structures (e.g., ridge, hairs or waxes); micro-and nano-cavities; elasticity of the structures. [8,18]ere we have artificially reproduced the hairs of the Salvinia Molesta leaf, with dimensions one order of magnitude lower than the natural counterpart (millimeter scale).In fact, the downscaling to the micrometer scale gives the possibility to exploit the microscale physics and obtain wettability behaviors not achievable at bigger scale.For natural sized hairs it has been demonstrated that the presence of a double chemical coating is necessary for super-hydrophobicity and pinning effect. [11]Meanwhile the dimension of the proposed microhairs is one order of magnitude higher than that investigated in our previous work, where we have demonstrated that similar patterns can determine hydrophobicity even if made with hydrophilic materials, showing the absolute relevance of geometrical parameters. [7,12]In the present work we focused on this intermediate dimensional scale (one hundred microns), analyzing the combined effects of different chemical coatings (i.e., surface energies) and morphologies on the wettability characteristics of the patterns.In particular, we fabricated three different bioinspired patterns: in hydrophilic material, covered with hydrophobic coating, and with double hydrophobic/hydrophilic coating in order to replicate the pinning effect.To this purpose we integrated DLL with chemical coating and microcontact printing that allow for the first time the replication of complex functional hierarchical microstructures that have direct effects on air retention and drag force reduction, the two aspects that we are investigating here.
The classic approach to relatively simple hierarchical microstructures consists in the fabrication of elementary features, such as micropillars, covered with micro-or nano-metric particles, [9] multiscale patterning via template-assisted procedures, [19] nanofilaments, [20] and nanotubes: [21] in these cases, the amount of trapped air is relatively scarce since the thickness of the layer is comparable to the roughness dimensional scale.24] Traditional techniques employed for the fabrication of superhydrophobic surfaces are based on random patterns made by spay-coating of micro-and nano-particles on flat substrates, [25][26][27] grids or meshes superimposed to structured surfaces, [28] micro-pillars, [29][30][31][32] micro-gratings, [33] and needle-like [34] patterns obtained by means of photolithographic techniques.Fabrication processes have a great impact on the wettability performances of the patterned surfaces that hardly translate into effective applications in low friction surface engineering, where the values of hydrophobicity, pressure resistance of air layers and low friction must be carefully defined and tuned.So, considering the most performing between the aforementioned pattern types, while being relatively easy to fabricate super-hydrophobic surfaces, it is still challenging to obtain surfaces with all these three characteristics, that are rarely considered simultaneously in scientific literature.Nanofilaments (so-called nanofur) are able to reduce the drag up to 50% but they are relatively weak in withstanding the hydrostatic pressure, with only 50% of a micrometric thin layer of air retained up to 0.5 atm. [20]rids on structured surfaces, that require the assembly of several components, can retain 60% of air at 0.7 atm of hydrostatic pressure. [28]Randomly patterned surfaces suffer the absence of a real 3D design and show the less significant results in terms of drag reduction (in the range 15%-30%) [25][26][27] and slip length (only 19 µm). [25]Results of the same order of magnitude are obtained with needle-like patterns with submicron periodicity, that present a small slip length of 20 µm. [34]Pillared patterns result to be more suitable for drag reduction, with a slip length of 70 µm, further increased to 90 µm when the micropillars are functionalized with hierarchical nanoposts.However, such type of pattern can retain air at only 600 Pa. [30]Similarly, extremely high values of slip length are associated to very low values of maximum sustainable hydrostatic pressure, like in the case of micropillars with nanometric roughness (≈400 µm of slip length but only 250 Pa of limit pressure for the air layer). [29]or all these reasons, more complex geometries have been investigated, also inspired to the Salvinia.Salvinia-like structures, made with 3D printing techniques cannot reach the same levels of spatial and superficial resolution of the DLL, especially at the selected dimensional scale investigated here. [35,36]Moreover, the study of their wettability properties is mainly limited to the contact angle analysis. [35,37,38]pplications of DLL have been limited to the fabrication of hydrophobic patterns [10,23] or to the investigation of the externally-induced air recovery phenomenon. [36]Finally, direct laser writing and direct laser interference patterning, have been employed to study the effect of etched patterns on contact angles, without considering real complex 3D shapes, on metals [39,40] and polymers, [41] extremely limiting the potentiality of such technique in additive manufacturing.
Therefore, in the present work we overcome the limitations of the current techniques for the fabrication of complex functionalized 3D micropatterns, by means of combined DLL and chemical functionalization.In particular, we developed novel multiscale hierarchical micropatterned surfaces, that have, simultaneously, five peculiar characteristics: i) super-hydrophobicity; ii) pinning effect; iii) long-term stability of the air layer; iv) resistance to pressure-driven water infiltration; v) drag force reduction.
The high reproducibility of the proposed method allowed to model and verify the effect of dimensional scale and chemical functionalization on wettability properties.
We proved that at the targeted dimensional scale hydrophobic coating can enormously enhance air retention and drag reduction.In detail, air retention is the capability to trap air under hydrostatic pressure and can be evaluated by means of the critical pressure, that is the pressure at which the air volume retained by the pattern starts to decrease.The drag reduction determines the energy saved by a patterned system in hydrodynamic conditions (with respect to a flat substrate) and it is related to kinetic friction.While drag reduction can be estimated from differential pressure between two points on a patterned surface subjected to a liquid flow, water infiltration resistance is related to the absolute pressure of the liquid phase and the critical pressure is the maximum value of pressure that the pattern can withstand.
