Article pubs.acs.org/Langmuir
Fog Deposition and Accumulation on Smooth and Textured Hydrophobic Surfaces Tony S. Yu,*,† Joonsik Park,‡ Hyuneui Lim,‡ and Kenneth S. Breuer† †
Brown School of Engineering, Brown University, 182 Hope Street, Providence, Rhode Island 02912, United States Department of Nature-Inspired Nanoconvergence Systems, Nano-Convergence Mechanical Systems Research Division, Korea Institute of Machinery and Materials, 171 Jang-dong, Yuseong-gu, Daejeon 305-343, Korea
‡
S Supporting Information *
ABSTRACT: We investigated the deposition and accumulation of droplets on both smooth substrates and substrates textured with square pillars, which were tens of micrometers in size. After being coated with a hydrophobic monolayer, substrates were placed in an air flow with a sedimenting suspension of micrometer-sized water droplets (i.e., fog). We imaged the accumulation of water and measured the evolution of the mean drop size. On smooth substrates, the deposition process was qualitatively similar to condensation, but differences in length scale revealed a transient regime not reported in condensation experiments. Based on previous simulation results, we defined a time-scale characterizing the transition to steady-state behavior. On textured substrates, square pillars promoted spatial ordering of accumulated drops. Furthermore, texture regulated drop growth: first enhancing coalescence when the mean drop size was smaller than the pillar, and then inhibiting coalescence when drops were comparable to the pillar size. This inhibition led to a monodisperse drop regime, in which drop sizes varied by less than 5%. When these monodisperse drops grew sufficiently large, they coalesced and could either remain suspended on pillars (i.e., Cassie−Baxter state) or wet the substrate (i.e., Wenzel state).
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settling.16 Furthermore, condensation of water vapor is governed by nucleation. Since vapor must overcome an energy barrier to nucleate, tuning the surface chemistry of a substrate is an effective method of directing water accumulation during condensation.15,17−19 Droplets, in contrast, will deposit wherever they land. Despite these difference, there are notable similarities between these processes, and this paper will draw comparisons to the extensive literature on condensation17,18,20−26 to illuminate the deposition process. Although there is extensive literature on the deposition of particles on surfaces,4,16,27 the study of deposition and accumulation of liquid droplets has mostly been limited to simulations28,29 and coarse measurements of the net water accumulation on macroscale structures.6−11 Previous deposition simulations showed that accumulated drops exhibited a steadystate growth regime, during which the mean drop-radius grew linearly in time and the drop-size distribution was selfsimilar.28,29 The simulations by Family and Meakin28 exhibited prolonged transient growth before reaching steady-state; the dynamics of this transient regime, however, were left unexplored by the authors. More recent work by Ulrich et al.29 discussed the transient regime in detail and suggested that the system does not reach steady-state until the fraction of
INTRODUCTION Surface roughness is frequently exploited to augment the hydrophobicity of a chemically hydrophobic surface. When a large drop is placed on a hydrophobic substrate that is textured with micropillars, it can stand atop these pillars (i.e., the Cassie−Baxter, or “fakir”, state) and, as a consequence, exhibits a larger contact angle than on a smooth substrate.1,2 If a droplet is smaller than the microtexture, however, it can deposit inbetween pillars. This intrusion can ruin the surface’s superhydrophobic and self-cleaning properties.3 In addition to wetting, the deposition of droplets (and particles) is critical to applications ranging from drug delivery in human respiratory tracts4,5 to water uptake in plants and animals.6−11 In this paper, we investigated the accumulation of water drops, on both smooth and microtextured surfaces, due to the deposition of droplets smaller than the size of the microtexture. (In what follows, “droplets” refers to water drops suspended in air, while “drops” refers to water drops that have accumulated on the substrate.) The ability of small droplets to deposit in-between pillars is similar to the tendency of vapor to condense in-between pillars.2,3,12−15 In fact, the deposition of water droplets is often conflated with condensation of water vapor despite notable distinctions between the two processes. For example, transport during condensation is dominated by the diffusion of water vapor, whereas diffusion of fog droplets, typically larger than 1 μm, is negligible compared to droplet inertia or gravitational © 2012 American Chemical Society
Received: May 9, 2012 Revised: July 27, 2012 Published: July 30, 2012 12771
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Figure 1. Bench-top wind tunnel in which the working fluid was air with a suspension of micrometer-sized water droplets. Pressurized air drove flow through an atomizer, which generated water droplets. The flow was guided toward a test section where a substrate was suspended. The test section was closed off with optical glass, and a microscope objective provided optical measurement.
