Nonmonotonic contactless manipulation of binary droplets via sensing of localized vapor sources on pristine substrates

Remote localized vapor sources manipulate binary droplets in a nonmonotonic way on pristine surfaces for various applications.


INTRODUCTION
Droplets moving on solid surfaces are at the heart of many pheno mena of fundamental and applied interest in physics, biophysics, chemistry, and materials science (1,2). Examples include "tears of wine" due to the Marangoni effect (3), rolling droplets on selfcleaning substrates (4), microfluidic liquid handling (5), as well as enhancing heat transfer (6), sensing (7), and printing technologies (8). Achieving realtime control over the directionality of moving droplets is therefore an important milestone toward harnessing them for applications in, e.g., printable materials (8), biological assays (9), and microreactors (10).
The main impediment to trigger droplet motion on solid surfaces comes from the hysteresis of the contact angle that pins the droplet's edge to the underlying substrate (11). The generation of gradients of surface energy on the substrate is a widespread strategy to overcome the pinning of the contact line and achieve motion (5,6,(12)(13)(14). Alternatively, thermal and solutal imbalances of surface tension can be directly induced on the droplet's free surface, thus inducing flows within the droplet that ultimately lead to its motion (7,15,16). For example, vapor fields can be used to induce such imbalances and influence droplet physics and motion (7,(17)(18)(19)(20)(21). In an emblematic recent example, multiple aqueous droplets of food coloring [con taining different concentrations of propylene glycol (PG) in water] showed a wealth of emerging spontaneous behaviors when placed on a glass substrate, including attraction, chasing, coalescence, and repulsion (7). By modifying the underlying substrate or by develop ing elaborate vapor traps with multiple droplets, various examples of dropletbased devices were also demonstrated (7).
Because of their widespread use in technology and their innate ability to overcome contact angle hysteresis (8,18), similar droplets of two (or more) liquid components of different volatilities are therefore prime candidates for applications that require control over droplet motion on surfaces. When it comes to controlling the di rectional transport of droplets (i.e., manipulating them), however, existing techniques rely on large gradients of surface energy (6,12), on carefully engineered substrates (5,14), or on tailored trapping potentials (7), thus limiting the level of control that one can achieve over droplet motion and its applicability on pristine substrates, for example, for printing technology.
Here, we demonstrate the nonmonotonic contactless longrange twodimensional (2D) manipulation of binary droplets of water and PG on solid pristine surfaces. These droplets spontaneously move in a directional manner in response to small imbalances of surface tension gradients induced by the presence of an external localized source of water vapor. Unexpectedly, unlike previous observations (7), a droplet of fixed initial composition can move either away or toward a vapor source of fixed composition depending on separa tion distance. We show with a simplified analytical model based on the 2D functional form of the surface tension gradient along the droplet's free surface that the viscous nature of the driving forces at play (<N) is paramount to capture the observed dual response (from attractive to repulsive) of the droplet with distance from the source. Our robust understanding of the underlying motion mech anism allows us to showcase its adaptability in a range of potential applications in materials science, including pattern formation, the printing of chemical gradients, and the mixing of reactive materials on pristine substrates (i.e., without requiring further modification of the underlying surface).

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of the pure liquids and a reduced hysteresis (23). When x s → ∞ (i.e., in the absence of the source), the twocomponent droplet with a spherical cap shape is stationary on a flat surface; however, in the presence of the source, because of the reduced hysteresis, the binary droplet can instead move, maintaining a spherical cap shape if the contact line is not pinned as in our case ( Fig. 1 and fig. S1). In par ticular, when placed afar (x s = 2 mm; Fig. 1B and movie S1), the droplet experiences an attractive force toward the source. This at tractive behavior is consistent with a relative larger local increase in humidity at the droplet's edge nearest to the source, which generates motion by slowing down evaporation and comparatively increasing the value of surface tension at that edge with respect to the opposite side, similar to previous observations (7,25). Such considerations based on differences of absolute values of surface tension would naturally lead one to expect a stable equilibrium position to appear directly beneath the source's center (x s = 0), as any displacement from x s = 0 would induce a restoring force. Instead, x s = 0 is an unstable equilibrium position from which the droplet gets easily repelled to an offcentered radial distance x e ( Fig. 1C and movie S2), where the droplet consistently settles near the end of the evapora tion whether it starts from afar the vapor source or below it (Fig. 1D). This dual response (i.e., from attractive to repulsive) of the droplet motion with distance from the source is fundamentally different from that observed in previous reports (7), where a binary droplet of water and PG with our initial composition always showed attrac tion to a pure source of water vapor.

