Self-propelling Microdroplets Generated and Sustained by Liquid-liquid Phase Separation in Confined Spaces

Flow transport in confined spaces is ubiquitous in technological processes, ranging from separation and purification of pharmaceutical ingredients by microporous membranes and drug delivery in biomedical treatment to chemical and biomass conversion in catalyst-packed reactors and carbon dioxide sequestration. In this work, we suggest a distinct pathway for enhanced liquid transport in a confined space via self-propelling microdroplets. These microdroplets can form spontaneously from localized liquid-liquid phase separation as a ternary mixture is diluted by a diffusing poor solvent. High speed images reveal how the microdroplets grow, break up and propel rapidly along the solid surface, with a maximal velocity up to ~160 um/s, in response to a sharp concentration gradient resulting from phase separation. The microdroplet self-propulsion induces a replenishing flow between the walls of the confined space towards the location of phase separation, which in turn drives the mixture out of equilibrium and leads to a repeating cascade of events. Our findings on the complex and rich phenomena of self-propelling droplets suggest an effective approach to enhanced flow motion of multicomponent liquid mixtures within confined spaces for time effective separation and smart transport processes.


Introduction
Microdroplets out of composition equilibrium can be seen as active matter, exhibiting autonomous motion without additional energy input from external sources [1]. These self-propelling droplets have drawn intensive research interest, as they show promise as programmable microcarriers in drug delivery [2], artificial units simulating chemotaxis and collective behaviours in living microorganisms [3,4,5], fast solvers of geometric mazes [6,7], microswimmers to extract metal ions [8,9], or automated bouncing droplets for stirring of the surrounding liquid [10], to name a few. The primary force driving autonomous microdroplet motion is typically a Marangoni stress arising from imbalanced forces along droplet surfaces [1]. The mobility of the droplets is governed by the interplay of droplet size, the viscosities of liquids inside and outside of droplet, and the interfacial tension gradient.
The response of microdroplets to small gradients in interfacial tension leads to autonomous motion via concentration gradients of chemical constituents adjacent to the droplet surface. Strategies have been developed to sustain one component out of equilibrium so that the droplets can travel in a designated direction over a large distance for an extended period of time [11,12,13]. A typical approach is the creation of a non-uniform distribution of molecular components on a droplet surface, for instance, from dissolution of a solid surfactant source [12], from local chemical and catalytic reactions [14,15,16] or solvent vapor emitted by neighbouring droplets [17,18]. Even simple combinations of different types of oil and aqueous solutions are able to yield diverse behaviors of the droplets that can only be completely probed through robotic experimental platforms and machine learning [19]. Droplet motion is further enhanced by coupling it with induced external liquid flow. As exemplified by a bouncing droplet in a stratified liquid [10], Marangoni stress at the droplet surface pulls down the bulk liquid, further strengthening the stress. The droplet jumps up once the stress exceeds gravity. The process repeats itself as gravity restores the system [10].
So far creation of self-propelling motion has mainly focused on droplets in a continuous liquid medium or on liquid surfaces with small resistance to droplet movement.
However, in the biological context or for technological processes, microdroplets evolve in compartmentalized environments. Examples include cases as diverse as coacervate droplets of biomolecules causing liquid-liquid phase separation in organelles within living cells, [20] and emulsion droplets in flooding fluid in enhanced oil recovery. [21] In addition to significant extra drag resistance along the boundary acting on the droplets, the confined space inherently introduces effects from the size, composition and motion of droplets on their surroundings. To explore the potential for self-propelled droplets in confinement, it is essential to identify an approach to sustain autonomous motion of droplets and to understand the coupled interactions between the droplets and their confined environment.
In this work, we reveal an effective pathway for rapid self-propelled transport of microdroplets in quasi-2D confined spaces. These microdroplets are secondary droplets formed during the rupture of a spreading drop arising from spontaneous liquid-liquid phase separation. The excess free energy released from phase separation is converted to the interfacial energy of the microdroplets and their kinetic energy. The resulting velocity of the propelling microdroplets reaches ∼ 160 µm/s at a maximum. The concentration gradients responsible for the formation and the initial spreading of the drop are intrinsically self-sustained through droplet dynamics along the wall surface and the induced liquid transport between the walls. We show that the phenomenon of self-propelling droplets is common for various unstable liquid mixtures even with high viscosity. Though a fully quantitative understanding of the rich and complex phenomena in the large space of control parameters is beyond the scope of this paper, we expect that the knowledge gained from this work will be valuable in designing new strategies for speeding up the transport in narrow spaces by leveraging the autonomous motions of microdroplets.  ethanol, respectively. Subsequently, the cleaned substrates were dried and incubated in a solution of OTS in hexane for 12 hr. Afterwards, the OTS coated Si wafers were sonicated for three times in OTS-free solvents for 10 min to remove loosely adsorbed OTS.
All chemicals were purchased and used as received.
The interfacial tension of water-lean and water-rich subphases after phase separation was measured by using a Spinning drop tensiometer (SDT) (Krüss, Germany). The two subphases were made by adding water to a solution of oleic acid/water/ethanol (4.2/28.8/67 by vol%) to drive phase separation.

