Solute-mediated interactions between active droplets

Phase-separated droplets swim to their dissolution

Biological macromolecules can condense into liquid domains. In cells, these condensates form membraneless organelles that can organize chemical reactions. However, little is known about the physical consequences of chemical activity in and around condensates. Working with model bovine serum albumin (BSA) condensates, we show that droplets swim along chemical gradients. Active BSA droplets loaded with urease swim toward each other. Passive BSA droplets show diverse responses to externally applied gradients of the enzyme's substrate and products. In all these cases, droplets swim toward solvent conditions that favor their dissolution. We call this behavior "dialytaxis", and expect it to be generic, as conditions which favor dissolution typically reduce interfacial tension, whose gradients are well-known to drive droplet motion through the Marangoni effect. These results could potentially suggest alternative physical mechanisms for active transport in living cells, and may enable the design of fluid micro-robots.

Billiards with Spatial Memory

Many classes of active matter develop spatial memory by encoding information in space. We present a framework based on mathematical billiards, wherein particles remember their past trajectories. Despite its deterministic rules, such a system is strongly nonergodic and exhibits intermittent statistics and complex pattern formation. We show how these features emerge from the dynamic change of topology. Our work illustrates how the dynamics of a single-body system can dramatically change with spatial memory, laying the groundwork to further explore systems with complex memory kernels.

Pair Interactions of Self-Propelled SiO2-Pt Janus Colloids: Chemically Mediated Encounters

Driven by the necessity to achieve a thorough comprehension of the bottom-up fabrication process of functional materials, this experimental study investigates the pairwise interactions or collisions between chemically active SiO2-Pt Janus colloids. These collisions are categorized based on the Janus colloids' orientations before and after they make physical contact. In addition to the hydrodynamic interactions, the Janus colloids are also known to affect each other's chemical field, resulting in chemophoretic interactions, which depend on the degree of surface anisotropy in reactivity of Janus colloid and the solute-surface interaction at play. Our study reveals that these interactions lead to a noticeable decrease in particle speed and changes in orientation that correlate with the contact duration and yield different collision types. Distinct configurations of contact during collisions were found, whose mechanisms and likelihood are found to be dependent primarily on the chemical interactions. Such estimates of collision and their characterization in dilute suspensions shall have a key impact in determining the arrangement and time scales of dynamical structures and assemblies of denser suspensions and potentially the functional materials of the future.

Shaping active matter from crystalline solids to active turbulence

Active matter drives its constituent agents to move autonomously by harnessing free energy, leading to diverse emergent states with relevance to both biological processes and inanimate functionalities. Achieving maximum reconfigurability of active materials with minimal control remains a desirable yet challenging goal. Here, we employ large-scale, agent-resolved simulations to demonstrate that modulating the activity of a wet phoretic medium alone can govern its solid-liquid-gas phase transitions and, subsequently, laminar-turbulent transitions in fluid phases, thereby shaping its emergent pattern. These two progressively emerging transitions, hitherto unreported, bring us closer to perceiving the parallels between active matter and traditional matter. Our work reproduces and reconciles seemingly conflicting experimental observations on chemically active systems, presenting a unified landscape of phoretic collective dynamics. These findings enhance the understanding of long-range, many-body interactions among phoretic agents, offer new insights into their non-equilibrium collective behaviors, and provide potential guidelines for designing reconfigurable materials.

Buoyancy-driven attraction of active droplets

For dissolving active oil droplets in an ambient liquid, it is generally assumed that the Marangoni effect results in repulsive interactions, while the buoyancy effects caused by the density difference between the droplets, diffusing product and the ambient fluid are usually neglected. However, it has been observed in recent experiments that active droplets can form clusters due to buoyancy-driven convection (Krüger et al. Eur. Phys. J. E, vol. 39, 2016, pp. 1-9). In this study, we numerically analyze the buoyancy effect, in addition to the propulsion caused by Marangoni flow (with its strength characterized by Péclet number Pe). The buoyancy effects have their origin in (i) the density difference between the droplet and the ambient liquid, which is characterized by Galileo number Ga, and (ii) the density difference between the diffusing product (i.e. filled micelles) and the ambient liquid, which can be quantified by a solutal Rayleigh number Ra. We analyze how the attracting and repulsing behaviour of neighbouring droplets depends on the control parameters Pe, Ga, and Ra. We find that while the Marangoni effect leads to the well-known repulsion between the interacting droplets, the buoyancy effect of the reaction product leads to buoyancy-driven attraction. At sufficiently large Ra, even collisions between the droplets can take place. Our study on the effect of Ga further shows that with increasing Ga, the collision becomes delayed. Moreover, we derive that the attracting velocity of the droplets, which is characterized by a Reynolds number Red, is proportional to Ra1/4/(ℓ/R), where ℓ/R is the distance between the neighbouring droplets normalized by the droplet radius. Finally, we numerically obtain the repulsive velocity of the droplets, characterized by a Reynolds number Rerep, which is proportional to PeRa-0.38. The balance of attractive and repulsive effect leads to Pe ~ Ra0.63, which agrees well with the transition curve between the regimes with and without collision.

