Spontaneous motion and deformation of a self-propelled droplet

Shear-induced dynamics of an active Belousov-Zhabotinsky droplet

Controlled navigation of self-propelled active matter in complex biological environments has remained a significant challenge in engineering owing to a multitude of interactions that persist in the process. Active droplets, being some of the several synthetic active matters, have garnered significant attention owing to their ability to exhibit dynamic shape changes, self-sustained motion, interact with external stimuli such as flows, and mimic biological active matter. Here, we explore the dynamics of a self-propelled active droplet powered by the oscillatory Belousov-Zhabotinsky (BZ) reaction in the presence of a shear flow. We adapt a multicomponent lattice Boltzmann method (LBM) in conjunction with the phase-field model to simulate the droplet's interaction with the surrounding fluid. We unravel the collective effect of droplet deformation, reaction kinetics, and strength of the surrounding shear flow on droplet dynamics. Our findings depict that the shear flow disrupts the initial isotropic surface tension, and produces concentration nucleation spots in the droplet. The asymmetry thus generated produces Marangoni flow that ultimately propels the droplet. Our findings provide valuable insights into the mechanisms governing active droplet behavior and open new avenues for designing controllable synthetic active matter systems with potential applications in microfluidics, targeted delivery, and biomimetic technologies. In addition, our framework can potentially be integrated with the physics-informed machine learning framework to develop more efficient mesh-free methods.

Dynamics of Aggregation in Systems of Self-Propelled Rods

We highlight camphene-camphor-polypropylene plastic as a useful material for self-propelled objects that show aggregation while floating on a water surface. We consider self-propelled rods as an example of aggregation of objects characterized by non-trivial individual shapes with low-symmetry interactions between them. The motion of rods made of the camphene-camphor-polypropylene plastic is supported by dissipation of the surface-active molecules. The physical processes leading to aggregation and the mathematical model of the process are discussed. We analyze experimental data of aggregate formation dynamics and relate them to the system's properties. We speculate that the aggregate structure can be represented as a string of symbols, which opens the potential applicability of the phenomenon for information processing if objects floating on a water surface are regarded as reservoir computers.

Marangoni Droplets of Dextran in PEG Solution and Its Motile Change Due to Coil-Globule Transition of Coexisting DNA

Motile droplets using Marangoni convection are attracting attention for their potential as cell-mimicking small robots. However, the motion of droplets relative to the internal and external environments that generate Marangoni convection has not been quantitatively described. In this study, we used an aqueous two-phase system [poly(ethylene glycol) (PEG) and dextran] in an elongated chamber to generate motile dextran droplets in a constant PEG concentration gradient. We demonstrated that dextran droplets move by Marangoni convection, resulting from the PEG concentration gradient and the active transport of PEG and dextran into and out of the motile dextran droplet. Furthermore, by spontaneously incorporating long DNA into the dextran droplets, we achieved cell-like motility changes controlled by coexisting environment-sensing molecules. The DNA changes its position within the droplet and motile speed in response to external conditions. In the presence of Mg2+, the coil-globule transition of DNA inside the droplet accelerates the motile speed due to the decrease in the droplet's dynamic viscosity. Globule DNA condenses at the rear part of the droplet along the convection, while coil DNA moves away from the droplet's central axis, separating the dipole convections. These results provide a blueprint for designing autonomous small robots using phase-separated droplets, which change the mobility and molecular distribution within the droplet in reaction with the environment. It will also open unexplored areas of self-assembly mechanisms through phase separation under convections, such as intracellular phase separation.

Self-emergent vortex flow of microtubule and kinesin in cell-sized droplets under water/water phase separation

By facilitating a water/water phase separation (w/wPS), crowded biopolymers in cells form droplets that contribute to the spatial localization of biological components and their biochemical reactions. However, their influence on mechanical processes driven by protein motors has not been well studied. Here, we show that the w/wPS droplet spontaneously entraps kinesins as well as microtubules (MTs) and generates a micrometre-scale vortex flow inside the droplet. Active droplets with a size of 10-100 µm are generated through w/wPS of dextran and polyethylene glycol mixed with MTs, molecular-engineered chimeric four-headed kinesins and ATP after mechanical mixing. MTs and kinesin rapidly created contractile network accumulated at the interface of the droplet and gradually generated vortical flow, which can drive translational motion of a droplet. Our work reveals that the interface of w/wPS contributes not only to chemical processes but also produces mechanical motion by assembling species of protein motors in a functioning manner.

