Interface‐Driven Spontaneous Differentiation‐Repulsion Behavior in Isochemical Droplet Populations

An important exercise for understanding the emergent behavior in biology is to study it using minimal synthetic systems. Current biomimetic systems involving directed motion and collective migration require at least three components: two immiscible solvents to form an emulsion, and external agent(s), usually surfactants, to give rise to asymmetric interactions and induce transient non‐equilibrium conditions. Here, the most minimal system thinkable, consisting of only two components, is presented, in the form of micron‐sized oil (1‐decanol) droplets dispersed in a finite water reservoir. Spontaneous emergent dynamics within chemically identical droplet populations is reported, in the form of physical differentiation of droplets in a stochastic manner leading to an immediate repulsive behavior amongst their neighbors. Using a microfluidic production platform, fluorescence microscopy experiments, and modelling, it is showed that this cyclic phenomenon of differentiation‐repulsion results from oil droplets entering the air‐water interface leading to Marangoni flows and their coupling with evaporative flux of decanol. The potential of this platform is illustrated by demonstrating control over the event frequency, its use as Marangoni tweezers to trap droplet clusters, and proof‐of‐principle reorganization of multi‐component assemblies. The presented collective behavior with exceptional chemical simplicity makes it amenable for potentially developing self‐assembled biomimetic and bioengineered structures.


Introduction
The emergence of life is among the key concepts at the intersection of chemistry, physics, and biology.
Referring to the notion of "the whole is more than the sum of its parts" 1 , emergent properties unite the study of living systems with the study of individual inanimate components.A conceptual and practical exploration of the concept requires studying simplistic model systems and understanding the involved dynamics under non-equilibrium conditions 2,3,4 .A current major effort is in the direction of constructing synthetic cells, artificial constructs that can mimic form and function of biological cells.
One of the hallmark properties to recreate in such a bottom-up fashion is motility and chemotaxis of individual units as well as their collective behavior within a population.
Along with membranous vesicles and aqueous phase separation-based containers, single emulsions (water-in-oil or oil-in-water droplets) are well-established and the simplest model systems to study bio-inspired behavior 5,6,7,8 .Using emulsions, numerous studies have looked at creating motile systems.Some recent examples include droplets with synthetic flagella-like extrusions which swim by surface phase transitions induced by temperature variations 9 and chemotactic movement of octanol droplets supported by self-reproducing lipids 10 .Along with external cues, encapsulated active substances can also induce directional movement, for instance, random motion of bacteria inside droplets can lead to directional self-locomotion 11 .
Even without external cues or active encapsulated components, droplets can be directionally driven utilizing either their physicochemical properties or hydrodynamics 12 .For instance, buoyancy from density differences 13 , drag from viscosity 14 , and discrepancy in surface tension 15 can all induce droplet motion.On the other hand, droplets' own diffusion in a surfactant solution 16 or evaporation of the surrounding multicomponent solution 17 can also indirectly affect the droplet movement 18 and collective behavior 19 .Based on the knowledge above, emulsion could either move in a straight-line trajectory 20 or find an optimal path in a microfluidic maze 21,22 .Furthermore, systems in which droplets affect each other's behavior have been observed, such as in 'predator-prey' attraction/repulsion 23 and chemotactic self-caging 24 .
All the above-mentioned examples need at least three components to exhibit a motile behavior, either to stabilize the droplet suspension or to create appropriate non-equilibrium conditions through gradients.The prominent presence of additives like surfactants 21 , or soft matter assemblies like liposomes 25 in fundamentally two-component emulsion systems poses a question whether three components is a minimum requirement to induce a collective motile behavior and transient nonequilibrium dynamics in emulsion systems.
In this study, we present a strictly two-component system, consisting of oil droplets in water, that exhibits spontaneous emergent dynamics at the air-water interface.We use a surfactant-free microfluidic platform to produce and collect micron-sized 1-decanol droplets.When dispersed in a water reservoir, these originally identical droplets spontaneously differentiate themselves at the water-air surface to give rise to various forms of complex emergent dynamics.Specifically, spontaneous physical transformation of one of the droplets produces Marangoni flows that temporarily repel the surrounding droplets.Coupled with evaporative flux of oil in the surrounding air, the resulting effect is sustained, and the transformation-repulsion cycle can be repeated numerous times.We provide a physical model that explains the phenomenon and we also show control over the system at the expense of adding a third component.We further demonstrate the potential of this platform for bioengineering by its proof-of-principle use as "Marangoni tweezers" to trap micron-sized objects through interfacial tension gradients and reorganization of densely packed emulsion population into tissue-like ordered structures.The presented two-component shows significant reduction in the chemical complexity and yet a rich collective behavior making it amenable to its use in further developing self-assembled biomimetic platforms.