Nonequilibrium structure formation in electrohydrodynamic emulsions

Application of an electric field across the interface of two fluids with low, but non-zero, conductivities gives rise to a sustained electrohydrodynamic (EHD) fluid flow. In the presence of neighboring drops, drops interact via the EHD flows of their neighbors, as well as through a dielectrophoretic (DEP) force, a consequence of drops encountering disturbance electric fields around their neighbors. We explore the collective dynamics of emulsions with drops undergoing EHD and DEP interactions. The interplay between EHD and DEP results in a rich set of emergent behaviors. We simulate the collective behavior of large numbers of drops; in two dimensions, where drops are confined to a plane; and three dimensions. In monodisperse emulsions, drops in two dimensions cluster or crystallize depending on the relative strengths of EHD and DEP, and form spaced clusters when EHD and DEP balance. In three dimensions, chain formation observed under DEP alone is suppressed by EHD, and lost entirely when EHD dominates. When a second population of drops are introduced, such that the electrical conductivity, permittivity, or viscosity are different from the first population of drops, the interaction between the drops becomes non-reciprocal, an apparent violation of Newton's Third Law. The breadth of consequences due to these non-reciprocal interactions are vast: we show selected cases in two dimensions, where drops cluster into active dimers, trimers, and larger clusters that continue to translate and rotate over long timescales; and three dimensions, where drops form stratified chains, or combine into a single dynamic sheet.

Simple model for self-propulsion of microdroplets in surfactant solution

We propose a simple active hydrodynamic model for the self-propulsion of a liquid droplet suspended in micellar solutions. The self-propulsion of the droplet occurs by spontaneous breaking of isotropic symmetry and is studied using both analytical and numerical methods. The emergence of self-propulsion arises from the slow dissolution of the inner fluid into the outer micellar solution as filled micelles. We propose that the surface generation of filled micelles is the dominant reason for the self-propulsion of the droplet. The flow instability is due to the Marangoni stress generated by the nonuniform distribution of the surfactant molecules on the droplet interface. In our model, the driving parameter of the instability is the excess surfactant concentration above the critical micellar concentration, which directly correlates with the experimental observations. We consider various low-order modes of flow instability and show that the first mode becomes unstable through a supercritical bifurcation and is the only mode contributing to the swimming of the droplet. The flow fields around the droplet for these modes and their combined effects are also discussed.

Hydrodynamic interactions between squirmers near walls: far-field dynamics and near-field cluster stability

Confinement increases contacts between microswimmers in dilute suspensions and affects their interactions. In particular, boundaries have been shown experimentally to lead to the formation of clusters that would not occur in bulk fluids. To what extent does hydrodynamics govern these boundary-driven encounters between microswimmers? We consider theoretically the symmetric boundary-mediated encounters of model microswimmers under gravity through far-field interaction of a pair of weak squirmers, as well as the lubrication interactions occurring after contact between two or more squirmers. In the far field, the orientation of microswimmers is controlled by the wall and the squirming parameter. The presence of a second swimmer influences the orientation of the original squirmer, but for weak squirmers, most of the interaction occurs after contact. We thus analyse next the near-field reorientation of circular groups of squirmers. We show that a large number of swimmers and the presence of gravity can stabilize clusters of pullers, while the opposite is true for pushers; to be stable, clusters of pushers thus need to be governed by other interactions (e.g. phoretic). This simplified approach to the phenomenon of active clustering enables us to highlight the hydrodynamic contribution, which can be hard to isolate in experimental realizations.