surface covered by drops, that is, the surface coverage, ϕ, reaches a critical value ϕ∗. This critical surface coverage was required for the system to reach the self-similar distribution of drop sizes found at steady-state.28,30 Based on the scaling results from Ulrich et al.,29 we found that the transient regime for deposition experiments lasted significantly longer than for typical condensation experiments. In this article, we first describe an experimental setup used to deposit micrometer-sized water droplets, that is, fog, onto substrates. Using this setup, we quantified the growth of drops on the surface: first for smooth substrates and then for substrates textured with a regular array of square pillars. On smooth substrates, the deposition process was qualitatively similar to condensation, but differences in length scale revealed a transient regime, which we characterized by a time constant. For textured substrates, we observed a series of drop-growth regimes that were characterized by changes in growth rates and spatial organization of drops. Finally, we present preliminary results on late-time coalescence, which occurred when drops became larger than the scale of the microtexture.
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illumination. This method of illumination minimized reflections, which could lead to spurious drop detection, and the bright edges were easy to detect using image analysis techniques. In this study, we used a circle-detection algorithm based on the Hough transform, as described by Illingworth and Kittler.33 Silicon substrates were patterned with alternating strips of smooth and textured regions; these strips allowed simultaneous measurement and direct comparison of results on both regions. The texture was produced by deep reactive-ion etching and consisted of a square lattice of 90 μm high square pillars with a high solid fraction (54 μm wide pillars with 12 μm gaps). After patterning, the samples were coated by vapor deposition of a fluoroalkylsilane (tridecafluoro-1,1,2,2-tetrahydrooctyltrichlorosilane, FOTS, Aldrich, St. Louis, MO) to reduce their surface energy.34,35 Water drops placed on the textured region exhibited a contact angle of 135° compared to 107° on the smooth region. The substrate was held with its surface parallel to the freestream flow, and a leading knife-edge (100 μm thick, 1 cm long) shifted entrance effects upstream of the substrate (see Figure 2). Images were captured near the center of the substrate to further mitigate edge effects. In the present study, gravitational settling, that is, sedimentation, was the dominant force for droplet motion near the substrate. The sedimentation velocity, vs, can be calculated by balancing gravity with viscous forces:4
EXPERIMENTAL SECTION
To study the deposition of micrometer-sized water droplets, we built a bench-top wind tunnel, as depicted in Figure 1. Pressurized air drove flow through an ultrasonic atomizer, which generated water droplets with diameter d ≈ 3−4 μm.31,32 The air flow carried suspended droplets through a 2.2 cm square-channel, which guided the flow toward a test section. The test section was closed off with a glass coverslip, which was coated with a commercial antifog coating (FogTech, MotoSolutions, Rodeo, CA) to maintain visibility during fog exposure. We suspended substrates in the test section and imaged them using a variable-zoom lens (TECHSPEC VZM 1000i, Edmund Optics, Barrington, NJ) attached to a digital camera (Prosilica GX1050, Allied Vision Technologies, Stadtroda, Germany). The microscope objective could be oriented horizontally, looking at the substrate edge-on (as shown in Figure 1), to measure droplet trajectories over the substrate, or vertically, looking top-down at the substrate (not shown), to measure the size of accumulated drops. To facilitate drop-size measurement, we used a ring illuminator to generate dark-field images: From the top-down perspective, the outer edge of drops appeared as bright circles due to the annular
vs =
ρw d 2g 18μa
≈ 0.4 ± 0.1mm/s (1)
where g is the gravitational constant, ρw is the density of water, and μa is the dynamic viscosity of air. This sedimentation velocity was verified with particle-tracking experiments (see, e.g., Figure 2). The flow through the channel can be characterized by the Reynolds number, which relates the inertial effects of the flow to the viscous effects:
Re =
ρa UL μa
(2)
For the bulk flow through the channel, the air velocity was U ≈ 1 cm/ s, the air density was ρa = 1.2 kg/m3, and the characteristic length was the channel size L = 2.2 cm; thus, Rebulk ∼ 10 such that the bulk flow was laminar. Furthermore, since the knife-edge shifted the entrance length upstream of the substrate, the flow over the substrate was fully developed Poiseuille flow.36 Close to the substrate, the flow scaled with the size of the microtexture, which was roughly 100 μm; at this scale, the flow was significantly reduced by viscous effects, such that 12772
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dominant on each pillar, as shown in Figure 3c. Drops on adjacent pillars eventually grew large enough to touch and coalesce. The resulting agglomerate drops spanned four, or more, pillars, as shown in Figure 3d, and could either remain suspended on pillars or wet the underlying substrate. As is common in condensation studies,14,20 we present experimental data in terms of the mean radius, as shown in Figure 4. The labels (a), (b), and (c) correspond to the images in Figure 3. The image in Figure 3d was outside the range of plotted data, which ended just before drops on adjacent pillars coalesced. On the smooth half of the substrate (black dots), the slope of the curve, that is, the growth rate, changed slightly, but continuously, with no sharp changes in growth. At early times, the mean radii on the textured half of the substrate (red dots) were similar to those on the smooth half. Note that the camera was focused on the