Decanol droplets undergo spontaneous and cyclic differentiation-repulsion behavior
We chose our two-component system to be a water reservoir (~4 µL) placed on a clean glass slide, with numerous (~10-1000), micron-sized (10-80 µm) oil droplets freely diffusing in the reservoir (Fig. 1a).We opted for 1-decanol (C10H21OH; referred simply as decanol from here onwards), a straightchain primary alcohol, as our oil-of-choice, owing to its very low solubility in water (37 mg/mL at 25 °C), its density being lower than water (830 kg/m 3 ) allowing the droplets to float, and its wide usage in biomimetic systems 19,20,26,27 .We used pure water without any additives (salts or surfactants), except for specific experiments.It should be noted that since the height of the water droplet is roughly 1 mm and since decanol microdroplets are buoyant, they are not in direct contact with the waterglass interface, making the water-air boundary the key interface in the experiments.
To obtain a monodispersed population of oil droplets within a biological cell size range, we used a microfluidic production setup (Fig. 1a-d; see Materials and Methods for details).Briefly, our production device consisted of a flow-focusing junction, where the middle decanol stream was pinched-off by two orthogonal water streams to produce ~30 µm decanol droplets (Fig. 1b).It is important to note here that unlike the widely used droplet production protocols that use surfactants in the water phase to stabilize the formed droplets 28,29 , this is a strictly two-component system.
Despite not using surfactants, we were able to obtain stable droplets without any appreciable coalescence.A possible explanation is because the produced droplets were immediately transferred into a bulk water reservoir to prevent on-chip prolonged physical contact (Fig. 1c), and the electrostatic repulsion between the droplets prevented their coalescence.Indeed, the zeta potential of decanol droplets was measured to be -15.3 ± 2.3 mV (see Materials and Methods for details).Similar magnitude of negative surface charge is reported for simple hydrophobic phases and seems to be a generic phenomenon.The origin this negative surface charge is proposed to be either due to the preferential adsorption of hydroxide ions at the interface, or minute amounts of surface-active Scale bar is 1 mm.(e) Spontaneous "popping" of a decanol droplet (indicated by the red arrow and then marked with a red circle in subsequent images) that immediately leads to a repulsive behavior of the neighboring droplets as they move away from the popped droplet.The repulsive droplet eventually moves to the edge of the water droplet (top-right), and a new droplet pops (indicated by the green arrow and then marked with a green circle in subsequent images), followed by the repulsive behavior of the surrounding droplets.The white boundary indicates the edge of the water droplet.Decanol droplets were stained with Nile red (0.01% w/v) and visualized using epifluorescence microscopy.Scale bar is 1 mm.contaminants 30,31,32 .We observed coalescence for densely packed droplet populations and for older samples, and thus strictly used freshly prepared decanol droplets to carry out the experiments.
To start the experiment, we added a tiny amount of decanol droplet suspension (0.2-0.4 µL) to the water droplet and recorded the droplet behavior (Fig. 1d).We stained the droplets with a fluorescent dye (Nile red, ≈0.01%w/v) for better visualization using epifluorescence microscopy.Along with the expected Brownian motion of the oil droplets, we made a surprising observation.Every now and then, one of the droplets suddenly became repellent, instantly pushing away the surrounding droplets (Fig. 1e; Supplementary Videos 1 and 2).We chose to name this phenomenon "popping", emphasizing the sudden, discontinuous nature of the change and the physical displacement of the popped droplet towards the air-water interface, as will become clear later in the text.Popping happened spontaneously and rapidly, within 30 ms, and the repelled droplets were pushed away at high speeds, in the order of ~1 cm/s.The repelled droplets eventually regrouped, and then another droplet popped, repeating the process (we recorded 44 consecutive events on one occasion).In the case of larger droplets, as can be seen in Fig. 1e, the popped droplet sometimes remained repulsive even after the next popping event.This "dance of droplets" sometimes continued till all droplets had, at one point, taken the role of the repellent droplet.It should be noted that the same popping behavior was observed using bulk-produced droplets, without the addition of Nile red, confirming that neither the microfluidic production nor the fluorescent dopant played any part in the phenomenon (Supplementary Video 3).

