SUPPLEMENTARY INFORMATION

Transcription

1 doi: /nature16956 Table of Contents I. Supplementary Methods I.1. Materials and Sample Preparation I.2. Contact Angle Measurements I.3. Thickness Characterization of Carnation Mineral Oil TM I.4. Condensation Experiment I.5. Optical Analysis of Droplet Growth II. Supplementary Control Experiments II.1. Effect of Radius of Curvature of Convex Topography Compared to the Effect of Surface Roughness II.2. Effect of Radius of Curvature of Convex Topography Compared to the Effect of Temperature Distribution across the Surface III. Supplementary Theoretical Modeling III.1 Theoretical Modeling of Focused Diffusion and Heat Flux on the Apex of Spherical- Cap-Shaped Bumps Using a Spherical Mass Sink and Source Geometry III.2 Numerical Calculation of Focused Diffusion Flux by Using COMSOL-Multiphysics III.3 Numerical Calculation of Total Free Energy of Droplet-Vapor-Bump System Using Surface Evolver IV. Importance of Multi-Scale Surface Structures and Asymmetry of Bumps for Facilitating Both Droplet Growth and Transport 1

2 RESEARCH SUPPLEMENTARY INFORMATION I. Supplementary Methods I.1. Materials and Sample Preparation Fabrication of Bumpy Surfaces The various bumpy surfaces studied in this work were molded by pressing a thin aluminum sheet (60 mm 55 mm mm, McMaster-Carr) between three-dimensionally printed polymer (Objet VeroBlue RGD840, Stratasys) molds prepared by Objet30 (Stratasys). The samples were then sonicated for 20 min with ~1 wt% solution of Alcojet (Alconox, Inc.) in MilliQ DI water, cleaned using acetone (VWR), and rinsed with MilliQ DI water. Surface Modification 1 Micro/Nano and Molecular Scale Textured Hydrophobic Surfaces Surface nanostructure (Fig. 3c) was created by immersing the cleaned aluminum sheet in boiling water for approximately 10 min 1. To make the surface hydrophobic, liquid-phase surface treatment [0.1 wt% CPE-K (Colonial Chem) in MilliQ DI water] was performed for 1 h at T = 70 C. After rinsing excess solution with DI water, Carnation mineral oil (Sonneborn, kinematic viscosity µ = 12.5 ± 1.5 mm 2 /s at 40 C, interfacial tension at oil-vapor interface γ OV = 28 ± 0.5 mn/m, interfacial tension at water-oil interface γ WO = 61 ± 3 mn/m at room temperature) was spun on the side of interest at 1,000 rpm (for Fig. 3d and Supplementary Movie 3 only) or 4,000 rpm for 2 min to create slippery coatings. In order to further reduce lubricant thickness, pressurized Tetrafluoroethane (Whoosh-Duster, VWR) was used as an inert gas to remove some of the spin-coated mineral oil from the test surfaces. To create the superhydrophobic surfaces used in Fig. 4a, the same bare aluminum sheet was first roughened with sandpaper (Sanding Sheet for Aluminum, 320 Grit, McMaster-Carr) before molding. Surfaces were cleaned by Alcojet, acetone, and MillQ DI water and made hydrophobic by a liquid-phase surface treatment [0.1 wt% CPE-K (Colonial Chem) in MilliQ DI water] for a few hours at T = 70 C and rinsed with DI water. Surface Modification 2 To minimize the effect of micro/nanoscale roughness smaller than the radius of curvature of bumps (see Supplementary Experimental below), polydimethylsiloxane (PDMS, 10:1 wt% of Sylgard 184 silicone elastomer base : Sylgard curing agent) was spun on the side of interest at 2,000 rpm for 2 min. The thickness of the deposited PDMS was 22.2 ± 3.3 µm, calculated from the measurement of mass difference before and after the deposition. Surface Modification 3 To prepare the hydrophobic surfaces used in Fig. S3 and Supplementary Movie 2, another liquid-phase surface treatment 1 [1 wt% solution of fluoroaliphatic phosphate ester fluorosurfactant (FS100, Mason Chemical Company) in 95:5 ethanol:water] for ~1 h at T = 70 C followed by a DI water rinse was performed after roughening by sandpaper (320 grit, McMaster- Carr), molding, and cleaning. Surfaces used for Fig. S4 and for the hydrophobic control in S7 were prepared without the surface roughening process. 2