tops of pillars, such that drops on the smooth half were slightly blurred (see, e.g., Figure 3a), and their measured mean radii were slightly larger (≈0.25 μm) than those on the textured half. Around t ≈ 100 s, a change in the relative slopes of the mean-radii curves suggested a slight increase in the growth rate of drops on the textured region of the substrate. Between t ≈ 243 and 318 s, drops on the textured region grew rapidly. At the end of this period, a single drop sat atop each pillar as pictured in Figure 3c, and the growth in mean radius slowed to ⟨r⟩ ∼ t1/3 (see Figure 7). In the following sections, we detail the physical mechanisms underlying the observed drop-evolution behavior. Deposition on Smooth Substrates. On smooth substrates, deposition, incorporation, and coalescence controlled the number and size of accumulated drops.29 This growth was reflected in a monotonically increasing mean radius, which is replotted from Figure 4 as red dots on the log−log plot shown in Figure 5. In addition, the figure shows a gray-filled region extending from the minimum measured radius to the maximum radius. Note that the sudden increases in the maximum radius (e.g., at t = 315 s and t = 426 s in Figure 5) corresponded to coalescence events; such jumps would be mitigated by larger sample sizes. The minimum drop size in Figure 5 is incorrect, since freshly deposited drops had a radius ≈2 μm. Their absence in this plot reflects a flaw of the drop-detection algorithm, which favored larger drops and overlooked many smaller drops, that is, drops less than about 2/3 of the measured mean size (Supporting Information, Figure S2). Note, however, that small drops can distort the mean radius: The numerous small drops dominate the fewer number of large drops, and the mean radius will plateau at late times.29 In fact, small drops represent new “generations” of drops, where the growth of each generation can be described by a scaling law with a different starting time (see Meakin,25 Beysens37 for further discussion). To mitigate the influence of small drops, researchers typically present simulation results based on an area- or volume-weighted mean radius (see, e.g., Ulrich et al.,29 Fritter et al.38). By detecting only the largest drops, we restricted analysis to the first generation of drops, which more accurately reflects previous results. The continuous change in the slope of the mean radius was surprising, since simulations of both condensation and deposition predict that the mean drop-radius should grow linearly in time.21,28,29,38 In simulations, this steady-state regime was accompanied by a self-similar drop-size distribution, which had a narrow distribution of large sizes and a polydisperse distribution of smaller sizes.28,39 Furthermore, in the self-similar regime, the surface coverage, ϕ, is predicted to reach a constant
Figure 2. Flow and droplet trajectories over substrate. Bottom: A leading knife-edge shifted entrance effects upstream of the substrate, such that the flow over the substrate was parabolic. Top: Droplet trajectories from particle tracking analysis over 150 sequential frames at 1 ms intervals. Drops followed the horizontal flow but, in addition, sedimented due to gravity. Note that the substrates used for accumulation measurements had the same pillar width as the above substrate, but here the gaps between pillars were 4.5 times larger. Unear ≈ 1 mm/s. The resulting Reynolds number was on the order of Renear ∼ 10−2, such that viscous effects dominated inertia near the substrate. All other effects (e.g., droplet inertia, Brownian diffusion4,16) were negligible. As a result, the flow delivered droplets uniformly over the substrate at a constant deposition rate, which was governed by the sedimentation velocity and droplet concentration, c ≈ 106drops/cm3.
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EXPERIMENTAL RESULTS Images of accumulated drops on smooth (bottom-half) and textured (top-half) regions were captured simultaneously on the same substrate, as shown in Figure 3. Initially, the substrate was dry, and sedimenting droplets deposited directly on the substrate. As water accumulated on the substrate, droplets tended to land on existing drops to produce larger drops, in a process known as incorporation.29 Over time, these growing drops touched and coalesced to form larger drops. These processes (deposition, incorporation, and coalescence) each contributed to the growth of the mean drop size displayed in Figure 4, which shows both drop radius and time in logarithmic scales. This study used textured substrates with relatively small gaps (54 μm pillars with 12 μm gaps), since the prominence of pillar-tops facilitated measurements of drop-size. Nevertheless, growth rates on substrates with larger gaps showed similar behavior (see Supporting Information Figure S1). The qualitative results from these experiments were similar to condensation experiments on textured substrates:12−15 droplets deposited both on-top-of and in-between pillars. At early times, deposition and growth on the tops of pillars were identical to that on smooth substrates. Over time, however, the edges of the pillars had an apparent aligning effect, which is somewhat visible in Figure 3a and readily apparent in Figure 3b. As drop sizes became comparable to the pillar size, a single drop became 12773
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Figure 3. Dark-field images of drops on a substrate with both textured (top-half) and smooth (bottom-half) regions. Note that these are not composite images: the smooth and textured halves were on the same substrate. These images show the substrate at four different times (a) t = 90 s, (b) t = 216 s, (c) t = 318 s, and (d) t = 930 s during the deposition process. The light source emphasized the edge of drops. Nevertheless, larger drops tended to focus and reflect scattered light, thus producing bright circles in the middle of some drops, as shown in (d).