Decanol droplets stochastically enter the air-water interface and get physically differentiated
Upon closer inspection, the popped droplets seemed to become slightly bigger (Fig. 2a).We checked this by measuring their size just before and after popping (see Materials & Methods for details).
Indeed, the droplet diameter increased by a factor of α = 1.23 ± 0.02 (n = 10; see Fig. 2b).This increase is not coupled to a decrease in size of other droplets, nor is there any other external source of decanol present in the system.We therefore ascribed this size change to a change in droplet shape.
Specifically, we hypothesized that the popped droplets entered the air-water surface and became lens-shaped, thereby increasing their apparent diameter (Fig. 2c).
To determine whether such a transition is thermodynamically favorable, we calculated the entering coefficient which is defined as 33
Therefore, for decanol droplets in water, E is always positive, ranging between 9-53 mN/m, implying a favorable transition regardless of the air-water interface coverage by decanol.Upon entering, the shape of the droplets is determined by the balance of forces that result from the three interfacial tensions (see Fig. 2c).In the extreme case of a complete decanol monolayer formation at the air-water interface, the popped droplet should take the form of a hemisphere, and in its transformation from a sphere, the droplet radius should grow by a factor of α = √2 3 = 1.260.In the experiments, the droplet is most likely lens-shaped and therefore, α is expected to be lower.Our measured value of α = 1.23 ± 0.02 corresponds very well to this expectation.To further confirm the entering of the popped droplet at the air-water interface, we visualized the popping event sideways, using a contact angle measurement setup (see Materials and Methods for details).While relatively hard to image, we captured a popping droplet significantly changing its appearance within 1.7 ms (Fig. 2d; Supplementary Video 4).Furthermore, the droplet was seen to move upwards upon overlapping the two images (Fig. 2e; before image in red, after image in green), further corroborating our hypothesis.

Differentiated decanol droplets repel neighboring droplets via Marangoni flow
Having clarified the spontaneous shape transformation during the popping of the decanol droplets, we turned our attention to the cause of the sudden repulsion of the surrounding droplets.Being an amphiphilic molecule, decanol can act as a surfactant, preferring to occupy the air-water interface compared to water molecules.We hypothesized that upon the entry of the droplet into the air-water interface, decanol molecules can directly move along the interface without being limited by its diffusion through bulk water phase.Through the establishment of a surface tension differential, a Marangoni flow will be generated that can quickly spread a decanol monolayer across the surface of the water droplet and causing the observed "repulsion" of the surrounding droplets as they get carried away by the Marangoni flow.To test our hypothesis, we used fluorescent beads (0.5 µm in diameter) to visualize the Marangoni flow induced by the popped droplets.While the beads initially diffused randomly throughout the sample, we observed an immediate radially outward motion upon a popping event (Supplementary Video 5).This motion of the beads away from the popped droplet can be seen clearly in the form of moving streaks and upon overlaying successive time frames (Fig. 3a).Here, the red streaks (initial time point) are closer to the droplet than the green streaks (latter time point).Also, upon focusing inside the water reservoir, 150 µm away from the air-water interface, we observe the opposite, i.e., the green streaks are closer to the droplet than the red streaks (Fig. 3b).This is due to a compensatory backflow within the sample that balances the outward Marangoni flow, again in line with our hypothesis (Fig. 3c).Side-view imaging in recent work showed similar flow-fields for oil droplets at the air-water interface 36 .

Marangoni flow-driven decanol influx and evaporative efflux drives the differentiation-repulsion cycle
If the efflux from the popped droplet was the only process affecting the decanol monolayer at the airwater interface, one would expect the Marangoni flow to quickly stop once the monolayer covers the entire water droplet surface, and we would expect no other droplets to enter the air-water surface, preventing further popping-repulsion cycles.As we observe multiple cycles within a single experiment, there must be another process at play that results in a continuous efflux.A reasonable candidate is evaporation.Although the vapor pressure of decanol is relatively low (1.13 pa at 25 C) 26 , and the evaporation rate will therefore be minimal, it may nevertheless be enough to drive the observed micron-scale processes, facilitated by the high area-to-volume ratio of a monolayer.
To determine whether evaporation may contribute significantly to the mass balance of decanol at the air-water interface, we assumed that the evaporation flux was directly proportional to the area through which evaporation occurred.