3 RESEARCH I.2. Contact Angle Measurements Static water contact angle (θ static ) and contact angle hysteresis (CAH) measurements shown in Table S1 were performed on various surfaces using drop shape analysis system DSA100 (Krüss, Germany). Small droplets of water (5 µl) were placed in multiple areas on the surfaces of each sample and observed using a video camera. The angle was then estimated from the still images using photo analysis software. The θ static, and CAH were obtained by measuring at least three different locations on the sample. Supplementary Table S1. Measured contact angles of water on different flat surfaces. θ static ( ) CAH ( ) PDMS-coated Hydrophobic Surfaces 120 ± 2 65 ± 1 Slippery Surfaces with Nanostructure 104 ± 1 < 5 Slippery Surfaces without Nanostructure 108 ± 1 < 5 Superhydrophobic Surfaces 155 ± 2 < 5 FS100-coated Hydrophobic Surfaces 136 ± 6 35 ± 1 I.3. Thickness Characterization of Carnation Mineral Oil TM The average thickness of Carnation mineral oil was calculated by measuring the mass of test surfaces before and after spincoating and additional removal of oils by applying airflow (Table S2). Supplementary Table S2. Calculated thickness of Carnation mineral oil TM. All the values are averaged from at least three measurements. Area of Aluminum Mass of Oil after Spincoating Oil Thickness Mass of Oil after Oil Thickness Sample [cm 2 ] at 1000 rpm (mg) (nm) Airblowing (mg) (nm)

4 RESEARCH SUPPLEMENTARY INFORMATION I.4. Condensation Experiment All the water condensation experiments were done in a custom humidity chamber, composed of a metallic frame with acrylic viewing windows and a door as shown in Fig. S1, that enabled regulation of relative humidity (RH = 60 ± 5%), by a microprocessor controller (Model , electro-tech systems Inc.) and ultrasonic humidifier (AOS 7146, Air-O-Swiss) and surrounding ambient temperature (T = 23 ± 2 C). Vertically positioned flat and bumpy test surfaces (T surface = 7.3 ± 0.6 C) were chilled through the thermal contact (3M TM Scotch Double Sided Conductive Copper Tape, 12.7 mm wide and 0.04 mm thick) with U-shaped copper tube (T tube = 2.3 ± 0.3 C). The temperature of surfaces and copper tube were measured with a digital thermometer (HH66U, OMEGA). Supplementary Figure S1. Experimental setup. I.5. Optical Analysis of Droplet Growth The diameter of the maximum droplets on the bumps and flat surfaces were measured by analyzing the images taken by a camera (EOS Rebel T4i, Canon) with a macro lens (MP-E 65mm, Canon). For one data point, at least three droplets on the same surface geometry in the same image were selected. For analyzing the amount of water collection on each surface, the diameters of shed droplets were measured using pixel-counting software (ImageJ) and were then converted to millimeters using a reference measurement. The volume of water was then calculated using an estimated contact angle (θ = 105 ). 4

5 RESEARCH II. Supplementary Control Experiments II.1. Effect of Radius of Curvature of Convex Topography Compared to the Effect of Surface Roughness Previous studies on condensation on topographically heterogeneous surfaces have found that the micro/nanoscale concave textures play a major role in preferential condensation if the textured surface is modified with a chemically homogeneous coating 2,3. To minimize the effect of the small length scale concave features that are formed on the Al plates upon pressing into the mold, we coated the bumpy surfaces with PDMS used in the experiments designed for Fig. 2 and Fig. S2b (see the Supplementary Methods section above for detailed coating condition) and checked the PDMS-coated surfaces using scanning electron microscopy (SEM) and profilometry. Whereas the uncoated surfaces exhibited microscale roughness, the PDMS-coated surfaces did not display the micro-roughness and were effectively smooth, as shown in Fig. S2. Supplementary Figure S2. (a) SEM and contact profilometer images of spherical-cap-shaped bumps without PDMS coating. (b) SEM and contact profilometer images of spherical-cap-shaped bumps with PDMS coating. To further compare the effect of the micro/nanoscale concave textures and that of millimetric convex topography on droplet growth during condensation, we have tested the same macroscopic geometry used in Fig. 2b, in which the flat surfaces around the bumps were significantly roughened with the 320 grit sandpaper before molding, cleaning and treating them with FS100. The bump, which did not undergo additional roughening by sandpaper shown in Fig. S3, still exhibited greater droplets on its apex compared to the highly roughened flat surfaces (see Supplementary Movie 2), thus ruling out the dominant effect of the surface nano/micro roughness on the observed preferential droplet growth at the apex of the structures. 5

