Quick Liquid Propagation on a Linear Array of Micropillars | Langmuir

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Cite This: Langmuir 2019, 35, 9139−9145

Quick Liquid Propagation on a Linear Array of Micropillars Lizhong Mu,†,‡ Harunori N. Yoshikawa,*,§ Farzam Zoueshtiagh,∥ Tetsuya Ogawa,⊥ Masahiro Motosuke,# and Ichiro Ueno*,¶

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†

Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, 2 Linggong Road, Ganjinzi District, Dalian 116024, China ‡ Research Institute for Science & Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan § Université Côte d’Azur, CNRS, Institut de Physique de Nice, 06100 Nice, France ∥ Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Valenciennes, UMR 8520IEMN, F-59000 Lille, France ⊥ Division of Mechanical Engineering, Graduate School of Science & Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan # Department of Mechanical Engineering, Faculty of Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika, Tokyo 125-8585, Japan ¶ Department Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan S Supporting Information *

ABSTRACT: The wetting process of a high energy surface can be accelerated locally through the capillary interaction of a liquid advancing front with a micro-object introduced to the surface (Mu et al., J. Fluid Mech, 2017, 830, R1). We demonstrate that a linear array of micropillars embedded in a fully wettable substrate can produce quick propagation of liquid along the array. It is observed that multiple interactions of a liquid front with pillars can induce the motion of liquid a hundred times faster than in the absence of pillars.

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INTRODUCTION Wetting of a solid surface by liquid has attracted widespread interest because of its relevance to industrial and technological applications. Numerous industrial applications involve lens coating, water-resistant fabric manufacturing, lab-on-a-chip device fabrication, inkjet printing, and pesticide deposition on plant leaves.2−5 Biological systems benefit from their functional surfaces thanks to particular wetting properties, for example, the self-cleaning ability of lotus leaves6 and protective surfaces of insects.7 They have also been motivating the research to understand the physics of wetting to develop biomimetic applications. Wetting occurs when it decreases the energy of a surface. The resulting energy profit is measured by the spreading parameter S0 = γSO − γSL − γ, where γSO, γSL, and γ are the areal energy densities of solid−gas, solid−liquid, and liquid−gas interfaces, respectively.3 A surface of large negative S0 repels liquid and is free from the contamination by the liquid, as seen in water-resistant fabrics. In contrast, liquid spreads spontaneously over a surface of a nonnegative S0, until the intermolecular forces between the solid and the liquid or some external mechanisms prohibit further liquid extension. Such fully wettable surfaces have applications in surface protection and in heat transfer. © 2019 American Chemical Society

Endowing a surface of a given substance with a desired value S0 of the spreading parameter is often realized by treating surfaces chemically. Another method is implementing particular geometrical structures to surfaces, as adopted in the fabrication of superhydrophobic surfaces, where micropillars are embedded for realizing the liquid−solid contact in the Cassie state.8,9 Surface microstructures also have significant effects on wetting.10−19 For example, the effective spreading parameter S0′ = r(γSO − γSL) − γ of a fully wettable surface with microstructures is larger than the spreading parameter of a smooth surface, where r (>1) is the roughness factor defined as the ratio of the real to apparent surface areas.18 Microstructures can thus improve the wetting on a wettable surface. The wetting of a surface with closely packed pillars has been investigated intensively20 because of its applicability to a wide range of technologies. It is, for example, concerned with the wicking process of textiles, as the liquid imbibition into the interfiber spaces decides the soiling and cleanability properties of textures.21 However, most studies have focused to static or quasi-static aspects only. The effect of interaction between Received: March 24, 2019 Revised: June 11, 2019 Published: June 16, 2019 9139

