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1 doi: /nature Freezing of Impacting Droplets Ice build-up from freezing rain is problematic for variety of applications including aircraft surfaces, wind turbines, and power lines. If a water drop were to bounce off a surface before it were to freeze, then ice build-up can be significantly reduced. When a liquid droplet impinges a solid surface that is kept below its freezing point, spreading and solidification of the droplet occur simultaneously 1-4. Whether a drop bounces or gets arrested on the surface depends on the extent of solidification, which in turn, depends on the contact time for a given set of temperatures and thermophysical properties of the droplet and substrate materials. 2,4 Here, we have carried out experiments to show that reducing contact time with macrotexture has a significant effect on whether or not the drop freezes on the surface. We have used liquid tin, rather than water, in these experiments due to experimental constraints associated with the sub-cooling that could be achieved in our set up. Liquid tin is a good model system for water since the timescales of bouncing and freezing are on the same order. Particularly, the bouncing timescale ( t c ρr 3 γ ) for identical drop sizes are almost equal as the ratio of density to surface tension for liquid tin and water are very close. Specifically, we show tin drops impacting a microscopically textured nonwetting surface with and without macrotextures under identical conditions. The drops bounce off of the macrotextured surface while they freeze on the surface without macrotextures. 1

2 Metal Droplet Impact Experiments The substrates were laser-ablated silicon, identical to the ones used for water droplet experiments described in Fig 2b,c. Liquid tin makes a large contact angle (~120 ) 5,6 with smooth silicon and therefore is able to bounce off the microscopically textured surfaces. The key parameter varied in these experiments was the substrate temperature as it controlled the amount of solidification of the impacting tin droplet. Since molten tin oxidizes rapidly in air, the experiments were conducted in a glove box, which could maintain oxygen concentration below 150 ppm 7. Droplets of molten tin with radius 1.25 mm were produced using a drop-on-demand droplet generator 7. The droplet impact velocity was controlled by setting the height, above the substrate surface, from which droplets ejected out of the droplet generator and was about 1.3 m/s, identical to its value for the water droplet experiments. The temperature of the droplet was about 250 C, above the melting point of tin (232 C). The substrate temperature was controlled by mounting it on a copper block (30 mm x 20 mm x 5 mm) having three cartridge heaters (5 W each) controlled via a temperature controller (CN 3112, Omega). A high thermal conductivity pad (Bergquist Gap Pad 1500) was inserted between the substrate and the copper block in order to minimize thermal contact resistance. A thermocouple kept below the thermal pad measured the substrate temperature while a high-speed camera captured droplet deformation during impingement on the substrate. Extended Data Fig. 1 shows tin droplets impacting silicon substrates without (top row of images) and with the macroscopic ridge (bottom row of images). In both cases, the droplets are able to bounce off of the substrate completely, however, the contact time when the droplet hits the substrate with the ridge is significantly less (6.8 ms) than that 2

3 without the ridge (11.9 ms). This is consistent to our experiments with water droplets shown earlier in the manuscript. We observed droplets to bounce-off completely for both cases until the substrates were cooled to 125 C (subcooling ~ 107 C) when droplets impacting the substrate without the ridge got severely arrested (Extended Data Fig. 2, top row) so that the contact time was infinite. However, droplets impacting the substrate with the macroscopic ridge continued to bounce-off (Extended Data Fig. 2, bottom row, Supplementary Video 5). In fact, droplets impacting the ridge continued to bounce off until the substrate was cooled to about 50 C, indicating that a significantly large subcooling ~182 C is needed to arrest the droplets on the ridge surface (Extended Data Fig. 3, bottom row). These experiments demonstrate that the contact time reduction achieved in our study by using designed macrostructures (ridges in the present case) is significant enough to change the outcome of the droplet impact process over a large range of temperature. The liquid tin experiments provide evidence that reducing drop contact time reduces the total heat transferred between the drop and the solid. These results can be extended to freezing water droplets impacting a cold surface, as well as metal droplet induced fouling observed in turbines and thermal spray coating systems. Similarly, one can extend this idea to other diffusion processes, such as chemical and particle transport that occur during droplet-based corrosion and fouling processes. 2. Droplet Splitting and Contact Time 3

