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Droplet Jumping: Effects of Droplet Size, Surface Structure, Pinning, and Liquid Properties Xiao Yan, Leicheng Zhang, Soumyadip Sett, Lezhou Feng, Chongyan Zhao, Zhiyong Huang, Hamed Vahabi, Arun K. Kota, Feng Chen, and Nenad Miljkovic ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b06677 • Publication Date (Web): 09 Jan 2019 Downloaded from http://pubs.acs.org on January 10, 2019
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Droplet Jumping: Effects of Droplet Size, Surface Structure, Pinning, and Liquid Properties Xiao Yan1, 2, Leicheng Zhang1, Soumyadip Sett1, Lezhou Feng1, Chongyan Zhao2, Zhiyong Huang2, Hamed Vahabi3, Arun K. Kota3,4,5, Feng Chen2, Nenad Miljkovic1,6,7,8* 1
Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL, 61801, USA 2 Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing, 100084, China 3 Department of Mechanical Engineering, Colorado State University, Fort Collins, CO 80523 USA 4 School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523 USA 5Department of Chemical Engineering, Colorado State University, Fort Collins, CO 80523 USA 6 Department of Electrical and Computer Engineering, University of Illinois at Urbana–Champaign, Urbana, IL, 61801, USA 7 Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801, USA 8 International Institute for Carbon Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka, 819-0395, Japan
*Authors to whom correspondence should be addressed. Electronic mail: Nenad Miljkovic:
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Abstract Coalescence-induced droplet jumping has the potential to enhance the efficiency of a plethora of applications. Although binary droplet jumping is quantitatively understood from energy and hydrodynamic perspectives, multiple aspects which affect jumping behavior including droplet size mismatch, droplet-surface interaction, and condensate thermophysical properties, remain poorly understood. Here, we develop a visualization technique utilizing microdroplet dispensing to study droplet jumping dynamics on nanostructured superhydrophobic, hierarchical superhydrophobic, and hierarchical biphilic surfaces. We show that on the nanostructured superhydrophobic surface, the jumping velocity follows inertial-capillary scaling with a dimensionless velocity of 0.26 and a jumping direction perpendicular to the substrate. A droplet mismatch phase diagram was developed showing that jumping is possible for droplet size mismatch up to 70%. On the hierarchical superhydrophobic surface, jumping behavior was dependent on the ratio between the droplet radius 𝑅 relative and surface structure length scale 𝐿. For small droplets (𝑅 ≤ 5𝐿), the jumping velocity was highly scattered, with a deviation of the jumping direction from the substrate normal as high as 80º. Surface structure length scale effects were shown to vanish for large droplets (𝑅 > 5𝐿). On the hierarchical biphilic surface, similar but more significant scattering of the jumping velocity and direction were observed. Droplet-size-dependent surface adhesion and pinning-mediated droplet rotation were responsible for the reduced jumping velocity and scattered jumping direction. Furthermore, droplet jumping studies of liquids with surface tensions as low as 38 mN/m were performed, further confirming the validity of inertial-capillary scaling for varying condensate fluids. Our work not only demonstrates a powerful platform to study droplet-droplet and droplet-surface interactions, it provides insights into the role of fluid-substrate coupling as well as condensate properties during droplet jumping.
Keywords: coalescence-induced droplet jumping, visualization, jumping velocity, directionality, superhydrophobic, biphilic, low-surface-tension liquid
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Coalescence-induced droplet jumping has received increased attention in the past few years due to its capacity to passively shed micro and nanoscale droplets, which can enhance anti-icing,1 defrosting,2 self-cleaning,3-6 and condensation heat transfer performance.7-12 During droplet coalescence, the rigid substrate breaks symmetry, resulting in momentum transfer away from the surface, driving the jumping process.13,14 Extensive studies have been conducted investigating the hydrodynamics of jumping droplet coalescence,7,14 jumping velocity,7,13-17 and directionality15,18 on various superhydrophobic surfaces. In pursuit of increased jumping velocity,19-21 decreased jumping droplet size,16,22,23 and controlled direction,18,24-26 surfaces have been carefully designed as a passive method to exert a delicate influence on coalescing droplets via surface interactions. During coalescence and departure, the surface topography,23,27,28 wettability,22 condensate fluid,29 and surrounding gas30 properties strongly affect the hydrodynamic processes governing jumping. To study droplet-surface interactions, several efforts using top-view and side-view visualization have attempted to observe droplet coalescence and jumping dynamics, with limited success. Top-view imaging is incapable of extracting jumping velocity, directionality, and surfacedroplet interfacial effects.15,31 Side-view imaging has difficulty eliminating the interference of neighboring droplets.7,14 Meanwhile, during condensation, the intrinsically small length scale of coalescing droplets (0.5 - 100 µm)22,32 leads to a capillary-inertial timescale13 approaching 40 ns, posing stringent requirements for imaging speed.33 Visualizing larger (~ 100 µm), manually generated droplets, without the need for condensation helps to elucidate key droplet-surface interactions and post-jumping behavior. Furthermore, artificial droplet generation methods can be extended to include condensate liquids other than water, such as low-surface-tension fluids and binary liquid mixtures.29,34,35 However, generating and positioning arbitrary sized microdroplets remains a challenge.17,19,29 Previous approaches have
