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Difference in growth and coalescing patterns of droplets on bi-philic surfaces with varying spatial distribution
Accepted Manuscript Difference in growth and coalescing patterns of droplets on bi-philic surfaces with varying spatial distribution Martand Mayukh Garimella, Sudheer Koppu, Shantanu Shrikant Kadlaskar, Venkata Pillutla, Abhijeet, Wonjae Choi PII: DOI: Reference:
S0021-9797(17)30765-8 http://dx.doi.org/10.1016/j.jcis.2017.06.099 YJCIS 22526
To appear in:
Journal of Colloid and Interface Science
Received Date: Revised Date: Accepted Date:
4 May 2017 29 June 2017 29 June 2017
Please cite this article as: M.M. Garimella, S. Koppu, S.S. Kadlaskar, V. Pillutla, Abhijeet, W. Choi, Difference in growth and coalescing patterns of droplets on bi-philic surfaces with varying spatial distribution, Journal of Colloid and Interface Science (2017), doi: http://dx.doi.org/10.1016/j.jcis.2017.06.099
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Difference in growth and coalescing patterns of droplets on bi-philic surfaces with varying spatial distribution Martand Mayukh Garimella, Sudheer Koppu, Shantanu Shrikant Kadlaskar, Venkata Pillutla, Abhijeet and Wonjae Choi* Department of Mechanical Engineering, University of Texas at Dallas, 800 W. Campbell Road, Richardson, TX 75080 * Corresponding author: [email protected]
Keywords: Condensation; water harvesting; bi-philic surfaces; hydrophobicity; hydrophilicity
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Abstract This paper reports the condensation and subsequent motion of water droplets on bi-philic surfaces, surfaces that are patterned with regions of different wettability. Bi-philic surfaces can enhance the water collection efficiency: droplets condensing on hydrophobic regions wick into hydrophilic drain channels when droplets grow to a certain size, renewing the condensation on the dry hydrophobic region. The onset of drain phenomenon can be triggered by multiple events with distinct nature ranging from gravity, direct contact between a droplet and a drain channel, to a mutual coalescence between droplets. This paper focuses on the effect of the length scale of hydrophobic regions on the dynamics of mutual coalescence between droplets and subsequent drainage. The main hypothesis was that, when the drop size is sufficient, the kinetic energy associated with a coalescence of droplets may cause dynamic advancing of a newly formed drop, leading to further coalescence with nearby droplets and ultimately to a chain reaction. We fabricate bi-philic surfaces with hydrophilic and hydrophobic stripes, and the result confirms that coalescing droplets, when the length scale of droplets increases beyond 0.2 mm, indeed display dynamic expansion and chain reaction. Multiple droplets can thus migrate to hydrophilic drain simultaneously even when the initial motion of the droplets was not triggered by the direct contact between the droplet and the hydrophilic drain. Efficiency of drain due to mutual coalescence of droplets varies depending on the length scale of bi-philic patterns, and the drain phenomenon reaches its peak when the width of hydrophobic stripes is between 800 m and 1 mm. The Ohnesorge number of droplets draining on noted surfaces is between 0.0042 and 0.0037 respectively. The observed length scale of bi-philic patterns matches that on the Stenocara beetle’s fog harvesting back surface. This match between length scales suggests that the surface of the insect is optimized for the drain of harvested water. 2
I. Introduction This paper discusses the heterogeneous condensation (simply ‘condensation’ hereafter, for brevity) of water on surfaces patterned with regions of different wettabilities. Condensation phenomenon is ubiquitous in nature. We observe condensation on solid surfaces where we observe temperature difference and moisture, such as window panes, cold drink bottles and various heat exchangers [1]. Condensation rate is highly associated with the wettability of solid surfaces. Hydrophilic surfaces (surfaces on which water forms a Young’s contact angle < 90°) promote initial condensation, because the high surface energy of hydrophilic surfaces facilitates the adhesion of water molecules on the surface. But the same hydrophilicity typically leads to the formation of a water film on the solid surface as condensation process continues. Such a film drastically lowers the subsequent condensation of water, due to the low heat conductivity of the water layer. In contrast, the initial condensation rate of water on a hydrophobic surface ( > 90°) is lower than on a hydrophilic surface, as a hydrophobic surface is more stable in a dry state [2]. Once a drop condenses on a hydrophobic surface, however, the drop beads up rather than spreads to form a film. Drops beading up on a tilted surface roll off with relative ease, exposing the dry hydrophobic surface for another cycle of condensation. Therefore, although the initial nucleation rate is lower, long-term steady-state condensation rate is higher on a hydrophobic surface [2]. Noted roll-off phenomenon of droplets is vital for a hydrophobic surface to renew its dry area for further condensation, so the critical radius for a drop to roll-off the surface heavily influences the efficiency of condensation heat transfer or water collection. On a hydrophobic surface tilted by a certain angle, a drop begins to roll when the gravitational pull is greater than the adhesive force due to the contact angle hysteresis. Gravity-driven roll-off of droplets has been a topic of academic interest for decades, and a model by Furmidge [3] (later revised by 3
Extrand and Gent [4]) can predict the critical size for a quasi-static drop to roll-off a tilted surface. The model predicts that, for example, a water drop would begin to roll at a diameter of 2.08 mm on a vertically tilted hydrophobic surface with a moderate hysteresis (PTFE-coated silicon wafer with = 112°, contact angle hysteresis = 23°). The issue is that it takes significant time (6 minutes on our PTFE coated silicon wafer) for a drop to grow by condensation to reach 2 mm diameter. Thus a method to facilitate the drain of nucleating droplets can have a significant impact on the efficacy of condensation and water collection. One approach to reduce the critical radius for a droplet to leave the hydrophobic region is to make bi-philic surfaces (Fig. 1) [5, 6, 7, 8], surfaces patterned with hydrophilic and hydrophobic regions. Bi-philic surfaces were originally inspired by Namib Stenocara beetle [6, 9], which collects fog water using its back surface patterned with hydrophilic and hydrophobic patches. Bi-philic surfaces offer dual advantage over homogeneous hydrophilic or hydrophobic surfaces for condensation process. First, one can localize the formation of liquid film only on the hydrophilic region, which will serve as a drain path for condensing water. Second, droplets nucleating on the hydrophobic region leave the area when the droplets contact the hydrophilic drains, renewing the dry hydrophobic region for subsequent nucleation. Eventually, bi-philic surfaces have potential to offer higher and sustainable rates of water collection or heat transfer [6, 10]. Bi-philic surfaces, therefore, have become a topic of significant interest recently [6, 7, 9, 11, 12, 10]. These papers have given quantitative evidence of selective condensation, improved condensation rates, efficiency of fog collection, or higher heat transfer coefficient. One interesting observation on natural bi-philic surfaces on Stenocara beetle, an insect that harvests fog droplet on its back, is that the hydrophobic and hydrophilic patches have specific length scale of 1 mm and 500 microns respectively [9]. Research using synthetic bi-philic surfaces also 4
revealed that the efficacy of water collection reaches its maximum when the length scale of patterned regions is around the noted values [11]. Although the deposition of fog droplets and the condensation of dew droplets are not exactly the same, the rates of both phenomena are affected by the efficiency of drainage [12, 13]. We thus hypothesized that the observed dependence of the efficiency of water collection on the length scale of bi-philic patterns is due to the difference in drain rate. This paper thus investigates the effect of the variation of the spatial distribution of biphilic patterns on the growth, coalescing patterns and draining motion of droplets. In particular, we focus on the mutual coalescence of droplets leading to subsequent coalescence with neighboring droplets (chain reaction), ultimately to the simultaneous drainage of multiple droplets. For better insight, we have maintained a constant areal ratio between the hydrophobic (67%) and hydrophilic (33%) regions, while changing only the length scale of patterns. In conjunction with the referred papers, our results would give proper direction in choosing optimized spatial distribution for applications intended. The scope of this paper includes the motion of water droplets on bi-philic surfaces and the corresponding increase of water collection, but the paper does not investigate the effect of bi-philic surfaces on heat transfer. Although it is not the focus of this paper, another way to enhance condensation is to use super-hydrophobic or super-hydrophilic surfaces [5, 14]. Textured surfaces with extreme wettability can lead to interesting phenomena such as jumping droplets [12, 14] or fast wicking [15, 16, 17]. Although there are some open questions on the practical applicability of noted phenomena (e.g., jumping droplet phenomenon occurs only at low condensation rate regime, as the liquid-air interface on textured surfaces lose its stability at high condensation rate [12]), such surfaces can potentially promote the condensation or water collection efficiency beyond that on smooth surfaces. We limit the scope of this paper to the condensation on smooth hydrophobic
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and hydrophilic surfaces, to maintain the complexity of the problem to be manageable. We believe the findings from this research are general enough to be applicable for textured surfaces as well.