Experimental setup and visualization of propelling droplets
The flow chamber was assembled by placing the Si substrate between a polycarbonate base and a cover glass sealed with a silicone rubber spacer with a thickness of 1 mm.
The distance from the top cover glass to the substrate surface was 20-30 µm after the chamber was assembled. The chamber was filled with the ternary solution from an inlet, followed by the injection of the displacing liquid (water, water/ethanol, or water/glycerol solutions) from one end of the side channel at a constant flow of 200 µL/min with a 4 syringe pump. The mixing of the ternary solution and the displacing liquid led to the droplets jetting phenomenon in the main microchannel.
The entire process of phase separation induced droplet propulsion was visualized using an optical microscope (Nikon H600L) equipped with a high speed camera (Photron Fastcam SA-Z) recording at 1000 frames-per-second (fps).
To obtain the fluorescence data, we added trace of Nile Red (0.02 %) to the binary solution (butyl paraben/ethanol = 10/90 wt/wt) with water as displacing liquid. The fluorescence intensity profiles around the hot spot was analyzed using self-written codes to convert the brightness in fluorescent images at different time points into normalized intensity. The composition map and intensity profiles were obtained along parallel lines at different locations. Also, the profile on the same location was tracked over a time period of 12 seconds.
A confocal microscope (SP5, Leica) was used to obtain an 3-dimensional image of self-propelled droplets after being pinned on the surface. The initial solution with the same concentration of Nile Red was prepared as the fluorescence experiment. A green HeNe laser was used to excite the fluorescent Nile Red dye. The contact angle of the pinned droplet was obtained from the 3D confocal image.

Data analysis
Droplets in all frames of a high-speed video were visualized and the positions of the droplets at different time were analyzed during the process from phase separation to droplet immobilization. Primary droplets spreading into a film and subsequent elongation into filaments, secondary droplets breaking off from the filament, and self-propelling were tracked manually using ImageJ. The droplets were tracked until they stagnated or coalesced with neighboring droplets. The data were processed to obtain displacement values, velocities and locations within the fluid cell.

Numerical simulation for diffusion of ethanol from solution A to solution B
Numerical simulation of the receding oil-rich region was done via immersed boundary methods. [24] Given the narrow thickness of the channel in the experiment setup, the two-dimensional diffusion equation Note that the velocity field is not modeled, so in this simple approach u( x, t) ≡ 0, i.e. pure diffusion.