DOI: 10.1021/acs.langmuir.9b00882 Langmuir 2019, 35, 9139−9145

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Figure 1. Liquid motion induced by a single pillar of height H = 140 μm. (a) Sequences of images in side and top views in the presence of a pillar of diameter 2a = 50 μm. (b) Positions X of the MCL along the x axis, as illustrated in panel (a), for pillars of different diameters. The result of the free spreading of a drop without the pillar is also shown for comparison. (c) Evolution of the MCL velocity U at different pillars of different diameters. The velocities have been computed from the data X = X(t) shown in panel (b). Their values may contain an error of 2 μm/s due to numerical differentiation of X(t). The left narrow panel shows U prior to the interaction with a pillar on a semi-log scale. The right panel shows U during the interaction with a pillar on a log−log scale. (d) Profiles of a meniscus developing on a pillar of diameter 2a = 50 μm at different instants. (e) Relaxation of the negative Laplace pressure measured from meniscus profiles. The behavior of the pressure is modeled by an exponential curve, exp[−(t − t0)/τp], where t0 is a time offset, and τp is the relaxation time of pressure decay. Determined values of τp are shown in the inset table.

affects the wetting dynamics around flexible pillars,27 would thus be negligible. We first confirm the acceleration produced by the interaction of liquid with single pillars of diameters ranging from 20 to 80 μm. We reveal the important dynamical role of the meniscus formed at pillar’s foot to draw liquid from the bulk liquid. We then investigate successive liquid−pillar interactions for a linear array of four pillars of a diameter of 50 μm. We demonstrate that the interactions produce a directional rapid liquid transport along the array and that the maximum velocity of MCL on the substrate can become a hundred times larger than on a smooth surface without pillars. The role of menisci as a liquid reservoir will be revealed. The effect of the interpillar distance on the MCL accelerated motion is also examined by a complementary experiment. These results are of primary importance for designing economical and low-energy consuming liquid transport devices in different technological applications, for example, in optimal designing of hemiwicking structures for heat pipe wicks28 and in performance improvement of lithium-ion batteries by structuring electrode surfaces.29

individual pillars on the dynamics of a contact line has attracted less attention. Recently, Kim et al.22 investigated the dynamics of a liquid climbing a fully wettable substrate patterned by cylindrical pillars. Balancing a driving capillary force with frictions on substrate and pillar surfaces, they explained successfully the diffusive dynamics of the liquid front. Mu et al.1 focused on the dynamical interaction of a macroscopic contact linea (hereafter referred to as MCL) with a single microparticle placed on a fully wettable substrate. It was observed that the wetting of a fully wettable particle induced the formation of a meniscus at its foot and produced a sharp acceleration of MCL motion. From this observation, one would expect that the interaction with an array of micrometersize objects would produce multiple accelerations of an MCL and yield a quick liquid propagation on the array. Indeed, we reported our first observation of multiple accelerations for an array of three spherical particles in a recent work.23 In the present article, we examine in detail the physical processes involved in the interaction of a thin liquid edge with micropillars on a substrate by an experiment. The surfaces of pillars and substrate are both fully wettable. The pillars are upright and cylindrical (different from refs 24 and 25) and embedded sparsely in order to examine individual liquid−pillar interaction in detail (different from refs24−26). They are rigid, made of the epoxy-based negative photoresist (SU8). The energy dissipation associated with pillar deformation, which

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RESULTS AND DISCUSSION Wetting of a Single Isolated Pillar. In the present experiment, a liquid drop spreads freely on a substrate surface due to its full wettability. The edge of the drop advances on the 9140


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liquids. The friction coefficient ζ is decided by the details of interactions between liquid and solid molecules32 and, depending on its relative importance to the liquid viscosity, the molecular friction could modify the behavior of MCL substantially.33 At the late stage of liquid−pillar interaction, X ≫ a and h ≈ a according to the experiment. We can then simplify eq 2 to Ẋ ≈ γa3/πμX3. The simplified equation gives power laws X ≈ (4γa3/πμ)1/4t1/4 and

surface to impact a pillar. Prior to the impact, the liquid motion is quasi-static and obeys to power law30,31 L ∝ t α , U ∝ t −(1 − α) ,

with

1 1 ≤α≤ 10 7

(1)