Dynamics of droplet's motion
To efficiently harness this mechanism, we have developed a simpli fied analytical model to better understand our counterintuitive ex perimental observations. This duality (attraction versus repulsion) in the interaction between droplet and source cannot be simply ex plained by arguments purely based on differences of absolute values of surface tension on opposing sides of the droplet or between its edge and an adjacent precursor film, for which the droplet would always move toward the vapor source (7,25). Instead, as can be seen in Fig. 2, both the magnitude and directionality of the net force ex perienced by the droplet can be modulated when we account for the full 2D functional form of the surface tension gradient along the droplet's free surface. Our analytical derivation relies on the initial estimation of the droplet's composition and compositiondependent physical parameters from our experimental data (see Materials and Methods).
To a first approximation, we can understand the whole process assuming a steady state for the diffusion of water vapor from the source toward the droplet's free surface. In the presence of the va por source, aqueous vapor saturates the atmosphere within a blunt needle [vapor pressure p s = 2.49 kPa at T = 21 ° C (26)] and diffuses toward the droplet's free surface, where it induces a local decrease in the evaporation rate proportional to the local water partial pressure, p H 2 O (r, , h), with r, , and h(r) being variables describing the free surface in cylindrical coordinates ( fig. S2A). Considering the source as a flat circular disc of radius R s at pressure p s and centered in (x s , y s , z s ) ( fig. S2A), neglecting any influence from the droplet on the diffusion from it and assuming the vapor to behave ideally, we can calculate p H 2 O (r, , h) as the sum of two terms (see derivation S1) where is the steadystate solution to the diffusion problem of water vapor from the disc source (27) at ambient relative humidity RH (eq. S1), and 2 ) is a correc tion term introduced to account for the presence of the substrate (eq. S2) (28). (29), and p RH is the partial pressure of water corresponding to RH. For simplicity, we have assumed that the presence of the droplet does not alter the solution of the diffusion problem from the source. This approximation becomes increasingly valid at higher droplet source separation distances, as the full coupling among the external vapor phase and the droplet's composition can be quite complex otherwise  (30). Nonetheless, as we will see below, there is good agreement be tween our model and our experimental data. The local decrease in evaporation rate due to p H 2 O (r, , h) induces local variations in composition  H 2 O (r, , h), and hence in local sur face tension (r, , h), along the droplet's free surface (see derivation S2). Given  H 2 O (r, , h), we can estimate (r, , h) with empirical formu lae (31) and use it to estimate the gradient in surface tension along the free surface ( fig. S3) to determine the forces acting on the droplet's contact line (Fig. 2). Neglecting intrinsic imbalances of composition due to the evaporation of the binary droplet (24) and assuming that the composition perturbations due to the source are small, we can thus express the local water composition along the free surface as the local mole fraction is a reference value for the timevarying bulk composi tion of the evaporating droplet (see derivations S2 and S3), is the molar volume of the mixture at x H 2 O  as estimated from empirical formulae (32), and kp H 2 O is the additional amount of water retained along the droplet's free surface due to the slower local evaporation that we assume proportional to p H 2 O (see derivation S2). The pro portionality constant k expresses the balance of the rate constants associated to the condensation and vaporization of the additional amount of water along the free surface when we assume an equilib rium between the two processes.
