Self-wrapping of an ouzo drop induced by evaporation on a superamphiphobic surface

Evaporation of multi-component drops is crucial to various technologies and has numerous potential applications because of its ubiquity in nature. Superamphiphobic surfaces, which are both superhydrophobic and superoleophobic, can give a low wettability not only for water drops but also for oil drops. In this paper, we experimentally, numerically and theoretically investigate the evaporation process of millimetric sessile ouzo drops (a transparent mixture of water, ethanol, and trans-anethole) with low wettability on a superamphiphobic surface. The evaporation-triggered ouzo effect, i.e. the spontaneous emulsification of oil microdroplets below a specific ethanol concentration, preferentially occurs at the apex of the drop due to the evaporation flux distribution and volatility difference between water and ethanol. This observation is also reproduced by numerical simulations. The volume decrease of the ouzo drop is characterized by two distinct slopes. The initial steep slope is dominantly caused by the evaporation of ethanol, followed by the slower evaporation of water. At later stages, thanks to Marangoni forces the oil wraps around the drop and an oil shell forms. We propose an approximate diffusion model for the drying characteristics, which predicts the evaporation of the drops in agreement with experiment and numerical simulation results. This work provides an advanced understanding of the evaporation process of ouzo (multi-component) drops.


Introduction
Drop evaporation is an omnipresent phenomenon in daily life. During this process, the liquid at the drop surface changes its phase and escapes as vapor into the ambient air. Dating back to Maxwell, the evaporation process of a drop in an ambient gas has been explored and considered mainly as a diffusion-controlled process 1 . The study of the evaporation process of sessile drops is important because of its crucial role in numerous technologies and applications, such as inkjet printing, coatings, patternings, deposition of materials, or DNA mapping [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . In the last two decades, numerous studies have focused on understanding the evaporation process of sessile drops on solid substrates experimentally, numerically and theoretically 14,15 . Surface properties [17][18][19][20] , thermal effects 21,22 , dispersed particles in the liquid 3,23 , surfactants at the liquid-gas interface [24][25][26] , and the liquid composition [27][28][29] were all found to have a contribution to the drop evaporation characteristics.
The evaporation of multi-component drops draws special interest because of its ubiquity in practice. The physicochemical properties of the drop solution dramatically enrich the system and give rise to an unexpected outcome: the different volatilities of the components lead to distinct evaporation stages with different evaporation rates and various types of wetting behavior 27,28 .
In a hydrodynamic context, flow transitions inside an evaporating binary mixture drop have been revealed, which are a result of the intense and complicated coupling of flow and the spatio-temporal concentration field 29,30 . By controlling these mechanisms, binary drop evaporation can offer a new physicochemical way for surface coatings 31 .
Recently, we used an ouzo drop as a model for a ternary liquid mixture and investigated its evaporation process on a hydrophobic surface 32 . The Greek drink Ouzo (or the French Pastis or the Turkish Raki) is a miscible solution and primarily consists of water, ethanol and anise oil.
When the water concentration is increased by adding water or by reducing ethanol, the solution becomes opaque due to the "ouzo effect", i.e. the spontaneous nucleation of oil microdroplets [33][34][35] . We discovered how the preferential evaporation of ethanol triggers the "ouzo effect" in an evaporating ouzo drop. Four life phases can be distinguished during its drying. As a remarkable phenomenon, we found that the evaporation-triggered nucleation starts at the rim of the ouzo drops.
It can be attributed to the drop geometry, namely the singularity at the rim. On the hydrophobic substrate, the ouzo drops maintain a contact angle θ smaller than 90 • (flat droplets) because of the low surface energy of ethanol in the ouzo solution. The singularity of the evaporation rate at the contact line of flat drops 5,36 and the higher volatility of ethanol induce a maximum in the local water concentration and thereby trigger the onset of the "ouzo effect" at this position. At a later stage, the microdroplets coalesce and form an oil ring at the rim of the drop, with a water drop sitting on it. Once also the water has evaporated, only an oil drop remains.
Based on the diffusion model by Popov 5 , changing the geometric configuration is a simple and direct way to change the evaporation profile and hence to induce a different concentration distribution along the liquid-air interface. In particular, a maximum evaporation rate should be found at the top of the drop when the drop has a large contact angle (θ > 90 • ). Thus, ouzo drops on substrates with low wettability should have the highest water concentration at the top of the drop rather than at the rim, and therefore the onset of nucleation should take place right there.
However, a comprehensive numerical model by Pan et al., who took into account the evaporative cooling effect and the buoyancy-driven convective flow in the drop and vapor domains, shows that the maximum evaporation rate of drops with low wettability is still located at the contact line due to temperature effects 22 . Both of these models are only applicable to single-component drops, but hitherto it little is known about the evaporation process of multi-component sessile drops with low wettability (θ > 90 • ). Here we explore where the evaporation-triggered nucleation process starts for evaporating ouzo drops with θ > 90 • , and find out the evaporation dynamics.
