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

Xuehua Zhang<EMAIL_ADDRESS>Jae Bem You111These authors contributed
equally to this work. Gilmar F. Arends222These authors contributed equally to
this work. Jiasheng Qian333These authors contributed equally to this work.
Yibo Chen  Detlef Lohse  John M. Shaw<EMAIL_ADDRESS>Department of
Chemical and Materials Engineering, University of Alberta, Alberta T6G 1H9,
Canada  Physics of Fluids Group, Max Planck Center Twente for Complex Fluid
Dynamics, JM Burgers Center for Fluid Dynamics, Mesa+, Department of Science
and Technology, University of Twente, Enschede 7522 NB, The Netherlands  Max
Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany

###### Abstract

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 $\sim$160 $\mu m/s$, 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.

###### keywords:

Self-propelling , microdroplets , concentration gradients , liquid-liquid
phase separation , 2D confinement

††journal: Chemical Engineering Journal

supporting

##  1 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 $\sim$ 160 $\mu$m/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.

##  2 Experimental section

###  2.1 Preparation of chemicals and substrates

Solutions consisting of butyl paraben ($>$99 %, Sigma-Aldrich) and ethanol
(histological grade, Fisher Scientific) were prepared at mass ratio of 8/92,
10/90 or 15/85. Similar solutions were prepared using oleic acid (90%, Alfa
Aesar) or 1-octanol ($>$99 %, Sigma-Aldrich). For experiments with increased
viscosity, glycerol (Fisher Scientific) was added (see supporting information
for table with detailed compositions). The viscosity of glycerol solutions
with 30 wt%, 50 wt%, and 70 wt% are 2.5, 6, and 25.5 cP, respectively [22].

Hydrophobic Silicon (Si) substrates were prepared by coating with
octadecyltrichlorosilane (OTS-Si) according to a previously reported
method.[23] Briefly, Si substrates were cleaned with piranha solution (30%
$H_{2}O_{2}$ \+ 70% $H_{2}SO_{4}$), de-ionized water (Mill-Q) and 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.

###  2.2 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 $\mu m$ 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 $\mu L/min$ with a
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.

###  2.3 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.

###  2.4 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

$\frac{\partial c}{\partial t}=D\nabla^{2}c$

was solved to obtain the temporal and spatial evolution of the concentration
gradient of the solvents. Here $D$ is the diffusion coefficient taken as 2
$\times 10^{-9}m^{2}/s$. The oil phase with concentration of 1 (c = 1) was
initially restricted to an equilateral triangle area with size length $=$ 350
$\mu m$. The domain size was $L_{x}\times L_{y}$ = 2 $mm$ $\times$ 1 $mm$.

At the wall of x = $L_{x}$, y = 0 and y = $L_{y}$, the concentration is set to
0. At the wall x = 0, the concentration obeys von Neumann boundary conditions,

$\frac{\partial c}{\partial y}=0$

Note that the velocity field is not modeled, so in this simple approach
$\vec{u}(\vec{x},t)\equiv{0}$, i.e. pure diffusion.

###  2.5 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 $K$.

##  3 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 $\sim$ 3 in
Table LABEL:composition_space). Initially, the ternary solution filled both
the microchamber (20 $\mu m$ in depth) and the side channel (1000 $\mu m$ in
depth) as sketched in Figure 1. The top wall of the microchamber was a
hydrophilic glass slide and the bottom wall, a smooth silicon substrate coated
with a hydrophobic layer. Water was injected into the deep side channel to
displace the ternary solution in the y-direction, and some of it diffused
transversely into the microchamber in the x-direction.

A sequence of fluorescence images revealed a smooth boundary formed between
the solution (doped with a dye) and water over time. However, there were
several triangular zones of solution protruding out from the smooth boundary
into the water on the surface of the hydrophobic wall. At the hot spots of the
triangle tips, microdroplet trails of several millimeters were left behind on
the surface. From confocal microscopic imaging, the base radius of the
microdroplets was found to range from $\sim$ 2 $\mu m$ to 25 $\mu m$, the
contact angle was around $15^{o}-20^{o}$, and the maximal height was 0.5
$\mu$m to 7 $\mu$m above the surface.