As a consequence of these local changes in composition, gradients of surface tension form over the droplet's free surface ( fig. S3) that drive the formation of Marangoni flows toward the areas of higher  (33), i.e., where the evaporation is slower. The estimated values in Fig. 2A show how the position of this maximum shifts along the droplet's free surface following the position of the source, moving from the droplet's apex for x s = 0 to its contact line when the source is far away (x s = 1.2R D ). For no displacement (x s = 0), the gradient in surface tension, and hence the corresponding Marangoni flows along the free surface, is radially symmetric and pointing inward toward the droplet's apex ( fig. S3). When we displace the source toward one edge, the flows in the droplet become radially asymmetric (34), strengthening under the source at first due to a steeper gradient in surface tension ( fig. S3). When the source is far away, the flows coming from the distal edge predominate instead due to the con fined geometry of the droplet. Between these two cases, the gradient in surface tension at the edge closer to the source changes direction ality ( fig. S3). Although the coupling between droplet composition, internal flows, and external vapor phase is rather simplified in our derivation (30), this change in surface tension gradient intuitively justifies the dual response of the droplet's motion to the position of the source (Fig. 1).
To formalize this intuition, we can integrate the viscous stress induced by the flows within the droplet on the liquidsolid interface to obtain a viscous driving force F x  in the direction x of motion. For a droplet of small constant contact angle  c that maintains a spher ical cap shape while moving at constant velocity v x along x, the liq uid flow within the droplet, in the lubrication approximation, is the superposition of a Poiseuille flow induced by the pressure gradient in the moving droplet and a Marangoni flow due to the gradient in surface tension at the droplet's free surface (35). Assuming no de formation of the droplet and small gradients, the viscous stress on the substrate in the direction of motion due to these flows is given by (35) where  is the dynamic viscosity of the mixture estimated with em pirical formulae at the droplet's composition (32), and u x is the pro jection of the local velocity of the contact line in the x direction. By integrating  xz (z = 0) over the droplet's basal area in polar coordi nates, we can calculate the total viscous force in the x direction as the sum of two terms, (see derivation S4), using the fact that dissipation (i.e., the viscous force) is dominated by the edge where the shear gradient is the sharpest (35). We thus obtain that the viscous drag force on the moving droplet is given by where ℓ n = 11.2 is a constant prefactor determined by the droplet's geometry and the molecular dimension of the liquid (7,35). The viscous driving force is instead given by In the absence of surface wettability gradients or external forces acting on the droplet (as in our case), the balance of forces requires Because of the symmetry in the prob lem, the net viscous force along the y direction is null instead. Our transport mechanism is entirely driven and dominated by viscous forces. Figure 2B shows how the integrated function in Eq. 5 (with units of force) varies along the contact line for three different source positions at the start of the evaporation. This quantity always points toward the source and intensifies in the parts of the contact line closer to it. These two considerations alone can formally explain our main observations in Fig. 1. When the source is just above the droplet's apex (x s = 0), there is no net force because of symmetry; this is, however, an unstable configuration as any small displace ment generates repulsion (x s = 0.6R D ). When the source crosses the contact line (x s = 1.2R D ), the droplet starts experiencing a net attrac tive force instead, and a stable equilibrium point is formed at the crossover between attraction to and repulsion from the source. Overall, this force primarily acts on the contact line, is a function of the gradient of surface tension, and has typical values <N consistent with previous reports (Fig. 3) (7). Last, by solving the force balance equation for the moving droplet, we can calculate its velocity v x in the vapor field generated by the source as Typical experimental values of v x range between a few and a few tens of m s −1 , and are well reproduced by our model (Fig. 4). Throughout our derivation, we have assumed that the droplet maintains the same spherical cap shape when attracted toward the source or repelled from it. This is a valid assumption even for the biggest vapor source considered here (fig. S1). Nonnegligible deform ations might, however, take place in the presence of even stronger vapor fields (34).