𝐽 𝑒𝑣𝑎𝑝 = 𝐾 𝑒𝑣𝑎𝑝 • 𝐴
Where   is the evaporation flux in mol/s,   is the evaporation constant in mol/m 2 .sand  is the evaporation area in m 2 .To estimate   , a 4 μl decanol droplet was left to evaporate at room temperature and the volume change over time was determined using a side-view imaging setup (Fig. 3d; see Materials and Methods for details).The obtained   (19.1 pmol/s) let us estimate   to be ~1.38⋅10 - mol/m 2 s.At room temperature, a decanol monolayer is in a liquid 2D lattice state, in which a decanol molecule takes up 24 Å 2 37 .Therefore, the maximum surface concentration of decanol, Γ monolayer , is 6,92⋅10 -6 mol/m 2 .Thus, one equivalent of a fully covered monolayer will evaporate very rapidly (  =   Γ  ), within 0.2 seconds.Thus, it is reasonable to say that decanol evaporation is likely contributing significantly to the effects we observe.
After a decanol droplet enters the air-water surface, an initial "burst state" in which the decanol monolayer is spread across the air-water surface by Marangoni flow is expected to be followed by a steady state, in which the evaporative decanol efflux from the surface equals the influx from the droplet.In previous studies, the speed of a monolayer in the burst state was found to follow the equation 38   = 35.79*  −0.399 With  being the distance to the droplet, and   the speed of the monolayer.For  = 1 cm (the length scale of the water reservoir), the speed would be 35.79cm/s, which far exceeds the top speeds (~1 cm/s) that we observe for the repelled droplets.While this might be due to the differences in the experimental setups and limitation of the analytical solution, this estimation suggests that the repulsion we observe may largely take place during the steady state.
To test this explanation of Marangoni flow coupled with evaporative flux causing the observed behavior, we derived a simplistic steady-state model (see Supplementary Information).We used the model to predict the speed of the decanol droplets being repelled from a popped droplet as a function of their distance from the popped droplet.We derived the following equation.
Here, we assumed the shape of the water droplet to be the cap of a sphere with radius .The droplet speed  is expressed in terms of , the angle between the droplet, the centre of the sphere, and the zenith of the sphere.The contact angle θ between the water, glass, and air phase was measured to be 51.7° ± 0.2°.A correction factor  is included to fit the predicted shape of the trendline over the experimental data using a least-squares regression method.The data for two independent experiments (each with three popping events), along with the model prediction, are plotted in Fig. 4a.
Despite being relatively simple and based on the assumption that the popped droplet is centrally placed in the water reservoir, our model correctly predicts the trendline (R 2 = 0.88) when compared to the experimental data.We find  = 4.1, suggesting that the model fits reasonably well and is within the correct order of magnitude.As  >1, the model predicts lower speeds that those observed experimentally.One explanation might be that decanol may evaporate more readily from a monolayer than from a decanol droplet, leading to an underestimation of   .droplets.The decanol monolayer that is spread across the interface during the process is rapidly evaporated, keeping the process in a steady state.Once the entered droplet is completely consumed or removed from the interface, the process repeats with another randomly chosen droplet.
We thus understand the popping-followed-by-repulsion behavior as follows (Fig. 4b): Decanol droplets enter the air-water interface spontaneously owing to a positive spreading coefficient and thermal fluctuations.Immediately upon entering, interfacial tension differential produces a Marangoni flow directed radially outwards of the popped droplets.This leads to the 'repulsive behavior' of the neighboring submerged droplets and facilitates the spreading of decanol monolayer across the air-water interface.The spread monolayer is rapidly evaporated leading to a steady-state condition which lasts till (i) the popped droplet is completely used up in the process, or (ii) is moved away from the interface, either to the boundary of the reservoir or back in bulk water, due to fluid flows induced by other popping events.