Below we show that interestingly these trails consist of pinned microdroplets
at the end of their propulsion. The motion of these self-propelling
microdroplets is a key step in a cascade of dynamic events originating from
liquid-liquid phase separation in 2D confinement as sketched in Figure 1e.

###  3.1 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(a)(b) 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 ($\sim 99\%$) 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 concentration gradient close
to the hot spot is more pronounced in the experiments than in the simulations.
The second difference lies in the trend in the temporal evolution of local
concentration gradients. In Figure 2e-h the concentration at the same location
is plotted at time $t_{0}$ to $t_{0}+26s$ for experiment and the same time
window for simulation. With time the simulated ethanol concentration gradient
decayed by diffusion at a fixed location. On the other hand, the ethanol
concentration gradient estimated from the composition map in the experiments
was unchanged over a long period of time. Within the same distance from a hot
spot, the concentration gradient of ethanol remained the same as the boundary
recedes. The presence of such a local sharp and persistent gradient of ethanol
clearly requires a pathway to supply water and to keep the mixture out of
equilibrium at the hot spots. Below we show that this pathway is possibly
through self-propelling microdroplets and the induced bulk flow. The ethanol
concentration gradient in the y-direction is symmetric from the hot spot in
both experimental and simulation results (Supporting Figure S1), which has
important implications for the dynamics of droplet movement.

###  3.2 Dynamics of self-propelling microdroplets

Our high speed images (Figure 3, Movie S1) capture the rich and complex
dynamics of droplets. At the start time ($t_{0}$), a thin line comprising
several droplets forms at the tip of the trail that subsequently merges to
form a larger drop with a diameter of 10 $\mu m$ at $t_{0}+90$ ms. This drop
becomes unstable at $t_{0}+210$ ms, rapidly spreading a symmetrically from the
hot spot under a stress from symmetrical distribution of local chemical
compositions. Over a span of 480 ms, the average speed of the spreading front
from six repeating events is similar in both +y and -y directions, with
$(90\pm 23)$ $\mu m/s$ and $(72\pm 21)$ $\mu m/s$, respectively. The distance
of the film front from the hot spot increases almost linearly with time ($\sim
t^{0.92}$) as shown in the logarithmic plot in Figure 3b.

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 $\pm$ 1) $\mu m$. Microdroplets pinch off and jet out from the
filaments, travelling at an initial velocity of $(73\pm 46)$ $\mu m/s$, 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 $\mu m/s$ (from 10 representative
droplets) in the first tens of milliseconds.

Self-propelling droplets slow down and evolve gradually to a crawling motion
(Figure 3g), due to resistance from both the surrounding liquid and the solid
wall surface. The displacement of the microdroplets from the breakup point
increases with time ($\sim t^{0.82}$). The crawling droplets are repeatedly
stretched away from the hot spot and relaxed to become spherical cap (Movie
S2), every 50 ms switching between pinning and depinning modes while moving
away with an instant velocity fluctuating around 60 $\mu m/s$. This crawling
motion of the droplets resembles a self-running droplet on a surface with
wettability gradient [30] or that of a light-driven droplet on a
photoresponsive surface[31], both driven by an interfacial tension gradient.
The crawling droplets coalesced with other slower or already-immobilized
droplets and formed a larger droplet. More microdroplets coalesced on the way
as the drop travels further until the droplets eventually reached the outer
rim of the droplet trail and became immobilized. Some droplets barely moved
after nucleation, forming the central line of the trail.

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.

###  3.3 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 Figure 4. Across
an area of a semi-circular sector towards the hot spot, this bulk flow is
manifested by the trajectory of very small oil droplets with a radius of
$\sim$ 1 $\mu m$ dispersed in the solution that act as tracers. By tracking
these droplet tracers suspended in the flow, the average velocity of the flow
was determined to be 34 $\mu m/s$ at the distance of $\sim$ 150 $\mu m$ from
the hot spot. Closer to the hot spot, the flow was faster, reaching an average
speed of (46 $\pm$ 15) $\mu m/s$. After reaching the hot spot, the flow
converged to a single stream, heading toward the side channel along the
droplet trail. This bulk flow brings fresh water to the hot spot continuously,
maintaining the sharp concentration gradient at the hot spot.