Finally, even if the bioinspired double hydrophilic/hydrophobic coating is still not enough to further increase the stability of the air layer, the proposed approach allows to tune the wettability characteristics and to obtain peculiar properties, such as super-hydrophobicity and higher roll-off angles.

Fabrication Results
Artificial hairs were fabricated via direct laser lithography, in a dimensional scale (10 −4 m) in between the two scales where geometry and chemical coating were proved to exert major effects on wettability (10 −5 m and 10 −3 m, respectively). [7,11]icro-hairs are composed of a stalk with diameter 10 µm and height 40 µm, ending in a 3D structure resembling the crownlike head of the Salvinia leaf hairs (Figure 1b).Three different geometries were designed for the heads, by changing the number of the constituent filaments: two, three, and four circumferences were intersected respectively at 90°, 60°, and 30°.The filament thickness is 4 µm and the diameter of the head is 60 µm, determining a total height of the hair of 100 µm.The arrays of artificial hairs, used in the hydrostatic and hydrodynamic experiments, are arranged by following a 2D hexagonal lattice configuration with a spacing of 100 µm between firstneighbor stalks and a minimum distance between the heads (spheres circumscribing the filaments) of 40 µm (Figure 1c).
Arrays of sides 5 × 5 mm 2 were fabricated for contact angle experiments, while a perimeter wall with re-entrant profile was added for air retention tests.Finally, rectangular patterns of sides 5 × 50 mm 2 were prepared for drag reduction experiments.
Figure 1d-f illustrates the results of the surface patterning made in a negative tone photoresist (IP-S, Nanoscribe GmbH).DLL demonstrated to be a highly reliable technique for the fabrication of complex 3D hierarchical microstructures, with outstanding results in terms of resolution, aspect ratio, structural stability, and reproducibility.The artificial hairs remained stable and did not collapse nor detach from the substrate also after being subjected to high hydrostatic pressures and laminar flows.
In order to find out the effect of chemical coatings on wettability, three different superficial functionalization (i.e., surface energies) were compared in every experiment: untreated bare hydrophilic photoresist (IP-S), hydrophobic coating (Polytetrafluoroethylene (PTFE)), and double hydrophilic/hydrophobic coating (IP-S/PTFE).The nanometric hydrophobic coating was obtained by dipping the samples in a Teflon AF1600 solu-tion in Fluorinert as illustrated in Figure 2a(i).Dual coating was instead made by means of a further step in which a small amount of hydrophilic photoresist was deposited on the tips of the heads through microcontact printing, resembling the hydrophilic patches on the hydrophobic wax of the natural model (Figure 2a(ii)).The hydrophilic area was 293 ± 38, 658 ± 97, and 719 ± 44 µm 2 per micro-hair (for N f = 4, 6, and 8, respectively) that correspond to 3.3% ,7.6%, and 8.3% of the total pattern (Figure 2c; Figure S2, Supporting Information).This values are of the same order of magnitude of the natural counterpart (2.2%). [11]Figure 2b-d shows the scanning electron microscopy images of the doubly functionalized micro-hairs, demonstrating the feasibility and precision of the proposed fabrication process.Moreover, the PTFE layer produced micro-and nano-wrinkles that further increase and sustain the hydrophobicity effect (Figure 2d).

Apparent Static Contact Angle and Roll-Off Angle
Artificial hairs were fabricated in a dimensional scale that was expected to determine a hydrophobic behavior almost independently from either low or high free energy of the component materials. [7]The evaluation of the apparent static contact angle (ASCA) of a water droplet has been employed to demonstrate the aforementioned wettability hypothesis about the micropatterned surfaces (Figure 3a).All the selected designs  resulted highly hydrophobic (ASCA in the range 140° -170°) and, in particular, the chemically functionalized structures behaved as strongly super-hydrophobic.This result verifies the initial hypothesis that starting from hydrophilic (IP-S) and hydrophobic materials (PTFE coating), it is possible to obtain, respectively, hydrophobic and super-hydrophobic surfaces if properly patterned. [7]igure 3b illustrates the results of the ASCA of a 5 µl water droplet on patterned surfaces that differ for designs and chemical coatings.They represent a great incrementation of the wettability performance, considering that the equilibrium SCA (static contact angle) measured on flat surfaces coated with IP-S photoresist and with PTFE is ≈70° ± 2° and 110° ± 2° respectively. [23,42]ASCA is clearly affected by the morphology of the crown-like heads (for each equal chemical treatment): as soon as the number of filaments increases, the higher number of solid-liquid interfaces and the consequent reduction of the air-liquid interface determine a lowering of the ASCA.For 4, 6, and 8 filaments respectively, it has been found: for untreated patterns (IP-S surface) ASCA value is 150.1° ± 2.5°, 145.2° ± 3.8°, and 139.3° ± 2.6°; for hydrophobic coating (PTFE surface) ASCA value is 170.6° ± 1.9°, 166.5° ± 2.4°, and 165.8° ± 1.9°; for hydrophilic/hydrophobic coating (IP-S/PTFE surface) ASCA value is 161.4° ± 2.2°, 153.4° ± 1.9°, and 151.5° ± 3.6°.In summary, for each type of chemical coating there is an average decrement of ≈5° each time that a couple of filaments in the head is added: this demonstrates how ASCA is extremely sensitive to the number of solidliquid interfaces in hierarchical microstructures.Moreover, this effect allows also to finely tune the value of ASCA of a pattern in order to precisely obtain desired wettability characteristics.As expected, chemical coating also affects the wettability of the hierarchical micropatterns.The presence of PTFE causes a 15% average increment of the ASCA with respect to untreated patterns, while the functional double coating a 7% average increment.