Prediction of excess Gibbs free energy using UNIFAC
The excess Gibbs free energies for butyl paraben-water-ethanol ternary mixture were predicted using the UNIQUAC Functional-group Activity Coefficients (UNIFAC) thermodynamic model [25]. For all paraben concentrations, the tie lines in the ternary diagram were assumed to have the same ethanol composition in oil-rich and water-rich subphases as reported elsewhere [26]. The mole fraction of the water-rich subphase was taken to be the point where dilution line meets the phase envelope. The mole fraction of oil-rich subphase was estimated to be at the point on the opposite end of the tie line where it meets the phase envelope. For the composition of unstable mixture that would exist -if no phase separation had taken place -was calculated by setting the mass of water-rich subphase to be 100 times the mass of oil-rich subphase, based on the ratio of these two subphases along the tie lines in the phase diagram. The group volume (R k ), surface area (Q k ) and interaction parameters (a mn ) used for UNIFAC are shown in Table   1 and 2, and temperature was taken as T = 298.15 K.

Results and discussion
The first ternary solution we tested consisted of butyl paraben (a hydrophobic compound), a cosolvent ethanol, and a poor solvent water (cases 1 ∼ 3 in Table ??). Initially, the ternary solution filled both the microchamber (20 µm in depth) and the side channel

Local concentration gradient and formation of self-propelling microdroplets
The spatial distribution of chemical composition was revealed by the fluorescence intensity of an oil-soluble dye (Nile red) doped in the ternary solution. The concentration ratio of ethanol to dye in the solution prior to phase separation was assumed to be constant as mixing with water dilutes them equally. Therefore, the fluorescence intensity indicates the concentration of both the dye and ethanol in the mixture. Figure 2 shows that at a given time, the ethanol concentration gradient across the mixing boundary becomes sharper near the tip of the triangular zone. The gradient is the sharpest at the hot spot and diminishes far away from the hot spot.
To mimic this key feature of the process, we simulated the diffusive mixing between the ternary solution and water in a triangular zone by solving the 2D diffusion equation, employing a finite difference code and the immerse boundary method [24]. For details, we refer the reader to the method section. Figure 2c shows the concentration field at t = 4s after ethanol starts diffusing uniformly from the triangular zone into water. The concentration distribution of ethanol is consistent with the experimental measurements: a sharper concentration gradient at the tip of the triangle, i.e. the hot spot.
Diffusive mixing with water reduces both the concentration and the solubility of paraben in the ternary solution. While supersaturation of paraben can be realized and sustained under a limited set of conditions, more typically as composition reaches saturation at the hot spot, the mixture undergoes spontaneous liquid-liquid phase separation [27]. A large fraction of the mixture (∼ 99%) forms a water-rich subphase, while a small fraction forms droplets of a water-lean subphase ( Figure 1a).
As the highest concentration gradient is located at the triangle tip, this is where microdroplets nucleate exclusively. The concentration gradients along the smooth receding boundary are not sharp enough for the phase separation to initiate. The exact location and number of the triangular zones and the hot spots are possibly determined by the initial conditions of mixing, such as the influence of imperfection on the edge of the side channel on the formation of very early droplets [28]. Once formed, the triangular zone sustains along the receding boundary. The droplets appear brightest in the fluorescence images, because of enrichment of the hydrophobic dye in the water-lean droplets through nanoextraction [28,29].
As noted above, the concentration profile in the simulations represents the effect from pure diffusion processes adjacent to the triangular zone. Differences between the experimental measurements and simulation results partly reflect effects beyond pure diffusion, for instance convective effect. The first difference is that the increase in the concentra-  Figure S1), which has important implications for the dynamics of droplet movement. The spreading film evolves into thin liquid filaments that then rupture at t 0 + 710 ms, breaking up into shorter fragments and microdroplets with a diameter of (5 ± 1) µm.