Gravitational settling of active droplets

The gravitational settling of oil droplets solubilizing in an aqueous micellar solution contained in a capillary channel is investigated. The motion of these active droplets reflects a competition between gravitational and Marangoni forces, the latter due to interfacial tension gradients generated by differences in filled-micelle concentrations along the oil-water interface. This competition is studied by varying the surfactant concentration, the density difference between the droplet and the continuous phase, and the viscosity of the continuous phase. The Marangoni force enhances the settling speed of an active droplet when compared to the Hadamard-Rybczynski prediction for a (surfactant free) droplet settling in Stokes flow. The Marangoni force can also induce lateral droplet motion, suggesting that the Marangoni and gravitational forces are not always aligned. The decorrelation rate (α) of the droplet motion, measured as the initial slope of the velocity autocorrelation and indicative of the extent to which the Marangoni and gravitational forces are aligned during settling, is examined as a function of the droplet size: correlated motion (small values of α) is observed at both small and large droplet radii, whereas significant decorrelation can occur between these limits. This behavior of active droplets settling in a capillary channel is in marked contrast to that observed in a dish, where the decorrelation rate increases with the droplet radius before saturating at large values of droplet radius. A simple relation for the crossover radius at which the maximal value of α occurs for an active settling droplet is proposed.

Self-Organization Emerging from Marangoni and Elastocapillary Effects Directed by Amphiphile Filament Connections

Self-organization of meso- and macroscale structures is a highly active research field that exploits a wide variety of physicochemical phenomena, including surface tension, Marangoni flow, and (elasto)capillary effects. The release of surface-active compounds generates Marangoni flows that cause repulsion, whereas capillary forces attract floating particles via the Cheerios effect. Typically, the interactions resulting from these effects are nonselective because the gradients involved are uniform. In this work, we unravel the mechanisms involved in the self-organization of amphiphile filaments that connect and attract droplets floating at the air-water interface, and we demonstrate their potential for directional gradient formation and thereby selective interaction. We simulate Marangoni flow patterns resulting from the release and depletion of amphiphile molecules by source and drain droplets, respectively, and we predict that these flow patterns direct the growth of filaments from the source droplets toward specific drain droplets, based on their amphiphile depletion rate. The interaction between such droplets is then investigated experimentally by charting the flow patterns in their surroundings, while the role of filaments in source-drain attraction is studied using microscopy. Based on these observations, we attribute attraction of drain droplets and even solid objects toward the source to elastocapillary effects. Finally, the insights from our simulations and experiments are combined to construct a droplet-based system in which the composition of drain droplets regulates their ability to attract filaments and as a consequence be attracted toward the source. Thereby, we provide a novel method through which directional attraction can be established in synthetic self-organizing systems and advance our understanding of how complexity arises from simple building blocks.

Chemically Tuning Attractive and Repulsive Interactions between Solubilizing Oil Droplets

Micellar solubilization is a transport process occurring in surfactant-stabilized emulsions that can lead to Marangoni flow and droplet motility. Active droplets exhibit self-propulsion and pairwise repulsion due to solubilization processes and/or solubilization products raising the droplet's interfacial tension. Here, we report emulsions with the opposite behavior, wherein solubilization decreases the interfacial tension and causes droplets to attract. We characterize the influence of oil chemical structure, nonionic surfactant structure, and surfactant concentration on the interfacial tensions and Marangoni flows of solubilizing oil-in-water drops. Three regimes corresponding to droplet "attraction", "repulsion" or "inactivity" are identified. We believe these studies contribute to a fundamental understanding of solubilization processes in emulsions and provide guidance as to how chemical parameters can influence the dynamics and chemotactic interactions between active droplets.

Chemotactic self-caging in active emulsions

The out-of-equilibrium dynamics of chemotactic active matter—be it animate or inanimate—is closely coupled to the environment, a chemical landscape shaped by secretions from the motile agents, fuel uptake, or autochemotactic signaling. This gives rise to complex collective effects, which can be exploited by the agents for colony migration strategies or pattern formation. We study such effects using an idealized experimental system: self-propelled microdroplets that communicate via chemorepulsive trails. We present a comprehensive experimental analysis that involves direct probing of the diffusing chemical trails and the trail–droplet interactions and use it to construct a generic theoretical model. We connect these repulsive autochemotactic interactions to the collective dynamics in emulsions, demonstrating a state of dynamical arrest: chemotactic self-caging.