Experiments performed up to 2 weeks after the fabrication of the samples showed comparable values of ASCA, resulting in the small standard deviation of the measurements, demonstrating the chemical durability in water of the structures, in addition to the thermodynamic durability discussed further on. [43,44]he theoretical approach to the wettability of hierarchical microstructures deals with the generalizations of the equations of the ASCA for standard rough surfaces.For a flat surface, Young equation expresses the contact angle (θ) of a liquid as a function of the liquid surface tension (γ L ), the surface free energy of the solid surface (γ S ), and the solid−liquid interfacial energy (γ SL ): For patterned surfaces, the contact between solid and liquid interphase involves more complex interactions, as described by Wenzel and Cassie-Baxter models. [45]In the case of a rough surface and in absence of trapped air pockets, the apparent SCA (θ) can be calculated by means of the Wenzel equation: where θ 0 is the equilibrium SCA on the flat surface and R is the roughness parameter calculated as the ratio between the effective surface of the contact area and its projection on the flat surface of the substrate.If air remains trapped between the liquid and solid phases, the relative extension of solid-liquid and liquid-air interface must be considered to predict the apparent SCA, according to the Cassie-Baxter equation: where F SL and F LA are the fraction of solid−liquid and liquid−air interface.Equation 3 allows for apparent SCA bigger than 90°, also for hydrophilic constituent materials, for specific values of ]. [7] For hierarchical microstructures, each level of hierarchy can affect the wettability in different ways according to its roughness and air trapping capability.In the case of the Salvinia-like hairs, four possible configurations of the solid-liquid-air interfaces are possible. [7]For the structures in the present study, experimental evidence proves that air remains trapped both inside the heads and between the stalks, in a double Cassie-Baxter configuration.In this configuration, illustrated in Figure 3c, θ CB CB is the apparent macroscopic SCA due to the double Cassie-Baxter state and it can be equally obtained from Equation 3: [7] F F SL SL Experimental values of the ASCA for different geometries and surface energies fit very well with the θ CB CB predicted by the aforementioned model (Figure 3e).The range of uncertainty for the predictions is related to the assumptions made for the calculation of F SL (Figure 3d).Solid-liquid contact area is assumed to be the upper hemisphere of the head for untreated hairs, the final tip for the PTFE-coated and the IP-S patch for the IP-S/PTFE-coated.Lower values of F SL come from the simplest approximation to the ratio between the projection of the solid-liquid contact area and the area of the unitary parallelogram cell.Upper limits of F SL are derived considering the actual spherical geometry of the crown-head and are calculated as the solid-liquid contact area divided by the unitary cell area.While being all inside the limiting range of prediction, the experimental values are slightly closer to the flat model approximation.All the calculated values of the geometrical and chemical parameters in Equation 4 are reported in detail in Figure S3 (Supporting Information).While the model well fits with experimental results, the accuracy could be further improved by measuring the liquid-solid contact interface with micrometric resolution, by means for example of confocal fluorescence microscopy.
Roll-off angle analysis has been carried out to further characterize the wettability of the proposed patterned surfaces in instable configurations (Figure 3 g).Even if the roll-off angle depends on the volume of the droplet, it generally correlates to the contact angle hysteresis and gives information about the capability of hydrophobic surfaces to hold back a water phase. [45]Hairs coated with PTFE have the lowest roll-off angle while the uncoated hairs have the highest.While roll-off angle tends to increase with the number of filaments in the head of the hairs, since it is related to the solid fraction which determines the amount of interaction at the level of the solid-liquid interface, this trend is actually minimized with functionalization (Figure 3f).In fact, functionalization determines a change in the surface energy that modulates the pinning effect.This means that untreated hairs with higher surface energy will be more affected by geometrical parameters while Teflon coated hairs, with lower surface energy, are enable to anchor the liquid phase, almost independently from the solid fraction of the pattern.Double coated hairs show a trend in increasing roll-off angle with the number of filaments in between the trend of the other types of patterns, since the surface of hydrophilic patches is in between that of the other two configurations.This effect is particularly evident in the case of 8 uncoated filaments: the patterned surface, while remaining hydrophobic, is able to hold the water droplet independently of the tilt, up to 90°.Considering the contact area of the water droplet on the surface, it is possible to determine the maximum adhesive sheer force of the patterns: where ρ is the density of water, g the gravitational acceleration, and V is the droplet volume.The results for each geometrical and chemical configuration are reported in Table 1.
Strong adhesion is evident only in the untreated hairs (with a coherent trend according to the number of filaments composing the heads) and, in a lesser extent, in the double-coated structures.All types of structures are hydrophobic or superhydrophobic.For this reason, it is possible to deduce that while hydrophobicity is mainly given by the geometry (as typical of 3D hierarchical microstructures), the chemical coating has a greater impact on the adhesive properties.Untreated and double-coated patterns present the wettability of those strongly hydrophobic adhesive surfaces that experience the Cassie impregnating wetting state (the so-called Petal-effect).Cassie impregnating wetting state can be considered as a global Wenzel state at the length scale of the micrometric features but locally is a Cassie-Baxter state, at the length scale of the smaller nanofolds. [46]However, in our case, the presence of air is not simply confined in the nanoscale roughness but involves the entire height of the structures, so that the effective wettability state is that of a Cassie-Baxter state (Figure 3a; Figure S4, Supporting Information).