where L is the radius of the drop on the substrate, and U is the velocity of the MCL: U = dL/dt. The law (1) is called Tanner’s law when α = 1/10. The apparent contact angle θ formed by the solid−liquid and liquid−air interfaces is a few degrees. Thus, the thickness of the liquid film at the pillar position varies only by a few micrometers during the passage of the drop edge at a pillar. The liquid−pillar interaction starts by the pinning of the MCL (Figure 1a), during which the liquid circumvents the pillar foot. Once the whole foot is wetted, a meniscus emerges and develops on the pillar (t = 4.7 s in Figure 1a). The meniscus is almost axisymmetric with respect to the pillar axis and its growth is accompanied by a quick advancement of the MCL at the downflow side (Figure 1b). This acceleration produces a maximum MCL velocity, Umax, 10 times larger than the incident velocity U0 (Figure 1c), as reported for spheres and for particles in other shapes.1,23 The pillar diameter does not affect Umax (Figure 1c), while the MCL acceleration starts later for pillars of larger diameters (Figure 1b). After attaining its maximum velocity, MCL decelerates through a slow relaxation process (Figure 1c) and retrieves the incident velocity. The velocity curves for pillars 2a = 40 and 50 μm almost collapse with each other. This might arise from residual contamination on one of the substrates used in these experiments, in particular, at the pillar foot. The observed accelerated motion of an MCL is driven by the force resulting from the capillary energy released through the wetting of the pillar surface. The dynamics of this motion would be modeled by balancing the driving capillary force Fd with the resistance force due to hydrodynamic friction, Fr, as Kim et al.22 successfully modeled the behavior of a liquid front during the hemiwicking on a hydrophilic surface covered by micropillar arrays. The model is based on the integral momentum equation in the low Reynolds number limit. For MCL motion observed in the present experiment, the driving capillary force is given by the capillary pressure γκ multiplied by the section of a meniscus Xh as in Kim et al.,22 where κ is the curvature of the meniscus, X is the position of MCL measured from the pillar axis along the x axis (Figure 1a), and h is the height of the meniscus. We have taken into account the experimental fact that the meniscus is almost symmetric around the pillar so that the transverse extension of a meniscus is also given by X. As κ ≈ h/X2, we have Fd ≈ γ(h/X2)·Xh = γh2/X. The resistance force Fr would have two contributions: one from the viscous shear μ(Ẋ /h) at the bottom area of the meniscus π(X2 − a2); the other from the viscous shear μ(Ẋ /X) at the pillar surface 2πah. We thus have Fr ≈ μ(Ẋ /h)·π(X2 − a2) + μ(Ẋ /X)·2πah. The balance Fd = Fr then gives γh3 ijj a2 2ah2 yzz 1− 2 + z j 3j πμX k X X3 z{

U = Ẋ ≈ (γa3/64πμ)1/4 t −3/4

The increase of X observed in the experiment is faster than that predicted by this power law (see the appendix provided in the Supporting Information). However, at the late stage of interaction, the MCL behavior (Figure 1c) approaches to and agrees with the power law (3). At the beginning of liquid−pillar interaction, in contrast, the theoretical model (2) gives an estimate Ẋ ≈ γ/8πμ ≈ 10−1 m/s for h ≈ a and X ≈ 2a, which is much larger than the observed MCL velocity (Figure 1c). In the experiment, it is also observed that menisci grow up with a time scale tmax (∼1 s) much larger than the capillary time τc = ρa3/γ ≈ 10−5 s, which is expected to characterize the formation of the meniscus on a vertical thin rod impinged in a liquid bath.34 These discrepancies arise from the severely limited liquid supply to a meniscus in the present experiment. In fact, the meniscus has a large curvature at the beginning of its formation (Figure 1d). The related Laplace pressure Δp, which would vanish quickly, at a time scale of τc, if the liquid supply was not limited,34 takes large negative values (−Δp ≈ γ/a = 102−103 Pa) at the early stage of meniscus growth and relaxes to zero over a larger time scale τp (∼0.1 s) than τc (Figure 1e). The measured relaxation time τp does not vary linearly with the pillar radius a (Figure 1e, inset table). There might be a threshold in pillar diameter, above which some effects of the global interaction of a pillar with a spreading drop would become significant. Wetting of a Linear Array of Pillars. When a liquid edge impacts a linear array of pillars perpendicularly (Figure 2),

Figure 2. Schematic illustration of an array of four cylindrical pillars P1, P2, P3, and P4. Liquid approaches the array from left. The diameter of pillars is 2a = 50 μm. The pillar height H is either 120 or 140 μm. The interpillar distance d is 250 μm.