First, we present an investigation of the evaporation characteristics of millimetric ouzo drops on a flat surface with a large contact angle. We performed evaporation experiments on a superamphiphobic surface, which is both superhydrophobic and superoleophobic, to achieve low wettability for the ouzo drops (θ > 150 • to start). We found that the "ouzo effect" induced by evaporation indeed preferentially takes place at the top of the drop, and two distinct stages with different evaporation rates exist. Moreover, a new remarkable phenomenon appears: part of the nucleated oil microdroplets form an oil shell wrapping up the ouzo drop, instead of forming a persistent oil ring at the contact line. Then a numerical model based on a finite element method presents additional insight into the process. Finally, we propose an approximate diffusion model for the evaporation characteristics of ouzo (multi-component) drops, and furthermore highlight and discuss the influences of Marangoni flow and the evaporative cooling effect. In summary, we provide a quantitive understanding of the evaporation process of ouzo drops experimentally, numerically and theoretically.  37,38 . These soot-templates surfaces are formed by collecting a fractal-like network of self-assembled nearly spherical carbon particles (diameter about 40 nm). The network is roughly 30 µm thick and homogeneous on length scales above 5 µm.
The soot particles are loosely connected by van der Waals forces. The network was stabilized by depositing roughly 30 nm of SiO2 using chemical vapor deposition (CVD) of tetraethyl orthosilicate (TEOS) for 24 h. The final porosity was 90 % 38 . The soot-templated superamphiphobic surface is optically transparent, so that the bottom side of the ouzo drop can be imaged while it evaporates. The static contact angles of Milli-Q water and trans-anethole oil on the substrate are 160 • ± 1 • and 157 • ± 0.5 • , respectively. Thus the ouzo drop with more than 60% ethanol can still initially hold ∼ 150 • static contact angle.

Experimental Setup
The evaporation experiments were performed in an empty room without any person in the room during data recording. In this sense, the entire lab can be considered as closed cell. An ouzo drop was deposited on a superamphiphobic surface through a teflonized needle (HAMILTON; 8646-02) by a motorized syringe pump (HARVARD; PHD 2000). Experiment recording started when the needle departed from the drop (defined as t 0 ). In practice there was a time delay (∼ 22 s) between starting to pump liquid out of the needle and taking the first snapshot of the drop (t 0 ), leading to premature evaporation. The time delay was caused by the difficulty of depositing a sessile ouzo drop on a superamphiphobic surface. Therefore, the initial ratios of ethanol and water of the recording data should be corrected. The correction for the ethanol composition can be estimated by extrapolating the ethanol composition of the prepared solution (66.5 % vol/vol) with respect to the delayed time and the initial volume loss rate (ref to Fig. 5A).
With this method, a −7.4 % correction is applied to the initial ethanol composition (7.4 % to water) for the data used in sections 4 and 5. The entire evaporation process of the ouzo drop was recorded by a CCD camera [XIMEA; MD061MU-SY, 3 frames per second (fps) at 1, 372 × 1, 100 pixel resolution] equipped with a high-magnification zoom lens system (THORLABS; MVL12X3Z) for side-view recordings and a CMOS [NIKON; D750, 24 frames per seconds (fps) at 1, 920 × 1, 080 pixels resolution] attached to an identical lens system for top-view recordings. We used a self-built collimated LED source system to illuminate the side-view recording. A powerful Hella LED light source was used for the top-view illumination to show the top of the drop (Figs. 1A-E). The relative humidity and temperature in the laboratory were monitored at a sampling rate of one per second with a universal handheld test instrument (OMEGA; HH-USD-RP1, accuracy relative humidity is ± 2 % over 10 to 90 % @25 • C and a temperature accuracy of ± 0.3 K @25 • C). The location of the probe was around 10 cm away from the droplet. A similar sketch of the setup is described in detail in reference 32 . Stereo-imaging was performed by a confocal microscope (Nikon Confocal   Figure 1A, the ouzo drop is transparent and concentrates illuminating light on the substrate. Around t = t 0 +167 s, the "ouzo effect" sets in at the top of the drop and a region with a cloudy white emulsion appears (Fig. 1B). The nucleated microdroplets scatter the light, giving them "milky" appearance. In Figures 1CD, the emulsion is more and more evident and spreading around the drop. Finally, the entire drop is opaque, and the bright spot on the substrate disappears completely (Fig. 1E). Experimental movies (SV1 and SV2) and numerical movie (SV3) are available as supplementary material.