4 For the ridge type macrostructure, the drop impact dynamics is modified in a way that leads to splitting the initial drop into two parts. Therefore, it is tempting to think that our paper does not break through the axisymmetric limit, but rather reduces the radius that one should incorporate in the axisymmetric limit. Indeed, if it were possible to reduce the size of the drop prior to impact, the dimensional contact time of the two axisymmetric drops would be shorter, even though the theoretical axisymmetric limit would still be observed. However, in most situations, it is impractical, if possible, to accomplish this mid-air break-up, especially through a passive mechanism. Our paper describes a practical way to achieve the contact-time-reduction benefits of mid-air split up, but it is critical to note that prior theory and experiments based on an axisymmetric drop geometry can not be applied directly. Here, we show in detail that it is incorrect to predict the contact time by simply substituting the radius of the split part in the current theoretical scaling t c ρr 3 /γ and simplistically considering the ridge case equivalent to that of two drops impinging with volumes equal to those of split parts. We demonstrate the above with the help of Extended Data Fig. 7 which lays out the two scenarios: the ridge case (Extended Data Fig. 7a) and the simplistic case (Extended Data Fig. 7b), the key difference being that in the former case the drop splits on the surface while retracting (subscript 1), whereas in the latter case it is split before impact (subscript 2). If the initial drop volume, Ω = 4 3 π R 3 1, is split into two equal parts, the radius of the split part is that the contact time 3 R 2 = 2. The simplistic approach therefore suggests 4

5 t = 2.2 ρ γ R 2 t c 2.2 and thereby = = 1.6. This value happens to be close to the measured value of 1.4, τ 2 but we argue that this is a mere coincidence. By considering the retraction time in both cases, we show that splitting on the surface and splitting before impact are two fundamentally different scenarios that lead to very different contact times. The retraction time scales as t r ~ R d V T C, where R d is the distance the film needs to travel to dewet and V T-C is the Taylor-Culick retraction velocity. Substituting in the velocity, this time can be rewritten as: t r ~ R d 2γ ρh, where h is the average thickness of the liquid film when retraction begins. The thickness h can be expressed in terms of the radius of the initial drop R and the maximum radius of the spread film R m by considering the conservation of droplet mass before impact and at the instant of maximum spread: R 2 m h ~ R 3. Combining these expressions and noting that 3 R 2 = 2, we find that the time for the two cases are different, highlighting that a nonaxisymmetric drop split on the surface has a different contact time than two axisymmetric drops split before contacting the surface: t r,1 ~ R m1 2 2γ ρh 1 = 1 2 2γ ρ t r,2 ~ γ ρ In general, if the spread out drop is split into n films of almost equal thickness (Extended Data Fig. 7c), then 5

6 h n h 1, t r,1 ~ 1 (1) n 2γ ρ whereas in the case of Extended Data Fig. 7b for n equal volume drops, t r,2 ~ 1 n. (2) 2γ ρ Equations (1) and (2) show that the retraction time for the drops split prior to axisymmetric impact scales as t~, whereas for the ridge case (when film splits on the surface) the retraction time scales as t~. The difference in scaling again demonstrates that these two cases are fundamentally different. Furthermore, the exact form of scaling could be affected due to non-trivial effects, such as Rayleigh-Plateau instabilities, zipping (Extended Data Fig. 7c), and complex geometries (Fig. 1e). References for Supplementary Information 1. Aziz, S.D. & Chandra, S. Impact, recoil, and splashing of molten metal droplets. Int. J. Heat Mass Transf. 43, (2000). 2. Mishchenko, L. et al. Design of Ice-free Nanostructured Surfaces Based on Repulsion of Impacting Water Droplets. Acs Nano 4, (2010). 3. Chandra, S. & Fauchais, P. Formation of solid splats during thermal spray deposition. J. Thermal Spray Tech. 18(2), (2009). 4. Dhiman, R. & Chandra, S. Freezing-induced splashing during impact of molten metal droplets with high Weber numbers. Int. J. Heat Mass Transf. 48, (2005). 6

7 5. De Jonghe, V. & Chatain, D. Experimental study of wetting hysteresis on surfaces with controlled geometrical and/or chemical defects. Acta Metall. Mater. 43(4), (1995). 6. Amirfazli, A., Chatain, D. & Neumann, A.W. Drop size dependence of contact angles for liquid tin on silica surface: line tension and its correlation with solidliquid interfacial tension. Colloids and Surfaces A. 142, (1998). 7. Cheng, S., Li T. & Chandra, S. Producing molten metal droplets with a pneumatic drop-on-demand generator. J. Mater. Process. Tech. 159(3), (2005). 7