−1

Ẋ ≈

(3)

successive liquid−pillar interactions occur (Figure 3a). The pinning of the MCL at the foot of each pillar is followed by the formation of a meniscus, which is accompanied by the MCL quick advancing motion (Figure 3b), as in the single pillar case. The MCL is sharply accelerated to a maximum velocity and, then, decelerates through a slow relaxation (Figure 3c). These processes are repeated for four pillars and, as a consequence, the liquid propagates along the pillar array. After a meniscus develops at the last pillar, the menisci at the four pillars grow as a whole until the liquid attains the pillar top. This collective

(2)

In the model (2), we have neglected the resistance force due to the frictions between liquid and solid molecules32 to the first approximation, as in the model of Kim et al.22 This molecular friction, which could be estimated by the friction per unit length ζẊ multiplied by the length of the contact line πX at the bottom of the meniscus (ζ: the friction coefficient), will be significant in wetting of a soft substrate by small viscosity 9141


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Figure 3. Wetting of an array of four pillars P1, P2, P3, and P4. The diameter 2a and the interpillar distance d are 50 and 250 μm, respectively. The height H of the pillars is 120 μm, except for (g) where H = 140 μm. (a) Sequences of images in side and top views. (b) Space−time diagram showing the position X(t) of an MCL on the x axis. The diagram has been constructed of chronologically arranged line images extracted from topview images. (c) Velocity U of an MCL computed from the data X(t) reported in (b). It may contain an error of 2 μm/s due to numerical differentiation. (d) Profiles of menisci at different pillars at the moments of maximum MCL velocity Umax. The horizontal coordinates (x) have been shifted by the positions of corresponding pillars, that is, by x1, x2, x3, x4 = 0, 250, 500, 750 μm. (e) Lateral extension l vs the height h of menisci during their growth. (f) Laplace pressure (Δp) of the menisci at the four pillars. Solid lines are exponential fits Δp ∝ exp[−(t − t0)/τp], where t0 is a time offset. The pressure relaxation time τp is found to be τp = 0.18, 0.0064, 0.0078, and 0.0067 s for the menisci at P1, P2, P3, and P4, respectively. The maximum velocity moments tmax are indicated by arrows. (g) Meniscus heights h measured at the downflow side of each pillar.

10. As a consequence, the MCL velocity attains a maximum value 200−300 times larger than in the absence of the pillar array. These differences should reflect the differences in the meniscus growth and in the associated Laplace pressure. The meniscus at P1 is almost axisymmetric during the interaction with the liquid front until the wetting of the next pillar starts. The interactions of P2, P3, and P4 with the front occur, in contrast, in the lack of the fore-and-aft symmetry in meniscus shapes because the meniscus upflow sides develop as a part of the liquid bridge connecting them to their previous pillar. Furthermore, throughout the evolution, the downflow−side profiles of the last three menisci are much sharper than the meniscus profile at P1 (Figure 3d,e). The relaxation time τp of the meniscus Laplace pressure takes values 0.18 s at P1 and

growth is produced by the capillary force associated with the large curvature of a liquid free surface imposed by the narrow space between pillars.35 Liquid can indeed rise over the pillar height H = 140 μm, which is larger than the rise height hstatic of a static meniscus on a vertical cylindrical rod.b Detailed examination of the MCL motion shows significant differences between the liquid−pillar interaction at the first pillar (P1) and the other ones (P2, P3, P4). Because an MCL accelerated by a pillar arrives at the next pillar before the completion of the relaxation process, the MCL incident velocities at pillars P2, P3, and P4 are larger than that at P1 (Figure 3c). The MCL acceleration produced by the last three pillars is much sharper than that by the first pillar (Figure 3b), and the velocity gain Gi = Umax,i/U0,i (i = 2, 3, 4) at P2, P3, and P4 is two times larger than the gain at P1: G1 = Umax,1/U0,1 ≈ 9142


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The distance d should thus be smaller than a critical value dc for successive liquid−pillar interactions to produce the maximum velocity larger than that by a single pillar. Under present experimental conditions, this critical distance dc is 510 μm according to eq 4. When the interpillar distance becomes small compared with the pillar diameter, the motion induced by the second pillar will be qualitatively different from that presented above. Liquid will rise up along the pillar axis to fill the interpillar space due to capillary effects before advancing further on the substrate surface. When the interpillar distance vanishes, no separated successive accelerations will be produced. Our preliminary experiment with a horizontal long rod placed on substrate surface showed, in fact, that liquid is pinned by the rod until its whole foot is wetted. The optimal distance between two successive pillars will be examined in our future work.