Regarding this aspect, it is worth noting the variety of wettability characteristics that can be achieved with 3D hierarchical microstructures and selective chemical coatings, from pure Cassie-Baxter configurations to a state in between a double Cassie-Baxter state (air between stalks and inside hairs) and a Cassie impregnating wetting state.

Air Retention
In the present study we demonstrate that the selected bioinspired micropatterns are able to efficiently stabilize the air layer so that they can perform air retention in a broad range of external overpressures.[49] In turn, a good capability in air retention is a necessary condition for drag force reduction.
Samples with a square pattern of sides 5 × 5 mm 2 (Figure 4a), with the same geometrical parameters and chemical coatings employed in ASCA experiments, were prepared for the air retention test, with the purpose to investigate how these characteristics affect the performance of the micropatterns.The patterns were surrounded by a wall with a T-shape profile with re-entrant corners (inset in Figure 4a): in this way it was possible to prevent the infiltration of the water from the base of the stalks, simulating a sort of infinite extension of the pattern.Moreover, compartmentation of the surface is often present in the biological systems since it seems essential for the stability of air retention under hydrostatic and hydrodynamic conditions: for this reason, compartmentation is seen as a promising strategy in surface patterning for technological applications. [23,28,50]The samples were submerged vertically just below the water level and the external pressure was increased up to 4 atm.At the beginning a layer of air remains trapped between the hairs of the pattern, resulting in silvery reflections (Figure S4, Supporting Information).At certain point, in correspondence of the critical pressure, the airliquid interface collapses and the water reaches the bottom of the substrate, starting to fill the cavities between the stalks.Once this process has started, as soon as the pressure increases, the percentage of the patterned area infiltrated by water becomes bigger till all the air that was present at the beginning is completely replaced by water, leading to a complete loss of hydrophobicity, and thus light reflection.An exemplary series of images taken at growing values of external pressure is illustrated in Figure 4b.The edges of the collapsed areas follow the directions defined by the hexagonal arrangement of the hairs, typical of such type of geometrically ordered surfaces. [51]igure 4c illustrates the typical experimental result (for N f = 8) of the amount of air, expressed as fractional area, that remains trapped inside the micropatterns while varying the external pressure.All the combinations of chemical coatings and geometries show very good results in term of air retention capability, compared to the most investigated nanofilaments, grid and micropillars. [20,28,51]As already aforementioned in the introduction, current patterned surfaces can retain 50% of the initial air layer under hydrostatic pressure well below 1 atm.Figure S5 (Supporting Information) illustrates the experimental results of air retention for all the combinations of designs and materials, showing how these parameters affect the performance of the patterns.For different geometries, untreated hairs (Figure S5d (Supporting Information), hydrophilic IP-S surface) are able to retain 45%-55% of the initial air at 1 atm, while at 4 atm 10%-15% of air is still present; double hydrophilic/hydrophobic coating allows to retain 50%-65% of air at 1 atm and 15% at 4 atm (Figure S5f, Supporting Information).PTFE-coated hairs performed outstanding results being able to prevent the water to fill the microcavities at least up to 1.8 atm (for N f = 8) and to lose on average only the 20%-30% at 4 atm (Figure S5e, Supporting Information).The main reason of such result seems to be the presence of an air layer visibly thicker than the height of the hairs that the superhydrophobic pattern is able to stabilize (Figure S6, Supporting Information).Chemical surface characteristics have an evident effect on the air retention: the presence of partial or total hydrophobic coating (PTFE) determines a higher capability to retain air since water infiltration between the cavities of the patterns is hindered by the lower surface energy compared to hydrophilic IP-S (Figure S5a-c, Supporting Information).The absence of a prominent difference in air retention between hairs made in hydrophilic IP-S and double coated hairs, can be caused in part by reduced air-liquid interfaces at the top of the crown-like head.Comparing this result to PTFE-coated hairs it seems evident that the double coating is not enough to further increase the stability of the air layer in hydrostatic conditions at the selected dimensional scale (10 −4 m).
On the other hand, the number of filaments composing the heads affects the air retention in a way that a minor number of solid elements reduces the formation of solid-liquid interfaces that help the water front to advance, once the infiltration has started (Figure S5d,f, Supporting Information).In the case of PTFE coating (Figure S5e, Supporting Information), the geometry affects the stability of the thick air layer formed on the top of the pattern: this is a different phenomenon (connected to the initial amount of trapped air) that is promoted by the number of filaments, explaining the reverse trend with respect to untreated and double coated hairs (Figure S5d,f, Supporting Information).Finally, a minor number of filaments in the heads determines also a decrease of the solid-liquid interfaces density.The energetic barrier for the collapse of the Cassie-Baxter state into Wenzel state is proportional to that density so that the system is less resistant to pressure fluctuations.This can be noticed from the dimension of the standard deviation in the experimental results (Figure S5, Supporting Information).