The pinned microdroplets on the wall surface altered the local velocity
profile of the replenishing flow. When the droplet tracers in the flow
approached a pinned microdroplet, they were trapped by a local flow near the
microdroplet surface. The revolving motion of the tracers is attributed to the
concentration gradient of solvent constituent around the droplets. In the
proximity to the pinned droplet, the Marangoni stress is strong enough to
overcome the directional flow in the bulk and to spin the tracers. Although
the ethanol concentration was too low to be reflected in the fluorescence
intensity, the variation of ethanol concentration in space was sufficient to
induce a gradient in the interfacial tension of the droplet surface and a
local Marangoni flow adjacent to the droplet.

###  3.4 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 LABEL:composition_space. The directional
flow and self-propelling droplets occur in a certain range of chemical
composition, viscosities and oil types on a hydrophobic wall surface. The
velocity of self-propelling droplets was related to the initial chemical
composition of the ternary solution (Figure 5). At a given concentration of
paraben, adding 10 % - 20 % ethanol in water as the displacing liquid does not
change the speed of the self-propelling droplets but reduces the number of
locations of phase separation. In the range of 8 % - 15 %, the droplets travel
a shorter distance but move faster at a low concentration of paraben. The
results show that tuning the chemical composition is another way to vary the
velocity of self-propelling droplets.

The same dynamics are observed in the solutions with higher viscosity (2.5 cP
to 25.5 cP) and in various ternary mixtures (such as 1-octanol or oleic acid
in isopropanol and water). How far a droplet travels before coalescence or how
fast a droplet moves was found to vary in each case. However, linear droplet
displacement $l$ with time ($l\sim t$) was observed for all cases. The results
suggest the mechanism for self-propelling microdroplets is general for liquid-
liquid phase separation of ternary systems.

The wettability of the wall surface plays an important role in self-propelling
microdroplets. In a microchamber with both walls being hydrophobic, the
velocity of self-propelling droplets can reach $(111\pm 6)$ $\mu m/s$ on
average, almost twice the speed of droplets where only the bottom surface is
hydrophobic. The droplet trail is absent as all droplets move away from the
hot spot. For a microchamber with both walls hydrophilic, all droplets are
pinned on surfaces and there is no enhanced fluid motion.

###  3.5 Mechanisms for self-propelling droplets and directional flow

In the proposed mechanism illustrated in Figure 1e, liquid-liquid phase
separation are induced bulk flow are linked in a self-sustained cycle. The
sharp concentration gradient leads to local liquid-liquid phase separation at
the hot spot where the concentration of ethanol fades away while water
concentration increases. The interfacial tension is negligible between the
water-rich subphase and water-lean droplets, but is substantial between water
and droplets. For instance, the interfacial tension is only $\sim$ 0.2 $mN/m$
between two equilibrium subphases formed from phase separation in the mixture
of water, ethanol and oleic acid. In contrast, the interfacial tension reaches
$\sim$ 11 $mN/m$ for an oleic acid droplet and water [32]. A positive
interfacial tension gradient away from the hot spot exerts a Marangoni stress
on the free surface of the droplet, leading to symmetrical spreading along the
y-direction. Under stress the spreading film eventually becomes unstable,
breaking up into smaller droplets.

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.

For a given droplet volume, the distance of the film front ($l$) under the
stress is linear in time, i.e. $l\sim t$, completely different from drop
spreading governed by capillary force according to Tanner’s law ($l\sim
t^{0.1}$). This linear relationship holds for the temporal evolution of the
spreading front, and initial movement of the self-propelling droplets after
break-off from the film in Figures 3 and 5. The linear increase with time is
also reported in spreading of aqueous surfactant drop on surfaces, enhanced by
the Marangoni stress from the concentration gradient of a surfactant [36]. The
balance between the Marangoni stress and viscous stress on the droplets leads
to the linear dependence $l\sim t$, as reported previously [36].