0.007 s at the other pillars (Figure 3f). It suggests that the menisci at the last three pillars drive liquid from the surrounding more easily than the meniscus at P1. Indeed, when a meniscus is growing at P2, P3, or P4, the menisci formed at the previous pillars serve as a liquid source. The time evolution of meniscus heights h measured at the downflow sides of different pillars confirms this point (Figure 3g). The meniscus height h1 at P1 continues to increase until the MCL arrives at the downflow side of P2. Once the meniscus emerges at P2, the height h1 decreases as the liquid is drawn to the second meniscus by its negative Laplace pressure. When a meniscus emerges at P3, the liquid bridge between P1 and P2 serves as a liquid reservoir, as indicated by the sharp decrease of h1. A gradual increase of the height h2 of the second meniscus is due to the formation of a liquid bridge between P2 and P3. Similar behavior of the meniscus heights at two preceding pillars is observed during the growth of the meniscus at P4. Effects of the Interpillar Distance. The experiment with an array of four pillars shows the propagation of liquid on the array driven by the capillary force. The growth of a meniscus at a pillar is affected by the previous meniscus through the formation of a liquid bridge, which serves as a liquid reservoir to allow a rapid development of the growing meniscus. This beneficial effects of the meniscus at preceding pillars would be less significant as the interpillar distance d is large. The range of influence λ of a pillar, beyond which the MCL retrieve its velocity prior to the interaction with the pillar, is of the order of a capillary length Sc (Figure 4a). An interpillar distance

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CONCLUSIONS We demonstrated experimentally that the wetting of a fully wettable surface is accelerated up to 300 times by an array of micropillars along the array direction. The liquid wets the extra surface area offered by each of the pillars and forms a meniscus on each pillar. The growth of the meniscus is accompanied by a quick advancing motion of the liquid edge. It was found that the liquid needed less than 3 s to travel over a distance of 600 μm thanks to the pillar array (Figure 3), while it will take more than half a minute on a flat surface. During the quick propagation of liquid, only the lower parts of pillars are wetted. The wetted height is approximately a pillar diameter so that pillars can be as low as 2a to produce a quick liquid motion. Detailed observation of the behavior of liquid showed a significant difference in the wetting processes of the first and the other pillars. The development of the meniscus on the first pillar is affected by severely limited liquid supply to the meniscus at the early stage of meniscus formation. The menisci formed on the other pillars are, in contrast, not concerned with this limitation because they can draw liquid from the preceding meniscus that serves as a reservoir of liquid. The ability of a pillar array to produce a large velocity through the multiple liquid−pillar interactions depends on interpillar distance d that decides whether a formed meniscus can be a liquid source for the next meniscus. This critical distance dc was estimated dc ≈ 510 μm for pillars of a diameter of 50 μm under the wetting condition examined in the present work. The constant maximum velocity produced by the second, third, and fourth pillars is encouraging. A quick and directional liquid transport over a long distance would be possible by implementing a long array of pillars at a fully wettable surface. The efficiency of the transport would be decided by the geometry of the pillar array. The present investigation provides key information for designing this liquid transport system.

Figure 4. Effects of the interpillar distance d. (a) Diagram showing the variation of the influence length λ of a single pillar in function of pillar diameter 2a. The motion of a MCL induced by a single pillar has velocity U larger than incident velocity U0 when distance X of the MCL is smaller than λ. Otherwise, U < U0. (b) Velocity of an MCL interacting with an array of two pillars. The diameters 2a of the first and second pillars are 50 and 60 μm, respectively. The velocity has been normalized by the maximum velocity produced by the first pillar, Umax,1.