From a theoretical point of view, the equilibrium condition of the triple interface is achieved when the pressure of the air trapped by the pattern and the capillary pressure are balanced by the hydrostatic pressure and the ambient external pressure (Figure 4e). [52]Increasing the external pressure causes an increase of the contact angle till it reaches the Young−Laplace contact angle: at this point the water starts to move along the solid sides of the microstructures, in correspondence of the critical pressure P cr . [53,54]Here, starting from established models in scientific literature we extended the results to the Salvinia-like micropatters in order to validate the experimental results. [52,55]or simplicity the space between the hairs has been approximated to circular holes: this approximation is not a limiting factor since equivalent capillary and geometric parameters have been introduced and hexagonal arrangement and geometrical features of the microhairs have been considered.The volume of water protruding into each equivalent pore can be expressed as (Figure 4f): where V cyl is the cylindrical volume of protruding water up to the solid-liquid interface, V men is the remaining water volume (approximated for a circular hole) bounded by the meniscus, R g_eq is the equivalent geometrical radius (Figure 4g), h is the amount of the protrusion, and θ is the ASCA. [55]The final air volume (V f ) inside the equivalent pore of height H results: At equilibrium the condition V 0 p ∞ = V f p f (ideal gas law at constant temperature, with V 0 and p ∞ initial air volume and pressure before submersion in water, p f air pressure after water protrusion) is satisfied together with the Young−Laplace equation: with p w hydrostatic pressure of the water, σ water surface tension (0.073 N m −1 ) and R c_eq equivalent capillary radius.Combining Equations 6,7,8 it is possible to obtain the general description of the relation between the variables involved in the triple interface: [55] p p h H R H R w g eq c eq 1 2 3sin sin 3cos In order to find the critical pressure at which the stability of the air-liquid interface is lost and the interface starts to move downward (at h = 0), it is sufficient to consider the balance between the pressures illustrated in Figure 4e: whit p air = p f (h = 0) and p cap = -2σ cosθ/R c_eq .Finally, the definitive expression for the P cr is: The value of the equivalent capillary radius R c_eq is defined as: [56] R A C c eq where A represents the interface projection area and C the length of contact line of the solid-liquid-air interface.In particular, for the Salvinia-like hairs (Figure 4 h): with L center-center distance between the hairs, R head radius of the crown-like head, and n the number of filaments sustaining the liquid phase in the unitary cell (n = 2, 3, 5 for N f = 4, 6, 8 respectively).It is possible to assume R head thanks to the experimentally verified double Cassie-Baxter configuration, which remains stable in the heads: the collapse of the triple interface leads in fact to a Wenzel (between the stalks) / Cassie-Baxter (inside the heads) states (Figure S7, Supporting Information).
The equivalent capillary radius results to be: Figure 4d reports the values of P cr predicted by the proposed model as a function of Φ, the heads fractional area calculated as the ratio between the projection of the heads and the total flat area of the substrate (φ = 0.33 for the proposed patterns).The curves of untreated and IP-S/PTFE-coated hairs follow a very similar behavior as expected from the air retention test, with IP-S/PTFE-coated hairs able to more strongly withstand water infiltration.In particular the predicted P cr for the selected geometries lies in the range 0.2-0.4atm, experimentally obtained for both untreated and IP-S/PTFE-coated hairs (Figure S8, Supporting Information): 0.2 atm, 0.2 atm, 0.21 atm (untreated, N f = 4, N f = 6, N f = 8 respectively), 0.27 atm, 0.24 atm, 0.27 atm (double coating, N f = 4, N f = 6, N f = 8 respectively).While the double hydrophilic/hydrophobic coating seems to ensure the same stability of the air layer, PTFE-coated hairs demonstrate to prevent water infiltration for higher pressures.In particular, the PTFE curve illustrated in Figure 4d has been obtained from Equation 11with p ∞ equal to 1.22 atm, 2.07 atm, and 6.75 atm (N f = 4, N f = 6, N f = 8 respectively, instead of 1 atm).This means that before reaching the condition h = 0, the pattern is able to retain a quantity of air higher than V 0 .This phenomenon was indeed observed during the experimental tests although it was not completely controllable.The amount of initial trapped air determines the variability of the air retention analysis for PTFEcoated hairs and explains their superior air trapping properties and represents a superior limit of the air retention capability while IP-S/PTFE-coated and untreated hairs represent the lower limit.
Finally, it is worth noting the complexity of the relation between geometrical parameters, chemical coating and critical pressure.Since these variables are related in a non-linear way, it is not intuitive to predict, for example, the effect of the change in the number of filament or the inter-stalk distance or other involved parameters without a theoretical model.This means that the qualitative considerations regarding the comparison between different N f are valid for the specific selected dimension of the heads.