where α(ϕ) is a constant determined by the desired surface coverage, and r0 is the radius of the wetted surface of a deposited droplet. For systems in which the contact angle is 90°, the critical surface coverage is ϕ∗ ≈ 0.62, which corresponds to α∗ ≈ 2.7 in simulations (see Ulrich et al.,29 Figure 12). Although the contact angle in our experiments was approximately 107°, their results provide a good approximation for the current study. Since the deposition rate in this study was constant, it can be expressed as
value.22,29 Because of the aforementioned limitations of our drop detection algorithm, we could accurately measure the narrow distribution of large drops but not the polydisperse distribution of small drops. This made quantitative estimates of the surface coverage, ϕ, difficult. Nevertheless, we qualitatively estimated that the surface coverage increased throughout the experiment, and we only saw the predicted self-similar distribution at late times in the experiment (see, e.g., the smooth region of Figure 3d). These observations strongly suggested that the present experiments were restricted to the transient regime of drop growth. Transient Regime. The transient regime was explored in simulations by Ulrich et al.29 They developed a criterion for the number of deposited droplets required to reach a desired surface coverage, ϕ, and found that the transition to steady-state growth occurred at a critical surface coverage, ϕ∗. The number of deposited droplets per unit area, n(ϕ), required to reach a surface coverage, ϕ, can be expressed as n=
α πr0 2
dn = cvs dt
(4)
where c is the concentration of droplets and vs is the sedimentation velocity given by eq 1. Integrating the deposition rate once and equating to eq 3 gives the critical time to reach steady state: α * τ = * cv πr 2 (5) s 0 Here, c ≈ 106 drops/cm3, r0 ≈ 2 μm, and vs ≈ 0.4 μm/s, which gives a time scale of τ∗ ≈ 10 min. This time scale is supported
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= 10 s (see also Fritter et al.22). Furthermore, r0 corresponds to the smallest drops in the system, which are approximately r0 ≈ 1 nm based on nucleation theory.15,37 Under these conditions, τ∗ ≈ 10 ms, which agrees with experimental observations that this transient time lasted less than 1 s.20,22 Note, however, that the transient regime can be extended by decreasing the flux of condensate (e.g., by reducing the flow rate of vapor or the degree of supersaturation). In the present deposition experiments, the longer transient regime corresponds to the time needed to develop the selfsimilar polydispersity observed in simulations22,28 and experiments:39,40 Here, the smallest drops are roughly three orders of magnitude larger than those in condensation. Thus, to develop the self-similar drop-size distribution, deposition must evolve significantly larger drops than those for condensation. As a result, condensation experiments typically focus on steady-state behavior, while the present deposition experiments were dominated by the transient regime and did not exhibit power-law behavior. Deposition on Textured Substrates. On the textured region, the mean-radii curve (red dots) in Figure 4 suggested three different growth regimes. This temporal evolution was due to spatial organization of accumulated drops. Thus, we first discuss the organizing effects of pillars before examining the temporal evolution of the mean drop size. Finally, we present preliminary results on late-stage coalescence, when drops on adjacent pillars touch. Spatial Organization. When drops were much smaller than the pillar tops, they were located randomly on the pillars, as they would be on smooth substrates. For larger drops, however, the pillars align drops and restrict them from spreading. In the top half of Figure 6, spatial histograms aggregate the locations of drop centers relative to the pillar width. Each histogram presents measurements for a different normalized radius, r̂ = r/ w, and the horizontal axis represents the x-(or y-)positions of drops along the width of the pillar, w. In the bottom half of the figure, representative drops touch opposite edges of a pillar; this graphic illustrates the tendency for small drops (Figure 6a and b) to cluster one radius away from the pillar edge. Note that drops smaller than r̂ = 0.1 (which were visible by eye but not identified by our drop detection method) were uniformly distributed over the substrate. As these undetected drops grew, however, the pillar edges appeared to enhance growth, and thus, we saw more drops of a detectable size (r̂ ≳ 0.1) near the edges. This alignment effect was somewhat visible with the small drops in Figure 3a and clearly visible with the larger drops in Figure 3b. As a small drop near the edge of a pillar grew, it was forced toward the center of the pillar; if, instead, the drop spread over the sharp edge of the hydrophobic pillar, the surface energy of that drop would increase. This enhanced drop movement promoted coalescence. As a result, drops near the edges of a pillar should grow faster than those near the center. While many drops appear near the center for r̂ = 0.1, few drops near the center were able to grow to r̂ = 0.2 before being absorbed by faster-growing drops near the edge. This effect was demonstrated by the modest peak in the center of Figure 6a and its disappearance in Figure 6b. As drops grew inward from the edges and reached a radius that was (on average) 1/4 of the pillar width, they coalesced to form significantly larger drops. If the two idealized drops in the bottom of Figure 6b grew simultaneously, they would touch when r̂ = 0.25. Since the pillar-tops were two-dimensional
Figure 4. Log−log comparison of mean drop radii for smooth and textured regions on the same substrate. For the smooth region (black dots), the mean radius grew continuously and smoothly. For the textured region (red dots), the mean radius exhibited three distinct regimes, each with a different slope (i.e., growth rate). The labels (a), (b), and (c) mark data corresponding to the images in Figure 3.