A common feature of biological self-organization is how active agents communicate with each other or their environment via chemical signaling. Such communications, mediated by self-generated chemical gradients, have consequences for both individual motility strategies and collective migration patterns. Here, in a purely physicochemical system, we use self-propelling droplets as a model for chemically active particles that modify their environment by leaving chemical footprints, which act as chemorepulsive signals to other droplets. We analyze this communication mechanism quantitatively both on the scale of individual agent–trail collisions as well as on the collective scale where droplets actively remodel their environment while adapting their dynamics to that evolving chemical landscape. We show in experiment and simulation how these interactions cause a transient dynamical arrest in active emulsions where swimmers are caged between each other’s trails of secreted chemicals. Our findings provide insight into the collective dynamics of chemically active particles and yield principles for predicting how negative autochemotaxis shapes their navigation strategy.

Reversible morphology-resolved chemotactic actuation and motion of Janus emulsion droplets

We report, for the first time, a chemotactic motion of emulsion droplets that can be controllably and reversibly altered. Our approach is based on using biphasic Janus emulsion droplets, where each phase responds differently to chemically induced interfacial tension gradients. By permanently breaking the symmetry of the droplets’ geometry and composition, externally evoked gradients in surfactant concentration or effectiveness induce anisotropic Marangoni-type fluid flows adjacent to each of the two different exposed interfaces. Regulation of the competitive fluid convections then enables a controllable alteration of the speed and the direction of the droplets’ chemotactic motion. Our findings provide insight into how compositional anisotropy can affect the chemotactic behavior of purely liquid-based microswimmers. This has implications for the design of smart and adaptive soft microrobots that can autonomously regulate their response to changes in their chemical environment by chemotactically moving towards or away from a certain target, such as a bacterium.

Artificial microswimmers can emulate the autonomous regulation of chemotactic motility of living organisms. Frank et al. realize a chemotactic locomotion of emulsion droplets, composed of two phase-separated fluids, that can be reversibly directed up or down a chemical concentration gradient.

Spontaneously rotating clusters of active droplets

We report on the emergence of spontaneously rotating clusters in active emulsions. Ensembles of self-propelling droplets sediment and then self-organise into planar, hexagonally ordered clusters which hover over the container bottom while spinning around the plane normal. This effect exists for symmetric and asymmetric arrangements of isotropic droplets and is therefore not caused by torques due to geometric asymmetries. We found, however, that individual droplets exhibit a helical swimming mode in a small window of intermediate activity in a force-free bulk medium. We show that by forming an ordered cluster, the droplets cooperatively suppress their chaotic dynamics and turn the transient instability into a steady rotational state. We analyse the collective rotational dynamics as a function of droplet activity and cluster size and further propose that the stable collective rotation in the cluster is caused by a cooperative coupling between the rotational modes of individual droplets in the cluster.

Self-avoidant memory effects on enhanced diffusion in a stochastic model of environmentally responsive swimming droplets

Enhanced diffusion is an emergent property of many experimental microswimmer systems that usually arises from a combination of ballistic motion with random reorientations. A subset of these systems, autophoretic droplet swimmers that move as a result of Marangoni stresses, have additionally been shown to respond to local, self-produced chemical gradients that can mediate self-avoidance or self-attraction. Via this mechanism, we present a mathematical model constructed to encode experimentally observed self-avoidant memory and numerically study the effect of this particular memory on the enhanced diffusion of such swimming droplets. To disentangle the enhanced diffusion due to the random reorientations from the enhanced diffusion due to the self-avoidant memory, we compare to the widely used active Brownian model. Paradoxically, we find that the enhanced diffusion is substantially suppressed by the self-avoidant memory relative to that predicted by only an equivalent reorientation persistence timescale in the active Brownian model. We attribute this to transient self-caging that we propose is novel for self-avoidant systems. Additionally, we further explore the model parameter space by computing emergent parameters that capture the velocity and reorientation persistence, thus finding a finite parameter domain in which enhanced diffusion is observable.