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smaller than λ is, however, not sufficient to produce a quick liquid propagation. It should be small enough for the previous meniscus to be capable to serve as a liquid reservoir for a growing meniscus. An experiment performed with two pillars by varying interpillar distance d shows that the maximum velocity Umax produced by the second pillar decreases with the distance d (Figure 4b). The measured maximum velocities Umax,2 induced by the second pillar are correlated with the distance d by Umax,2 Umax,1

iay = (1.02. ± 0.11) × 102 ·jjj zzz kd{

EXPERIMENTAL SECTION

Setup. Micropillars are fabricated on a polished silicon wafer of 76 mm diameter. The pillar embedding is done by the classical lithography process, that is, spin-coating of a UV-epoxy (SU8permanent epoxy negative photoresist), exposition to UV light, and development in solvent bath. Single pillars and linear arrays of four pillars of diameters 2a ranging from 20 to 100 μm and height, H, of 120 or 140 μm were created at different zones of the wafer. In the linear arrays, pillars are regularly spaced with a constant interpillar distance d = 250 μm. Prior to each experiment, this substrate is cleaned by acetone and by a plasma cleaner (PDC 32G, Harrick Plasma) during 10 min and installed horizontally in the test section.

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(4) 9143


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Langmuir The test liquid is silicone oil of a density of ρ = 873 kg/m3, a kinematic viscosity of ν = 2.00 mm2/s, and a surface tension of γ = 18.3 mN/m at 25 °C. The corresponding capillary length Sc = γ /ρg is 1.46 mm, where g denotes the gravitational acceleration. The surfaces of the wafer and the pillars are fully wettable to this oil. In each experiment, a drop of the oil of volume Vdrop is deposited on the substrate by a syringe pump through a hypodermic needle (Figure 5) at a distance L from the closest pillar. The drop first

ξzz 2 3/2

(1 + ξz )

−

Δp 1 =− 2 1/2 γ ξ(1 + ξz )

(5)

where ξ is the radial coordinate of a meniscus surface. The shape of the meniscus has been assumed to be locally independent of the azimuthal angle around the pillar axis so that the surface is given by r = ξ(z). This assumption is consistent with the fact that the MCL at the downstream side of a meniscus remains circular throughout the meniscus development (Figure 1a). The first and second derivatives of ξ with respect to z have been denoted by ξz and ξzz, respectively. The boundary condition to the surface is ξ|z = 0 = R ,

ξ|z = H = a

ξz|z = 0 = − cot θs ,

(6a)

ξz|z = H = tan θp

(6b)

where R is the distance of MCL from the pillar axis measured along the x axis: R = X for an isolated pillar; R = X − xi for Pillar i (=1, ..., 4) in an array. The angles θs and θp are the apparent contact angles at the substrate surface and at the pillar surface, respectively. Equation 5 under the boundary condition (6a) generates a series of surface shapes for different values of Δp. By seeking for the value of Δp that produces the best fitting to an observed surface shape at a given instant, one can estimate Δp. This method is applicable only until the meniscus foot reaches, if any, the next pillar.

Figure 5. Sketch of the experimental setup.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.9b00882. Details on the power law behavior of MCLs induced by single pillars (PDF)

Figure 6. Spreading of a drop on a polished silicon wafer substrate in the absence of any pillar. The volume of the drop is 2 mm3. The evolution of the spreading radius L in function of time t elapsed from the drop deposition follows the power law (1) with an exponent 1/8.7 at the late stage of spreading (L > 2500 μm). The deviation of the exponent from that of Tanner’s law, that is, 1/10, would be due to either non-negligible gravity31 or molecular friction.33 The position of pillars (the first pillar in the case of pillar arrays) is indicated by a horizontal line.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (H.N.Y.). *E-mail: [email protected] (I.U.). ORCID