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II. Materials and Methods Fabrication of bi-philic surfaces: Four inch test grade p-type silicon wafers, purchased from University Wafers, with thickness of 500–525 m were used in this research. Native oxide layer was removed by 2-minute treatment with hydrofluoric acid in the acid hood, followed by a UVozone treatment in Samco UV ozone stripper/cleaner at UT Dallas clean room laboratory. Standard photolithography with S1813 photoresist and MF 319 developer was performed using CEE spin coater and Karl Suss MA6B Contact Printer provided in the clean room, to define patterns for regions with different wettability. PTFE layer was then deposited on samples through a 10 minute sputtering process at 100 W power and 4·10 -7 mTorr in A.J.A. Orion sputtering equipment. Photoresist layer was then stripped by acetone cleaning, to expose hydrophilic regions. The thickness of PTFE layer was measured by Dektak 8 profile meter, to be ~ 20 nm. Surface characterization: Rame-Hart 260 goniometer as used to determine contact angles of water droplets on surfaces. Water contact angle on PTFE-covered hydrophobic area was 112°±3° and the angle on (UV-ozone treated) hydrophilic area was ~0° respectively. While the contact angle on PTFE-covered area was constant after 48 hours, the angle on hydrophilic area increased up to ~20° over 10 hours. In this study, all observations on drop coalescence and condensation were performed within 3 hours after sample fabrication so that the contact angle on hydrophilic area remained below 10°.
Condensation: Silicon wafers with bi-philic patterns were mounted vertically, with a vaporizer unit placed 5 cm below, and 3 cm away, to prevent any mist droplets from vaporizer to reach surfaces. Steam required for condensation was developed using commercial vaporizer V150SGN 7
(KAZ incorporated) that was maintained at 95°~97° and 100% relative humidity. Backside of the wafers was exposed to room temperature, and all experiments were performed at atmospheric pressure. High speed image capture and analysis: The enhancement of efficiency of water collection has already been proven through measuring the amount of water collected by bi-philic surfaces [8, 11]. The focus of this study is, however, the mechanism that causes noted enhancement. For this goal, it is necessary to capture the dynamic motion of water droplets on bi-philic surfaces. Image analysis provides us with pictorial evidence of chain coalescence, and droplet wicking, and how they contribute towards enhancing condensation efficiency of bi-philic surfaces, as compared to homogeneous hydrophilic and hydrophobic surfaces. Sample surfaces were exposed to steam generated using a vaporizer and the growth patterns of droplets were captured at different stages of condensation using SA4 Photron high speed camera, at the resolution of 1024 × 1024 pixels and 2000 fps. Most images and movie clips were used to understand the dynamic motion of droplets. Data for the graph in Figure 8 were generated using Measure and Analyze add-on of ImageJ software.
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III. Results and Discussion Coalescence-induced motion of sessile drops: Shortly after the beginning of condensation process, droplets start to coalesce with nearby droplets. When two very small, quasi-static droplets (i.e., the flow remains in Stokes regime) coalesce on a hypothetical, hysteresis-free surface, a simple calculation based on the weighted average of the centers of the masses of parent drops may predict the center of the merger [18]. In this scenario, the outer perimeter of the merger (dotted line in Fig. 2) contracts from the perimeters of the parents along the axial direction (L in Fig. 2) and expands along the transverse direction (W in Fig. 2) [19]. Therefore, such a hypothetical coalescence can lead to subsequent coalescence with a neighboring droplet located along the transverse direction (see droplet G in Fig. 2), but not with a droplet along the axial direction (droplet R). Noted limited chance for the chain reaction leads the growth by coalescence to quickly saturate, that is, after one or two coalescence events, merger drops can grow only by further condensation or by trivial coalescence with tiny neighboring droplets that form by later condensation. As a result, prolonged condensation typically results in the formation of large and quasi-static drops (see Fig. 2C), who cover large portion of the surface and function as an insulation layer due to the low heat conductivity of water. Such a saturated state can be renewed only when these drops grow sufficiently large (e.g., ~ 2.1 mm as was discussed in section I) and roll off the surface. This renewal by gravity is, however, inefficient because the growth of a drop drastically slows down as its size increases. One of the key findings of this research is that one can overcome this limitation by using the bi-philic surfaces with appropriate length scale. Our experiments suggest that, the mutual coalescence between droplets, when their diameter is around 200 m or larger, leads to various types of chain reaction some of which are not expected by the simple model shown in Fig. 2. Empirical results show that the chain reaction 9
can occur along the axial as well as transverse directions, facilitating simultaneous drain of multiple droplets. Fig. 3 shows one example of the mutual coalescences between two droplets, leading to a chain reaction with another droplet that is located along the axial direction of the two parent droplets. Drop A and B merge by direct contact, forming a merger (Drop D). Drop D oscillates after the coalescence, and touches its neighbor (Drop C) that is located along the axial direction of the original coalescence. The second coalescence leads to the formation of the final merger, Drop E. Note that the observed chain reaction is not predicted by the simple model shown in Fig. 2. It is also interesting that the center of the mass of the final merger E is significantly off the location of the center of three parent drops. There are two mechanisms that may cause noted dynamic coalescence and subsequent chain reaction. First, the difference in surface energies of the two parent drops and the merger partially converts into a dynamic flow inside the merger. Multiple studies investigated this phenomenon [18, 20] and used the dimensionless Ohnesorge number [21] to characterize the flow associated with the coalescence of two equal-sized drops. The Ohnesorge number in this research is defined as:
Oh =
d
(1)
Where, Oh is the Ohnesorge number, μ and ρ are dynamic viscosity and density of water, σ is the surface tension of water and d is the diameter of the merger drop. The Ohnesorge number associated with merger Drop D in Fig. 3 is estimated to be 0.0015, which suggests the kinetic energy of the coalescing flow is sufficient for Drop D to overcome the viscous dissipation and to display substantial translation or oscillation. Note that the Ohnesorge number for commonly 10
occurring 3 mm-sized raindrops drops is ~ 0.002. For two equal-sized drops, the kinetic energy can only create symmetric motions, such as oscillations without any change in the center of mass. For two unequal-sized drops, the merger can exhibit both oscillatory motion and translational motion leading to subsequent coalescence with neighboring drops: asymmetric translational motion can occur because the coalescence-induced flow inside the merger can be asymmetric between two droplets when the sizes of the parent droplets are unequal. Such coalescence typically causes the smaller droplet to flow into the larger droplet due to the difference in Laplace pressures inside two drops. Indeed, comparing Figs. 3A and 3G clearly shows that the center of mass of Drop D is significantly different from the weighted average between Drops A and B. Although the anisotropic coalescence may lead to the transition of the merger, the degree of drop expansion per se, a measure of kinetic energy stored in the merger drop, is primarily related to the Ohnesorge number not the anisotropy between the sizes of parent drops (see Fig. S1 in Supporting Materials). Second, the neck formation in the early phase of coalescence generates a fast moving capillary wave (Figs. 3B~C and 3H~I). The speed of the neck formation is determined by the Reynolds number of the coalescence process [22], which in turn depends on the Ohnesorge number. This surface wave can reach the outer edge of a drop before the bulk flow makes the drop shrink [23, 24, 25, 26]. This effect is clear between Fig. 3G and 3K, where the outer periphery of the merger E momentarily extends beyond that of the parent Drop C (see the red dashed line). Although such a momentary expansion quickly dissipates between Fig. 3K and 3L, the same phenomenon can lead to subsequent coalescence if there is a neighboring drop. Noted axial expansion of the merger drop is a counterpart to a well-known “jumping droplet” phenomenon, a phenomenon that the merger displays strongly transverse expansion due to the
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difference in surface energy when two equal-sized droplets merge [14]. These two mechanisms – the bulk motion of the merge due to excessive surface energy, and the surface waves from neck formation – can make each coalescing event to lead to another, ultimately to a long chain of coalescence events along various directions.