Differentiation-repulsion behavior can be tuned and utilized to reorganize multiparticle assemblies
After deciphering the popping mechanism, we wondered if one could tune this phenomenon and further utilize it to design and control soft matter assemblies.We started with tuning the popping frequency.We noted that a pristine water-air interface is negatively charged .Since the decanol droplets are also negatively charged, the resulting electrostatic repulsion between the surface charges may act as a significant barrier for the decanol droplets to enter the air-water surface.If this is indeed the case, addition of decanoate, a negatively charged amphiphile that is expected to adsorb at the surface of the decanol droplets as well as at the air-water interface, will make the interfaces even more negatively charged and therefore decrease the popping frequency.On the other hand, presence of monovalent salts should shield surface charges and increase the popping frequency.The experiments confirmed our predictions, as shown in the frequency plot in Fig. 5a: At a low concentration of decanoate (~30 μM) and no salt, the popping frequency was 0.13 Hz.Increasing the decanoate concentration to 10 mM decreased the frequency by a factor of 3.8.Addition of salt had the opposite effect, with 50 mM NaCl dramatically increasing the frequency nearly 50-fold, despite the low amount of decanoate (~30 μM) present (Fig. 5b; also see Supplementary Video 6).Even at high decanoate concentrations (10 mM), presence of salt increased the frequency 2.6-fold, compared to samples containing 10 mM decanoate but without salt.Thus, addition of salt dramatically increased the popping frequency, whereas the addition of decanoate decreased it, showing that the popping can be tuned over two orders of magnitude by adding a third component (surfactants or salts) to the system.Next, we demonstrated a novel way of spatially controlling a group of droplets using popped droplets.
We observed that in case of multiple popping events in close succession, each of the popped droplets generated their own Marangoni flows, pushing each other away, and stabilizing themselves at the vertices of an equilateral polygon.An arrangement with five popped droplets is shown in Fig. 6a, with the assembly lasting up to 90 seconds (See Supplementary Video 7).An interesting consequence of this is that the produced flow-fields can trap the remaining decanol droplets in the middle.Thus, the Marangoni flows induced through interfacial tension gradients may be applied to build "Marangoni tweezers", allowing manipulation of microparticles, similar to the optical tweezers that use lasers to hold and move micron-sized objects.
Finally, we probed the benefits of such spontaneous popping events to induce structural reorganizations within a dense population of decanol droplets.We used a polydisperse droplet population with a high number density to check the effect of popping events on the overall droplet organization (Fig. 6b; Supplementary Video 8).Interestingly, the individual randomly placed popping events not only resulted in the expected repulsion behavior but led to a dramatic inter-droplet reorganization.Prior to the first pop, the droplets were scattered and freely diffusing as individual units, albeit the bigger droplets being situated more towards the center owing to higher buoyancy forces.However, after the first pop, the local repulsion of the droplets was followed by a regrouping event in which droplet speed, due to the buoyancy force, was highly size-dependent.The result was a cluster of larger droplets tightly packed in the center, surrounded by smaller droplets forming relatively tight ring around this central formation.After the second popping eventin which multiple droplets became repulsivethe droplets formed one tightly packed assembly, in which the size of droplets decreases radially outwards.The structure closely resembled a biological tissue in its appearance and remained stable within the time frame of the experiment (~2 min).The stability of the structure was likely facilitated by the Marangoni tweezers created by five popped droplets present outside the assembly (not visible in Fig. 6b), keeping the assembly at the center of the water reservoir.
Thus, the presented popping behavior has the potential to spontaneously organize a droplet population into a more ordered structure without the need of any external force.