Harunori N. Yoshikawa: 0000-0003-4472-4425 Ichiro Ueno: 0000-0003-1616-3683 Notes

spreads at the substrate due to its inertia. When the edge of the drop reaches the pillar location, however, any effect related to the drop deposition process has vanished. The spreading is then driven either by capillarity or gravity, following the power law (1) with an exponent 1/8.7 (Figure 6) for the spreading radius L. The volume Vdrop = 2 mm3 and the distance L ≈ 3 mm are chosen for the drop edge to arrive at the pillar position, within experimentally tractable time, without any transient behavior related with initial conditions. The dynamics of MCL at the proximity of the pillars is observed from top and side views (Figure 5) with, respectively, ×300 and ×600 objective lenses using two high-speed cameras (Photron, FastcamMini) at a typical frame rate of 250 fps. The top view aims at characterizing the deformation and the motion of the contact line during the interaction with pillars. The side view aims at monitoring the liquid ascending motion on pillars and the profile of the liquid free surface. Lighting systems consist of a 100 W halogen light source (MORITEX, MegaLight 100) for top-view observation and of a 350 W metal-halide lamp (Photron, HVC-SL) for side-view observation. Laplace Pressure Measurement. The Laplace pressure Δp at the downflow side of a meniscus can be estimated from the balance of normal stresses at the meniscus surface, (p0 + Δp) − p0 = 2γκ , where p0 is the air pressure, p0 + Δp is the pressure inside the meniscus, and κ is the local mean curvature. Viscous stresses have been neglected because of a small capillary number (Ca ≈ 10−6). This balance gives the following equation

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Reiya Ono for the fabrication of the pillars used in the present experiment. This work was partially supported by Grant-in-Aid for Challenging Exploratory Research from Japan Society for the Promotion of Science (JSPS, grant no. 16K14176) and by a grant from the French National Research Agency (ANR) through the program “Fluid Engineering for Food Security” (grant no. ANR-18-CE210010-02). Authors acknowledge the financial support from MAE (French Ministry of Foreign Affairs and International Development) and from JSPS through the PHC Sakura program “Wetting dynamics in the presence of particles”. I.U. acknowledges the support by Fund for Strategic Research Areas from Tokyo University of Science.

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ADDITIONAL NOTES We adopt this terminology to avoid any confusion arising from the full wettability of surfaces, since a precursor film will be present ahead of a liquid front. b hstatic = 122 μm for a fully wettable rod of a diameter 50 μm.3 a

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(26) Xiao, R.; Wang, E. N. Microscale liquid dynamics and the effect on macroscale propagation in pillar arrays. Langmuir 2011, 27, 10360−10364. (27) Yuan, Q.; Zhao, Y.-P. Wetting on flexible hydrophilic pillararrays. Sci. Rep. 2013, 3, 1944. (28) Dunn, P. D.; Reay, D. Heat Pipes, 3rd ed.; Pergamon Press, 1982. (29) Pfleging, W. A review of laser electrode processing for development and manufacturing of lithium-ion batteries. Nanophotonics 2018, 7, 549−573. (30) Tanner, L. H. The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 1979, 12, 1473−1484. (31) Lopez, J.; Miller, C. A.; Ruckenstein, E. Spreading kinetics of liquid drops on solids. J. Colloid Interface Sci. 1976, 56, 460−468. (32) Blake, T. D.; de Coninck, J. The influence of solid-liquid interactions on dynamic wetting. Adv. Colloid Interface Sci. 2002, 96, 21−36. (33) Yuan, Q.; Huang, X.; Zhao, Y.-P. Dynamic spreading on pillararrayed surfaces: Viscous resistance versus molecular friction. Phys. Fluids 2014, 26, 092104. (34) Clanet, C.; Quéré, D. Onset of menisci. J. Fluid Mech. 2002, 460, 131−149. (35) Velev, O. D.; Denkov, N. D.; Paunov, V. N.; Kralchevsky, P. A.; Nagayama, K. Direct measurement of lateral capillary forces. Langmuir 1993, 9, 3702−3709.