Dynamics of self-propelling microdroplets
Microdroplets pinch off and jet out from the filaments, travelling at an initial velocity of (73 ± 46) µm/s, a similar velocity to that of the front of the stretching film.
The film spreading and breakup of offspring microdroplets proceeds symmetrically in the y-direction, signifying symmetry in the stress acting on the water-lean subphase.
These self-propelling droplets continue to travel along the y-direction shown in Figure   3d. Self-propelling droplets reach a maximum velocity of roughly 110 to 160 µm/s (from 10 representative droplets) in the first tens of milliseconds.
Self-propelling droplets slow down and evolve gradually to a crawling motion ( The above results show that on the two rims, microdroplets come to the end of the motion of self-propulsion. The width of the droplet trail is determined by the longest distance travelled by the microdroplets from the hot spot. Next we analyze the local chemical composition in space and time to reveal why the phase separation only takes place at the hot spot, and why the droplets move away from the hot spot.

Induced directional flow in the bulk between the walls
In the direction opposite to that of the self-propelling droplets, we observed a slower flow in the bulk between the walls that is induced by self-propelling droplets due to mass conservation in the confined space, see

Generality of self-propelling microdroplets
We now further explored the generality of the self-propelling droplets with a parametric investigation. The parameters included the chemical composition, the type, and viscosity of the ternary mixtures, and the wettability of the wall surfaces, as summarized in Table ??

Mechanisms for self-propelling droplets and directional flow
In the proposed mechanism illustrated in Figure 1e The driving force for droplet spreading in our experiments is similar to film spreading enhanced by a concentration gradient of a surfactant or an organic solvent in the formation of Marangoni flowers [33], or spreading on a liquid surface driven by solvent evaporation [34,35]. In all cases a small volume of liquid is exposed to a concentration gradient of the external constituents. We now focus on the source of energy input to the cycle. Spontaneous phase separation of the unstable mixture releases excessive Gibbs free energy. We estimated the excess Gibbs free energies of the ternary system in the states before and after phase separation using the UNIFAC model. The model enables prediction of activity coefficients based on the interaction of functional groups found in each component in a mixture. [25] Using UNIFAC, the ∆G E at initial oil concentration is estimated to be 1.89 J/mol at 8 % paraben, and decreases to 1.66 J/mol at 10 %, and further to 1.19 J/mol at 15 % (Table ??).
A substantial portion of the excessive free energy from the phase separation is converted to interfacial energies in forming three interfaces: 1) the solid-liquid interface be-14 tween water-rich subphase and substrate, 2) the solid-liquid interface between water-lean subphase and substrate, and 3) the liquid-liquid interface between the two subphases.
The interfacial energies gained by the system from forming the three interfaces can be estimated by the difference between the interfacial energies between the unstable mixture and the substrate before and after phase separation, and the interfacial energies between the droplet and the surrounding liquid (Supporting Information). The total energy gain from the interfaces is approximately 0.5 J/mol, on the same order of magnitude as excessive free energy from phase separation estimated from UNIFAC.
We take different oil concentrations as the example to estimate whether the energy supplied from phase separation is sufficient to drive self-propelling droplets. The kinetic energy of droplets were calculated by E k ∼ 1 2 mv 2 where m is the mass and v is the velocity. The mass of each droplet was obtained using a density estimated based on the water-lean subphase composition and the volume of the droplet. The kinetic energy of autonomous droplets listed in Table ?? and is on the same order of magnitude as that for droplets driven by other means such as surface chemical gradient [38] or catalytic motor [13]. The kinetic energy of propelling droplets accounts for only ∼ 1 millionth of the total amount of the free energy released from phase separation at given chemical composition. Such low efficiency in the energy conversion to kinetic energy is an expected result, considering the large proportion of energy converted to interfacial energy.