Mutual coalescence leading to simultaneous drainage of multiple droplets: Fig. 4 shows a typical example that a chain reaction leads to the simultaneous drainage of multiple droplets. Droplets A and B coalesce at time = 0 ms, and the merger (Drop C) expands laterally to contact its neighbor (Drop D; see t = 2 ms to 3 ms). Subsequent coalescence of Drop C and Drop D leads to the formation of merger E, which displays axial expansion (arguably due to surface waves) to contact the hydrophilic channel (note the bulging meniscus on the channel to the left of Drop E; t = 4 ms). Same drop also expands laterally to contact droplet F (t = 5 ms), and finally merger G drains into the hydrophilic region driven by the difference in surface wettability (t = 9 ~ 12 ms). All these coalescing motions occur within 12 ms, suggesting that this simultaneous drainage was triggered only by the first coalescence, not by additional condensation or gravity. Noted chain reaction renews a large area (Circled area in the last panel of Fig. 4) for fresh nucleation. Chaudhry et.al reported a similar renewal phenomenon accelerated by the mutual coalescence of droplets [27]. Their work was, however, based on a hydrophobic surface with surface energy gradient so that any coalescence between droplets becomes converted into a directional motion of mergers. Our work, on the other hand, investigates a random motion of mergers leading to the simultaneous drain of multiple droplets occurring on bi-philic surfaces. Chain reaction due to axial and lateral expansion can propagate across multiple hydrophobic regions. Fig. 5 shows an example. Drop A and B coalesce at time = 0 ms, and the 12
merger (drop C) laterally expands to contact hydrophilic regions (regions H and E at t = 30 ms ~ 60 ms). The majority of drop mass flows to region H, as the drop contacts this region first. Due to the substantial inertia of the motion of merger C, the frontal end of the drop surpasses the boundary of hydrophilic region H, ultimately to touch a next drop (Drop D; t = 60 ms). New merger (Drop G) repeats the expansion and touch the next hydrophilic strip (region F; t = 70 ms), although the majority of the mass flows to the first hydrophilic drain (H). Observed expansion (Drop G to region F) to a direction opposite to motion of the main drop (Drop G to region H), is arguably due to the surface wave discussed previously (see Fig. 3). Effect of length scale on the efficacy of chain reaction: The strength of both mechanisms that drive chain reaction – i) the conversion of the interfacial energy to the bulk motion of the merger, and ii) the surface waves momentarily extending the outer periphery of the merger – depend on the non-dimensional viscosity or the Ohnesorge number (Oh). Figs. 6 and 7 show the coalescing patterns of droplets on four surfaces with bi-philic patterns of same areal ratio (67% hydrophobic, 33% hydrophilic) but with different length scales. One length scale is chosen to be similar to that of Namib Stenocara beetle (1 mm and 0.5 mm for the hydrophobic and hydrophilic stripes). Assuming that the diameter of commonly occurring droplets to be roughly half of the width of hydrophobic stripes (see Fig. 6), Oh numbers for water droplets on the four surfaces are, in the ascending order of the length scale of patterns, 0.0083, 0.0042, 0.0037 and 0.0026 respectively. The initial nucleation and coalescence on bi-philic surfaces with different length scales is shown in Fig. 6. On surface A, droplets on the hydrophobic stripes wick into hydrophilic channels mostly through direct contact, because droplets can grow only up to 200 μm before they contact the drain. Time for a droplet to grow to 200 μm is relatively short (~5 seconds), so the 13
condensation is constantly renewed during the initial phase. However, on the same surface, as the hydrophilic channel is very narrow (100 μm), the drain flow is insignificant (the cross sectional area of an open channel flow is proportional to the cube of its width). Insufficient drainage causes large drops to appear on hydrophilic channels [28] (see Fig. 6A). Once these drops appear, their further growth decreases the Laplace pressure inside the drop, reducing the driving force for drain even lower. As a result, these drops remain in a quasi-static state until gravity pulls them down. On Surfaces B and C, each of which has 800 m / 400 m and 1 mm / 0.5 mm pattern widths, droplets nucleate, coalesce and grow on the hydrophobic stripes. Proximity between the droplets on the hydrophobic stripes leads to the chain reaction of coalescence which causes those droplets to either form a merger drop at the center of the hydrophobic stripes or wick into the hydrophilic channels as shown in Figs. 4 and 5. As the hydrophilic channels are much wider on Surfaces B and C than on A, water can easily flow along such channels and thus clogging of the hydrophilic channels by large drops occurs in rarity (see Figs. 6B, 6C). Even when it occurs, unlike the drops on Surface A, drops that clog the hydrophilic channels on Surfaces B and C roll down the surface with relative ease (see Fig. S2 in Supporting Materials). This difference is because the resistance against drop rolling is proportional to the number of the hydrophilic stripes beneath the drop: the borderlines between hydrophobic and hydrophilic stripes are not perfectly straight, and the meniscus of a water drop becomes pinned on the asperities at the borderlines [29, 30]. Each rolling-off drop carries the surrounding droplets with them (see Fig. S2), clearing a large chunk of space for fresh nucleation. Surface D with 2 mm (hydrophobic) and 1 mm (hydrophilic) pattern widths do not display any sign of channel clogging. However, the probability of the chain reaction on 14
hydrophobic stripes reaching hydrophilic channels also diminishes due to the excessively large width of hydrophobic channels, and thus large drops, similar to the ones in Fig. 2C, begin to form at the center of hydrophobic stripes (compare Fig. 6D and Fig. 7D). A steady state is reached on all patterns by 15 minutes of condensation. The state shown in Fig. 7 remains essentially the same after 15 minutes, as the condensation and drain phenomena balance one another. In the case of Surface A, the condensation of droplets becomes drastically inefficient as large drops form over multiple hydrophobic stripes and hydrophilic channels (Fig. 7A). The diameters of these drops are of the scale of 2 mm (average). These drops function as condensation barrier due to the poor thermal conductivity of water, and also block the hydrophilic drains [28]. Although these drops eventually roll off Surface A to wipe out large chunks of area, the frequency of drop shedding is very low as the rate of growth of those large drops is insignificant. Surfaces B and C deliver best results with regards to droplet shedding. Due to the chain reaction of droplet coalescences and the subsequent drainage of multiple droplets into hydrophilic channels, the surface is ensured to be relatively dry compared to other surfaces (see Fig. 7B and 7C). Even though a similar chain reaction among droplet coalescences exists on surface D, the renewal of hydrophobic regions is much slower on Surface D due to the excessive width of hydrophobic stripes. On Surface D, chain reactions tend to cause the formation of bigger drops in the middle of hydrophobic stripes rather than the drainage into hydrophilic stripes (see Fig. 7D). Once formed, these drops do not readily drain into hydrophilic channels even when in contact with newly formed small droplets. These drops leave the surface only when the drop is large enough to fall due to gravity, which takes as long time as the large drops shown in Fig. 7A. 15
Analysis on the fraction of dry area: Water collection through condensation is heavily affected by the fraction of the dry area available for the nucleation of droplets. Therefore, an experimental analysis was performed to compare the areal fraction of the dry region on Surfaces A, B, C and D; the analysis was performed twice with the condensation patterns obtained at 5 and 15 minutes from the start of condensation. Only the hydrophobic area was used for computation, as all hydrophilic channels become fully wetted shortly after the initial phase of the experiment. Considering the fact that drop growth drastically slows down with its size, it is reasonable to assume that the area covered by large drops is essentially not useful for further condensation. 240 μm in diameter is chosen as the threshold size to determine such ‘large drops.’ The choice of 240 m is based on the observation that droplets reach that size within tens of seconds by condensation. Also, the resolution limit of obtained images did not allow accurate calculation of droplet area for small droplets below 240 m diameter. (Note that an analysis based on the threshold value of 300 m leads to different values for the areal fractions on four surfaces, but the relative rank of surfaces does not change; see Fig. S3). One needs to be extra cautious to analyze the condensation pattern on Surface A (200 m / 100 m pattern widths), as there cannot be any droplets reaching 240 µm diameter on Surface A unless drops cover multiple channels. Therefore, only such large drops were taken into account to calculate the areal fraction on Surface A. Fig. 8 shows the result: at 5 minutes from the start of condensation, the areal fraction of the dry region is 45-65% of the total hydrophobic area (dark gray bars in Fig. 8) for Surfaces A to D. All surfaces thus allow substantial amount of condensation of new droplets. With time, however, the areal fraction of the dry region drastically reduces to 13% and 11% on Surface A 16
and Surface D respectively, while the fraction remains relatively the same on Surface B and Surface C (76% and 60% of the hydrophobic region remains dry as shown with light gray bars in Fig. 8). It can be inferred that patterns on Surface B (800 m and 400 m widths for hydrophobic and hydrophilic channels) provide best results in terms of droplet drainage and the renewal of hydrophobic region. Interestingly, the length scale of bi-philic patterns on Surfaces B and C matches that of the hydrophobic / hydrophilic patterns on the Stenocara beetle’s fog harvesting back surface. This match between length scales supports our hypothesis that the wetting / non-wetting patterns on the insect’s back have evolved to maximize the efficiency of water harvesting through optimal drainage. It should be noted that the outcome from this experiment should be taken only as a qualitative guideline for designing bi-philic surfaces, and the optimum length scale for any specific bi-philic pattern would vary depending on the shape of hydrophobic / hydrophilic regions.