The physical origin of the phenomenon has two aspects. One is the maximum local evaporation rate at the top of the drop. On a superamphiphobic substrate, the ouzo drop maintains its high contact angle (∼ 150 • ) during the evaporation process. Under the assumption of a small temperature gradient along the liquid-air interface, this geometric configuration gives the highest local evaporation flux at the top of the drop 5,15,36 (Fig. 1F). The thermal gradient along the liquid-air interface is reduced by the strong solutal and thermal Marangoni convection, as discussed in detail in section 5. The average temperature at the interface is lower than ambient temperature due to evaporative cooling (section 5).
The second aspect is that the component ethanol in the ouzo drop has a higher volatility than water, while trans-anethole is non-volatile. As the drop evaporates, the highest water concentration initially appears at the drop top with the highest local evaporation flux. Hence, the evaporation- Evaporation Phases We monitored evaporating ouzo drops with initial volumes V init of 0.82, 0.93 or 0.92 µL to study its evaporation characteristics, including the transient drop volume V , the contact angle θ, and the radius of the contact line r c (as annotated in Figure 2E). Here, we nondimensionalized the temporal evolution of the drop volume as follows: we define a nondimensional volume V * by dividing the drop transient volume V by the original amount V init . A nondimen-sional time t * for the first three phases is determined by dividing time t by the total time of the water/ethanol evaporation time (∼ 660 s, ∼ 727 s and ∼ 736 s for Data-1, Data-2, and Data-3, respectively). After the non-dimensionalization, the three temporal evolution curves overlap, as shown in Figure 2A.
Like on flat hydrophobic surfaces 32 two distinct time regimes could be distinguished for drops evaporating from superamphiphobic surfaces ( Fig. 2A). The similar feature also exists for an evaporating water-ethanol drop in gas [27][28][29] and a dissolving sessile drop in an ouzo system 39 . The difference of evaporation/diffusion rates of the components in the drop determines this feature. In the first period (t * < 0.2) of the volume evolution curves in Figure 2A, the ouzo drop undergoes a transition from phase I to phase II, i.e. from transparent (first snapshot column in  40 . We note that not only the left and right contact angles of a single drop coincide, but also the contact angles of different drops. Furthermore, three-phase intersection points in the side-view contour, which were reported in our previous study on flat evaporating ouzo drops 32 , are now absent. When most of the ethanol has evaporated, the evaporation of water dominates and determines the less steep slope of phase III. The ouzo drop is milky during the whole phase III (the third and fourth snapshot columns in Fig. 2D). There is no phase inversion from oil droplets in water to water droplets in oil as was reported for flat evaporating ouzo drops 32 . The nucleated oil emulsion microdroplets fill up the ouzo drop and remain stable. After some time, the contact angle increases and the contact area simultaneously shrinks to a smaller base radius (Figs. 2BC), i.e. the CRmode ceases. As the water is evaporating, its concentration in the drop continues to decrease until there is not enough water to maintain the stability of oil emulsion microdroplets in the bulk. The microdroplets then start to coalesce (last snapshot column in Fig. 2D), leaving behind a small transanethole drop. The capillary force at the contact line on the surface can damage the soot coating layer. The residual trans-anethole drop rolls up the damaged layer, resulting in a non-spherical-cap shape in the end.
Wrapping of Nucleated Oil As discussed before, the drop initially is in CR-mode 40 in the early stages of the evolution (for example, t * < 0.5 for Data-1). To further investigate this behavior, we used a confocal microscope to image the contact region of an evaporating ouzo drop.  and wraps up the ouzo drop at some point when the drop has a small ethanol concentration and a high surface energy. Smith et al. 41 and Schellenberger et al. 42 have reported the same phenomenon before. The spreading coefficient gives a criterion for the occurrence of the wrapping process 41 . It is defined as S ta,l ≡ γ l,a − γ ta,a − γ l,ta , where γ is the interfacial tension between different phases, l is short for the ouzo drop liquid, a is for air, and ta is for trans-anethole 43 . If S ta,w is positive, the trans-anethole-air interface and trans-anethole-liquid together have a lower energy than the liquid-air interface and thus trans-anethole can wrap up the drop 44 . Table 1 lists the interfacial tension between water and air (γ w,a ), trans-anethole and air (γ ta,a ), and water and transanethole (γ w,ta ). If the drop liquid is water, the spreading coefficient S ta,w is positive. Consequently, the spreading parameter predicts total wetting and the trans-anethole wraps up the ouzo drop completely. As shown in Figure 3D, a bright oil shell appears. An experimental movie (SV4) created by confocal microscope is available as supplementary material. To have an observation inside the ouzo drop at high resolution, we performed a 2D scan with an 60× oil immersion objective in the confocal microscope system. Figure 3E shows a snapshot, where we find numerous nucleated oil microdroplets with ∼ 2 µm diameter size by the continuous oil shell. Here, only fluorescent dye was added for trans-anethole.

