Electronic Supplementary Material (ESI) for Soft Matter. This journal is The Royal Society of Chemistry 2017 Self-wrapping of an Ouzo Drop Induced by Evaporation on a Superamphiphobic Surface Supplementary Material Tan, Diddens, Versluis, Butt, Lohse, and Zhang S.1 Phase diagram of the trans-anethole-ethanol-water system Figure S.1 is the ternary diagram of the trans-anethole-ethanol-water system. The blue solid line is the measured phase-separation curve. The gray dashed lines indicate the composition paths of the titration experiments. The titration was conducted at a temperature of around 22 C. 0.0 0.2 0.6 Water (wt%) 0.4 0.6 Ethanol (wt%) 0.4 0.2 0.0 0.0 0.2 0.4 0.6 Trans-anethole (wt%) Figure S.1: Phase diagram for the trans-anethole-ethanol-water system. The blue dots present the measured miscibility limit. 1
. S.2 Parameters used in the FEM model S.2.1 List of symbols A description of all symbols used in the FEM model can be found in Table S.2.1. For quantities that are constant during the simulation, also the corresponding values are given. S.2.2 S.2.2.1 Relations for non-constant quantities Saturation pressure p ν,sat The temperature-dependence of the saturation pressure is calculated by the Antoine equation, i.e. by B ν log 10 (p ν,sat [in mmhg])=a ν C ν + T[in C], where the constants A ν, B ν and C ν read [2] S.2.2.2 A ν B ν C ν water 8.07131 1730.63 233.426 ethanol 8.20417 1642.89 230.300 Composition-dependent properties (S.1) In the droplet, the physical properties depend on the mixture composition. Due to the low initial concentration of trans-anethole, the composition-dependence of all quantities in the ouzo droplet was approximated based on a binary water-ethanol mixture. To that end, experimental data for the mass density ρ [5], the dynamic viscosity µ [5], the surface tension σ [6], the diffusivity D [7], the specific heat capacity c p [10] and the thermal conductivity λ [11] was fitted. The activity coefficients γ ν were determined by AIOMFAC [8, 9]. The extracted experimental data and the corresponding fits are depicted in Figure S.2. 2
Symbol Description value and/or unit c ν vapor concentration of species ν kg/m 3 c ν, ambient vapor concentration of species ν kg/m 3 c ν,vle vapor-liquid equilibrium concentration kg/m 3 c p specific heat capacity J/(kgK) D mutual diffusivity in the liquid m 2 /s D vap ν,air vapor diffusion coefficient D vap w,air = 0.260cm2 /s [1] D vap e,air = 0.135cm2 /s [1] H relative humidity of water 42 % j ν mass transfer rate of species ν kg/(m 2 s) J ν diffusive liquid flux at the interface kg/(m 2 s) Jν gas diffusive vapor flux at the interface kg/(m 2 s) M ν molar mass of species ν M w = 18.015gmol 1 [2] M e = 46.069gmol 1 [2] M ta = 148.21gmol 1 [3] p ν,sat saturation pressure of component ν Pa r c base radius m R universal gas constant 8.314 459 8 J/(molK) t time s T temperature C T ambient temperature 23 C u mass-averaged liquid velocity ms 1 V droplet volume m 3 x ν mole fraction of component ν in the liquid y ν mass fraction of component ν in the liquid γ ν activity coefficient of component ν δ Γ delta function at the liquid-air interface 1/m 2 θ contact angle λ thermal conductivity W/(mK) Λ ν latent heat of evaporation Λ w = 2438kJ/kg [2] Λ e = 918kJ/kg [2] ν component index ν = w, e, ta ρ mass density kg/m 3 ρ gas mass density of air 1.183kg/m 3 [4] Table S.1: A table containing all quantities entering the FEM model. If the quantity is constant during the simulation, also the corresponding value is given. 3
(a) ρ [g/cm 3 ] 1.1 0.9 ρ σ 80 70 60 50 40 30 σ [mnm 1 ] (b) D [10 9 m 2 /s] 1.50 1.25 0 0.75 0.50 D µ 2.5 2.0 1.5 µ [mpas] 0.7 20 0.0 0.2 0.4 0.6 ethanol mass fraction y e 0.25 0.5 0.0 0.2 0.4 0.6 ethanol mass fraction y e (c) γν 5.0 4.5 4.0 3.5 γ w γ e 3.0 2.5 2.0 1.5 0.5 0.0 0.2 0.4 0.6 ethanol mole fraction x e (d) cp [kj/(kgk)] 4.5 4.0 3.5 3.0 2.5 c p λ 2.0 0.0 0.0 0.2 0.4 0.6 ethanol mass fraction y e 0.6 0.4 0.2 λ [W/(mK)] Figure S.2: Composition-dependent properties based on a water-ethanol mixture. (a) Mass density ρ [5] and surface tension σ [6]. Note that the surface tension is also a function of the temperature. However, since the temperature-dependence of the surface tension is only in the order of 0.14mNm 1 K 1, it is not plotted for the sake of visibility. (b) Dynamic viscosity µ [5] and diffusivity D [7]. (c) Activity coefficients γ ν calculated by AIOMFAC [8, 9]. (d) Specific heat capacity c p [10] and thermal conductivity λ [11]. S.2.2.3 Thermal properties of air and substrate The thermal properties of the gas phase and the substrate used in the simulation read ρ [kg/m 3 ] c p [J/(kgK)] λ [W/(mK)] gas phase (air) 1.183 [4] 1005 [12] 0.026 [4] substrate (quartz glass) 2648 [4] 739 [4] 1.36 [13] 4
S.3 Temperature and relative humidity Figure S.3 presents the temperature T and relative humidity H in the laboratory during the experiments. The sampling rate is one per second with a relative humidity accuracy of ± 2 % over 10 to 90 % @25 C and a temperature accuracy of±0.3 K @25 C). ambient temperature [ o C] 28 26 24 22 20 Data-1: 2µL Data-2: 0.93µL Data-3: 0.92µL 18 0 200 400 600 800 time [second] relative humidity [%] 48 46 44 42 40 Data-1: 2µL Data-2: 0.93µL Data-3: 0.92µL 38 0 200 400 600 800 time [second] Figure S.3: Measured ambient temperature T and relative humidity H during the evaporation experiments. 5
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