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used micropipettes or syringes to dispense droplets having radii > 450 µm, further triggering coalescence with air flow or wire pushing.19,29 These past methods tend to be invasive, introducing undesired external disturbances, and affecting coalescence hydrodynamics. More importantly, past strategies have limits on the lower boundary of the droplet sizes, preventing the study of dropletsurface interactions. To generate droplets of varying sizes, complicated techniques including solenoid actuator dispensing (radii > 300 µm), droplet explosion (100 µm < radii < 300 µm), and gating control (20 µm < radii 5𝐿),
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droplets departed perpendicular to the surface (𝜃 ≈ 90º), similar to what we observed for the majority of jumping events on the superhydrophobic CuO surface (Figure 2d). Comparing the velocity and direction of jumping droplets from the two surfaces, it is evident that the addition of microstructures acts to scatter both jumping velocity and direction of small droplets (𝑅 ≤ 5𝐿). To further investigate the effects of microstructures on jumping direction, we dispensed two equally sized droplets with varying sizes near a micro-asperity (≈ 80 µm in width) (Figure 4d-f). As the droplet radius increased from ≈ 45 µm to ≈ 60 µm to ≈ 125 µm, 𝜃 increased from ≈ 4° (Figure 4d) to ≈ 50° (Figure 4e, see Video S3) to ≈ 90° (Figure 4f), respectively. Due to the comparable size of the droplets and the surface roughness length scale, the first droplet residing on the microstructure top and second in the valley had different heights. When the droplets merged, the radially expanding liquid bridge impacted the local structure feature, which imparted nonsurface-normal momentum to the merged droplet, thus affecting the jumping direction. Nonperpendicular jumping droplets tend to sweep adjacent droplets, and this explains why higher frequency of multi-droplet jumping on hierarchical surfaces was observed during condensation when compared to single tier structures.32,49 The quantitative dependence of droplet jumping angle on microstructured surfaces could be understood by considering the geometric shape of the structures and coupling them to the droplet position and size dependent coalescence dynamics (see Figure S9 and Section S9, Supporting Information). Additionally, the scattered jumping velocity was also related to the exact location of the droplets with respect to the local surface topography, which affected the coalescence process at different stages depending on the specific geometric features of the surface. When the local surface feature engaged in the liquid bridge expansion at an early stage, the jumping velocity was enhanced, which has been confirmed for droplets jumping on hydrophobic fibers51 and also at corners of micro-square-posts.47 In contrast, when the local
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surface structure engaged in the liquid bridge expansion at later stages of coalescence, the jumping velocity was reduced.47 For large droplets (𝑅 > 5𝐿), it was the collective counteraction from multiple micro-asperities that determined the droplet coalescence and jumping behavior, and therefore, the role of local topography was less important.
Droplet Jumping on Hierarchical Biphilic Surfaces: Effects of Pinning Compared with superhydrophobic surfaces, biphilic surfaces with wettability contrast exploit the advantages of combining hydrophobicity and hydrophilicity.52,53 However, droplet jumping dynamics on surfaces having spatially contrasting wettability remain to be explored. To study jumping performance on biphilic surfaces, we fabricated laser etched Cu micro-hill structures with CuO nanowires on top of these micro-hills (Figure 5a). The center-to-center spacing of the microhills, 𝐿, was measured to be 48.2 ± 0.6 µm using SEM. After fabrication, the surfaces were hydrophilic, with 𝜃
≈ 0°. Upon exposing the fabricated surface to ambient laboratory air for
≈ 3 weeks, the surface became globally superhydrophobic with 𝜃
= 162 ± 1.2º and 𝜃
= 120
± 3.2º due to adsorption of airborne volatile organic compounds (VOCs) (see Methods).54,55 Biphilicity was realized by the roughness variation resulting from the curvature-dependent nanowire features.55 Nanowires were long and dense in the valley and ridge areas, while hilltops were barren with few nanowires. Therefore, the hilltops were less hydrophobic than the valley and ridge regions since the extent of roughness governs wettability.23,54,55 Wettability contrast was confirmed by optical microscopy condensation experiments (Figure S4, see Section S6, Supporting Information). The hilltops with higher wettability acted as pinning spots towards condensing or deposited droplets.