Drag Force Reduction
Air retention mediated by a stable Cassie-Baxter state is a necessary condition for drag force reduction. [57]In fact, this represents the main limiting factor for several artificial surfaces employable in limited time and conditions. [49,58]From a theoretical point of view the boundary conditions of a flow confined between micro-and nano-structures, determine its effectiveness in reducing the drag force and consequently providing energy efficiency.Three hydrodynamic configurations are possible on the patterned surface: no-slip, partial slip, and slip conditions.Ignoring the partial slip condition that mainly occurs in case of lubricant-infused patterned surfaces, the other two are illustrated in Figure 5a.In the no-slip boundary condition the fluid velocity profile is zero at the flat surface, while in correspondence of air pocket trapped by microstructures the fluid experience non-zero velocity at the surface, with consequent drag force reduction.In other words, effective slip can be seen as the equivalent slip required on a flat surface that can reproduce the same flow conditions far from the surface. [59]Natural Salvinia's hairs have demonstrated to behave according to this last model. [11]rag force reduction tests were performed in a microfluidic chip (Figure 5b,c) since it is an excellent platform to investigate boundary flow conditions and detect microscale interfacial slip. [59]To perform this experiment, the configuration with N f = 8 was selected because of its slightly higher theoretical critical  pressure, its superior resistance to water infiltration for PTFE coating and for its smaller standard deviation in the air retention tests measurements (thus less subject to random pressure fluctuation consequences).A glass slide patterned with Salvinia-like hairs was used as the bottom side of a polydimethylsiloxane (PDMS) microchannel of dimensions L = 50 mm, w = 5 mm, and h = 500 µm.The effects of the different chemical functionalization have been analyzed by means of the pressure drop versus flow rate method.Water was pumped in the microfluidic circuit at certain flow rates according to selected Reynold's numbers in the range 5-250.Flow velocity has been set therefore as v = Re ν D h , where Re is the Reynold's number, ν the kinematic fluid viscosity, and D h the hydraulic equivalent diameter that for channel with rectangular section is defined as D h = 2 w h/(w +h). [60]The pressure drop was then measured by a differential pressure sensor.
Figure 5d illustrates the experimental results, that are coherent with those from air retention tests and with adhesion sheer force values (Table 1).Regarding the latter aspect, it is important to specify that all the experimental acquisitions were made at the stationary state, with the flow in the laminar regime.Although friction forces between the liquid phase and the surface are different depending on the static or dynamic regime, [61] the kinetic friction estimated from drag force reduction tests resulted coherent with the static friction inferable from adhesion sheer force values.
The control surface is a flat surface made in IP-S that is the constituent material of all the tested patterns.As expected, PTFE-coated hairs showed to be more effective compared to untreated and IP-S/PTFE-coated hairs, even if the performance in drag reduction of all the micropatterned surfaces is remarkable compared to the control.In fact, the pressure drop along the flat surface is higher with respect to the Salvinia-like patterned ones.
To quantitatively describe this effect, the drag reduction factor (DR) can be introduce and, in the case of pressure drop (pd) versus flow rate method analysis, DR pd is defined as: [59] where Δp ns is the pressure drop in case of non-slip condition (flat control) and Δp exp is the pressure drop experimentally measured for patterned surfaces.In particular, DR p is 34% for untreated hairs, 41% for PTFE-coated hairs, and 37% for IP-S/ PTFE-coated hairs.As consequence we found that the pinning effect due to double hydrophilic/hydrophobic chemical coating is not really effective at the studied dimensional scale, where super-hydrophobicity is sufficient for ensuring drag reduction sustained by strong air retention.The drag reduction factor represents a comparative estimation of the energy saved by transporting the fluid through a system with slip (Salvinia-like pattern) with respect to the same system containing zero slip (flat control in our case).This factor changes with the scale of the system.On the contrary, the slip length (s l ) is a property of the surface itself so that it is not expected to depend on system size.In particular, s l resulted to be 103 µm for untreated hairs, 147 µm for PTFE-coated hairs, and 123 µm for IP-S/PTFE-coated hairs.The slip length, has been derived from DR p since the two parameters are related according to the following expression, valid for rectangular cross-sectional channels (with high aspect ratio w/h): [59] DR h s pd l Comparing the slip length of different patterns is more meaningful for a correct estimation of the real low friction performance.30] This means that for a given slip length the reduction of the dimensional scale leads to an increase of the energetic efficiency that makes the proposed surfaces extremely suitable for technological applications like in the microfluidics field.

Conclusion
In the present study we integrated 3D laser lithography with traditional microfabrication techniques (dip-coating, microcontact printing) for the replication of functional micropatterned surfaces with complex 3D hierarchical structures inspired to the hairs present on the Salvinia Molesta leaves.The artificial surfaces have peculiar characteristics: super-hydrophobicity, pinning effect, long-term stability of the air layer, resistance to pressure-driven water infiltration, and drag force reduction capability.The biomimetic approach gives the possibility to artificially implement natural phenomena, exploiting the strong relation between design and chemical surface properties.For the first time both the morphology and the chemical coating of the natural counterpart have been mimicked, thanks to the integrated microfabrication method.We evaluated the performance of the proposed microstructures in terms of wettability characteristics in hydrostatic and hydrodynamic conditions, in order to validate the reproduction of the so-called Salviniaeffect at the microscale.Three different designs for the artificial hairs were fabricated by changing the number of filaments forming the crown-like heads.They were made in hydrophilic IP-S and underwent to three different chemical functionalization: untreated, hydrophobic PTFE, and bioinspired dual hydrophilic/hydrophobic IP-S/PTFE coating.Apparent static contact angle analysis demonstrated that all the samples were hydrophobic or super-hydrophobic almost independently from the superficial free energy, thanks to the hierarchical design that ensures a stable Cassie-Baxter state.Roll-off angle tests were carried out to evaluate the capability of the proposed micropattern to hold water droplet and to validate the pinning effect.