Interactions in active colloids

The past two decades have seen a remarkable progress in the development of synthetic colloidal agents which are capable of creating directed motion in an unbiased environment at the microscale. These self-propelling particles are often praised for their enormous potential to self-organize into dynamic nonequilibrium structures such as living clusters, synchronized super-rotor structures or self-propelling molecules featuring a complexity which is rarely found outside of the living world. However, the precise mechanisms underlying the formation and dynamics of many of these structures are still barely understood, which is likely to hinge on the gaps in our understanding of how active colloids interact. In particular, besides showing comparatively short-ranged interactions which are well known from passive colloids (Van der Waals, electrostatic etc), active colloids show novel hydrodynamic interactions as well as phoretic and substrate-mediated 'osmotic' cross-interactions which hinge on the action of the phoretic field gradients which are induced by the colloids on other colloids in the system. The present article discusses the complexity and the intriguing properties of these interactions which in general are long-ranged, non-instantaneous, non-pairwise and non-reciprocal and which may serve as key ingredients for the design of future nonequilibrium colloidal materials. Besides providing a brief overview on the state of the art of our understanding of these interactions a key aim of this review is to emphasize open key questions and corresponding open challenges.

Two-dimensional numerical model of Marangoni surfers: From single swimmer to crystallization

We numerically study the dynamics of an ensemble of Marangoni surfers in a two-dimensional and unconfined space. The swimmers are modeled as Gaussian sources of surfactant generating surface tension gradients and are shown to follow the Marangoni flow filtered at their spatial scale in the lubrication regime, an unstable situation leading to spontaneous motion as soon as the Marangoni effect is intense enough. As the system is fully unconstrained, it is possible to study the various dynamical regimes from single swimmer, two-body interaction, to the many-particles case characterized by an efficient particle dispersion. We show that, although the present model is very simple, it reproduces the experimentally observed transition between a regime of dispersion by random agitation when the number of swimmers is moderate to the regime of crystallization with imperfect hexagonal lattice at high density.

Interfacially-adsorbed particles enhance the self-propulsion of oil droplets in aqueous surfactant

Understanding the chemo-mechanical mechanisms that direct the motion of self-propulsive colloids is important for the development of active materials and exploration of dynamic, collective phenomena. Here, we demonstrate that the adsorption of solid particles on the surface of solubilizing oil droplets can significantly enhance the droplets' self-propulsion speeds. We investigate the relationship between the self-propulsion of bromodecane oil droplets containing silica particles of varying concentration in Triton X-100 surfactant, noting up to order of magnitude increases in propulsion speeds. Using fluorescently labeled silica, we observe packing of the particles at the oil-water interfaces of the rear pole of the moving droplets. For bromodecane oil droplets in Triton X-100, the highest droplet speeds were achieved at approximately 40% particle surface coverage of the droplet interface. We find particle-assisted propulsion enhancement in ionic surfactants and different oil droplet compositions as well, demonstrating the breadth of this effect. While a precise mechanism for the propulsion enhancement remains unclear, the simple addition of silica particles to droplet oil-water interfaces provides a straightforward route to tune active droplet dynamics.

Alignment and scattering of colliding active droplets

Active droplets emit a chemical solute at their surface that modifies their local interfacial tension. They exploit the nonlinear coupling of the convective transport of solute to the resulting Marangoni flows in order to self-propel. Such swimming droplets are by nature anti-chemotactic and are repelled by their own chemical wake or their neighbours. The rebound dynamics resulting from pairwise droplet interactions was recently analysed in detail for purely head-on collisions using a specific bispherical approach. Here, we extend this analysis and propose a reduced model of a generic collision to characterise the alignment and scattering properties of oblique droplet collisions and their potential impact on collective droplet dynamics. A systematic alignment of the droplets' trajectories is observed for symmetric collisions, when the droplets interact directly, and arises from the finite-time rearrangement of the droplets' chemical wake during the collision. For more generic collisions, complex and diverse dynamical regimes are observed, whether the droplets interact directly or through their chemical wake, resulting in a significant scattering.

Lamellar to Micellar Phases and Beyond: When Tactic Active Systems Admit Free Energy Functionals

We consider microscopic models of active particles whose velocities, rotational diffusivities, and tumbling rates depend on the gradient of a local field that is either externally imposed or depends on all particle positions. Despite the fundamental differences between active and passive dynamics at the microscopic scale, we show that a large class of such tactic active systems admit fluctuating hydrodynamics equivalent to those of interacting Brownian colloids in equilibrium. We exploit this mapping to show how taxis may lead to the lamellar and micellar phases observed for soft repulsive colloids. In the context of chemotaxis, we show how the competition between chemoattractant and chemorepellent may lead to a bona fide equilibrium liquid-gas phase separation in which a loss of thermodynamic stability of the fluid signals the onset of a chemotactic collapse.