As the droplet's geometry and composition are changing due to evaporation ( fig. S2 and derivation S3), both force and velocity vary in time too (Figs. 3 and 4). The experiments in Fig. 4 show how the droplet's velocity evolves in time and with the distance x s from the source as a function of the source size R s . Qualitatively, these maps show the same common features, which are well reproduced by our model. At the beginning of the evaporation process, a small region of null speed and force (white, Figs. 3 and 4) in the proximity of the droplet's edge separates a repulsive area (blue) from an attractive one (red). As the droplet's radius is initially shrinking (fig. S2B), the stable equilibrium point of null speed, and hence the limit of the repulsive zone, shifts toward the droplet's center with time, giving way to the attractive zone. When moving away from the droplet's edge, this attractive region presents a timedependent maximum around 〈x s 〉 ≈ 1.3R D as the strength of the attractive force fades when the distance from the source increases due to the weaker vapor fields around the droplet. Although the force strengthens toward the end of the evaporation (Fig. 3), speed drops eventually to zero as the droplet becomes richer in PG over time (and its viscosity increases) so that substantially higher forces are needed to set it in motion. As can be seen in the simulated maps (Figs. 3 and 4), a region of null speed and force emerges also for x s ≈ 0. As previously observed (Fig. 1), this represents an unstable equilibrium point, which is sur rounded by a region of repulsive forces (Fig. 3). We can attribute all qualitative differences (also reproduced by our model) to the source size, i.e., the strength of its influence at a given x s (Fig. 4). In particular, larger sources exert larger attractive forces (Fig. 3) and, as a conse quence, droplets move faster and experience the source influence from further away and for longer during their evaporation. To keep a fixed distance x s between droplet and source over time, we per formed these experiments by continuously moving the microscope stage to compensate for the droplet's motion (see Materials and Methods). When droplets are free to move on the substrate as in Fig. 1, they follow trajectories on the maps in Fig. 4 with a timevarying velocity consistent with the underlying functional form of these velocity surfaces ( fig. S4) until they settle in the stable region of null speed.

Applications of moving droplets under an external vapor source
Next, we demonstrate the performance and versatility of our method for possible applications, ranging from printing and depositing materials to controlling reactions in space and time on pristine sub strates, i.e., without requiring further modification of the underlying surface (Figs. 5 and 6). Figure 5 shows deposits from water/PG droplets containing different polymer concentrations. We guided these droplets with a large vapor source (R s = 640 m) placed at their leading edge to overcome the higher viscosity induced by the pres ence of the polymer (Materials and Methods). Figure 5A shows polymer trails left behind by moving droplets containing different concentrations of polyvinyl alcohol (PVOH), a polymer used for coating and printing applications. Visually, higher concentrations of polymer lead to thicker deposits with narrower line widths as a result of an increase in the droplet's overall viscosity and contact angle  c . The height profiles in Fig. 5B and the measurements in Fig. 5C confirm these observations quantitatively. Figure 5B also shows that typical measured thicknesses span at least two orders of magnitude with deposits as thin as ≈5 nm. For a given PVOH con centration, the resolution achievable by this printing technique in terms of average line width depends on the characteristic length of the droplet as w ∝ 3 √ ─ V D , with smaller droplets thus depositing thin ner lines (Fig. 5C and fig. S5). The addition of a second degree of freedom to the inplane displacement of the droplet allows printing arbitrary patterns in two dimensions such as sinuous lines (Fig. 5D and movie S3) and the cursive letters "ucl," notably including double pass portions (Fig. 5E and movie S4). Last, Fig. 5F and fig. S6 demonstrate the possibility of controlling the orientation of a poly crystalline polymer, such as polyethylene glycol (PEG) (36), thus leading to the formation of patterns within the deposit itself with ≈100nm high features ( fig. S6B). PEG quickly supersaturates in the deposit printed by the droplet (due to the evaporation of its more volatile component) and starts to crystallize as soon as a de fect is generated (movie S5) (37). The resulting polycrystalline phase forms physical ridges perpendicular to a moving front whose shape depends on the droplet's speed and determines the topography of the final pattern ( fig. S6): For slower moving droplets, the front matches the droplet's circular shape, leaving a scallop shell pattern behind, while, as the droplet speed increases, the moving front de forms into a triangular shape, which leaves a herringbone structure behind instead. Beyond depositing material in a controlled manner (Fig. 5), our technique also allows redissolving previously deposited material within a second droplet, thus facilitating the controllable deposition of chemical reactions in space and time. For example, Fig. 6A shows the final deposits left behind by water/PG droplets containing a pH indicator (bromothymol blue) after they retrace previous deposits by basic water/PG droplets with varying concentrations of NaOH (movie S6). As a pH indicating droplet (initially yellow) retraces a previous deposit at constant speed (here v x = 25 m s −1 ), it uptakes NaOH from the substrate, its pH increases, and its color turns from yellow to blue through green, thus printing a color gradient. We were able to regulate the steepness of this gradient, and thus the spatial variation of the printed colors, through the rate of uptake of the first deposited reactant (here NaOH), e.g., by varying its con centration in the first droplet (Fig. 6A).
