Self-wrapping of an Ouzo Drop Induced by Evaporation on a Superamphiphobic Surface Supplementary Material

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1 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 Water (wt%) Ethanol (wt%) Trans-anethole (wt%) Figure S.1: Phase diagram for the trans-anethole-ethanol-water system. The blue dots present the measured miscibility limit. 1

2 . 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 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 A ν B ν C ν water ethanol 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

3 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 = gmol 1 [2] M e = gmol 1 [2] M ta = gmol 1 [3] p ν,sat saturation pressure of component ν Pa r c base radius m R universal gas constant 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

4 (a) ρ [g/cm 3 ] ρ σ σ [mnm 1 ] (b) D [10 9 m 2 /s] D µ µ [mpas] ethanol mass fraction y e ethanol mass fraction y e (c) γν γ w γ e ethanol mole fraction x e (d) cp [kj/(kgk)] c p λ ethanol mass fraction y e 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 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) [4] 1005 [12] [4] substrate (quartz glass) 2648 [4] 739 [4] 1.36 [13] 4

5 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 C and a temperature accuracy of±0.3 C). ambient temperature [ o C] Data-1: 2µL Data-2: 0.93µL Data-3: 0.92µL time [second] relative humidity [%] Data-1: 2µL Data-2: 0.93µL Data-3: 0.92µL time [second] Figure S.3: Measured ambient temperature T and relative humidity H during the evaporation experiments. 5

6 References [1] C. Y. Lee and C. R. Wilke. Measurements of vapor diffusion coefficient. Ind. Eng. Chem., 46(11): , [2] Dortmund Data Bank [3] National Center for Biotechnology Information. PubChem Compound Database; CID= [4] John Dean. Lange s handbook of chemistry. McGraw-Hill, New York, [5] Begoña González, Noelia Calvar, Elena Gómez, and Ángeles Domínguez. Density, dynamic viscosity, and derived properties of binary mixtures of methanol or ethanol with water, ethyl acetate, and methyl acetate at T=(293.15, , and )K. J. Chem. Thermodyn., 39(12): , [6] Gonzalo Vazquez, Estrella Alvarez, and Jose M. Navaza. Surface tension of alcohol water + water from 20 to 50 C. J. Chem. Eng. Data, 40(3): , [7] Stanislav Pařez, Gabriela Guevara-Carrion, Hans Hasse, and Jadran Vrabec. Mutual diffusion in the ternary mixture of water + methanol + ethanol and its binary subsystems. Phys. Chem. Chem. Phys., 15(11):3985, [8] A. Zuend, C. Marcolli, B. P. Luo, and T. Peter. A thermodynamic model of mixed organic-inorganic aerosols to predict activity coefficients. Atmos. Chem. Phys., 8(16): , [9] A. Zuend, C. Marcolli, A. M. Booth, D. M. Lienhard, V. Soonsin, U. K. Krieger, D. O. Topping, G. McFiggans, T. Peter, and J. H. Seinfeld. New and extended parameterization of the thermodynamic model AIOMFAC: calculation of activity coefficients for organic-inorganic mixtures containing carboxyl, hydroxyl, carbonyl, ether, ester, alkenyl, alkyl, and aromatic functional groups. Atmos. Chem. Phys., 11(17): , [10] J.-P. E. Grolier and Emmerich Wilhelm. Excess volumes and excess heat capacities of water + ethanol at K. Fluid Phase Equilibr., 6(3-4): , [11] Ryuzi Yano, Yukio Fukuda, and Tsuneo Hashi. Thermal conductivity measurement of water-ethanol solutions by the laser-induced transient grating method. Chem. Phys., 124(2): ,

7 [12] J. Hilsenrath, C.W. Beckett, and W.S. Benedict. Tables of Thermal Properties of Gases: National Bureau of Standards. Number Nr Literary Licensing, LLC, [13] O. A. Sergeev, A. G. Shashkov, and A. S. Umanskii. Thermophysical properties of quartz glass. J. Eng. Phys., 43(6): ,

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