Autonomous mesoscale positioning emerging from myelin filament self-organization and Marangoni flows

Out-of-equilibrium molecular systems hold great promise as dynamic, reconfigurable matter that executes complex tasks autonomously. However, translating molecular scale dynamics into spatiotemporally controlled phenomena emerging at mesoscopic scale remains a challenge-especially if one aims at a design where the system itself maintains gradients that are required to establish spatial differentiation. Here, we demonstrate how surface tension gradients, facilitated by a linear amphiphile molecule, generate Marangoni flows that coordinate the positioning of amphiphile source and drain droplets floating at air-water interfaces. Importantly, at the same time, this amphiphile leads, via buckling instabilities in lamellar systems of said amphiphile, to the assembly of millimeter long filaments that grow from the source droplets and get absorbed at the drain droplets. Thereby, the Marangoni flows and filament organization together sustain the autonomous positioning of interconnected droplet-filament networks at the mesoscale. Our concepts provide potential for the development of non-equilibrium matter with spatiotemporal programmability.

Out-of-Equilibrium Colloidal Assembly Driven by Chemical Reaction Networks

Transient assembled structures play an indispensable role in a wide variety of processes fundamental to living organisms including cellular transport, cell motility, and proliferation. Typically, the formation of these transient structures is driven by the consumption of molecular fuels via dissipative reaction networks. In these networks, building blocks are converted from inactive precursor states to active (assembling) states by (a set of) irreversible chemical reactions. Since the activated state is intrinsically unstable and can be maintained only in the presence of sufficient fuel, fuel depletion results in the spontaneous disintegration of the formed superstructures. Consequently, the properties and behavior of these assembled structures are governed by the kinetics of fuel consumption rather than by their thermodynamic stability. This fuel dependency endows biological systems with unprecedented spatiotemporal adaptability and inherent self-healing capabilities. Fascinated by these unique material characteristics, coupling the assembly behavior to molecular fuel or light-driven reaction networks was recently implemented in synthetic (supra)molecular systems. In this invited feature article, we discuss recent studies demonstrating that dissipative assembly is not limited to the molecular world but can also be translated to building blocks of colloidal dimensions. We highlight crucial guiding principles for the successful design of dissipative colloidal systems and illustrate these with the current state of the art. Finally, we present our vision on the future of the field and how marrying nonequilibrium self-assembly with the functional properties associated with colloidal building blocks presents a promising route for the development of next-generation materials.

Adsorption inhibition by swollen micelles may cause multistability in active droplets

Experiments indicate that microdroplets undergoing micellar solubilization in the bulk of surfactant solution may excite Marangoni flows and self-propel spontaneously. Surprisingly, self-propulsion emerges even when the critical micelle concentration is exceeded and the Marangoni effect should be saturated. To explain this, we propose a novel model of a dissolving active droplet that is based on two fundamental assumptions: (a) products of the solubilization may inhibit surfactant adsorption; (b) solubilization prevents the formation of a monolayer of surfactant molecules at the droplet interface. We use numerical simulations and asymptotic methods to demonstrate that our model indeed features spontaneous droplet self-propulsion. Our key finding is that in the case of axisymmetric flow and concentration fields, two qualitatively different types of droplet behavior may be stable for the same values of the physical parameters: steady self-propulsion and steady symmetric pumping. Although stability of these steady regimes is not guaranteed in the absence of axial symmetry, we argue that they will retain their respective stable manifolds in the phase space of a fully 3D problem.

Life-Like Motion of Oil Drops at the Air-Liquid Interface

Generally, interactions of oil drops at the air-liquid interface mainly have two features, namely, attraction and repulsion. However, in our study, we find that the oil drops at the air-liquid interface have other interacting features, that is, the atomic-like motion and the "capture" motion. For the atomic-like motion, oil drops attract each other at a long distance, but repel when they are about to come into contact with each other. For the "capture" motion, a big oil drop can actively "capture" oil droplets like a zooplankton. In our research, we analyze interfacial forces among the oil drops. Based on the experiments and analyses, we demonstrate that the atomic-like motion of oil drops is mainly due to the lateral capillary force and the surface tension force, and the "capture" motion is mainly due to the unbalanced impact force of flow fluid around the drops. In addition, based on our results, we use the oil drops to perform many functions at the air-liquid interface. For example, the oil drops can drive an object with linear and rotational motion. When a carbon tetrachloride drop is suspended above the air-liquid interface, it can be used to control an oil droplet to pass through serpentine grooves and obstacles. In addition, the suspended carbon tetrachloride drops also can be used to rank multiple droplets with a special shape. Based on the results, our study makes it possible to use oil drops to transport materials, drive objects, and even collect droplets at the air-liquid interface.