6 RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure S3. (a) The apex region of a spherical-cap-shaped bump without additional roughening by sandpaper. (b) The roughened flat region with the same height. II.2. Effect of Radius of Curvature of Convex Topography Compared to the Effect of Temperature Distribution across the Surface We designed two different PDMS-coated bumps and a conical pipe in which curvature gradually increases (radius decreases) from left to right; at the same time, we applied a temperature gradient across the bumpy surface and pipe, such that T increases from left to right (Fig. S4). Supplementary Figure S4. (a) An image of water droplets condensed on two different PDMS-coated bumps with the same height, under a gradually increasing surface temperature (T) from left to right. The largest droplet on each bump is denoted by a yellow dotted circle. The droplets on the flat region are denoted by red circles. (b) Condensation on a conical, pipe-like geometry. Top: an image (t = sec) of water droplets condensed on a conical surface with a gradually increasing surface temperature (T) from left (T = 8.13 ± 0.05 C at x = 0 mm) to right (T = ± 0.15 C at x = 17.6 mm). Bottom: a family of averaged droplet sizes (2r avg ) as a function of position. Purple circles, blue squares, green triangles, and red diamonds represent t = , , , and sec, respectively. Gravitational force is downward in the optical images. All error bars, 1 s.d. 6

7 RESEARCH In contrast to the trend in the droplet size on the flat region that follows the direction of the surface temperature gradient (i.e. more efficient condensation and therefore larger droplets on the colder region, as denoted by red dotted circles on the bottom of Fig. S4a), droplets on the smaller bump show facilitated growth compared to that on the larger bump (denoted by the yellow dotted circles in Fig. S4a). More interestingly, on the conical geometry, non-monotonic droplet size distribution is observed. Within the region where the radius of the pipe is large enough (far left, 0 x 6 mm, in Fig. S4b), droplet diameter decreases as temperature increases from left to right. However, as the radius of the pipe decreases further, the effect of the curvature overcomes the effect of temperature and the droplet sizes begin to increase against the temperature gradient, becoming progressively larger according to the new mechanism preferential droplet growth at highly curved convex surfaces. Supplementary Table S3. Radius of curvature of various bumps used in Fig. 2 from the profilometer images. Radius of curvature (mm) Spherical-cap-shaped bump Spherical-cap-shaped bump Spherical-cap-shaped bump Rectangular bump 0.18 III. Theoretical Modeling III.1 Theoretical Modeling of Focused Diffusion and Heat Flux on the Apex of Spherical- Cap-Shaped Bumps Using a Spherical Mass Sink and Source Geometry Within a narrow region represented by the green rectangle in Fig. S5a, the concentration gradient near the apex of spherical-cap-shaped bumps can be approximately estimated by converting the bump topography to a sphere with the same radius of curvature (Fig. S5b) and calculating the concentration distribution created by a mass sink and its mirror image with the same magnitude and the opposite sign (i.e., corresponding mass source that has the same distance from its center to the depletion layer), as shown in Fig. S5c. The concentration distribution at an arbitrary point on the line between the centers of the mass source and sink can be obtained by the superposition of two independent concentration distributions created by the source and sink, respectively. In the following, the analytical expressions of the two independent concentration distributions are derived respectively, and they will then be superposed. To calculate the concentration distribution created by a spherical mass sink with the radius of curvature (κ -1 ), we can start with the diffusion equation that describes the threedimensional concentration distribution in the spherical coordinate system. d dr r dc 2 dr =

