On supercooled water drops impacting on superhydrophobic textures

Transcription

1 of On supercooled water drops impacting on superhydrophobic textures Tanmoy Maitra, Carlo Antonini, Manish K. Tiwari a, Adrian Mularczyk, Zulkufli Imeri, Philippe Schoch and imos Poulikakos * Laboratory of Thermodynamics in merging Technologies, Mechanical and Process ngineering epartment, TH Zurich, 8092 Zürich, Switzerland These authors contributed equally to this study a Current address: Mechanical ngineering, University College London, Torrington Place, London, WCI 7J * Corresponding author: dpoulikakos@ethz.ch Page 1 of 10

2 1. escription of the experimental setup Supercooled drop impact experiments were performed inside a chamber with controlled environmental conditions. The chamber was cooled by supply of cold nitrogen gas, both by direct flow into the chamber from the top, and by indirect cooling through a U-shaped aluminum channel (see Figure S1). The nitrogen flow inside the chamber was kept low enough, to avoid any disturbance to drop fall trajectory. Tests were performed at different environmental temperatures from room temperature, i.e. 23 C, down to -16 C. The low temperature limit was imposed by water freezing by heterogeneous nucleation at the drop dispenser tip, made of high-purity perfluoroalkoxyalkane (PFA), with external diameter 360 µm, and internal diameter 150 µm (part number 1933, Upchurch Scientific). The environmental humidity was kept at 0% by dry nitrogen flow, as mentioned in the main paper, to avoid frost formation on the sample and on the dispenser tip, limiting drop freezing events while dispensing the drop. Tests were performed after reaching isothermal conditions in the chamber, so that environmental, T, and surface temperature, T S, were equal. ue to evaporation effects, the drop temperature, T, was lower than the environment. The difference between the two was measured directly by a thermocouple immersed in the drop, during separate calibration tests (see Figure 2 in the main paper). When performing impact experiments, all tests were repeated at least 3 times on each sample for a given impact condition to ensure reproducibility. Page 2 of 10

3 Figure S1: xperimental setup for drop impact experiment at supercooling conditions. Page 3 of 10

4 2. Contact angle measurement Table S1: Advancing and receding contact angles, and contact angle hysteresis of the two different micropillar superhydrophobic textured surfaces used for the impact experiments. Surface Advancing contact angle ( o ) Receding contact angle ( o ) Hysteresis ( o ) µ 162.4± ± ± µ 162.4± ± ± Temperature effect on / max o for the 13.0 µ 4.5 superhydrophobic surface Figure S2: (a) Images of drop before impact and at maximum spreading. (b) scanning electron microscopic image 13.0 of surface µ (c) / max o as function of droplet temperature, T, for the surface µ 4.5 and for three different impact velocities, 1.6 m/s, 1.3 m/s and 0.7 m/s. Page 4 of 10

5 4. xperimental data for / max o against existing analytical models xperimental values of maximum spreading, / max o, were compared to two models available in the literature: an energy based model from Mao et al. 1, and a hydrodynamic model from Roisman et al. 2. On the basis of energy conservation from the moment of impact to maximum drop spreading, Mao et al. 1 proposed that drop non-dimensional maximum spreading, / max o, can be found from: We max We max 2 ( θ) Re cos = 0 (S1) The coefficients for the term accounting for the viscous dissipation, the original paper to best fit experimental data from millimeter water drop impact tests We Re, were derived in Roisman et al. 2 developed a theoretical model to predict the evolution of the drop diameter, starting from classical hydrodynamic balance equations. Under the assumption of 2-axisymmetric flow, the mass and momentum balance for the motion of the rim in the radial direction, appearing at the edge of the liquid film (lamella), can be written as: 1 dwr 2π dt ρwr d V 2π dt r ( V ) = R h V (S2) r l l r ( ) 2 = ρr h V V Rσ + R F R F (S3) r l l r r r w r µ where W r is the total volume of the rim, V r is the rim radial velocity, V l is the velocity of the liquid in the lamella, h l is the thickness of the lamella, ρ is the density of the liquid, σ is the surface tension, Fw = σ cosθ is the capillary force at the interface, F µ is the viscous drag force and t is the time. As can be seen from the right-hand side of q. S3, the model takes into account the capillary effects, wettability Page 5 of 10

