Evaporation-triggered segregation of sessile binary droplets
Yaxing Li, Pengyu Lv, Christian Diddens, Huanshu Tan, Herman Wijshoff, Michel Versluis, Detlef Lohse
EEvaporation-triggered segregation of sessile binary droplets
Yaxing Li, Pengyu Lv, Christian Diddens,
1, 2
Huanshu Tan, Herman Wijshoff,
2, 3
Michel Versluis, and Detlef Lohse
1, 4, ∗ Physics of Fluids group, Department of Science and Technology,Mesa+ Institute, and J. M. Burgers Centre for Fluid Dynamics,University of Twente, P.O. Box 217,7500 AE Enschede, The Netherlands Department of Mechanical Engineering,Eindhoven University of Technology, P.O. Box 513,5600 MB Eindhoven, The Netherlands Oc´e Technologies B.V., P.O. Box 101, 5900 MA Venlo, The Netherlands Max Planck Institute for Dynamics and Self-Organization, 37077 G¨ottingen, Germany
Abstract
Droplet evaporation of multicomponent droplets is essential for various physiochemical applica-tions, e.g. in inkjet printing, spray cooling and microfabrication. In this work, we observe andstudy phase segregation of an evaporating sessile binary droplet, consisting of a mixture of waterand a surfactant-like liquid (1,2-hexanediol). The phase segregation (i.e., demixing) leads to areduced water evaporation rate of the droplet and eventually the evaporation process ceases due toshielding of the water by the non-volatile 1,2-hexanediol. Visualizations of the flow field by particleimage velocimetry and numerical simulations reveal that the timescale of water evaporation at thedroplet rim is faster than that of the Marangoni flow, which originates from the surface tensiondifference between water and 1,2-hexanediol, eventually leading to segregation. i a r X i v : . [ phy s i c s . f l u - dyn ] J a n he evaporation of a sessile droplet has attracted a lot of attention over the past years [1–15], not only from a fundamental scientific perspective, but also because of many technolog-ical and biological applications, such as inkjet printing [16], nanopatterning depositions [17],and DNA stretching [18]. Within the whole class of problems, the so-called ”coffee-stain ef-fect” which was presented to the scientific community 20 y ago [2], has become paradigmatic.The problem and its variations keep inspiring the community. This holds not only for theevaporation of liquids with dispersed particles [12, 19], but also for that of liquid mixtures,including binary and ternary mixtures [15, 20–23]. In recent work on an evaporating Ouzodrop (a ternary mixture of water, ethanol and anise oil), Tan et al . [15] showed that a phasetransition and the nucleation of oil microdroplets can be triggered by evaporation. Thereason for the nucleation lies in the varying solubility of oil in the ethanol-water mixtures:the high evaporation rate at the rim of the droplet together with the higher volatility ofethanol as compared to water causes an oil oversaturation at the rim, leading to localizedoil microdroplet nucleation. The oil microdroplets are advected over the whole drop byMarangoni flow and further droplets later nucleate in the bulk. Finally, the microdropletsare jammed and coalesce during the further evaporation process, eventually leading to theformation of a separated oil phase in the remaining binary water/oil droplet. Liquid-liquidphase separation during evaporation not only occurs for Ouzo droplets, but is omnipresentin nature and technology [24–27].In this work, we study segregation within an evaporating 1,2-hexanediol/water misciblebinary droplet. 1,2-hexanediol is used in a variety of applications, such as co-surfactant formodifying the sodium dodecyl sulfate (SDS) micelles [28] and oil solubilization in ternarysystems [29]. The features of its aqueous solution are widely studied in many previouspapers [30–32], which show that 1,2-hexanediol molecules form micelle-like aggregates char-acterized by a critical micelle concentration (CMC) in aqueous solutions, leading to analmost constant surface tension above the CMC [33]. Compared with water, 1,2-hexanediolis non-volatile under room conditions, implying a preferred evaporation of the more volatilewater during the drying process. However, to the best of our knowledge, the segregationof the miscible 1,2-hexanediol and water during the evaporation process has never beenobserved, nor studied. In this paper, we explore experimentally and numerically the mecha-nism of segregation of 1,2-hexanediol from the miscible water, that is found to be triggeredby selective evaporation. iie begin with the visualization of the distribution of the mixture components duringevaporation by labelling water and 1,2-hexanediol with the fluorescent dyes dextran andnile red, respectively. A dyed 0.5 µ L binary droplet with initial 10% mass concentrationof 1,2-hexanediol (around the CMC [33]) is deposited on a transparent hydrophobic