The bioinspired micropatterns successfully proved underwater air retention, sustained by stable Cassie-Baxter state under external hydrostatic pressure up to 4 atm.Air retention mediated by a stable Cassie-Baxter state is a necessary condition for drag force reduction for applications in hydrodynamic conditions.Drag force reduction tests were performed in a microfluidic chip.We demonstrated that at the targeted dimensional scale hydrophobic coating can enormously enhance air retention and drag reduction.Moreover, the bioinspired functionalization with a double hydrophilic/hydrophobic coating allows to tune the wettability characteristics of the surface, providing super-hydrophobicity and higher roll-off angles.Experimental findings were supported by theoretical models that demonstrated the complex relation between geometrical parameters and chemical coating, and drag reduction and water infiltration resistance.These phenomena are both influenced by chemistry and morphology, but they cannot be correlated each other in direct way.

Experimental Section
Design and Microfabrication: The bioinspired micro-hairs were modeled using the software Blender (Blender Foundation) and processed with the software DeScribe (Nanoscribe GmbH), for the definition of the fabrication parameters.Three different shapes were designed for the heads, resembling the natural model but with the superimposition of a final spheroidal tip in order to locally promote the chemical functionalization (Figure S9a, Supporting Information).
The patterns were fabricated on a glass substrate by means of a Photonic Professional system (Nanoscribe GmbH), using the negative tone IP-S photoresist (Nanoscribe GmbH).Each substrate was rinsed with acetone, isopropyl alcohol (IPA), and deionized water, and a drop of IP-S photoresist was cast on it.The objective (25×, NA 0.8) of the instrument was put in immersion in the photoresist that was exposed to a femtosecond laser beam (Calman laser source) with a center wavelength of 780 nm.The microstructures were fabricated, using a slice by slice method (300 nm of slicing distance), with a writing speed of 10 mm s -1 and a laser power of 20 mW.The sample was then developed for 15 min in propylene glycol methyl ether acetate (PGMEA, Sigma-Aldrich) and rinsed with IPA and deionized water for 10 min.For contact angle, roll-off analysis, and for air retention tests, square patterns of size 5 × 5 mm 2 were fabricated on circular glass slide with diameter 30 mm.The patterns for air retention tests were surrounded by a wall with a T-shape profile with re-entrant corners.For drag reduction experiments rectangular patterns of sides 5 × 50 mm 2 were fabricated on rectangular slide (25 × 75 mm 2 ).In order to establish a laminar flow inside the microchannel, the rectangular patterns were preceded and followed by a 2 mm long ramp of height 100 µm.
Chemical Functionalization: The patterns employed for the experiments were functionalized in two ways: with a hydrophobic coating and with a bioinspired double coating consisting of a hydrophobic layer with hydrophilic patches in correspondence of the tips of the microhairs.The hydrophobic nanometric layer was obtained by dip-coating the samples into a 0.125% w/v solution of PTFE AF 1600 (Sigma-Aldrich) in Fluorinert FC-770 (Sigma-Aldrich).Using scanning electron microscopy (SEM), the efficacy of this technique was verified detecting the presence of the Teflon layer, and its effects on the eventual subsequent hydrophilic functionalization (Figure S9b,c, Supporting Information).
The double coating was obtained with a subsequent step of functionalization via microcontact printing by means of a micromanipulator.The device was composed of two parallel plates that can be put in contact with micrometric precision.A layer of IP-S photoresist was spun coated on a glass slide that was mounted on the mobile plate while the patterned sample was mounted on the fixed plate.The functionalization was carried out approaching the two surfaces at the proper distance and waiting few seconds in order to allows the IP-S to impregnate the spheroidal tips of the hairs without any chemical promoter.The result was then checked using the optical microscope (Figure S2, Supporting Information).Finally, the sample was exposed to UV light for IP-S polymerization on the tips.
To further investigate the effectiveness of the selective functionalization a very simple test whose result is illustrated in Figure S9 (Supporting Information) was performed.The IP-S functionalization was performed without the previous dip-coating in the Teflon solution.Comparing Figure S9b (Supporting Information) and Figure S9c (Supporting Information), it is evident how, without Teflon (b), IP-S pours along the filaments, covering most of the superior part of the heads with a thinner layer, completely different from the semispherical shape when Teflon is present (c).Moreover, in Figure S9b (Supporting Information), it is clearly visible the line of discontinuity between the bulk IP-S (with the visible lines of the laser fabrication) and the added IP-S (smooth).
Microscopy Imaging: Scanning electron microscopy images were acquired by means of EVO LS10 scanning electron microscope (Zeiss, Germany).Optical microscopy was performed using a Hirox KH-8700 digital microscope (Hirox, Japan).
Apparent Static Contact Angle and Roll-Off Angle Analysis: Contact angles analysis was carried out using an optical tensiometer (Attension Theta, Biolin Scientific).The tests were performed using a 5 µl droplet of deionized water.For the measure of the roll-off angle a tiltable stage was employed, recording the angle at which the water droplet started to slide.Five samples for each type of functionalization were tested five times in both experiments.Analysis of the experimental data and the measure of the hydrophilic area in IP-S/PTFE functionalized hairs was carried out with Matlab (MatWoks).
The contact area for the calculation of the adhesive sheer force was measured with the optical microscope.Tests were performed in both controlled and standard laboratory atmospheric condition, proving the absence or negligible effect of atmosphere-mediated super-hydrophobicity via hydrophobic volatile organic compounds adsorption. [44]ir Retention Test: The patterned samples were mounted on a holder and vertically immersed below the water level inside a tank.The tank was then pressurized up to 4 atm with 0.2 atm of incremental steps.Ten seconds were waited before each increment to ensure the stabilization of the system.Four samples for each type of functionalization were tested twice.Images of the samples were taken using a high-resolution camera (Canon, Japan).Images were then analyzed using a custom image processing script in Matlab (MatWorks) that allowed to detect the area of the air trapped in the patterns.Data analysis was performed with Matlab.