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Conclusion This paper gives a scaling analysis to understand the enhancement of water collection on biphilic surfaces, a phenomenon that has recently attracted interest from fluid physicists and engineers [5-11]. We tested a hypothesis that the water collection efficiency on bi-philic surfaces changes in response to the change in the length scale of the hydrophobic region. The hypothesis was based on an observation that the mutual coalescence of water drops generates the momentary expansion of the merger along both the axial and transverse directions, leading to subsequent coalescence with nearby drops. Such a chain reaction can greatly improve the water collection efficiency as multiple droplets can simultaneously move toward the hydrophilic regions on a bi-philic surface, renewing a large area for fresh nucleation of water droplets. We demonstrated that noted expansion of a merger is driven by two mechanisms: i) the translational motion of the merger when two droplets of distinct sizes merge and ii) the surface waves originating from the neck formation in the early phase of the coalescence. The efficacy of the droplet expansion and the consequential chain reaction among multiple droplets is thus affected the non-dimensional Ohnesorge number [21]. The Ohnesorge number (Oh) for the majority of coalescence events can be controlled by tuning the size of the hydrophobic area, where the dropwise condensation occurs. We have thus investigated the effect of the Ohnesorge number on the drain efficiency, by comparing the behavior of water droplets on four bi-philic surfaces with different length scales: The bi-philic surfaces with hydrophobic stripes of 800 ~ 1,000 m width (Oh of 0.0042 ~ 0.0037) remained mostly dry after a prolonged exposure to steam, while the surfaces with hydrophobic stripes of 200 m (Oh ~ 0.0083) or 2,000 m (Oh ~ 0.0026) became flooded with large, quasi-static drops. Observed optimum length scale for the hydrophobic area (800 m width of hydrophobic stripes ensures 76% of the area remains dry in steady state) 18
matches that of fog-harvesting Stenocara beetle [9], suggesting that the bi-philic surface on the back of the beetle has evolved to maximize the efficiency of water drainage [6, 10]. From the result, one can infer that the coalescence-induced expansion of a merger and the subsequent group drainage play a vital role in the droplet shedding on bi-philic surfaces. We believe the outcome from the scaling analysis in this work can aid researchers to optimize bi-philic surfaces for water condensation.
Acknowledgements This project was carried out as part of the U.S. Office of Naval Research (ONR) MURI (Multidisciplinary University Research Initiatives) program (Grant No. N00014-16-1-2239).
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13277, 2013. [14] J. Boreyko and C.-H. Chen, "Self-propelled dropwise condensate on superhydrophobic surfaces," Physical Review Letters, vol. 103, no. 18, p. 184501, 2009. [15] F. Cebeci, Z. Wu, L. Zhai, R. Cohen and M. Rubner, "Nanoporosity-driven superhydrophobilicity: A means to create multifunctional antifogging coatings," Langmuir, vol. 22, no. 6, pp. 2856-2862, 2006. [16] L. Zhang, N. Zhao and J. Xu, "Fabrication and application of superhydrophilic surfaces: A review," Journal of Adhesion Science and Technology, vol. 28, no. 8-9, pp. 769-790, 2014. [17] H. Chen, P. Zhang, L. Zhang, H. Liu, Y. Jiang, Z. Deyuan, Z. Han and L. Jiang, "Continuous directional water transport on the peristome surface of Nepenthes alata," Nature, vol. 532, no. 7597, pp. 85-89, 2016. [18] C. Andrieu, D. Beysens, V. Nikolayev and Y. Pomeau, "Coalescence of sessile drops," Journal of Fluid Mechanics, vol. 453, pp. 427-438, 2002. [19] R. Narhe, D. Beysens and V. Nikolayev, "Dynamics of drop coalescence on a surface: The role of initial conditions and surface properties," International Journal of Thermophysics, vol. 26, no. 6, pp. 1743-1757, 2005. [20] R. Li, N. Ashgriz, S. Chandra, J. Andrews and S. Drappel, "Coalescence of two droplets impacting a solid surface," Experiments in Fluids, vol. 48, no. 6, pp. 1025-1035, 2009. [21] C. Mundo, M. Sommerfield and C. Tropea, "Droplet wall collisions: Experimental studies of the deformation and breakup process," International Journal of Multiphase Flow, vol. 21, no. 2, pp. 151-173, 1995. [22] S. Thoroddsen, K. Takehara and T. Etoh, "The coalescence speed of a pendent and a sessile drop," Journal of Fluid Mechanics, vol. 527, pp. 85-114, 2005. [23] A. Menchaca-Rocha, A. Martinez-Davalos, Nunez-R, S. Popinet and S. Zaleski, "Coalescence of liquid drops by surface tension," Pysical Review E, vol. 63, no. 4, p. 046309, 2001. [24] R. Enright, N. Miljkovic, J. Sprittles, K. Nolan, R. Mitchell and E. Wang, "How coalescing droplets jump," ACS Nano, vol. 8, no. 10, pp. 10352-10362, 2014. [25] R. Narhe, D. Beysens and V. Nikolayev, "Contact line dynamics in dropc coalescence and spreading," Langmuir, vol. 20, no. 4, pp. 1213-1221, 2004. [26] M. Sellier and E. Trelluyer, "Modeling the coalescence of sessile droplets," Biomicrofluidics, vol. 3, p. 022412, 2009.
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[27] M. Chaudhury, A. Chakrabarti and T. Tibrewal, "Coalescence of drops near a hydrophilic boundary leads to long range directed motion," Extreme Mechanics Letters, vol. 1, pp. 104113, 2014. [28] P. Jansen, O. Bliznyuk, S. Kooij, B. Poelsema and H. J. Zandvliet, "Simulating anisotropic droplet shapes on chemically striped patterned surfaces," Langmuir, vol. 28, no. 1, pp. 499505, 2012. [29] J. Joanny and P. De Gennes, "A model for contact angle hysteresis," Journal of Chemical Physics, vol. 81, no. 1, p. 552, 1984. [30] M. Reyssat and D. Quere, "Contact angle hysteresis generated by strong dilute defects," Journal of Physical Chemistry B, vol. 113, no. 12, pp. 3906-3909, 2009.
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Figure 1. A. Water drop on a hydrophobic (Si wafer coated with PTFE) surface, forming a contact angle θ=112°. B. Water contacting a hydrophilic (Si wafer, plasma treated) surface, forming a contact angle θ ≈ 0°. Scale bars in A and B are 1 mm. C. Condensation pattern on a biphilic surface, patterned with alternating stripes of hydrophobic and hydrophilic regions. Red and black lines at the bottom are inserted for visual guide, and represent hydrophobic (width = 2 mm) and hydrophilic regions (width = 1 mm) respectively. D. Condensation pattern on a bi-philic surface with a different length scale, with hydrophobic (width = 200 μm) and hydrophilic regions (width = 100 μm). Scale bars in panels C and D are 2 mm and 1.5 mm respectively.
Figure 2. A. A schematic representing the coalescence of equal-sized droplets. B. A schematic representing the coalescence of unequal-sized droplets. C. Droplets condensing on a hydrophobic surface, when the condensation process reaches saturation. Droplet coalescence becomes infrequent at this point, and further condensation is slow due to the insulational effect of large water drops. Scale bar in C is 1 mm.