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Jumping velocities of equally sized binary water droplets on the hierarchical biphilic surface are shown in Figure 5b. For droplets having similar radii, the jumping velocities were lower than that observed on the superhydrophobic CuO surface. Furthermore, the velocities were scattered significantly when compared to both the superhydrophobic CuO (Figure 2a) and hierarchical superhydrophobic surfaces (Figure 4b). The scatter was especially pronounced in the small droplet size range (𝑅 ≤ 250 µm, ≈ 5𝐿). For small droplets (𝑅 ≤ 120 µm, ≈ 2𝐿), there existed a probability of ≈ 0.6 that the coalesced droplets will not jump (inset in Figure 5b). For large droplets ( 𝑅 ˃ 250 µm, ≈ 5 𝐿 ), the jumping velocities approached those characterized on the superhydrophobic CuO and hierarchical superhydrophobic surfaces. The observed deviation of jumping velocity for droplets departing the hierarchical biphilic surface can be understood from the size-dependent wetting properties. As the droplet grew in size from ≈ 50 µm (≈ 𝐿), the droplet base adhered to the surface and remained nearly unchanged until the droplet exceeded a critical radius 𝑅
,
≈ 250 µm (≈ 5𝐿), below which the droplet contact angle
increased from ≈ 140º to ≈ 160º (Figure S5, see Section S6, Supporting Information). Simultaneously, resembling growing droplets during condensation,60,61 the basal area of the growing droplet on the hierarchical biphilic surface expanded in a stepwise manner due to the discrete hydrophilic hilltops acting as pinning spots. The droplet basal area, characterized by the droplet base radius 𝑟 , could be predicted by the geometric pattern of microhills (Figure S6, see Section S7, Supporting Information). Considering a droplet with an initial base radius 𝑟 , . As the droplet radius 𝑅 grew, the apparent contact angle, 𝜃 contact angle 𝜃
corresponding to a droplet radius 𝑅
when 𝑅 exceeded 𝑅
,
, increased to the apparent advancing ,
. Since 𝜃
is the upper limit of 𝜃
,
, the triple-phase contact line at the droplet base advanced until it reached
the next pinning spots, with the droplet base radius jumping from 𝑟
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,
to 𝑟
,
and 𝜃
dropping
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from 𝜃
. Afterwards, the droplet base remained pinned until 𝑅 increased to 𝑅
droplet reached 𝜃
again. With the array of 𝑟
,
, at which the
determined (Table S1, see Section S7,
,
Supporting Information), the contact angle dependence on the droplet size can be expressed as:42 𝜃
where 𝑅 ∈ 𝑅 , , 𝑅
,
𝑟, 𝑅
= cos
+
π , 2
(4)
, subscript k=0, 1, 2… The jumping velocity of the pinned droplet, 𝑣 ,
can be solved by energy conservation: 1 𝜌𝑉𝑣 ≈ 2𝐴 − 𝐴 𝛾𝜂 − 2𝐴 𝜑 2
,
+ 1−𝜑
,
𝜑 (1 + cos 𝜃
(5)
)𝛾 ,
where the left side of the equation is the kinetic energy term, the first term on the right side is the available excess surface energy for jumping and the second term is the work of adhesion.22 The term 𝑉 represents the final jumping droplet volume (𝑉=2𝜋𝑅 (cos 𝜃
− 1) (cos 𝜃
+ 2)⁄3),
𝐴 , 𝐴 , and 𝐴 are the liquid-vapor surface areas of the initial droplets (𝐴 = 2𝜋𝑅 (1 − cos 𝜃 jumping droplet (𝐴 = 4𝜋(3𝑉 ⁄4𝜋) The term 𝜑
,
/
), and initial droplet base (𝐴 ≈ 𝜋𝑅 sin 𝜃
)),
), respectively.
represents the surface solid fraction56 with respect to microhills, corresponding to
the droplet basal radius 𝑟
,
, and 𝜑 represents the surface solid fraction determined by the
nanowires (see Section S7, Supporting Information). Assuming 𝜂 = 5.6% based on the experimental results on the superhydrophobic CuO surface, we calculated 𝑣 for droplets on the hierarchical biphilic surface as a function of 𝑅 , which was in excellent agreement with the experimental values (Figure 5b). Note that the discontinuity of the model velocity results arose from the presence of pinning and relaxation of the triple-phase contact line, resulting in the stepwise growth of the droplet basal radius and contact angle (see Section S7, Supporting Information). The initial position of the deposited droplets with respect to the microstructures is vital when determining the droplet base radius. In one case, droplets (~ 10 µm) were dispensed
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onto a hydrophilic hilltop, where the adhesive hilltop acted as the expansion center of the droplet basal area as the droplet volume grew due to the addition of subsequent dispensed droplets. The evolution of the basal radius could be determined geometrically assuming that the periphery of the droplet base (contact line) was pinned to the hilltop edges before it reached the adjacent neighboring hilltops (Figure S6a, see Section S7, Supporting Information). Similarly, when deposited droplets landed between two adjacent hydrophilic hilltops (Figure S6b, see Section S7, Supporting Information), or on superhydrophobic valleys surrounded by four hydrophilic hilltops (Figure S6c, see Section S7, Supporting Information), the droplet base would expand following alternate pathways (Table S1, see Section S7, Supporting Information). The modeled velocities corresponding to the three typical aforementioned initial conditions of the droplets were all modeled (Figure 5b), successfully capturing the scatter in the experimental velocity data and nonjumping cases in the small droplet radii range (𝑅