8 RESEARCH SUPPLEMENTARY INFORMATION A general solution to the differential equation is given as C = A r + B. If J 0 is the diffusion flux at the surface of the spherical mass sink (r = r 0 =κ -1 ), J 0 = J(r = r 0 ) = D dc dr r=r0 ( ), = D Ar 0 2 where D is the diffusion coefficient, which is assumed to be a constant in this first approximation estimate, then A can be expressed by A = J r D = Q 4πD, where Q is the total diffusion flux through the surface of the spherical mass sink. Supplementary Figure S5. (a) Schematic illustration (cross-sectional view) of depletion layer (represented by red dotted line) and a spherical-cap-shaped bumped surface (represented by blue solid line). The green rectangle and point represent the area and point of interest, respectively. (b) A spherical mass sink corresponding to the spherical-cap-shaped bump. (c) The spherical mass sink and its mirror image (a corresponding spherical mass source represented by red dotted line) used to calculate the concentration distribution and gradient near the point of interest. The concentration at an arbitrary point on the z axis created by the mass sink can be obtained by C 1 = C 0,1 Q 1 1 4πD r 1 r 0, where C 0,1 is the concentration at the surface of the spherical mass sink. By considering the the mass flux with the opposite sign, 8

9 RESEARCH ( ) Q = 4πD C C r 2 r 0, the concentration at the point created by the mass source can be obtained as follows: C 2 = C 0,2 + Q 1 1 4πD r 2 r 0. If the two concentration distributions are superposed, C = C 1 + C 2 = ( C 0,1 + C 0,2 ) + Q 1 1 4πD r 2 r 1. In that equation, C 0,1 +C 0,2 (the concentration at the depletion layer when r 1 = r 2 ) can be regarded as constants and Q/4πD =ΔC (κ -1 ) / (1-κ -1 /2d) is substituted 4, then 1 ΔC κ 1 C = a κ 1 2d r 2 r 1. ( ) Here ΔC is the difference in concentration between the bumpy surface and depletion layer thickness and d = δ + κ -1. By substituting r 2 = κ δ - h and r 1 = κ -1 + h because H<<δ, we get: 1 ΔC κ 1 C = a + 1 κ 1 2d κ 1 + 2δ h 1 κ 1 + h. ( ) The concentration gradient near the apex of the spherical-cap-shaped bump (h à 0) is obtained by differentiating the above equation and by substituting h = 0 as follows: dc ΔC κ 1 1 ( 1) = dh h 0 1 κ 1 2d (κ 1 + 2δ h) (κ 1 + h) 2 ( ) ΔC κ 1 = ( 1 κ 1 2d) (κ 1 ) 2 (1+ 2δ κ 1 ) 2 = ΔC κ 1 (1+ 2δ κ 1 ) 2 1 2(1+ δ κ 1 ). Note that when δ /κ -1 >>1, the concentration gradient near the apex of the spherical-cap-shaped bump is inversely proportional to κ -1. The following final form of scaling description of diffusion flux is used in the manuscript: J C ~ dc ~ 1 dh h 0 κ. 1 Using the same method, first approximation estimate of heat flux near the apex of spherical-capshaped bumps can be obtained, and the dependence of the temperature gradient on the radius of curvature is the same as the concentration gradient: J T ~ dt ~ 1 dh h 0 κ

10 RESEARCH SUPPLEMENTARY INFORMATION III.2 Numerical Calculation of Focused Diffusion Flux by Using COMSOL-Multiphysics Models for steady state transport of dilute species were used to simulate the magnitude of diffusion flux. The depletion layer thickness (δ ~ 10 mm > H ~ 1 mm) calculated based on previous studies 2,5 (see Fig. 2a) was used. We employed axisymmetric coordinates and twodimensional coordinates for spherical-cap-shaped bumps and rectangular bumps, respectively. The magnitude of the maximum diffusion flux focused at the apex of bumps does not decrease more than 5%, if P pattern /R bump > 2.5 (see Fig. 2c). III.3 Numerical Calculation of Total Free Energy of Droplet-Vapor-Bump System Using Surface Evolver The total free energy of a water droplet-vapor-asymmetric bump composite system was calculated using the Surface Evolver 6 software under user-specified initial conditions (Fig. S6). We kept the volume of the water droplet constant and calculated the energy of the system as the droplet moves to the equilibrium position and shape as the iteration proceeds. During the iterations, local water contact angle is kept constant along the three phase contact line and no contact angle hysteresis is assumed. The distortion near the contact line when the droplet is far from the equilibrium position arises from the curved shape of the solid-liquid boundary. Supplementary Figure S6. An oblique view of the Surface Evolver model used in this work. 10