Last, Fig. 6 (B and C) shows the simultaneous control of differ ent droplets with more than one vapor source, which can be useful to trigger the mixing and the reaction of materials dissolved or suspended within them in space and time. As can be seen in Fig. 6B and movie S7, the coalescence of two droplets can be guided by controlling the separation distance between two vapor sources (see Materials and Methods). The flows in the resulting droplet are substantially differ ent from the radially symmetric flows in a standard sessile binary droplet (7) and, after flowing outwards along the liquidliquid in terface between the two coalesced droplets, recirculate toward the closest source in each compartmentalized quarter ( fig. S7). As a consequence, after solute exchange has occurred at the interface predominantly via diffusion, these flows promote mixing within each quarter until the coalesced droplet becomes essentially uniform in composition. Beyond mixing, we can also implement chem ical reactions by the same principle. As an example, Fig. 6C and movie S8 show the acidbase neutralization reaction of NaOH and HCl: Before coalescence, the two droplets are very acidic (pH ≈ 1) and basic (pH ≈ 13), respectively; on coalescence, neutralization starts to occur at the interface where a gradient of pH forms as highlighted by the full color spectrum of the pH indicator; as the reaction proceeds, the coalesced droplet eventually reaches neutral pH uniformly.

DISCUSSION
These examples illustrate the robustness and versatility of our method for the nonmonotonic contactless, longrange 2D  Figure S6 shows higher speeds. All PVOH droplets contain rhodamine B for visualization. We subtracted the background from all color images. In the photographs, black triangles indicate the direction of motion. Scale bars, 1 mm. manipulation of binary droplets on pristine substrates. From a fundamental side, our observation of symmetry breaking in the stable equilibrium position of the same sourcedroplet system highlights the intrinsic complexity of the transport mecha nisms behind evaporating droplets subject to Marangoni flows. Our simplified analytical model reproduces well this symmetry breaking, and further qualitative and quantitative insight could be gained by considering the full coupling among the external vapor phase, the droplet's composition, and the flows within it (30). Be yond our experimental implementation, we can expect a similar complexity to naturally emerge in the transport of droplets of any shape driven by Marangoni flows of thermal or solutal origin. In this context, the local and tunable nature of the perturbation intro duced by the vapor source makes it ideal for fundamental studies of droplet motion (21,25,38). Because of its high sensitivity, our technique's principle could be adapted to develop force (from nN to N) and gas sensors. Similarly, beyond the sample applications demonstrated here, we envisage that our technique, as it does not require further substrate modification, could be used for coating applications, in printable electronics and optoelectronics, for manufacturing, as well as for the development of chemical reac tors, diagnostic tools, and bioassays based on small volume liquid handling on pristine substrates (10, 39-41).