Figure 5. Evolution of the mean radius for drops on the smooth region of the substrate. The red dots mark the mean radii, and the gray region extends from the minimum to the maximum measured radii. Note that the 3/4 slope on this log−log plot is only meant as a reference; the slope grew continuously from roughly 2/3 to 0.9 during this time period. Periodically, the maximum measured radius jumped due to coalescence, e.g., at t = 315 and 426 s.
by the data presented in Figure 5: Toward the end of the experiment, the slope on the log−log plot increases to 0.9, approaching the linear behavior predicted for the self-similar regime. For comparison, we estimate the time required to reach the self-similar regime in condensation experiments. Since condensation does not involve deposition of droplets, we rewrite eq 5 in terms of the volumetric flux of condensate, Q: αr τ ∼ 0 * Q (6) This flux can be estimated from experiments as Q ∼ ϕΔ⟨r⟩/Δt, where Δ⟨r⟩ is the change in the mean radius a over time period Δt. To estimate τ∗, we focused on condensation experiments by Beysens and Knobler,20 where ϕ ≈ 0.4 and Δ⟨r⟩ ≈ 5 μm at Δt 12775
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Figure 6. Locations of drop centers relative to pillar edges. Each histogram (top) collects drops of a given radii ranging from (a) 1/10 to (e) 1/2 of the pillar width. Symbolic drops (bottom) represent the measured radii and are drawn touching the left and right edges of each pillar. Dotted vertical lines highlight the center location of hypothetical drops touching the edge of each pillar. These histograms aggregate measurements on 66 pillars from images taken over the course of 700 s at 3 s intervals. The x- and y-coordinates of drop centers were considered separate measurements such that each detected drop was counted twice in these histograms.
different growth regimes, which we named (1) weakly organized growth, (2) fast growth, and (3) monodisperse growth. The weakly organized regime describes the enhanced drop-growth along pillar edges, as observed in Figure 6a and b. The mean-radius measurements in Figure 4, however, suggested only a small increase in the growth rate compared to smooth substrates during this regime (i.e., from t = 100s to 240s). As discussed in the previous section, when the mean dropradius reached approximately 1/4 of the pillar width, crowding forced rapid coalescence, and this coalescence typically involved four drops. Thus, the mean drop radius on each pillar grew by approximately 60% in less than 1 s. Because this coalescence transition occurred at different times for each pillar, however, the fast-growth regime spanned approximately 80 s (t ≈ 240− 320 s). The variation in transition times was reflected by a jump in the standard deviation of the drop radii (blue triangles in Figure 7). At t ≈ 350 s, the minimum and maximum radii collapsed onto the mean radius; this monodisperse distribution was observed when the last small drops coalesced and left a single drop atop each pillar. (The growth rate of the mean diminished before the collapse of the minimum/maximum radii because the last few coalescences had a small affect on the mean radius.) Note that the increase in the mean drop radius was accompanied by a reduction in the total number of drops, since the deposition rate was constant. After the fast-growth regime, a single drop sat atop each pillar. The resulting drops were highly monodispersed: the radii in the monodisperse regime of Figure 7 had a standard deviation of 0.5 μm, which was less than a one-pixel difference in images. This highly ordered pattern formation was reminiscent of condensation on chemically patterned surfaces.17−19 Accompanying this organization was a sharp reduction in growth rate to ⟨r⟩ ∼ t1/3, which can be rationalized as follows: Since the monodisperse drops occupied most of the pillar surface, they incorporated all droplets impinging on the pillar. For a constant deposition rateor equivalently, volumetric fluxthe volume of each drop grew linearly in time, such that the radius grew as t1/3. Coalescence of Drops on Adjacent Pillars. When monodisperse drops grew sufficiently large to touch drops on adjacent pillars, they coalesced to form larger drops that spanned multiple pillars, as shown in Figure 8. Note that these preliminary results, unlike all other experimental results in this