6 effects due to the substrate, as well as viscous effects. The model was derived from first principles and does not contain any tuning parameter to fit the data, as is the case for all energy based models. Figure 3 in the main paper illustrates the comparison between experimental data and predicted value for max /, using the energy based model by Mao et al. (Figure 3(a)), and the hydrodynamic model by o Roisman et al. (Figure 3(b)). xperimental data include both water drop impact tests at different temperatures, as well as water-glycerol drop impact tests (see Table S1 for properties of tested mixtures) at room temperature, to simulate the increase of viscosity of supercooled water drops. xperimental data are in very good agreement with the energy based model (average deviation is 5%), and also in good agreement with the hydrodynamic model (average deviation is 11%). 5. Contact angles with water-glycerol mixtures The advancing and receding contact angles were measured on the superhydrophobic microtextured surface, µ, and on the corresponding smooth silicon surface (with root mean square roughness ~0.2 nm), both functionalized by 1H,1H,2H,2H-Perfluorodecyltrichlorosilane (FTS) (96% Alfa Aesar) in n- hexane solution, at four different concentrations of glycerol (0%, 20%, 30% and 40% by weight) in water. The data in Figure S3 shows that the advancing contact angle is barely affected by addition of glycerol, whereas the receding contact angles decreases up to 15 on both surfaces by addition of glycerol on both microtextured and smooth surfaces. Page 6 of 10

7 Figure S3: Advancing and receding contact angles of water-glycerol mixtures at four different concentrations of glycerol (0%, 20%, 30% and 40% by weight) on the superhydrophobic microtextured surface, µ, and on the smooth functionalized silicon surface. Tests were performed at room temperature. Page 7 of 10

8 6. Liquid properties Table S2: viscosity of water-glycerol mixture at three different concentrations of glycerol and comparison to water at specific temperatures. Wt.% of glycerol In water-glycerol mixture Viscosity of water-glycerol mixture (mpas) 4 Surface tension of water-glycerol mixture (mn/m) 4 Viscosity of water at the specified temperature (mpas) at 5 o C at -5 o C at -15 o C Page 8 of 10

9 7. Captions for Videos Video 1: Side-by-side view of water drop impact on the µ surface at two different environmental temperatures, 23 C and -13 C, with impact velocity of 2.7 m/s (below the critical velocity of 2.8 m/s measured at room temperature). The video was recorded using side-view. The video shows that at T = -13 C the drop recoiling dynamics is significantly slower compared to 23 C. Thus, the contact time increases from ~13.3 ms at T = 23 C up to ~22.6 ms at T = -13 C. Video 2: Side-by-side view of water drop impact on the µ surface at two different environmental temperatures, 23 C and -10 C, with impact velocity of 3.1 m/s (above the critical velocity measured at room temperature, i.e. 2.8 m/s). The video was recorded using side-view. The size of the impaled drop remaining attached to the substrate is larger at T = 23 C compared to T =-10 C. Video 3: Side-by-side view of water drop impact on the µ surface for room temperature water and waterglycerol mixture (40% by weight), mimicking supercooled water at -15 C, at the impact velocity of 3.8 m/s (above the critical velocity measured at room temperature, i.e. 2.8 m/s). The video was recorded using top-view. For room temperature water, there are three different circles around the impact point, which correspond to bubble entrapment, partial penetration and full penetration, respectively. Interestingly, the diameter corresponding to full penetration matches the size of the droplet fragment remaining on the surface. However, with water-glycerol mixture (40% by weight), only two circles (regimes) are observed, corresponding to partial penetration and full penetration, with no bubble entrapment. Page 9 of 10

10 RFRNCS (1) Mao, T.; Kuhn,.; Tran, H. Spread and Rebound of Liquid roplets upon Impact on Flat Surfaces. AICh J. 1997, 43, (2) Roisman, I. V.; Rioboo, R.; Tropea, C. Normal Impact of a Liquid rop on a ry Surface: Model for Spreading and Receding. Proceedings of the Royal Society A: Mathematical, Physical and ngineering Sciences, 2002, 458, (3) Clanet, C.; Béguin, C.; Richard,.; Quéré,. Maximal eformation of an Impacting rop. J. Fluid Mech. 2004, 517, (4) uvivier,.; Seveno,.; Rioboo, R.; Blake, T..; Coninck, J. e. xperimental vidence of the Role of Viscosity in the Molecular Kinetic Theory of ynamic Wetting. 2011, (5) Hallett, J. The Temperature ependence of the Viscosity of Supercooled Water. Proceedings of the Physical Society, 2002, 82, Page 10 of 10