Figure 3. Time-lapse images representing group coalescing and expansion of droplets, on a PTFE-sputtered hydrophobic surface. Scale bar in panel L represents 2 mm.
Figure 4. Time-lapse images representing group coalescing and wicking of droplets. Scale bar on 12 ms panel represents 1.5 mm.
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Figure 5. Time-lapse images showing the group drainage of droplets occurring across multiple drain channels. The dashed lines and arrows on 10 ms and 60 ms frames represent axial and lateral expansions respectively. Scale bar on 300 ms frame represents 1.2 mm.
Figure 6. Distribution of droplets in the early phase of condensation, at 5 minutes from the start of experiment. Images of bi-philic surfaces of different length scales, featuring initial nucleation and coalescing on Surface A: hydrophobic / hydrophilic patterns of 200 m / 100 m widths, Surface B: 800m / 400 m, Surface C: 1 mm / 0.5 mm, and Surface D: 2 mm / 1 mm. Scale bars in A, B, C are 1.2 mm, and scale bar in D is 1.5 mm.
Figure 7. Distribution of droplets in the steady state phase of condensation, at 15 minutes from the start of experiment. Images of bi-philic surfaces of different length scale, featuring steadystate nucleation and drainage on Surface A: hydrophobic/hydrophilic patterns of 200 m / 100 m widths, Surface B: 800 m / 400 m, Surface C: 1 mm / 0.5 mm, and Surface D: 2 mm / 1 mm (hydrophobic/hydrophilic). Length of scale bars is 1.2 mm.
Figure 8. The areal fraction of dry region on Surface A, B, C and D, calculated at 5 minute (dark gray) and 15 minute (light gray) after the beginning of the experiment. Each calculation is performed using multiple images similar to Figs. 6 and 7 respectively. Threshold diameter of a droplet is 240 micron. Error bars are based on 5% uncertainty of measuring diameters.
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Graphical Abstract:
Group drainage of multiple droplets occurring on a bi-philic surface.
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S0021-9797(17)30765-8 http://dx.doi.org/10.1016/j.jcis.2017.06.099 YJCIS 22526
To appear in:
Journal of Colloid and Interface Science
Received Date: Revised Date: Accepted Date:
4 May 2017 29 June 2017 29 June 2017
Please cite this article as: M.M. Garimella, S. Koppu, S.S. Kadlaskar, V. Pillutla, Abhijeet, W. Choi, Difference in growth and coalescing patterns of droplets on bi-philic surfaces with varying spatial distribution, Journal of Colloid and Interface Science (2017), doi: http://dx.doi.org/10.1016/j.jcis.2017.06.099
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Difference in growth and coalescing patterns of droplets on bi-philic surfaces with varying spatial distribution Martand Mayukh Garimella, Sudheer Koppu, Shantanu Shrikant Kadlaskar, Venkata Pillutla, Abhijeet and Wonjae Choi* Department of Mechanical Engineering, University of Texas at Dallas, 800 W. Campbell Road, Richardson, TX 75080 * Corresponding author: [email protected]
Keywords: Condensation; water harvesting; bi-philic surfaces; hydrophobicity; hydrophilicity
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Abstract This paper reports the condensation and subsequent motion of water droplets on bi-philic surfaces, surfaces that are patterned with regions of different wettability. Bi-philic surfaces can enhance the water collection efficiency: droplets condensing on hydrophobic regions wick into hydrophilic drain channels when droplets grow to a certain size, renewing the condensation on the dry hydrophobic region. The onset of drain phenomenon can be triggered by multiple events with distinct nature ranging from gravity, direct contact between a droplet and a drain channel, to a mutual coalescence between droplets. This paper focuses on the effect of the length scale of hydrophobic regions on the dynamics of mutual coalescence between droplets and subsequent drainage. The main hypothesis was that, when the drop size is sufficient, the kinetic energy associated with a coalescence of droplets may cause dynamic advancing of a newly formed drop, leading to further coalescence with nearby droplets and ultimately to a chain reaction. We fabricate bi-philic surfaces with hydrophilic and hydrophobic stripes, and the result confirms that coalescing droplets, when the length scale of droplets increases beyond 0.2 mm, indeed display dynamic expansion and chain reaction. Multiple droplets can thus migrate to hydrophilic drain simultaneously even when the initial motion of the droplets was not triggered by the direct contact between the droplet and the hydrophilic drain. Efficiency of drain due to mutual coalescence of droplets varies depending on the length scale of bi-philic patterns, and the drain phenomenon reaches its peak when the width of hydrophobic stripes is between 800 m and 1 mm. The Ohnesorge number of droplets draining on noted surfaces is between 0.0042 and 0.0037 respectively. The observed length scale of bi-philic patterns matches that on the Stenocara beetle’s fog harvesting back surface. This match between length scales suggests that the surface of the insect is optimized for the drain of harvested water. 2
I. Introduction This paper discusses the heterogeneous condensation (simply ‘condensation’ hereafter, for brevity) of water on surfaces patterned with regions of different wettabilities. Condensation phenomenon is ubiquitous in nature. We observe condensation on solid surfaces where we observe temperature difference and moisture, such as window panes, cold drink bottles and various heat exchangers [1]. Condensation rate is highly associated with the wettability of solid surfaces. Hydrophilic surfaces (surfaces on which water forms a Young’s contact angle < 90°) promote initial condensation, because the high surface energy of hydrophilic surfaces facilitates the adhesion of water molecules on the surface. But the same hydrophilicity typically leads to the formation of a water film on the solid surface as condensation process continues. Such a film drastically lowers the subsequent condensation of water, due to the low heat conductivity of the water layer. In contrast, the initial condensation rate of water on a hydrophobic surface ( > 90°) is lower than on a hydrophilic surface, as a hydrophobic surface is more stable in a dry state [2]. Once a drop condenses on a hydrophobic surface, however, the drop beads up rather than spreads to form a film. Drops beading up on a tilted surface roll off with relative ease, exposing the dry hydrophobic surface for another cycle of condensation. Therefore, although the initial nucleation rate is lower, long-term steady-state condensation rate is higher on a hydrophobic surface [2]. Noted roll-off phenomenon of droplets is vital for a hydrophobic surface to renew its dry area for further condensation, so the critical radius for a drop to roll-off the surface heavily influences the efficiency of condensation heat transfer or water collection. On a hydrophobic surface tilted by a certain angle, a drop begins to roll when the gravitational pull is greater than the adhesive force due to the contact angle hysteresis. Gravity-driven roll-off of droplets has been a topic of academic interest for decades, and a model by Furmidge [3] (later revised by 3
Extrand and Gent [4]) can predict the critical size for a quasi-static drop to roll-off a tilted surface. The model predicts that, for example, a water drop would begin to roll at a diameter of 2.08 mm on a vertically tilted hydrophobic surface with a moderate hysteresis (PTFE-coated silicon wafer with = 112°, contact angle hysteresis = 23°). The issue is that it takes significant time (6 minutes on our PTFE coated silicon wafer) for a drop to grow by condensation to reach 2 mm diameter. Thus a method to facilitate the drain of nucleating droplets can have a significant impact on the efficacy of condensation and water collection. One approach to reduce the critical radius for a droplet to leave the hydrophobic region is to make bi-philic surfaces (Fig. 1) [5, 6, 7, 8], surfaces patterned with hydrophilic and hydrophobic regions. Bi-philic surfaces were originally inspired by Namib Stenocara beetle [6, 9], which collects fog water using its back surface patterned with hydrophilic and hydrophobic patches. Bi-philic surfaces offer dual advantage over homogeneous hydrophilic or hydrophobic surfaces for condensation process. First, one can localize the formation of liquid film only on the hydrophilic region, which will serve as a drain path for condensing water. Second, droplets nucleating on the hydrophobic region leave the area when the droplets contact the hydrophilic drains, renewing the dry hydrophobic region for subsequent nucleation. Eventually, bi-philic surfaces have potential to offer higher and sustainable rates of water collection or heat transfer [6, 10]. Bi-philic surfaces, therefore, have become a topic of significant interest recently [6, 7, 9, 11, 12, 10]. These papers have given quantitative evidence of selective condensation, improved condensation rates, efficiency of fog collection, or higher heat transfer coefficient. One interesting observation on natural bi-philic surfaces on Stenocara beetle, an insect that harvests fog droplet on its back, is that the hydrophobic and hydrophilic patches have specific length scale of 1 mm and 500 microns respectively [9]. Research using synthetic bi-philic surfaces also 4
revealed that the efficacy of water collection reaches its maximum when the length scale of patterned regions is around the noted values [11]. Although the deposition of fog droplets and the condensation of dew droplets are not exactly the same, the rates of both phenomena are affected by the efficiency of drainage [12, 13]. We thus hypothesized that the observed dependence of the efficiency of water collection on the length scale of bi-philic patterns is due to the difference in drain rate. This paper thus investigates the effect of the variation of the spatial distribution of biphilic patterns on the growth, coalescing patterns and draining motion of droplets. In particular, we focus on the mutual coalescence of droplets leading to subsequent coalescence with neighboring droplets (chain reaction), ultimately to the simultaneous drainage of multiple droplets. For better insight, we have maintained a constant areal ratio between the hydrophobic (67%) and hydrophilic (33%) regions, while changing only the length scale of patterns. In conjunction with the referred papers, our results would give proper direction in choosing optimized spatial distribution for applications intended. The scope of this paper includes the motion of water droplets on bi-philic surfaces and the corresponding increase of water collection, but the paper does not investigate the effect of bi-philic surfaces on heat transfer. Although it is not the focus of this paper, another way to enhance condensation is to use super-hydrophobic or super-hydrophilic surfaces [5, 14]. Textured surfaces with extreme wettability can lead to interesting phenomena such as jumping droplets [12, 14] or fast wicking [15, 16, 17]. Although there are some open questions on the practical applicability of noted phenomena (e.g., jumping droplet phenomenon occurs only at low condensation rate regime, as the liquid-air interface on textured surfaces lose its stability at high condensation rate [12]), such surfaces can potentially promote the condensation or water collection efficiency beyond that on smooth surfaces. We limit the scope of this paper to the condensation on smooth hydrophobic
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and hydrophilic surfaces, to maintain the complexity of the problem to be manageable. We believe the findings from this research are general enough to be applicable for textured surfaces as well.