Design strategies for engineering soluto-inertial suspension interactions

Soluto-inertial (SI) suspension interactions allow colloidal particles to be driven large distances over sustained periods of time. These interactions involve soluto-inertial "beacons" that establish and maintain solute fluxes over long times by slowly absorbing or emitting solutes in response to changes in the surrounding solution. Suspended particles then migrate in response to solute fluxes via diffusiophoresis (DP). Beacon materials must be chosen to maintain these solute fluxes, with range and duration in mind. Here we present a general strategy to facilitate qualitative design and quantitative prediction of SI interactions for a given beacon-solute pair. Specifically, we look at two classes of SI beacons: those that partition solute and those that associate with solute. We identify the design parameters for these systems to construct a parameter space map, calculate characteristic timescales over which SI fluxes persist, and generate approximate analytical expressions for solute concentration profiles. Further, we use these expressions to predict the DP velocity of colloids interacting with beacons, noting qualitative differences between beacon sources that release solute and beacon sinks that absorb solute. Proof-of-principle experiments of beacon sources and sinks, of partitioning, and associating types highlight the basic findings. More broadly, the conceptual approach outlined here can be adapted to treat SI interactions mediated by other materials such as dissolving solids, gases, evaporating liquids, ion-exchange resins, and others.

Orientational instability and spontaneous rotation of active nematic droplets

In experiments, an individual chemically-active liquid crystal (LC) droplet submerged in the bulk of a surfactant solution may self-propel along a straight, helical, or random trajectory. In this paper, we develop a minimal model capturing all three types of self-propulsion trajectories of a drop in the case of a nematic LC with homeotropic anchoring at the LC-fluid interface. We emulate the director field within the drop by a single preferred polarization vector that is subject of two reorientation mechanisms, namely, the internal flow-induced displacement of the hedgehog defect and the droplet's rotation. Within this reduced-order model, the coupling between the nematic ordering of the drop and the surfactant transport is represented by variations of the droplet's interfacial properties with nematic polarization. Our analysis reveals that a novel mode of orientational instability emerges from the competition of the two reorientation mechanisms and is characterized by a spontaneous rotation of the self-propelling drop responsible for helical self-propulsion trajectories. In turn, we also show that random trajectories in isotropic and nematic drops alike stem from the advection-driven transition to chaos. The succession of the different propulsion modes is consistent with experimentally-reported transitions in the shape of droplet trajectories as the drop size is varied.

Individual and Collective Behavior of Emulsion Droplets Undergoing Ostwald Ripening

Ostwald ripening (OR) is the dominating phase separation mechanism in nanoemulsions consisting of the mass exchange between separated droplets by dissolution and absorption of molecules. Here, we propose a model based on a stochastic equation for the mass exchange coupled to a Brownian dynamics algorithm. Our model accounts for the simultaneous gain and loss of mass within a medium, where the presence of sources and sinks leads to a complex distribution of dissolved oil molecules. Also, a criterion for possible nucleation zones based on the definition of a saturation area around the droplets is found. The predictions of the collective behavior are constructed on the individual contributions of each droplet with its own environment. Individual droplets undergoing molecular exchange exhibited anomalous diffusion, whereas when performing the collective analysis, such a behavior was disguised. We used reported experiments under diverse conditions to validate and test the scope of our model, including the modification to the interfacial tension via Gibbs elasticity, finding close agreements. Our results imply that saturation is not conditional for the occurrence of OR. The ability of this model to extend the limitations imposed by traditional treatments to a broader number of physicochemical conditions makes it a useful complementary tool for predicting and understanding experimental results of emulsions experiencing OR.