11 RESEARCH IV. Importance of Multi-Scale Surface Structures and Asymmetry of Bumps for Facilitating Both Droplet Growth and Transport Supplementary Figure S7. Droplet growth curve on four surfaces macroscopic asymmetric bumps with nanostructure (without lubricant, r, slope = 0.64), macroscopic asymmetric bumps with molecularly smooth lubricant (without nanostructure, p, slope = 0.78), flat slippery coatings (without macroscopic bump,, slope = 0.79), and flat hydrophobic surfaces (as a control,, slope = 0.86). Whereas slippery flat surfaces showed shedding at t ~ sec, the other three surfaces did not display shedding for more than t ~ sec. The slopes of all the lines are similar to each other because when condensed droplet size is smaller than the radius of curvature of the underlying convex structure, the effect of curvature does not significantly affect the droplet growth exponent as suggested by the dimension arguments in a previous study 2. All error bars, 1 s.d. Supplementary Figure S8. Images of droplets condensed on slippery spherical-cap-shaped bumps (a) and rectangular bumps (b). Even with slippery coatings, the bumps used in Fig. 2f,h did not shed the droplets, even though the droplets are greater than the shedding droplet diameter (denoted by purple dotted horizontal line) measured on flat surfaces, showing the importance of the asymmetric topography of bumps for an efficient droplet transport. All error bars, 1 s.d. 11

12 RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure S9. Fast growth and transport of droplets on slippery asymmetric bumps as compared to the droplets at the bottom edge regions, from Supplementary Movie 6. Each data point outside the green circles represents the average size of at least the three largest droplets on each surface. The green circles show the enhanced growth rate for the first three droplets that begin to move down by coalescence-driven growth and capillary-driven motion before leaving the bump and shedding solely by gravity. Each data point inside the green circles represents the diameter of the largest droplet on each of the bumps, obtained by tracking the same droplet on each of three different bumps. This plot demonstrates the superior drop growth behavior on the apex of bumps, compared to the bottom edge region and rules out the edge-effect as the reason for droplet growth. All error bars, 1 s.d. Supplementary Figure S10. Long-term steady state water collection on bumpy (denoted by p and black solid line) and flat (denoted by and blue dotted line) slippery surfaces. (a) Collected water. (b) Average rate of water collection. These extended data demonstrate that the control slippery surface, while significantly outperforming any other state-of-the-art surfaces (see Fig. S7 and ref. 7), must undergo a highly delayed triggering event before water collection can begin, and then shows lower continuous turnover rate compared to the bumpy slippery surface that has a higher continuous turnover rate, which yields substantially more water over time. 12

13 RESEARCH References 1. Kim, P. et al. Liquid-infused nanostructured surfaces with extreme anti-ice and anti-frost performance. ACS Nano 6, (2012). 2. Beysens, D. Dew nucleation and growth. C. R. Phys. 7, (2006). 3. Qian, M. & Ma, J. Heterogeneous nucleation on convex spherical substrate surfaces: a rigorous thermodynamic formulation of Fletcher s classical model and the new perspectives derived. J. Chem. Phys. 130, (2009). 4. Hahne, E. & Grigull, U. A shape factor scheme for point source configurations. Int. J. Heat Mass Transfer. 17, (1974). 5. Gebhart, B. & Pera, L. The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion. Int. J. Heat Mass Transfer. 14, (1971). 6. Brakke, K. A. The Surface Evolver. Exp. Math. 1, (1992). 7. Xiao, R., Miljkovic, N., Enright, R. & Wang, E. N. Immersion condensation on oil-infused heterogeneous surfaces for enhanced heat transfer. Sci. Rep. 3, 1988 (2013). 13