Conclusion
We have presented a system consisting of only two componentsdecanol microdroplets in a water reservoir devoid of any additional agentsthat exhibits unusual collective motile behavior.The oil droplets spontaneously enter the air-water interface, producing Marangoni flows balanced by evaporative flux and repelling the surrounding droplets.The observed differentiation-repulsion cycles proceed without needing an external energy source or changes to the environment.As opposed to using two chemically different droplet populations that interact with each other in a defined manner, the presented system exhibits spontaneous differentiation amongst a single droplet species in a stochastic manner, which is immediately detected and reacted upon by the rest of the population.
The popping (entering) of the decanol droplet is a stochastic phenomenon that changes the droplet shape as well as its physical behavior.We show that the energy barrier to pop can be significantly tuned by adding a third component, in the form of a dedicated surfactant, or salts to screen the charges.We also build a steady-state physical model that corroborates well with the experimental data.Using this two-component system, we show possibilities to control and reorganize multi-unit assemblies.
While this study has focused on understanding the physical mechanism behind differentiation-andrepulsion, in future it would be worth exploring how the chemical composition affects the phenomenon.It will be of interest to know how unique the popping event is to decanol and whether other hydrophobic oils also exhibit similar trend as long as the popping barrier remains sufficiently low.
An exciting way to utilize this phenomenon would be in developing biomimetic systems with life-like characteristics.Imparting collective motility and responsiveness to physicochemical stimuli for synthetic cells 8,40,41 will be particularly interesting given potential applications in targeted drug/cargo delivery 42,43 and pollutant purification 44,45 .For example, using microfluidic double emulsiontemplated techniques that use alcohols like 1-octanol as the lipid-carrying phase 28,46 would provide a natural gateway to utilize the popping-repulsion cycles to synthetic containers.A biocompatible vesicle with an external decanol pocket that can trigger a collective motility signal within a population may provide opportunities for bioengineering applications.

Microfabrication
Microfluidic devices were made using PDMS stamps, with engraved channels, bonded to a glass coverslip.First, a master wafer with the desired designs was prepared using soft lithography as described elsewhere 47 .Briefly, a negative photoresist SU-8 was coated on a clean silicon wafer to obtain a height of 40 μm and the designs were printed using MicroWriter ML3 Pro as described elsewhere 47 .Next, PDMS pre-polymer was thoroughly mixed with curing agent in a 10:1 weight ratio and poured on the master to a height of roughly 1 cm and incubated at 70 °C overnight.The designs were cut out, inlet and outlet holes were punched, and the PDMS slab was bonded to glass coverslip by activating the surfaces using a plasma cleaner (12 MHz, 30 seconds).After baking the bonded devices for 2 h, the post-junction channel was coated with PVA similar to as described in 47 , with PVA being supplied through the water inlet, and air through the decanol inlet.In case of no PVA treatment, the device was immediately used for droplet production.

Zeta potential measurements
Decanol droplets were generated by mixing 50 μl of decanol with 950 μl of MilliQ and shaking vigorously.The zeta potential was determined by taking the average of ten readings using the Malvern Zetasizer Nano instrument at 25 °C.

Contact angle measurements
The contact angle of water droplets placed on a clean glass slide was measured using the KRÜSS Drop Shape Analyser-DSA30E with KRÜSS Advance software using the Ellipse (Tangent-1) fitting method with an automatic baseline.Five droplets were measured, each with five runs.

Image processing
To show the size change upon popping (Fig. 2b), an intensity profile was measured using ImageJ for an individual droplet before and after popping.The profile was normalized by dividing over the total sum intensity.The size of the droplets was defined as and determined by taking the full-width halfmaximum of the profiles.The size change factor  was found by dividing the size after popping by the size prior to popping.To plot the time-distance curve (Fig. 4a), ImageJ was used to determine the distance between the center of the popped droplet and the repulsive droplets starting at the frame directly prior to the one where the repulsion started.Popped droplets were arbitrarily chosen from those that were sufficiently centrally located, not in contact with other droplets, and remaining roughly immobile after popping.The speeds were determined by subtracting the distances between consecutive frames and dividing by the time interval between them.Instead of using the former or latter position, the average droplet position was used to prevent biasing the data towards either position.

Figure 1 .
Figure 1.A population of decanol microdroplets floating on a water droplet show a repetitive "popping-followed-by-repulsion" behavior.(a) Schematic of the experimental set up showing decanol

Figure 2 .
Figure 2. The popped decanol droplets enter the air-water surface before they start repelling other

Figure 3 .
Figure 3.After entering the air-water interface, decanol droplets produce Marangoni flow and the

Figure 4 .
Figure 4.A simplistic model based on a steady-state assumption corresponds well to the

Figure 5 .
Figure 5. Droplet popping can be tuned by the addition of surfactants and salt.(a) A bar chart

Figure 6 .
Figure 6.The emergent differentiation-repulsion behavior can be used to create spatial control and