surfaces (instead of the one-dimensional projection depicted in Figure 6), this coalescence typically involved four drops (e.g., notice that four drops sit atop most of the pillars in Figure 3b), which meant that drops would grow by a factor of 4 in volume and 60% in radius. This typical jump in size led to a scarcity of intermediate-size drops (Figure 6c), since drops jump from roughly 0.24w to 0.38w at this stage. A similar coordination of coalescence was observed when drops were spatially ordered during condensation (see e.g., Gau and Herminghaus19). This fast-growth regime was accompanied by a rapid transition from bimodal to unimodal histograms, since large drops (Figure 6d and e) occupied most of the pillar top and had to be near the center of the pillar. Temporal Evolution on Textured Substrates. The spatial organization described above influenced the evolution of the mean radius, which is replotted from Figure 4 as red dots on the log−log plot shown in Figure 7. As in Figure 5, a gray-filled region extends from the minimum detected radius to the maximum. Here, the slope of the mean-curve suggested three
Figure 7. Evolution of mean radius for drops on textured regions of the substrate. The mean radius of drops exhibited three growth regimes: (1) early time, weakly organized growth, during which pillars slightly enhanced spatial organization; (2) intermediate-time, fast growth, when crowding of drops enhanced coalescence; and (3) latetime, slow growth, during which drops were monodisperse. In the monodisperse regime, the minimum and maximum drop radii were nearly equal to the mean radius and growth was slowed to ⟨r⟩ ∼ t1/3. Note that this plot shows both radius and time on logarithmic scales. 12776
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Figure 8. Late-time coalescence on substrates with different pillar spacing (increasing pillar spacing from left to right). The higher curvature of suspended drops reflected more light at drop edges and produced brighter drops. These transparent substrates were prone to light scattering, producing bright rings visible in the middle of drops. Smaller pillar spacing reduced the likelihood of a wetting transition upon coalescence: (left) all drops remained suspended on pillars for small gaps, and (right) all drops wet the substrate for large gaps. Intermediate gaps (middle) supported both wetting and suspended drops, as highlighted by the inset schematics.
paper, were from substrates made of polydimethylsiloxane. When the pillar spacing was small (15 μm), the increased contact-line density increased the surface’s resistance to wetting,41 and all drops coalesced into the Cassie−Baxter state. For larger pillar spacing (27 μm), the resistance to wetting was reduced and coalescence led to wetting. At intermediate spacings (21 μm), drops could coalesce into either the Cassie−Baxter or Wenzel state, as observed in condensation experiments.13 It is interesting to note that the present experiments did not reveal the “drying” transitions observed by Narhe and Beysens,14 in which suspended drops flowed into the gaps between pillars and left the tops of pillars dry. Drops can wet the underlying substrate due to static or dynamic effects. In the static case, drops can “sag” (or “droop”) due to their Laplace pressure and transition to the Wenzel state.42,43 In the present study, this phenomenon was exacerbated by drops deposited in-between pillars that reduced the effective pillar height. In addition to this static effect, the dynamics of the coalescence process could also promote wetting. The high fluid pressures and velocities generated by coalescing drops44−47 could drive a transition to the Wenzel state, much like the wetting transitions observed in drop impacts on microtextured surfaces.48,49 A more detailed study would be required to determine the relative importance of static and dynamic effects.
coalesce and pattern formation in deposited films. When these drops grew large enough to span multiple pillars, they coalesced into either the Cassie−Baxter or Wenzel states. On closely spaced pillars, drops preferred the Cassie−Baxter state over the duration of these experiments, but longer time scales are worth consideration: As deposition progresses, drops will fill the troughs between pillars and could pull suspended drops down from the tops of pillars (see Narhe and Beysens 14). Alternatively, the suspended drops could pull drops out from the troughs (see Dorrer and Rühe13). Further study of late time behavior will shed light on the robustness of superhydrophobic surfaces in foggy conditions.
CONCLUSION In this paper, we investigated the deposition of water droplets on both smooth and textured substrates. On smooth substrates, the behavior was qualitatively similar to condensation experiments in the literature, but deposition experiments were dominated by a transient regime of growth, instead of the selfsimilar regime typically observed in condensation experiments. Estimates of the surface coverage were consistent with expectations for the transient regime, but more meticulous drop-size measurements are required to produce convincing measurements of the surface coverage. On textured substrates, square pillars induced a monodisperse regime, during which a single drop sat atop each pillar. This enhanced spatial organization suggests a promising tool for controlling drop
ACKNOWLEDGMENTS This research was supported by the Korea Institute of Machinery and Materials.