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II. Materials and Methods Fabrication of bi-philic surfaces: Four inch test grade p-type silicon wafers, purchased from University Wafers, with thickness of 500–525 m were used in this research. Native oxide layer was removed by 2-minute treatment with hydrofluoric acid in the acid hood, followed by a UVozone treatment in Samco UV ozone stripper/cleaner at UT Dallas clean room laboratory. Standard photolithography with S1813 photoresist and MF 319 developer was performed using CEE spin coater and Karl Suss MA6B Contact Printer provided in the clean room, to define patterns for regions with different wettability. PTFE layer was then deposited on samples through a 10 minute sputtering process at 100 W power and 4·10 -7 mTorr in A.J.A. Orion sputtering equipment. Photoresist layer was then stripped by acetone cleaning, to expose hydrophilic regions. The thickness of PTFE layer was measured by Dektak 8 profile meter, to be ~ 20 nm. Surface characterization: Rame-Hart 260 goniometer as used to determine contact angles of water droplets on surfaces. Water contact angle on PTFE-covered hydrophobic area was 112°±3° and the angle on (UV-ozone treated) hydrophilic area was ~0° respectively. While the contact angle on PTFE-covered area was constant after 48 hours, the angle on hydrophilic area increased up to ~20° over 10 hours. In this study, all observations on drop coalescence and condensation were performed within 3 hours after sample fabrication so that the contact angle on hydrophilic area remained below 10°.
Condensation: Silicon wafers with bi-philic patterns were mounted vertically, with a vaporizer unit placed 5 cm below, and 3 cm away, to prevent any mist droplets from vaporizer to reach surfaces. Steam required for condensation was developed using commercial vaporizer V150SGN 7
(KAZ incorporated) that was maintained at 95°~97° and 100% relative humidity. Backside of the wafers was exposed to room temperature, and all experiments were performed at atmospheric pressure. High speed image capture and analysis: The enhancement of efficiency of water collection has already been proven through measuring the amount of water collected by bi-philic surfaces [8, 11]. The focus of this study is, however, the mechanism that causes noted enhancement. For this goal, it is necessary to capture the dynamic motion of water droplets on bi-philic surfaces. Image analysis provides us with pictorial evidence of chain coalescence, and droplet wicking, and how they contribute towards enhancing condensation efficiency of bi-philic surfaces, as compared to homogeneous hydrophilic and hydrophobic surfaces. Sample surfaces were exposed to steam generated using a vaporizer and the growth patterns of droplets were captured at different stages of condensation using SA4 Photron high speed camera, at the resolution of 1024 × 1024 pixels and 2000 fps. Most images and movie clips were used to understand the dynamic motion of droplets. Data for the graph in Figure 8 were generated using Measure and Analyze add-on of ImageJ software.
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III. Results and Discussion Coalescence-induced motion of sessile drops: Shortly after the beginning of condensation process, droplets start to coalesce with nearby droplets. When two very small, quasi-static droplets (i.e., the flow remains in Stokes regime) coalesce on a hypothetical, hysteresis-free surface, a simple calculation based on the weighted average of the centers of the masses of parent drops may predict the center of the merger [18]. In this scenario, the outer perimeter of the merger (dotted line in Fig. 2) contracts from the perimeters of the parents along the axial direction (L in Fig. 2) and expands along the transverse direction (W in Fig. 2) [19]. Therefore, such a hypothetical coalescence can lead to subsequent coalescence with a neighboring droplet located along the transverse direction (see droplet G in Fig. 2), but not with a droplet along the axial direction (droplet R). Noted limited chance for the chain reaction leads the growth by coalescence to quickly saturate, that is, after one or two coalescence events, merger drops can grow only by further condensation or by trivial coalescence with tiny neighboring droplets that form by later condensation. As a result, prolonged condensation typically results in the formation of large and quasi-static drops (see Fig. 2C), who cover large portion of the surface and function as an insulation layer due to the low heat conductivity of water. Such a saturated state can be renewed only when these drops grow sufficiently large (e.g., ~ 2.1 mm as was discussed in section I) and roll off the surface. This renewal by gravity is, however, inefficient because the growth of a drop drastically slows down as its size increases. One of the key findings of this research is that one can overcome this limitation by using the bi-philic surfaces with appropriate length scale. Our experiments suggest that, the mutual coalescence between droplets, when their diameter is around 200 m or larger, leads to various types of chain reaction some of which are not expected by the simple model shown in Fig. 2. Empirical results show that the chain reaction 9
can occur along the axial as well as transverse directions, facilitating simultaneous drain of multiple droplets. Fig. 3 shows one example of the mutual coalescences between two droplets, leading to a chain reaction with another droplet that is located along the axial direction of the two parent droplets. Drop A and B merge by direct contact, forming a merger (Drop D). Drop D oscillates after the coalescence, and touches its neighbor (Drop C) that is located along the axial direction of the original coalescence. The second coalescence leads to the formation of the final merger, Drop E. Note that the observed chain reaction is not predicted by the simple model shown in Fig. 2. It is also interesting that the center of the mass of the final merger E is significantly off the location of the center of three parent drops. There are two mechanisms that may cause noted dynamic coalescence and subsequent chain reaction. First, the difference in surface energies of the two parent drops and the merger partially converts into a dynamic flow inside the merger. Multiple studies investigated this phenomenon [18, 20] and used the dimensionless Ohnesorge number [21] to characterize the flow associated with the coalescence of two equal-sized drops. The Ohnesorge number in this research is defined as:
Oh =
d
(1)
Where, Oh is the Ohnesorge number, μ and ρ are dynamic viscosity and density of water, σ is the surface tension of water and d is the diameter of the merger drop. The Ohnesorge number associated with merger Drop D in Fig. 3 is estimated to be 0.0015, which suggests the kinetic energy of the coalescing flow is sufficient for Drop D to overcome the viscous dissipation and to display substantial translation or oscillation. Note that the Ohnesorge number for commonly 10
occurring 3 mm-sized raindrops drops is ~ 0.002. For two equal-sized drops, the kinetic energy can only create symmetric motions, such as oscillations without any change in the center of mass. For two unequal-sized drops, the merger can exhibit both oscillatory motion and translational motion leading to subsequent coalescence with neighboring drops: asymmetric translational motion can occur because the coalescence-induced flow inside the merger can be asymmetric between two droplets when the sizes of the parent droplets are unequal. Such coalescence typically causes the smaller droplet to flow into the larger droplet due to the difference in Laplace pressures inside two drops. Indeed, comparing Figs. 3A and 3G clearly shows that the center of mass of Drop D is significantly different from the weighted average between Drops A and B. Although the anisotropic coalescence may lead to the transition of the merger, the degree of drop expansion per se, a measure of kinetic energy stored in the merger drop, is primarily related to the Ohnesorge number not the anisotropy between the sizes of parent drops (see Fig. S1 in Supporting Materials). Second, the neck formation in the early phase of coalescence generates a fast moving capillary wave (Figs. 3B~C and 3H~I). The speed of the neck formation is determined by the Reynolds number of the coalescence process [22], which in turn depends on the Ohnesorge number. This surface wave can reach the outer edge of a drop before the bulk flow makes the drop shrink [23, 24, 25, 26]. This effect is clear between Fig. 3G and 3K, where the outer periphery of the merger E momentarily extends beyond that of the parent Drop C (see the red dashed line). Although such a momentary expansion quickly dissipates between Fig. 3K and 3L, the same phenomenon can lead to subsequent coalescence if there is a neighboring drop. Noted axial expansion of the merger drop is a counterpart to a well-known “jumping droplet” phenomenon, a phenomenon that the merger displays strongly transverse expansion due to the
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difference in surface energy when two equal-sized droplets merge [14]. These two mechanisms – the bulk motion of the merge due to excessive surface energy, and the surface waves from neck formation – can make each coalescing event to lead to another, ultimately to a long chain of coalescence events along various directions.