Numerical Modeling of the Evaporation Process with a Finite Element Method
Additional insight in the entire process can be obtained by numerical modeling. Since the initial contact angle is higher than 90 • , the lubrication theory model of references 32, 45 cannot be used.
To overcome this limitation and to provide an accurate prediction of the flow velocity even at high contact angles, a new finite element method (FEM) model has been developed. Here, we only give an outline of this model, and details can be found in reference 46 . In order to allow for acceptable calculation times, the model assumes axisymmetry. Furthermore, it is assumed that the drop is always in a spherical-cap shape and consists of a miscible liquid mixture. When the ouzo effect occurs, the latter assumption is still valid as long as the oil microdroplets are small compared to the entire drop. In the simulations, the ouzo effect is defined to happen when the local composition is in the experimentally determined ouzo effect regime of the ternary phase diagram of reference 32 .
The model solves the coupled processes of multi-component evaporation, Stokes flow in the droplet driven by solutal and thermal Marangoni flow and convection-diffusion equations for the spatio-temporal liquid composition and the temperature. The composition-dependence of the liquid properties, i.e. mass density, viscosity, surface tension, diffusivity and thermodynamic activities, are taken into account. However, since these relations are not available for the ternary mixture, experimental data of binary water-ethanol mixtures [5][6][7] have been fitted to model the compositiondependence. The thermodynamic activities of water and ethanol were calculated by AIOMFAC 8,9 .
Plots of the fitted relations and description of all used parameters can be found in supplementary material.
The evaporation rate for component ν (ν = w,e for water and ethanol, respectively) are calculated by solving the vapor diffusion equation ∂ t c ν = D vap ν,air ∇ 2 c ν in the gas phase, where D vap ν,air is the vapor diffusivity of ν in air and c ν is the vapor concentration, i.e. the partial density. With the ideal gas law, one can express the ambient water vapor concentration by where H is the relative humidity, R is the ideal gas constant, T ∞ is the room temperature and p w,sat is the saturation pressure, which temperature-dependence given by the Antoine equation. There is no ambient ethanol vapor present, i.e. c e,∞ = 0. At the liquid-gas interface, the vapor-liquid equilibrium according to Raoult's law has to hold, By virtue of equation 2, the evaporation rates are coupled with the local drop composition at the interface via the liquid mole fraction x ν and the activity coefficient γ ν and furthermore with the local temperature T . From the diffusive vapor fluxes J gas ν = −D vap ν,air ∂ n c ν at the interface, the mass transfer rates j w and j e can be determined from the coupled mass transfer jump conditions Here, the mass density ρ air of the gas phase is assumed to be constant and given by the value of humid air.
The drop is assumed to be in a spherical-cap shape, where the base contact radius r c was ρ (∂ t y ν + u · ∇y ν ) = ∇ · (ρD∇y ν ) − J ν δ Γ , with the mixture diffusivity D and the mass transfer source/sink term imposed at the liquid-gas interface Γ. The source/sink term is given by The mass fraction y ta of trans-anethole oil is obtained by y ta = 1 − y w − y e .
Finally, the following temperature equation has to be solved: Here, Λ ν is the latent heat of evaporation, ρ is the mass density, c p the specific heat capacity and λ where r = rc sinh α cosh α+cos θ is the radial coordinate at the surface of the drop, r c is the contact radius The evaporation rate of the drop massṁ is given byṁ = ṁ ν = ρ νVν , whereV ν is the evaporation rate of each component volume. When the small volume-change caused by the mixture of miscible liquids is ignored, the evaporation rate of the drop volumeV can be expressed as, In the application of the generalized diffusion model for the evaporation process of an ouzo drop, we assume that the trans-anethole (ν = ta) is non-volatile and has no influence on the evaporation of water (ν = w) and ethanol (ν = e). For water (ν = w), the ambient vapor concentration c w,∞ is given by In our case, the ouzo drop has a large contact angle. It is vital to take account of the temperature reduction caused by evaporative cooling effects. But something different happens here. As discussed in section 5, the appearance of the strong Marangoni flow uniformizes the temperature field. It is possible to have a thermal boundary layer along the substrate surface. The estimation of its thickness is ∼ 100 µm, given by P e = 1. And as a result there is no distinct temperature difference in most parts of the drop, as displayed in Figures 4AB. Therefore it is reasonable to assume an isothermal drop with a reduced temperature value.

Conclusions
The evaporation of an ouzo drop on a superamphiphobic surface is characterized by three features:      For quantities that are constant during the simulation, also the corresponding values are given.
Relations for non-constant quantities S.7.0.1 Saturation pressure p ν,sat The temperature-dependence of the saturation pressure is calculated by the Antoine equation, i.e. by where the constants A ν , B ν and C ν read 2  during the simulation, also the corresponding value is given.

S.7.0.2 Composition-dependent properties
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