Further away from the hot spot, the gradient in ethanol concentration
smoothens out, thus less stress propels the droplets. At the rim of the
droplet trail, the stress from $\Delta\gamma$ is balanced by the viscous drag
force from the surrounding fluid (now mostly water) and the friction from the
wall surface. Finally, due to the viscous drag and frictional forces, the
self-propelling droplet becomes pinned on the surface. The effect from the
wall wettability on self-propelling droplets is evident as no self-propulsion
takes place on a hydrophilic surface where the droplet cannot overcome the
large static friction force and displace the external water-rich liquid on the
surface [37].

The induced flow enhances the sharp concentration gradient at the hot spot for
further phase separation. At the same time, the mass loss at the hot spot of
the self-propelling droplets and the outflux along the droplet trail is
compensated by influx of the directional flow to the hot spot. In this way, a
self-sustained cycle completes and repeats itself from liquid-liquid phase
separation at the hot spot.

To summarize, we note that the cycle consists of several interconnected steps
on different time and length scales. The diffusive boundary moves away from
the side channel for several 102 s in time and over centimeters in length
scale. The formation and propulsion of droplets occurs in 10-3 s over
micrometers in distance. The induced flow travels over centimeters to reach
the hot spot, several orders of magnitude faster than the receding boundary.
This replenishing flow is 2-3 times faster than the diffusiophoretic transport
induced by chemical gradient or catalytic reactions reported in the literature
[13, 38]. Such enhanced transport may have important implications for mass
transfer involving liquid-liquid phase separation in confined spaces.

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 $\Delta
G^{E}$ 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 LABEL:energies).

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 between 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
$E_{k}\sim\frac{1}{2}mv^{2}$ 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 LABEL:energies 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 $\sim$ 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.

##  4 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.

## Acknowledgement

The project is supported by the Natural Science and Engineering Research
Council of Canada (NSERC) and Future Energy Systems (Canada First Research
Excellence Fund). This research was undertaken, in part, thanks to funding
from the Canada Research Chairs program. DL acknowledges the support from the
European Research Council - Advanced Grant under Project Number 740479 and
from the European Research Council - Proof-of-Concept Grant under Project
Number 862032.

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Figure 1: Experimental configuration for self-propelling droplets and enhanced
transport in a 2D chamber. (a) Ternary phase diagram for butyl
paraben/ethanol/water system. Reproduced from Ref. [26] (Copyright 2015
Elsevier). (b) Sketch of the 2D chamber with top view and cross-section of the
main and side channels. The surface of the bottom plate was hydrophobic while
the top surface was hydrophilic. Solution A is initially encased in the
microchamber with the composition as indicated in the solubility diagram.
Water flows to the side of the encased solution and diffuses into it. The
boundary between water and the oil solution moves from the side channel into
the 2D main channel. The composition of the mixture is indicated by the
dilution line (red dotted line in the phase diagram). An oil-rich subphase
(red circle) and a water-rich subphase (blue star) form from liquid-liquid
separation in response to oversaturation of paraben. (c)Confocal image showing
the oil-rich subphase droplets formed on the hydrophobic wall of the
microchamber. (d) Time-lapse fluorescence images show that the oil-rich
subphase droplets are propelled along the bulk water flow while the mixing
front moves toward the main channel. (e) Artistic sketch of the dynamical
events occurring at a hot spot triggered by spontaneous phase separation.