Osmosis, from molecular insights to large-scale applications

Osmosis is a universal phenomenon occurring in a broad variety of processes and fields. It is the archetype of entropic forces, both trivial in its fundamental expression - the van 't Hoff perfect gas law - and highly subtle in its physical roots. While osmosis is intimately linked with transport across membranes, it also manifests itself as an interfacial transport phenomenon: the so-called diffusio-osmosis and -phoresis, whose consequences are presently actively explored for example for the manipulation of colloidal suspensions or the development of active colloidal swimmers. Here we give a global and unifying view of the phenomenon of osmosis and its consequences with a multi-disciplinary perspective. Pushing the fundamental understanding of osmosis allows one to propose new perspectives for different fields and we highlight a number of examples along these lines, for example introducing the concepts of osmotic diodes, active separation and far from equilibrium osmosis, raising in turn fundamental questions in the thermodynamics of separation. The applications of osmosis are also obviously considerable and span very diverse fields. Here we discuss a selection of phenomena and applications where osmosis shows great promises: osmotic phenomena in membrane science (with recent developments in separation, desalination, reverse osmosis for water purification thanks in particular to the emergence of new nanomaterials); applications in biology and health (in particular discussing the kidney filtration process); osmosis and energy harvesting (in particular, osmotic power and blue energy as well as capacitive mixing); applications in detergency and cleaning, as well as for oil recovery in porous media.

Biological active matter aggregates: Inspiration for smart colloidal materials

Aggregations of social organisms exhibit a remarkable range of properties and functionalities. Multiple examples, such as fire ants or slime mold, show how a population of individuals is able to overcome an existential threat by gathering into a solid-like aggregate with emergent functionality. Surprisingly, these aggregates are driven by simple rules, and their mechanisms show great parallelism among species. At the same time, great effort has been made by the scientific community to develop active colloidal materials, such as microbubbles or Janus particles, which exhibit similar behaviors. However, a direct connection between these two realms is still not evident, and it would greatly benefit future studies. In this review, we first discuss the current understanding of living aggregates, point out the mechanisms in their formation and explore the vast range of emergent properties. Second, we review the current knowledge in aggregated colloidal systems, the methods used to achieve the aggregations and their potential functionalities. Based on this knowledge, we finally identify a set of over-arching principles commonly found in biological aggregations, and further suggest potential future directions for the creation of bio-inspired colloid aggregations.

Memory-Induced Transition from a Persistent Random Walk to Circular Motion for Achiral Microswimmers

We experimentally study the motion of light-activated colloidal microswimmers in a viscoelastic fluid. We find that, in such a non-Newtonian environment, the active colloids undergo an unexpected transition from enhanced angular diffusion to persistent rotational motion above a critical propulsion speed, despite their spherical shape and stiffness. We observe that, in contrast to chiral asymmetric microswimmers, the resulting circular orbits can spontaneously reverse their sense of rotation and exhibit an angular velocity and a radius of curvature that nonlinearly depend on the propulsion speed. By means of a minimal non-Markovian Langevin model for active Brownian motion, we show that these nonequilibrium effects emerge from the delayed response of the fluid with respect to the self-propulsion of the particle without counterpart in Newtonian fluids.

Compositional ripening of particle-stabilized drops in a three-liquid system

We present experimental studies of two aqueous drops, stabilized by colloidal silica, which are placed close to each other in a bath of toluene, ethanol and surplus colloidal silica. If one of the drops is enriched in ethanol while the other is pure water then we observe the spontaneous formation of small droplets at the surface of the water drop closest to its neighbour. These droplets are then observed to form all along the path to the ethanol enriched drop until they make a complete bridge. We relate this behaviour to the diffusion pathways on the underlying three-fluid phase diagram. We argue that the phenomena is a version of compositional ripening where the transfer of the dispersed phase leads to the spontaneous formation of droplets in the continuous phase. We show that, while the large drops are particle-stabilized, the spontaneously formed droplets are not. Instead the presence of surplus particles leads to the droplets gelling as an elastic bridge. The phenomenology at long times and at low particle concentrations becomes increasingly surprising.

Van't Hoff's law for active suspensions: the role of the solvent chemical potential

We extend Van't Hoff's law for the osmotic pressure to a suspension of active Brownian particles. The propelled particles exert a net reaction force on the solvent, and thereby either drive a measurable solvent flow from the connecting solvent reservoir through the semipermeable membrane, or increase the osmotic pressure and cause the suspension to rise to heights as large as micrometers for experimentally realized microswimmers described in the literature. The increase in osmotic pressure is caused by the background solvent being, in contrast to passive suspensions, no longer at the chemical potential of the solvent reservoir. The difference in solvent chemical potentials depends on the colloid-membrane interaction potential, which implies that the osmotic pressure is a state function of a state that itself is influenced by the membrane potential.