Drag Force Reduction Test: The microfluidic channel was fabricated by means of molding technique.The mold was made in Teflon using a CNC (computer numerical control) machine.PDMS was prepared from monomer and reticulation agent in a 1:5 ratio (Sylgard 185, Dow Corning) and then was cast in the mold and cured at 100 °C for 35 min.For the test with patterned samples the channel mold had a height of 600 µm while for the flat control 500 µm.The reason was that the pattern was 100 µm height so the flow experiences the same hydraulic section but in one case the bottom was flat and on the other results to be patterned.The total length of the channel was 64 mm with the inlet and outlet at the extremities and two connectors for the pressure sensor at a distance of 45 mm.Connections were made using silicone transparent tubes.The bottom of the channel, that is the patterned rectangular glass slide was aligned with the PDMS channel.On the top side of the system a 4 mm thick slice of Plexiglass was added to give robustness to the system.Once sealed, the microfluidic chip was connected to a syringe pump (AL-4000 WPI, USA) and a final reservoir.The flow was set according to selected Reynold's numbers and the pressure drop was measured by the differential sensor (BPS110 Series, Bourns Inc.).Each sample was tested three times.Data analysis was performed with Matlab.

Figure 1 .
Figure 1.a) Pinning effect on a water droplet retained by crown-like hairs in the natural Salvinia Molesta leaf.b) Design of the artificial hierarchical hair (H is the height of the structure, D is the diameter of the head, and N f the number of filaments composing the head).c) Optical image of an example of the hexagonal arrangement of the patterns (scale bar in the magnified image in the inset is 100 µm).d-f) Scanning electron microscopy of the results of the microfabrication process via direct laser lithography for patterns with hairs with d) 4, e) 6, and f) 8 filaments.

Figure 2 .
Figure 2. a) Chemical functionalization process: i) for the hydrophobic coating, the pattern is dipped in a Teflon AF1600 solution in Fluorinert; ii) for the bioinspired coating, hydrophilic photoresist was deposited on the tips of the heads via microcontact printing; ii) scheme of the final dual functionalization.b-d) Scanning electron microscopy images of the biomimetic doubly functionalized micro-hairs.

Figure 3 .
Figure 3. a) Example of apparent static contact angle measurement, using a 5 µl water droplet onto a PTFE coated pattern.b) Results of the ASCA analysis for different designs of the hairs and surface chemical treatments.c) Scheme of the double Cassie-Baxter state with air trapped both inside the heads and between the stalks.d) Assumptions made for the calculation of F SL for different designs of the hairs and surface chemical treatments: the solid area (solid-liquid interface) is in between the flat projection and the curved contact area that represent the range of uncertainty used in the theoretical model.e) Measured ASCA (black data) and related predictions (colored bars) according to the proposed double Cassie-Baxter state model.f) Results of the roll-off angle analysis for different designs of the hairs and surface chemical treatments.g) Example of a roll-off angle measurement, using a 5 µl water droplet; the scheme reports the equilibrium forces at the moment of the detachment used for the calculation of the adhesion sheer force.

Figure 4 .
Figure 4. a) Square pattern of sides 5 × 5 mm 2 employed in air retention tests; in the inset the T-shape section of the perimeter wall.b) Optical images series of the pattern with infiltrating water for growing values of external hydrostatic pressure: the collapsed areas follow the directions defined by the hexagonal arrangement.c) Example (for N f = 8) of the amount of trapped air, expressed as fractional area, inside the micropatterns for different external hydrostatic pressure values.d) Theoretical curves for the critical pressure P cr predicted, for the different surface chemical treatments and designs, by the proposed model as a function of Φ (the heads fractional area calculated as the ratio between the projection of the heads and the total area); experimental values of P cr for untreated and IP-S/PTFE-coated hairs agree with the model, while the curves for PTFE-coated hairs have been used to estimate the initial amount of air trapped by the pattern.e) Scheme of the pressures at the water-air interface used in the theoretical model.f) Model of the protrusion of water in the equivalent circular hole approximating the artificial hair.g) Definition of the equivalent geometrical diameter of the model.h) Definition of the parameters for the calculation of the equivalent capillary diameter of the model.

Figure 5 .
Figure 5. a) Scheme of the flow profile in case of slip (i) and no-slip (ii) conditions: while in the no-slip boundary condition the fluid velocity profile is zero at the flat surface, the presence of air pocket makes the fluid experience non-zero velocity at the surface; the consequent drag force reduction can be correlated to the slip value s l .b) Sketch of the microfluidic channel: colored elements represent the cavities of the PDMS device (the blue thin area is the patterned channel, orange tubes are connected to a differential pressure sensor, yellow tubes are the inlet and outlet of the water flow); the patterned channel is longer than the distance between the points of the drop pressure measurement in order to guarantee the establishment of a stable laminar flow.c) Final assembled microfluidic chip.d) Experimental results of the pressure drop at different Reynold's numbers for untreated (green), hydrophobic PTFE (blue), and bioinspired dual hydrophilic/hydrophobic IP-S/PTFE (red) coatings in comparison to the flat hydrophilic substrate (black) made in IP-S.

Table 1 .
Adhesion sheer force values for different designs of the hairs and surface chemical treatments.Tests were carried out with 5 µL droplets.