oc-tadecyltrichlorosilane (OTS)-glass surface, while monitoring its evaporation under ambientconditions with confocal microscopy from side and bottom (see supporting information).The contact angle of the droplet varies between 43 ◦ and 23 ◦ during the whole evaporationprocess, measured by bright-field imaging from side view. Fig. 1 presents the segregationprocess of the evaporating binary droplet. In the beginning the droplet is homogeneouslymixed, as revealed by the uniformed green colour over the surface and on the bottom (Fig.1 A ,1 A (cid:48) ). About 34 s after deposition, 1,2-hexanediol microdroplets nucleate at the rim ofthe droplet, revealed by the yellow colour (Fig. 1 B ,1 B (cid:48) ). During further evaporation, thenucleated microdroplets of 1,2-hexanediol grow and coalesce, which forms star-shape binarymixture area revealed in blue colour (Fig. 1 C ,1 C (cid:48) ). Eventually, 1,2-hexanediol covers thewhole surface of the droplet and the evaporation process stops with some water being en-trapped by the 1,2-hexanediol (Fig. 1 D ,1 D (cid:48) ). From comparing the initial and the final size,we calculate that approximately 96% of the water has evaporated while 4% got trapped.To obtain insight into the segregation process, we record the evolution of the flow fieldwithin the evaporating binary 1,2-hexanediol/water droplet by particle image velocimetry(PIV) combined with confocal microscopy. For a first qualitative understanding, we added1 µm diameter fluorescent particles at a concentration of 5 × − vol%, which is much lessthan the particle concentration required for a quantitative PIV measurement [22, 23]. Thewhole droplet and all particles were illuminated: particles near the substrate (pink colour)were in focus of the camera; the grey or transparent objects were out-of-focus particles andreside in the upper part of the droplet.Initially, the flow is directed radially outwards near the substrate (see Fig 2A). In thisphase, only water evaporates from the binary droplet and the droplet is thin, H/L (cid:28) H is approximately 60 µ m and droplet footprint diameter L is about600 µ m. Therefore, due to the relative high concentration of 1,2-hexanediol caused by thesingularity of the water evaporation rate at the rim of the sessile droplet [6], a Marangoniflow is driven from the contact line to the apex of the droplet by the surface tension gradient,which originates from the concentration variation along the surface. Note that the surfaceiii .1 mm A’ B’ C’ D’A B C D
FIG. 1: Confocal images of the segregation process during droplet evaporation in a side (A-D)and bottom (A’-D’) view taken at the same times. (A-D) The confocal microscope scans therectangular box with the volume 590 µ m × µ m × µ m. Water (blue) and 1,2-hexanediol(yellow) are labeled with different dyes for the observation. (A and A’) In the beginning, thedroplet is homogeneously mixed. (B and B’) At about 34 s after recording started, 1,2-hexanediolnucleates at the contact line of the droplet, which is revealed as yellow round shapes. (C andC’) The nucleated microdroplets of 1,2-hexanediol gradually grow and coalesce. (D and D’) Theevaporation ends when 1,2-hexanediol fully covers the surface of the droplet. tension of 1,2-hexanediol aqueous solution is monotonously decreasing with 1,2-hexanediolconcentration when it is lower than the CMC [33]. As a consequence, a convective flow insidethe droplet is driven by the Marangoni flow and water is transported to the contact line byradial outflow near the substrate. However, here the convective flow within the droplet isnot sufficient to compensate for the evaporative water loss near the contact line. The typicaloutwards flow velocity shortly after deposition is U ≈ µ m/s, implying a Reynolds number Re = ρHU/µ ≈ − , where ρ ≈ kg/m is the liquid density and µ ≈
10 mPa s is theviscosity. We compare the time scales of evaporation t ev ∼ ρLH/ ( D w , air ∆ c w ) [34] with that ofconvective Marangoni flow t Ma ∼ L/U on the surface: t ev /t Ma ∼ ρHU/ ( D w , air ∆ c w ) ≈ − ,where D w , air = 2 . × − m /s is the diffusion coefficient of water vapor at room temperatureivnd ∆ c w ≈ − kg/m is the vapor concentration difference from the air-liquid interfaceto the surrounding air. The small ratio t ev /t Ma (cid:28) ρgL /σ ≈ − , where g = 9 . / s gravity and σ ≈