Figure 2: (a) Intensity field of a receding mixing front at a fixed time
obtained from fluorescence imaging. (b) Plot showing the intensity of
fluorescence along lines 1 to 5 on the concentration field. The intensity
along each line decays according to the error function, $I(x)\sim
I_{0}e^{-(x/a)^{2}}$ where $I_{0}$ is taken as 1 and a is a constant. The
fitted curves are shown as black dotted curves on the plot. The slope of
intensity gradient becomes steeper as the location of the line in (a)
approaches the tip (lines 5 to 1). This suggests that the concentration
gradient is the sharpest at the hot spot where phase separation occurs. (c)
Similar results are observed from a concentration field of ethanol at time t0
= 4s obtained by numerical simulation. Here, the domain size is $L_{x}\times
L_{y}$ = 450 $\mu m$ $\times$ 450 $\mu m$. (d) Concentration profiles along
the lines 1 to 4 obtained from the concentration field. In agreement with
experimental results, the slope for the concentration profile becomes steeper
as the location of the line approaches the tip. (e) Time-lapse fluorescence
images of intensity field over 26s and (f) intensity profile along the white
dotted lines on the images. The intensity gradient at fixed location in the
mixing front remains unchanged thanks to the replenishment of fresh water by
recirculating flow. (g) Concentration field and (h) profiles on line 3 at
various times obtained from numerical simulation. Unlike the experimental
results, the stimulated concentration gradient smooths out over time.

Figure 3: Microscopic dynamics of the process. (a) Time-lapse high-speed
images showing water-lean subphase film spreading in $\pm$ y direction as a
result of spontaneous phase separation at the hot spot. (b) Plot showing
displacement vs. time for films spreading during 6 consecutive events. Filled
and hollow dots represent the top and bottom half portions of the film with
respect to the center indicated by the red dotted line in (a). The dynamics of
the film spreading is consistent with early dynamics of a drop spreading on a
surface, i.e $x\sim t^{n}$, with $n\sim$ 1\. Time-lapse high-speed images
showing (c) the splitting of a film into several branches after sufficient
spreading and (d) droplets being pinched off from a branch. (e) Plot showing
displacement vs. time for 10 individual droplets pinched off from branches.
The dynamics of droplets is similar to that of a spreading film, but with
lower exponent, i.e. $x\sim t^{n}$ where $n\sim 0.82$. (f) Time-averaged
velocities of droplets pinched off the branches. (g) Time-lapse images of
droplets coalescing with each other after traveling a certain distance. Thanks
to the drag from the surface, they eventually come to a stop.(h) Instantaneous
point-to-point velocities of self-propelled droplets tracked over 1 s. The red
curve shows the mean data obtained from 10 self-propelled droplets and the
gray colored area shows the maximum and minimum velocities at each instant in
time.  Figure 4: (a) High-speed time-lapse images demonstrating the presence
of replenishing flows visualized by tiny oil droplets traveling towards the
hot spot. (b) Plot showing the displacement vs. time of returning oil droplets
and the receding mixing front. The timescales of the two are vastly different.
The replenishing flow travels at $\sim$ 34 $\mu m/s$ whereas the receding
mixing front only travels at $\sim$ 6.4 $\mu m/s$. (c) The motion of tiny oil
droplets in the replenishing flow is influenced by the Marangoni flow around
large pinned droplets occurring due to the ethanol concentration gradient. As
a result, once tiny oil droplets are close enough to the large droplets, the
competition between replenishing flow and Marangoni flow drives the tiny oil
droplets in a circulatory motion around the large droplets as captured by
high-speed time-lapse images. (d) Schematics showing the presence of bulk flow
and Marangoni flow around a large pinned droplet.

Figure 5: (a) The self-propulsion of droplets driven by phase separation
occurs regardless of initial paraben concentration as shown by the time-lapse
high-speed images. (b) Plot showing the displacement vs time of 10 individual
droplets for initial paraben concentrations of 8%, 10% and 15%. All data
follow a similar trend as that of a spreading film, i.e. x $\sim$ tn where n
$\sim$ 1\. (c) The dynamics shown in this work also holds for various oil
types, compositions of Solution B, and viscosities of both Solutions A and B.
Again, the data follow a similar trend. (d) Surface wettability is critical
for the phenomena shown in this work. Optical images of droplet formation in a
chamber with both top and bottom surfaces hydrophilic (left) and hydrophobic
(right).