Mutual coalescence leading to simultaneous drainage of multiple droplets: Fig. 4 shows a typical example that a chain reaction leads to the simultaneous drainage of multiple droplets. Droplets A and B coalesce at time = 0 ms, and the merger (Drop C) expands laterally to contact its neighbor (Drop D; see t = 2 ms to 3 ms). Subsequent coalescence of Drop C and Drop D leads to the formation of merger E, which displays axial expansion (arguably due to surface waves) to contact the hydrophilic channel (note the bulging meniscus on the channel to the left of Drop E; t = 4 ms). Same drop also expands laterally to contact droplet F (t = 5 ms), and finally merger G drains into the hydrophilic region driven by the difference in surface wettability (t = 9 ~ 12 ms). All these coalescing motions occur within 12 ms, suggesting that this simultaneous drainage was triggered only by the first coalescence, not by additional condensation or gravity. Noted chain reaction renews a large area (Circled area in the last panel of Fig. 4) for fresh nucleation. Chaudhry et.al reported a similar renewal phenomenon accelerated by the mutual coalescence of droplets [27]. Their work was, however, based on a hydrophobic surface with surface energy gradient so that any coalescence between droplets becomes converted into a directional motion of mergers. Our work, on the other hand, investigates a random motion of mergers leading to the simultaneous drain of multiple droplets occurring on bi-philic surfaces. Chain reaction due to axial and lateral expansion can propagate across multiple hydrophobic regions. Fig. 5 shows an example. Drop A and B coalesce at time = 0 ms, and the 12
merger (drop C) laterally expands to contact hydrophilic regions (regions H and E at t = 30 ms ~ 60 ms). The majority of drop mass flows to region H, as the drop contacts this region first. Due to the substantial inertia of the motion of merger C, the frontal end of the drop surpasses the boundary of hydrophilic region H, ultimately to touch a next drop (Drop D; t = 60 ms). New merger (Drop G) repeats the expansion and touch the next hydrophilic strip (region F; t = 70 ms), although the majority of the mass flows to the first hydrophilic drain (H). Observed expansion (Drop G to region F) to a direction opposite to motion of the main drop (Drop G to region H), is arguably due to the surface wave discussed previously (see Fig. 3). Effect of length scale on the efficacy of chain reaction: The strength of both mechanisms that drive chain reaction – i) the conversion of the interfacial energy to the bulk motion of the merger, and ii) the surface waves momentarily extending the outer periphery of the merger – depend on the non-dimensional viscosity or the Ohnesorge number (Oh). Figs. 6 and 7 show the coalescing patterns of droplets on four surfaces with bi-philic patterns of same areal ratio (67% hydrophobic, 33% hydrophilic) but with different length scales. One length scale is chosen to be similar to that of Namib Stenocara beetle (1 mm and 0.5 mm for the hydrophobic and hydrophilic stripes). Assuming that the diameter of commonly occurring droplets to be roughly half of the width of hydrophobic stripes (see Fig. 6), Oh numbers for water droplets on the four surfaces are, in the ascending order of the length scale of patterns, 0.0083, 0.0042, 0.0037 and 0.0026 respectively. The initial nucleation and coalescence on bi-philic surfaces with different length scales is shown in Fig. 6. On surface A, droplets on the hydrophobic stripes wick into hydrophilic channels mostly through direct contact, because droplets can grow only up to 200 μm before they contact the drain. Time for a droplet to grow to 200 μm is relatively short (~5 seconds), so the 13
condensation is constantly renewed during the initial phase. However, on the same surface, as the hydrophilic channel is very narrow (100 μm), the drain flow is insignificant (the cross sectional area of an open channel flow is proportional to the cube of its width). Insufficient drainage causes large drops to appear on hydrophilic channels [28] (see Fig. 6A). Once these drops appear, their further growth decreases the Laplace pressure inside the drop, reducing the driving force for drain even lower. As a result, these drops remain in a quasi-static state until gravity pulls them down. On Surfaces B and C, each of which has 800 m / 400 m and 1 mm / 0.5 mm pattern widths, droplets nucleate, coalesce and grow on the hydrophobic stripes. Proximity between the droplets on the hydrophobic stripes leads to the chain reaction of coalescence which causes those droplets to either form a merger drop at the center of the hydrophobic stripes or wick into the hydrophilic channels as shown in Figs. 4 and 5. As the hydrophilic channels are much wider on Surfaces B and C than on A, water can easily flow along such channels and thus clogging of the hydrophilic channels by large drops occurs in rarity (see Figs. 6B, 6C). Even when it occurs, unlike the drops on Surface A, drops that clog the hydrophilic channels on Surfaces B and C roll down the surface with relative ease (see Fig. S2 in Supporting Materials). This difference is because the resistance against drop rolling is proportional to the number of the hydrophilic stripes beneath the drop: the borderlines between hydrophobic and hydrophilic stripes are not perfectly straight, and the meniscus of a water drop becomes pinned on the asperities at the borderlines [29, 30]. Each rolling-off drop carries the surrounding droplets with them (see Fig. S2), clearing a large chunk of space for fresh nucleation. Surface D with 2 mm (hydrophobic) and 1 mm (hydrophilic) pattern widths do not display any sign of channel clogging. However, the probability of the chain reaction on 14
hydrophobic stripes reaching hydrophilic channels also diminishes due to the excessively large width of hydrophobic channels, and thus large drops, similar to the ones in Fig. 2C, begin to form at the center of hydrophobic stripes (compare Fig. 6D and Fig. 7D). A steady state is reached on all patterns by 15 minutes of condensation. The state shown in Fig. 7 remains essentially the same after 15 minutes, as the condensation and drain phenomena balance one another. In the case of Surface A, the condensation of droplets becomes drastically inefficient as large drops form over multiple hydrophobic stripes and hydrophilic channels (Fig. 7A). The diameters of these drops are of the scale of 2 mm (average). These drops function as condensation barrier due to the poor thermal conductivity of water, and also block the hydrophilic drains [28]. Although these drops eventually roll off Surface A to wipe out large chunks of area, the frequency of drop shedding is very low as the rate of growth of those large drops is insignificant. Surfaces B and C deliver best results with regards to droplet shedding. Due to the chain reaction of droplet coalescences and the subsequent drainage of multiple droplets into hydrophilic channels, the surface is ensured to be relatively dry compared to other surfaces (see Fig. 7B and 7C). Even though a similar chain reaction among droplet coalescences exists on surface D, the renewal of hydrophobic regions is much slower on Surface D due to the excessive width of hydrophobic stripes. On Surface D, chain reactions tend to cause the formation of bigger drops in the middle of hydrophobic stripes rather than the drainage into hydrophilic stripes (see Fig. 7D). Once formed, these drops do not readily drain into hydrophilic channels even when in contact with newly formed small droplets. These drops leave the surface only when the drop is large enough to fall due to gravity, which takes as long time as the large drops shown in Fig. 7A. 15