24 mN/m is the surface tension of the 1,2-hexanediol aqueoussolution above the CMC [33]. In the final phase, when 1,2-hexanediol almost entirely coversthe surface and the evaporation ceases, particles flow irregularly and eventually are depositeduniformly with no particles accumulating at the edge when evaporation fully stops (Fig. 2D).To obtain a quantitative analysis of the flow field during evaporation, we add 520 nmdiameter fluorescent particles at a concentration of 2 × − vol% into the droplet. The flowspeed U and the wall-normal vorticity ω = ∂ x u y − ∂ y u x for the in-plane velocity ( u x , u y ) aremeasured during the whole evaporation process. Also from the evolution of the mean vortic-ity ¯ ω , the different life phases of the evaporation can be identified, now even quantitatively,see Fig. 3. In the early phase, there is almost only outward radial flow, resulting in constantlow vorticity. After de-staining of the particles, there are some small vortices appearingnear the droplet rim due to the receding contact line. When segregation starts, the vorticitysharply increases due to a series of vortices forming in the nucleated microdroplets of 1,2-hexanediol, see also in Fig. 1C. During coalescence of the growing nucleated microdroplets,small vortices merge and form larger vortices. When the growing microdroplets reach thearea where floating particle reside, the particles flow down to the bottom. Finally the flowv arangoniflowsHigher surfacetensionHigher 1,2-Hexanediolconcentration Flow down θ L/2
E. Before segregation: (A-B) F. After segregation: (C-D)
Flow down
B C D A Particles leave edge
FIG. 2: (A-D) Bottom-view snapshots of the droplet seeded with fluorescent particles in differentlife phases. (A) The flow is directed radially outwards near the substrate, as shown by particlestransported to the contact line (blue arrows). (B) All the particles are released from the contactline and flow to the upper center (orange circle) of the droplet (red arrows). (C) Particles floatingon the upper layer form a star shaped pattern (purple lines) and flow downward through thefingers of the star (green arrows). (D) When the droplet stops evaporating, the particles aredeposited homogeneously on the substrate, without leaving a coffee-stain. (E-F) Schematics ofthe flow inside the binary droplet at different phases. (E) Before segregation, the surface tensiongradient drives a Marangoni flow from the edge to the apex of the droplet. (F) After segregation,the nucleated microdroplets of 1,2-hexanediol grow and coalesce. At the same time, water-richliquid from the upper layer of the droplet flows down through the streams between neighbouringnucleated microdroplets. becomes irregular and then vanishes at the end of the evaporation process.Sessile droplet evaporation is a diffusion-dominated process driven by the concentrationgradient of the droplet’s constituent(s) from the droplet interface towards the surroundings.The case of a pure evaporating sessile droplet has analytically been solved by Popov [5], seethe supporting information.For a droplet consisting of more than one component, the situation gets more complicatedvi
IG. 3: Particle image velocimetry results showing the flow field near the substrate in terms ofvelocity vectors and vorticity, allowing to identify evaporation stages. The five vertical lines showthe moments of the five snapshots. (Blue line: 10s; red line: 80s; yellow line: 112s; purple line:122s; green line: 167s.) and can only be treated numerically. Several generalizations are necessary to adopt Popov’smodel to a multi-component droplet. Since these generalizations are described in detail inseveral recent publications [15, 23, 36–38], only a brief overview of the model is given in thefollowing, focusing on the case of the present binary mixture.As 1,2-hexanediol is non-volatile, only the evaporation rate of water has to be determined.However, in contrast to the case of a pure water droplet, where the water vapor concentration c w is saturated directly above the liquid-gas interface, i.e. c w = c w,s , in the case of adroplet, consisting of two miscible liquids, the vapor concentration is given by the vapor-liquid equilibrium. This equilibrium can be expressed by Raoult’s law, i.e. c w = γ w X w c w,s ,where X w is the mole fraction of water in the liquid and γ w is the activity coefficient ofwater for the 1,2-hexanediol/water mixture. The water vapor concentration is in generalnon-uniform along the interface and changes over time. The evaporation process is modeledviiy the quasi-steady vapor diffusion equation ∇ c w = 0. We use Raoult’s law at the liquid-gas interface and the ambient vapor concentration c w = c w , ∞ far away from the dropletas Dirichlet boundary conditions. The evaporation rate of water J w is then given by thediffusive flux at the interface, i.e. J w = − D w,air ∂ n c w .In case of a pure droplet, or for a multicomponent droplet in the presence of a veryintense Marangoni flow, it is sufficient to keep track of the total mass of each species overtime to predict the volume evolution [36, 38]. Here, however, the Marangoni flow is weakand segregation occurs, so that an explicit spatio-temporal dependence of the local liquidcomposition emerges. Hence, the convection-diffusion equation for the water mass fraction Y w has to