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ASSOCIATED CONTENT
S Supporting Information *
Figure S1 showing the monodisperse growth regime for a substrate with a wide pillar-spacing, and Figure S2 showing example results from the automated drop detection algorithm. This material is available free of charge via the Internet at http://pubs.acs.org/.
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Bico, J.; Marzolin, C.; Quere, D. Pearl drops. Europhys. Lett. 1999, 47, 220−226. (2) Lafuma, A.; Quere, D. Superhydrophobic states. Nat. Mater. 2003, 2, 457−460. (3) Wier, K.; McCarthy, T. Condensation on ultrahydrophobic surfaces and its effect on droplet mobility: Ultrahydrophobic surfaces are not always water repellant. Langmuir 2006, 22, 2433−2436. (4) Guha, A. Transport and deposition of particles in turbulent and laminar flow. Annu. Rev. Fluid Mech. 2008, 40, 311−341.
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(5) Kwok, P. C. L.; Chan, H.-K. Electrostatics of pharmaceutical inhalation aerosols. J. Pharm. Pharmacol. 2009, 61, 1587−1599. (6) Hamilton, W. J.; Seely, M. K. Fog basking by namib desert beetle, onymacris-unguicularis. Nature 1976, 262, 284−285. (7) Seely, M. K.; Hamilton, W. J. Fog catchment sand trenches constructed by tenebrionid beetles, lepidochora, from namib desert. Science 1976, 193, 484−486. (8) Seely, M. Irregular fog as a water source for desert dune beetles. Oecologia 1979, 42, 213−227. (9) Parker, A. R.; Lawrence, C. R. Water capture by a desert beetle. Nature 2001, 414, 33−34. (10) Martorell, C.; Ezcurra, E. The narrow-leaf syndrome: A functional and evolutionary approach to the form of fog-harvesting rosette plants. Oecologia 2007, 151, 561−573. (11) Vogel, S.; Muller-Doblies, U. Desert geophytes under dew and fog: The “curly-whirlies” of Namaqualand (South Africa). Flora 2011, 206, 3−31. (12) Chen, C.-H.; Cai, Q.; Tsai, C.; Chen, C.-L.; Xiong, G.; Yu, Y.; Ren, Z. Dropwise condensation on superhydrophobic surfaces with two-tier roughness. Appl. Phys. Lett. 2007, 90, 173108. (13) Dorrer, C.; Rühe, J. Condensation and wetting transitions on microstructured ultrahydrophobic surfaces. Langmuir 2007, 23, 3820− 3824. (14) Narhe, R. D.; Beysens, D. A. Growth dynamics of water drops on a square-pattern rough hydrophobic surface. Langmuir 2007, 23, 6486−6489. (15) Varanasi, K. K.; Hsu, M.; Bhate, N.; Yang, W.; Deng, T. Spatial control in the heterogeneous nucleation of water. Appl. Phys. Lett. 2009, 95, 094101. (16) Epstein, N. Elements of particle deposition onto nonporous solid surfaces parallel to suspension flows. Exp. Therm. Fluid Sci. 1997, 14, 323−334. (17) Lopez, G. P.; Biebuyck, H. A.; Frisbie, C. D.; Whitesides, G. M. Imaging of features on surfaces by condensation figures. Science 1993, 260, 647−649. (18) Kumar, A.; Whitesides, G. Patterned condensation figures as optical diffraction gratings. Science 1994, 263, 60−62. (19) Gau, H.; Herminghaus, S. Ripening of ordered breath figures. Phys. Rev. Lett. 2000, 84, 4156−4159. (20) Beysens, D.; Knobler, C. Growth of breath figures. Phys. Rev. Lett. 1986, 57, 1433−1436. (21) Viovy, J.; Beysens, D.; Knobler, C. Scaling description for the growth of condensation patterns on surfaces. Phys. Rev. A 1988, 37, 4965−4970. (22) Fritter, D.; Knobler, C.; Beysens, D. Experiments and simulation of the growth of droplets on a surface (breath figures). Phys. Rev. A 1991, 43, 2858−2869. (23) Briscoe, B.; Galvin, K. The evolution of a 2d-constrained growth system of droplets - breath figures. J. Phys. D: Appl. Phys. 1990, 23, 422−428. (24) Briscoe, B.; Galvin, K. Growth with coalescence during condensation. Phys. Rev. A 1991, 43, 1906−1917. (25) Meakin, P. Droplet deposition growth and coalescence. Rep. Prog. Phys. 1992, 55, 157−240. (26) Cueille, S.; Sire, C. Droplet nucleation and Smoluchowski’s equation with growth and injection of particles. Phys. Rev. E 1998, 57, 881−900. (27) Adamczyk, Z.; Siwek, B.; Zembala, M.; Belouschek, P. Kinetics of localized adsorption of colloid particles. Adv. Colloid Interface Sci. 1994, 48, 151−280. (28) Family, F.; Meakin, P. Kinetics of droplet growth-processes: Simulations, theory, and experiments. Phys. Rev. A 1989, 40, 3836− 3854. (29) Ulrich, S.; Stoll, S.; Pefferkorn, E. Computer simulations of homogeneous deposition of liquid droplets. Langmuir 2004, 20, 1763−1771. (30) Blackman, J.; Brochard, S. Polydispersity exponent in homogeneous droplet growth. Phys. Rev. Lett. 2000, 84, 4409−4412.