We prepared water/PG stock solutions by combining the two components in the correct mass to give the desired mole fraction (x H 2 O ). For example, we made the solution at x H 2 O = 0.95 by mixing PG (2.0 g, 26.3 mmol) with DI water (9.0 g, 500 mmol). We then used these solutions as a base for the preparation of the following stock solutions from which we made the droplets used in the exper iments. We prepared a 10 mM poly(vinyl alcohol) stock solution by dissolving poly(vinyl alcohol) (95 mg) in water/PG (1 ml, x H 2 O = 0.95). We made a 20 mM rhodamine B stock solution by dissolving rhodamine B (48 mg) in water/PG (5 ml, x H 2 O = 0.95). We prepared a 100 mM PEG stock solution by dissolving PEG 4000 (0.20 g) in water/PG (0.5 ml, x H 2 O = 0.95). We prepared a 2 M NaOH stock solution by dissolving NaOH (0.20 g) in water/PG (2.5 ml, x H 2 O = 0.95). We prepared a 1 M NaOH stock solution by dissolving NaOH We added a few drops of 1 M NaOH stock solution (x H 2 O = 0.85) to help improve the solubility of the dyes and make the solution pH neutral (green). We then added DI water (11.45 g) and diluted the solution to 25 ml using a water/PG mixture (x H 2 O = 0.85).

Sample preparation
We cleaned glass slides by sonicating sequentially in a 2 M NaOH ethanolic solution for 10 min, DI water for 5 min, a 1 M HCl aque ous solution for 10 min, and, finally, DI water for 5 min three times.  fig. S7. In (B), the droplets contain 100 mM NaOH and a dye, either methyl red (yellow, left) or bromothymol blue (blue, right); their contents mix as evidenced by the coalesced droplet turning green (movie S7). In (C), the droplets contain a pH universal indicator and either 100 mM NaOH (left) or 100 mM HCl (right); upon coalescing, an acid-base neutralization reaction occurs (inset) until the coalesced droplet turns uniform as the indicator shows qualitatively (movie S8). We subtracted the background from all images. Scale bars, 1 mm.
We then dried each slide by withdrawing it from the last water bath while exposing its surface to ethanol vapor (Marangoni drying) (19), and removed any remaining water with a nitrogen gun. In Figs. 1 and 4 Fig. 5 (A and B), we instead prepared droplets with 6 mM poly(vinyl alcohol) and 10 mM rhodamine B by directly dissolving poly(vinyl alcohol) (28.5 mg) in 20 mM rhodamine B stock solution (2.5 ml) and water/PG (2.5 ml, x H 2 O = 0.95). In Fig. 5F and fig. S6, we prepared droplets containing PEG directly from the 100 mM PEG stock solution. In Fig. 6A

Experimental design
Unless stated otherwise, we performed each experiment by deposit ing a 0.5l binary droplet of water and PG (with or without additives) on a clean glass slide placed on a homemade inverted microscope with the possibility of switching between brightfield and darkfield illumination and equipped with a complementary metaloxide semiconductor (CMOS) camera for monochrome (Thorlabs, DCC1545M) or color (Thorlabs, DCC1645C) imaging. A custom made environmental chamber (Okolab) enclosed the microscope to shield the system from external air flows as well as to control tem perature (T = 21 ± 0.5 ° C) and relative humidity (RH = 50 ± 5%). The entire setup was mounted on a floated optical table to reduce vibrations. The vapor source consisted of a glass capillary (640 m inner radius) terminated with a blunt metal needle of variable size at one end. We fixed the needle to the capillary with a siliconebased seal ant. The opposite end contained 20 l of DI water held in place through capillary forces by sealing the open end with wax. Alterna tively, when a stronger vapor field was required (Figs. 5 and 6 and figs. S5 and S6), we used the same capillary on its own with DI water directly placed at its lower opening. We mounted the capillary on a threeaxis micrometric stage so that we could accurately position it in space. We fixed the vertical distance of the capillary from the substrate at z s = 0.5 mm. To determine this distance and the drop let's contact angle  c , a periscope together with a flip mirror allowed us to switch optical path so as to visualize the droplet's side view instead of its basal plane on the CMOS cameras.