be solved inside the droplet: ρ ( ∂ t Y w + (cid:126)u · ∇ Y w ) = ∇ · ( ρD ∇ Y w ) − J w δ interf. (1)The mass density of the liquid ρ and the diffusivity D are composition-dependent quantities,i.e. ρ ( Y w ) and D ( Y w ). The evaporation rate of water enters Eq. (1) as interfacial sink term δ interf. .The advection velocity (cid:126)u is obtained from the Stokes equation, subject to a no-slip bound-ary condition at the substrate, the kinematic boundary condition considering evaporation,the Laplace pressure in normal direction at the liquid-gas interface, and the Marangoni shearstress that arises due to the composition-dependent surface tension σ ( Y w ) in tangential di-rection at the liquid-gas interface. Furthermore, the composition-dependence of the dynamicviscosity µ ( Y w ) has to be considered. For the composition-dependence of the liquid’s ma-terial properties, we have fitted experimental data and/or used models. More details andplots of these relations can be found in the supplementary information.The resulting set of coupled equations can be solved numerically with a finite elementmethod [23, 37, 38]. We restrict ourselves to axial symmetry. Since the evolution of thecontact angle is determined by microscopic interactions at the contact line, it cannot bepredicted by the model. Instead, the experimentally measured evolution of the contactangle was imposed throughout the simulation, see Fig. 4A.In Fig. 5, these snapshots of the simulation for the droplet consisting of an initial 10%1,2-hexanediol are depicted. While initially a considerable Marangoni flow is present andthe profile of the evaporation rate resembles the case of a pure water droplet, the situationdrastically changes at later times: The Marangoni flow ceases due to the nearly constantviii A FIG. 4: Experimental (data points) and numerical results (solid line) for the temporal evolutionof the geometrical parameters (A): footprint dimater L , contact angle θ and (B): volume V fromexperiment and numerical simulation. The error bars are deduced from the experimental accuracy. surface tension at lower water concentrations. Towards the end of the evaporation pro-cess, the evaporation rate suddenly decreases once the water concentration Y w falls belowa threshold of about 10%. Since this transition sets in near the contact line, the profile ofthe evaporation rate shows a remarkable deviation from the case of a pure droplet with apronounced evaporation at the apex in this stage. The evaporation-triggered segregationeffect in radial direction is well captured by the model. Finally, a remaining water residue isentrapped in the bulk of the droplet (4% of the initial water content) which can only reachthe interface by diffusion. The comparison between simulation and experimental data showsan excellent quantitative agreement as shown in Fig. 4B.To summarize, segregation within a binary droplet in spite of the simplifying asym-metry, triggered by selective evaporation is observed during the drying process of a 1,2-hexanediol/water mixture droplet. The small surface tension differences cannot drive astrong enough Marangoni flow on the surface to induce a high enough convection within thedroplet to obtain perfect mixing. Therefore a locally high concentration of 1,2-hexanediolaccumulates near the contact line of the droplet, leading to segregation. The evolution ofthe vorticity field indicates different life stages of the evaporating droplet. We quantitativelycompare the experimental data with a numerical simulation, showing excellent agreement.While the model perfectly predicts the water and diol concentrations in the inner center andouter layer of the droplet, respectively, note that it cannot predict the phase separation ofix =
10 s evaporation ratewater . / (m s) 0 .
25 mm velocity [ µ m / s ] . . . . . water vapor concentration [ g / m ] .
16 12 .
48 12 .
80 13 .
12 13 . % ] t=
145 s 0 .
25 mm . . . . water vapor concentration [ g / m ] . . . . . % ] t=
180 s 0 .
25 mm . . . . . velocity [ µ m / s ] FIG. 5: These snapshots from the simulation of an evaporating droplet with initially 10% of 1,2-hexanediol with the axisymmetric finite element model at different times t . In the gas phase, thewater vapor concentration c w is shown and the corresponding evaporation rate J w is indicated bythe arrows at the interface. Inside the droplet, the mass fraction of 1,2-hexanediol (left) and thevelocity (right) is depicted. Note the very different phenomena at t = 10s (upper) and at the twolater times t = 145s, and t = 180s (lower). the two liquids due to the complexity of the diol’s solubility in water. Indeed, 1,2-hexanediolcan mix with water at any concentration without phase separation in equilibrium due to theformation of micelles-like aggregates. 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