Conclusions
We show that microdroplets from liquid-liquid phase separation self propel and induce a fast flow in a quasi-2D microchamber. The microdroplets form spontaneously from diffusive mixing of a ternary mixture and a poor solvent, spread rapidly, and travel across the wall surface. The self-propulsion of the droplets induces a replenishing flow to the location of phase separation, which sustains the chemical concentration gradients in further phase separation. Our thermodynamic estimation shows that excessive free energy from the phase separation is more than sufficient to account for the kinetic energy of the propelling droplets. The phenomena studied in this work may have significant implications for a wide range of practical processes, as they are general, taking place in liquid mixtures of different concentrations, solution viscosities and solvent combination.
Our findings highlight the possibility of fast and smart fluid transport by controlling phase separation behaviors in confined spaces, which is of major interest for extraction of liquids from porous media, separation by membrane technology, phase transfer catalysis, or biphasic chemical reactions.

Declaration of Competing Interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Estimation of interfacial energies
Upon phase separation, a significant portion of the Gibbs free energy is used up in forming three interfaces: 1) solid-liquid interface between water-rich subphase and substrate, 2) solid-liquid interface between water-lean subphase and substrate, and 3) liquid-liquid interface between the two subphases. The energy required to form the three interfaces can be estimated by the difference between the interfacial energies between the mixture and the substrate before and after phase separation. Prior to phase separation, the interfacial energy between the unstable ternary mixture and the substrate (E 1 ) is given by the product of interfacial tension (γ ternary−S ) with contact area (A), Once phase separation takes place and the three interfaces form, the total interfacial energy (E 2 ) becomes the sum of the product of interfacial tensions and contact areas: L1, L2, and S denote water-lean subphase, water-rich subphase and substrate, respectively. The γ denote the interfacial tensions between respective interfaces. A 1 and A 2 denote the contact area of water-lean and water-rich subphases with the substrate, respectively, such that A = A 1 + A 2 . A interf ace is the interfacial area between the two subphases (See Figure S2). The energy E required to form the three interfaces is then the difference between the two states E = E 2 − E 1 .
Because the composition of each subphase is not exactly known, here we estimate the interfacial energy for the extreme case of an oil droplet (i.e. 1-octanol) surrounded by * Corresponding author * * Corresponding author Email addresses: xuehua.zhang@ualberta.ca (Xuehua Zhang), jmshaw@ualberta.ca (John M. Shaw) 1 These authors contributed equally to this work.
water. Therefore, in the following discussions, octanol and water are taken as L 1 and L 2 , respectively. With this assumption, γ L1−S and γ L2−S can be obtained using the Young's equation as shown below (see also Figure S2): where the surface tensions of octanol (γ L1 ) and water in air (γ L2 ), and the surface tension of OTS-coated substrate (γ S ) in air are known from literature. The static contact angle (θ) of each liquid on the substrate with air as the surrounding is θ octanol ∼ 42 o and θ water ∼ 110 o . Table S4 lists the values of surface tension as well as solid-liquid interfacial tensions for each liquid. The interfacial tension between the liquids is also known from literature.
Once the interfacial tensions are known, the total energy can be calculated by multiplying the γ values with the contact area. Here, the volume of surrounding phase (i.e. water) is estimated to be 100 times that of the oil, based on the ratio of the two subphases from phase separation along a tie line, see Figure 1a and the reference [1]. Thus, with an oil droplet of 2.5 µm in radius, the contact areas with the substrate for both oil and water are A 1 ∼ 1.96 × 10 −11 m 2 and A 2 ∼ 1.34 × 10 −10 m 2 , respectively. The interfacial area between the two liquids is A interf ace ∼ 5.4 × 10 −12 m 2 .
With these values, the total energy required for forming the three interfaces is E = E 2 − E 1 ∼ 0.49 J/mol. The energy approximated here is likely to be higher than the actual interfacial energy since the experimental value for interfacial tension between the subphases is very small (i.e. ∼0.2 mN/m for oleic acid, ethanol, water mixture). However, this analysis demonstrates that most of the energy from phase separation is spent for the formation of new interfaces.   Figure S1. Concentration profiles are symmetric along the y-axis