At the start of each experiment, we gently deposited the droplet under study on the clean slide with a pipette using either a disposable lowretention pipette tip (Brand, Z740080) or, for more viscous solutions (Figs. 5 and 6 and figs. S5 and S6), a standard pipette tip (Eppendorf). We carefully positioned droplets at the desired initial distance from the source of water vapor using the microscope stage, which we controlled with motorized actuators (Thorlabs, Z812B ac tuators with 29nm minimum step) to guarantee the possibility of translating the droplet with respect to the source in all planar direc tions. We then recorded the droplet's dynamics with low magnifica tion with the CMOS cameras either at 1 fps (frames per second) for the droplet tracking experiment or at 10 fps elsewhere. In Fig. 4, we performed the realtime tracking of droplet motion over large dis tances by inputting the direct stream from the camera into a custom Matlab script, which located the droplet's center and automatically moved the motorized stage continuously so as to maintain its rela tive distance x s from the source at the initial set value. This displace ment of the stage as a function of time provided the droplet's velocity. We also performed the deposition experiments in Fig. 5 (A to E) and fig. S5 in a similar way, i.e., by moving the stage to keep the distance between droplet and source constant. We guided all drop lets by holding the water vapor source at their leading edge. In Figs. 5F and 6A and fig. S6, we moved the stage in a straight line or according to a preprogrammed pattern at a constant speed. In Fig. 5F and fig. S6, we manually nucleated PEG crystallization in the supersaturated deposit with a metallic needle (movie S5). In Fig. 6 (B and C), we made two droplets coalesce by placing one droplet under a fixed vapor source (R s = 640 m) and a second droplet under a second identical source approximately 10 mm away, which we could move relative to the first. By reducing the intersource distance to 3.5 mm, we could make the two droplets approach grad ually until coalescence.

Estimation of droplet's geometry and physical quantities
In our model, we obtained the spherical cap geometry of the droplet (i.e., radius R D , contact angle  c , and volume V D ) directly from our experimental data ( fig. S2) and used it to estimate the droplet's bulk composition (Eq. S3) and the local composition of the droplet's free surface (Eq. 2) in time. From these composition values, we could then estimate the following physical quantities from empirical for mulae: the molar volume V m of the binary mixture in the droplet (32), the local value of the surface tension  at droplet's free surface (31), and its dynamic viscosity  (32). We obtained the value of the constant k = 0.15 mol Pa −1 m −3 in Eq. 2 by fitting Eq. 6 to all the experimental data on droplet's velocity in Fig. 4. Any other aspect and equation in the model are the result of a mathematical deriva tion, which we have solved numerically.

Profilometry
We measured the height profiles of the deposits in Fig. 5B and fig.  S6B on the DektakXT Surface Profilometer (Bruker) with a 5m stylus at 5mg force. In Fig. 5B, each profile is the average of five different profiles, which we acquired 4 m apart using a scan reso lution of 0.5 m/point, then leveled, and smoothed them with a Hampel filter (window size: 100 data points) to remove large ran dom spikes. We obtained the 2D profiles in fig. S6B by acquiring 1D profiles (5 m apart in the direction perpendicular to the scan direction) with the same parameters. We leveled the data points and then smoothed them using a Gaussianweighted moving average (window size: 30 data points along the scan direction and 4 in the perpendicular direction).

Particle tracking velocimetry
We visualized the flows within the droplets in fig. S7 by tracking 5m polystyrene microparticles using a custom Matlab script. At every instant, we determined the position of these microparticles by applying a sequence of three filters to the raw images. First, we used a tophat filter with a 3pixel radius disc structuring element to ob tain a uniform background. Then, we renormalized each pixel to the 3 pixel × 3 pixel window around it to set the centroid corre sponding to each particle to a value of one. Last, we extracted parti cle positions by applying a binary threshold to the processed images after excluding false positives. We obtained trajectories from these data using a nearest neighbor algorithm between consecutive frames.