REFERENCES

(1) Mu, L.; Kondo, D.; Inoue, M.; Kaneko, T.; Yoshikawa, H. N.; Zoueshtiagh, F.; Ueno, I. Sharp acceleration of a macroscopic contact line induced by a particle. J. Fluid Mech. 2017, 830, R1. (2) Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Wetting and spreading. Rev. Mod. Phys. 2009, 81, 739−805. (3) de Gennes, P. G.; Brochard-Wyart, F.; Quéré, D. Gouttes, Bulles, Perles et Ondes; Belin: Paris, 2002. (4) Snoeijer, J. H.; Andreotti, B. Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 2013, 45, 269−292. (5) Popescu, M. N.; Oshanin, G.; Dietrich, S.; Cazabat, A.-M. Precursor films in wetting phenomena. J. Phys.: Condens. Matter 2012, 24, 243102. (6) Bhushan, B.; Jung, Y. C.; Koch, K. Self-cleaning efficiency of artificial superhydrophobic surfaces. Langmuir 2009, 25, 3240−3248. (7) Wagner, T.; Neinhuis, C.; Barthlott, W. Wettability and contaminability of insect wings as a function of their surface sculptures. Acta Zool. 1996, 77, 213−225. (8) Callies, M.; Quéré, D. On water repellency. Soft Matter 2005, 1, 55−61. (9) Quéré, D. Non-sticking drops. Rep. Prog. Phys. 2005, 68, 2495− 2532. (10) Bico, J.; Tordeux, C.; Quéré, D. Rough wetting. Europhys. Lett. 2001, 55, 214−220. (11) Cassie, A. B. D.; Baxter, S. Wettability of porous surfaces. Trans. Faraday Soc. 1944, 40, 546−551. (12) Cazabat, A. M.; Cohen Stuart, M. A. Dynamics of wetting: effects of surface roughness. J. Pharm. Chem. 1986, 90, 5845−5849. (13) Dash, S.; Alt, M. T.; Garimella, S. V. Hybrid surface design for robust superhydrophobicity. Langmuir 2012, 28, 9606−9615. (14) Li, X.; Ma, X.; Lan, Z. Dynamic behavior of the water droplet impact on a textured hydrophobic/superhydrophobic surface: the effect of the remaining liquid film arising on the pillars’ tops on the contact time. Langmuir 2010, 26, 4831−4838. (15) Liu, Y.; Moevius, L.; Xu, X.; Qian, T.; Yeomans, J. M.; Wang, Z. Pancake bouncing on superhydrophobic surfaces. Nat. Phys. 2014, 10, 515−519. (16) Papadopoulos, P.; Deng, X.; Mammen, L.; Drotlef, D.-M.; Battagliarin, G.; Li, C.; Müllen, K.; Landfester, K.; del Campo, A.; Butt, H.-J.; Vollmer, D. Wetting on the microscale: shape of a liquid drop on a microstructured surface at different length scales. Langmuir 2012, 28, 8392−8398. (17) Wang, J.; Do-Quand, M.; Cannon, J. J.; Yue, F.; Suzuki, Y.; Amberg, G.; Shiomi, J. Surface structure determines dynamic wetting. Sci. Rep. 2015, 5, 8474. (18) Wenzel, R. N. Resistance of solid surfaces to wetting by water. Ind. Eng. Chem. 1936, 28, 988−994. (19) Yuan, Q.; Zhao, Y.-P. Multiscale dynamic wetting of a droplet on a lyophilic pillar-arrayed surface. J. Fluid Mech. 2013, 716, 171− 188. (20) Quéré, D. Wetting and roughness. Annu. Rev. Mater. Res. 2008, 38, 71−99. (21) Parada, M.; Vontobel, P.; Rossi, R. M.; Derome, D.; Carmeliet, J. Dynamic wicking process in textiles. Transp. Porous Media 2017, 119, 611−632. (22) Kim, J.; Moon, M.-W.; Kim, H.-Y. Dynamics of hemiwicking. J. Fluid Mech. 2016, 800, 57−71. (23) Mu, L.; Yoshikawa, H. N.; Kondo, D.; Ogawa, T.; Kiriki, M.; Zoueshtiagh, F.; Motosuke, M.; Kaneko, T.; Ueno, I. Control of local wetting by microscopic particles. Colloids Surf., A 2018, 555, 615− 620. (24) Kim, T.-i.; Suh, K. Y. Unidirectional wetting and spreading on stooped polymer nanohairs. Soft Matter 2009, 5, 4131−4135. (25) Chu, K.-H.; Xiao, R.; Wang, E. N. Uni-directional liquid spreading on asymmetric nanostructured surfaces. Nat. Mater. 2010, 9, 413−417. 9145


Quick Liquid Propagation on a Linear Array of Micropillars | Langmuir

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