Analysis on the fraction of dry area: Water collection through condensation is heavily affected by the fraction of the dry area available for the nucleation of droplets. Therefore, an experimental analysis was performed to compare the areal fraction of the dry region on Surfaces A, B, C and D; the analysis was performed twice with the condensation patterns obtained at 5 and 15 minutes from the start of condensation. Only the hydrophobic area was used for computation, as all hydrophilic channels become fully wetted shortly after the initial phase of the experiment. Considering the fact that drop growth drastically slows down with its size, it is reasonable to assume that the area covered by large drops is essentially not useful for further condensation. 240 μm in diameter is chosen as the threshold size to determine such ‘large drops.’ The choice of 240 m is based on the observation that droplets reach that size within tens of seconds by condensation. Also, the resolution limit of obtained images did not allow accurate calculation of droplet area for small droplets below 240 m diameter. (Note that an analysis based on the threshold value of 300 m leads to different values for the areal fractions on four surfaces, but the relative rank of surfaces does not change; see Fig. S3). One needs to be extra cautious to analyze the condensation pattern on Surface A (200 m / 100 m pattern widths), as there cannot be any droplets reaching 240 µm diameter on Surface A unless drops cover multiple channels. Therefore, only such large drops were taken into account to calculate the areal fraction on Surface A. Fig. 8 shows the result: at 5 minutes from the start of condensation, the areal fraction of the dry region is 45-65% of the total hydrophobic area (dark gray bars in Fig. 8) for Surfaces A to D. All surfaces thus allow substantial amount of condensation of new droplets. With time, however, the areal fraction of the dry region drastically reduces to 13% and 11% on Surface A 16
and Surface D respectively, while the fraction remains relatively the same on Surface B and Surface C (76% and 60% of the hydrophobic region remains dry as shown with light gray bars in Fig. 8). It can be inferred that patterns on Surface B (800 m and 400 m widths for hydrophobic and hydrophilic channels) provide best results in terms of droplet drainage and the renewal of hydrophobic region. Interestingly, the length scale of bi-philic patterns on Surfaces B and C matches that of the hydrophobic / hydrophilic patterns on the Stenocara beetle’s fog harvesting back surface. This match between length scales supports our hypothesis that the wetting / non-wetting patterns on the insect’s back have evolved to maximize the efficiency of water harvesting through optimal drainage. It should be noted that the outcome from this experiment should be taken only as a qualitative guideline for designing bi-philic surfaces, and the optimum length scale for any specific bi-philic pattern would vary depending on the shape of hydrophobic / hydrophilic regions.
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Conclusion This paper gives a scaling analysis to understand the enhancement of water collection on biphilic surfaces, a phenomenon that has recently attracted interest from fluid physicists and engineers [5-11]. We tested a hypothesis that the water collection efficiency on bi-philic surfaces changes in response to the change in the length scale of the hydrophobic region. The hypothesis was based on an observation that the mutual coalescence of water drops generates the momentary expansion of the merger along both the axial and transverse directions, leading to subsequent coalescence with nearby drops. Such a chain reaction can greatly improve the water collection efficiency as multiple droplets can simultaneously move toward the hydrophilic regions on a bi-philic surface, renewing a large area for fresh nucleation of water droplets. We demonstrated that noted expansion of a merger is driven by two mechanisms: i) the translational motion of the merger when two droplets of distinct sizes merge and ii) the surface waves originating from the neck formation in the early phase of the coalescence. The efficacy of the droplet expansion and the consequential chain reaction among multiple droplets is thus affected the non-dimensional Ohnesorge number [21]. The Ohnesorge number (Oh) for the majority of coalescence events can be controlled by tuning the size of the hydrophobic area, where the dropwise condensation occurs. We have thus investigated the effect of the Ohnesorge number on the drain efficiency, by comparing the behavior of water droplets on four bi-philic surfaces with different length scales: The bi-philic surfaces with hydrophobic stripes of 800 ~ 1,000 m width (Oh of 0.0042 ~ 0.0037) remained mostly dry after a prolonged exposure to steam, while the surfaces with hydrophobic stripes of 200 m (Oh ~ 0.0083) or 2,000 m (Oh ~ 0.0026) became flooded with large, quasi-static drops. Observed optimum length scale for the hydrophobic area (800 m width of hydrophobic stripes ensures 76% of the area remains dry in steady state) 18
matches that of fog-harvesting Stenocara beetle [9], suggesting that the bi-philic surface on the back of the beetle has evolved to maximize the efficiency of water drainage [6, 10]. From the result, one can infer that the coalescence-induced expansion of a merger and the subsequent group drainage play a vital role in the droplet shedding on bi-philic surfaces. We believe the outcome from the scaling analysis in this work can aid researchers to optimize bi-philic surfaces for water condensation.
Acknowledgements This project was carried out as part of the U.S. Office of Naval Research (ONR) MURI (Multidisciplinary University Research Initiatives) program (Grant No. N00014-16-1-2239).
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Figure 1. A. Water drop on a hydrophobic (Si wafer coated with PTFE) surface, forming a contact angle θ=112°. B. Water contacting a hydrophilic (Si wafer, plasma treated) surface, forming a contact angle θ ≈ 0°. Scale bars in A and B are 1 mm. C. Condensation pattern on a biphilic surface, patterned with alternating stripes of hydrophobic and hydrophilic regions. Red and black lines at the bottom are inserted for visual guide, and represent hydrophobic (width = 2 mm) and hydrophilic regions (width = 1 mm) respectively. D. Condensation pattern on a bi-philic surface with a different length scale, with hydrophobic (width = 200 μm) and hydrophilic regions (width = 100 μm). Scale bars in panels C and D are 2 mm and 1.5 mm respectively.
Figure 2. A. A schematic representing the coalescence of equal-sized droplets. B. A schematic representing the coalescence of unequal-sized droplets. C. Droplets condensing on a hydrophobic surface, when the condensation process reaches saturation. Droplet coalescence becomes infrequent at this point, and further condensation is slow due to the insulational effect of large water drops. Scale bar in C is 1 mm.
Figure 3. Time-lapse images representing group coalescing and expansion of droplets, on a PTFE-sputtered hydrophobic surface. Scale bar in panel L represents 2 mm.
Figure 4. Time-lapse images representing group coalescing and wicking of droplets. Scale bar on 12 ms panel represents 1.5 mm.
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Figure 5. Time-lapse images showing the group drainage of droplets occurring across multiple drain channels. The dashed lines and arrows on 10 ms and 60 ms frames represent axial and lateral expansions respectively. Scale bar on 300 ms frame represents 1.2 mm.
Figure 6. Distribution of droplets in the early phase of condensation, at 5 minutes from the start of experiment. Images of bi-philic surfaces of different length scales, featuring initial nucleation and coalescing on Surface A: hydrophobic / hydrophilic patterns of 200 m / 100 m widths, Surface B: 800m / 400 m, Surface C: 1 mm / 0.5 mm, and Surface D: 2 mm / 1 mm. Scale bars in A, B, C are 1.2 mm, and scale bar in D is 1.5 mm.
Figure 7. Distribution of droplets in the steady state phase of condensation, at 15 minutes from the start of experiment. Images of bi-philic surfaces of different length scale, featuring steadystate nucleation and drainage on Surface A: hydrophobic/hydrophilic patterns of 200 m / 100 m widths, Surface B: 800 m / 400 m, Surface C: 1 mm / 0.5 mm, and Surface D: 2 mm / 1 mm (hydrophobic/hydrophilic). Length of scale bars is 1.2 mm.
Figure 8. The areal fraction of dry region on Surface A, B, C and D, calculated at 5 minute (dark gray) and 15 minute (light gray) after the beginning of the experiment. Each calculation is performed using multiple images similar to Figs. 6 and 7 respectively. Threshold diameter of a droplet is 240 micron. Error bars are based on 5% uncertainty of measuring diameters.
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Graphical Abstract:
Group drainage of multiple droplets occurring on a bi-philic surface.
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