(31) Donnelly, T. D.; Hogan, J.; Mugler, A.; Schommer, N.; Schubmehl, M.; Bernoff, A. J.; Forrest, B. An experimental study of micron-scale droplet aerosols produced via ultrasonic atomization. Phys. Fluids 2004, 16, 2843−2851. (32) Donnelly, T. D.; Hogan, J.; Mugler, A.; Schubmehl, M.; Schommer, N.; Bernoff, A. J.; Dasnurkar, S.; Ditmire, T. Using ultrasonic atomization to produce an aerosol of micron-scale particles. Rev. Sci. Instrum. 2005, 76, 113301. (33) Illingworth, J.; Kittler, J. The adaptive hough transform. IEEE Trans. Pattern Anal. Mach. Intell. 1987, 9, 690−698. (34) Hozumi, A.; Ushiyama, K.; Sugimura, H.; Takai, O. Fluoroalkylsilane monolayers formed by chemical vapor surface modification on hydroxylated oxide surfaces. Langmuir 1999, 15, 7600−7604. (35) Lim, H.; Jung, D.; Noh, J.; Choi, G.; Kim, W. Simple nanofabrication of a superhydrophobic and transparent biomimetic surface. Chin. Sci. Bull. 2009, 54, 3613−3616. (36) Kundu, P.; Cohen, I. Fluid Mech. 2004. (37) Beysens, D. The formation of dew. Atmos. Res. 1995, 39, 215− 237. (38) Fritter, D.; Knobler, C. M.; Roux, D.; Beysens, D. Computer simulations of the growth of breath figures. J. Stat. Phys. 1988, 52, 1447−1459. (39) Zinke-Allmang, M.; Feldman, L.; Van Saarloos, W. Experimental study of self-similarity in the coalescence growth regime. Phys. Rev. Lett. 1992, 68, 2358−2361. (40) Søndergård, E.; Kofman, R.; Cheyssac, P.; Stella, A. Production of nanostructures by self-organization of liquid Volumer-Weber films. Surf. Sci. 1996, 364, 467−476. (41) Extrand, C. Model for contact angles and hysteresis on rough and ultraphobic surfaces. Langmuir 2002, 18, 7991−7999. (42) Patankar, N. A. Consolidation of Hydrophobic Transition Criteria by Using an Approximate Energy Minimization Approach. Langmuir 2010, 26, 8941−8945. (43) Jung, Y. C.; Bhushan, B. Wetting transition of water droplets on superhydrophobic patterned surfaces. Scr. Mater. 2007, 57, 1057− 1060. (44) Eggers, J.; Lister, J.; Stone, H. Coalescence of liquid drops. J. Fluid Mech. 1999, 401, 293−310. (45) Menchaca-Rocha, A.; Martnez-Dávalos, A.; Nunez, R.; Popinet, S.; Zaleski, S. Coalescence of liquid drops by surface tension. Phys. Rev. E 2001, 63, 046309. (46) Boreyko, J. B.; Chen, C. H. Self-propelled dropwise condensate on superhydrophobic surfaces. Phys. Rev. Lett. 2009, 103, 184501. (47) Eiswirth, R.; Bart, H.; Ganguli, A.; Kenig, E. Experimental and numerical investigation of binary coalescence: Liquid bridge building and internal flow fields. Phys. Fluids 2012, 24, 062108. (48) Bartolo, D.; Bouamrirene, F.; Verneuil, É.; Buguin, a.; Silberzan, P.; Moulinet, S. Bouncing or sticky droplets: Impalement transitions on superhydrophobic micropatterned surfaces. EPL 2006, 74, 299. (49) Deng, T.; Varanasi, K. K.; Hsu, M.; Bhate, N.; Keimel, C.; Stein, J.; Blohm, M. Nonwetting of impinging droplets on textured surfaces. Appl. Phys. Lett. 2009, 94, 133109.
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dx.doi.org/10.1021/la301901m | Langmuir 2012, 28, 12771−12778