Hydrodynamics of a confined active Belousov-Zhabotinsky droplet

Self-sustained locomotion of synthetic droplet swimmers has been of great interest due to their ability to mimic the behavior of biological swimmers. Here we harness the Belousov-Zhabotinsky (BZ) reaction to induce Marangoni stresses on the fluid-droplet interface and elucidate the spontaneous locomotion of active BZ droplets in a confined two-dimensional channel. Our approach employs the lattice Boltzmann method to simulate a coupled system of multiphase hydrodynamics and BZ-reaction kinetics. Our investigation reveals the mechanism underlying the propulsion of active BZ droplets, in terms of convective and diffusive fluxes and deformation of the droplets. Furthermore, we demonstrate that by manipulating the degree of confinement, strength, and nature of coupling between surface tension and active species' concentration, the motion of the BZ droplet can be directed. In addition, we are able to capture two different kinds of droplet behaviors, namely, sustained and stationary, and establish conditions for the sustained long-time motion. We envisage that our findings can be used not only to understand the mechanics of biological swimmers but also to design reaction-driven self-propelled systems for a variety of biomimetic applications.

pH-Sensitive Controlled Motion of Micrometer-sized Oil Droplets in a Solution of Surfactants Containing Fumaric Acid Derivatives

Self-propelled droplets are of considerable interest as an appropriate model for understanding the self-propulsion of objects in the fields of nonequilibrium physics and nonlinear science. Several research groups have reported the monodirectional motion of droplets, that is, chemotaxis, using stimuli-responsive materials. However, the precise control of chemotaxis remains challenging from the perspective of synthetic chemistry because chemotactic motion is primarily induced by the consumption of reactive oil or surfactants. Herein, we report a chemical system containing pH-responsive fumaric acid derivatives, in which the oil droplet exhibited positive chemotaxis over a wide pH range-from basic to acidic conditions. From the measurements of the interfacial tension between the oil and aqueous phases, it was deduced that the positive chemotaxis was due to heterogeneity in the interfacial tension of the droplet surface, which was accompanied by the production of surface-active compounds in the pH gradient in a linear-type channel.

Complexity and bifurcations in the motion of a self-propelled rectangle confined in a circular water chamber

We consider the motion of a self-propelled object of rectangular shape inside a circular water chamber. The mathematical model of self-motion includes equations for the orientation and location of the rectangle and reaction-diffusion equation with an effective diffusion coefficient for the time evolution of the surface concentration of active molecules. Numerical simulations of motion were performed for different values of the ratio between the supply rate S and the evaporation rate a of active molecules. Treating S₀ = S/a as a control parameter, we found the critical behavior in variables characterizing the trajectory and identified different types of motion. If the value of S₀ is small, the rectangle rests at the chamber center. For larger S₀, a reciprocal motion during which the rectangle passes through the center is observed. At yet higher supply rates, the star-polygonal motion appears, and the trajectory remains at a distance from the chamber center. In the experiments with a rectangle made of camphor-camphene-polypropylene plastic moving in a Petri dish, we observed the transition from the star-polygonal motion to the reciprocal motion in time. This transition can be understood on the basis of the developed model if we assume that the supply rate decreases in time.

Statistics for an object actively driven by spontaneous symmetry breaking into reversible directions

Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained until a large enough impulse by an additional stochastic force reverses it. Examples may be provided by self-propelled droplets, gliding bacteria stochastically reversing their propulsion direction, or nonpolar vibrated hoppers. The magnitude of active forcing is regarded as constant, and we include the effect of inertial contributions. Interestingly, this situation can formally be mapped to stochastic motion under (dry, solid) Coulomb friction, however, with a negative friction parameter. Diffusion coefficients are calculated by formal mapping to the situation of a quantum-mechanical harmonic oscillator exposed to an additional repulsive delta-potential. Results comprise a ditched or double-peaked velocity distribution and spatial statistics showing outward propagating maxima when starting from initially concentrated arrangements.

A camphene-camphor-polymer composite material for the production of superhydrophobic absorbent microporous foams

In a recently published paper (doi.org/10.3390/molecules26113116) on self-propelled motion of objects on the water surface, we described a novel surface-active plastic material obtained by dissolution of camphor and polypropylene in camphene at 250 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ$$\end{document}∘C. The material has wax-like mechanical properties, can be easily formed to any moldable shape, and allows for longer and more stable self-propelled motion if compared with pure camphor or pure camphene or of a camphene-camphor wax. Here we use scanning electron microscopy to visualize and characterize the microporous structure of the solid polypropylene foam formed in the plastic for different polypropylene contents. The topology of foams remaining in the material after camphor and camphene molecules have been removed through evaporation or dissolution is similar to polypropylene foams obtained using thermally-induced phase separation. We show that the foams have a superhydrophobic surface but strongly absorb non-polar liquids, and suggest an array of potential scientific and industrial applications.

A Perfect Plastic Material for Studies on Self-Propelled Motion on the Water Surface

We describe a novel plastic material composed of camphene, camphor, and polypropylene that seems perfectly suited for studies on self-propelled objects on the water surface. Self-motion is one of the attributes of life, and chemically propelled objects show numerous similarities with animated motion. One of important questions is the relationship between the object shape and its motility. In our paper published in 2019, we presented a novel hybrid material, obtained from the solution of camphor in camphene, that allowed making objects of various shapes. This hybrid material has wax-like mechanical properties, but it has a very high tackiness. Here, we report that a small amount of polypropylene removed this undesirable feature. We investigated the properties of camphor–camphene–polypropylene plastic by performing the statistical analysis of a pill trajectory inside a Petri dish and compared them with those of camphor-camphene wax. The plastic showed the stable character of motion for over an hour-long experiment. The surface activity of objects made of plastic did not significantly depend on the weight ratios of the compounds. Such a significant increase in usefulness came from the polypropylene, which controlled the dissipation of camphor and camphene molecules.

Marangoni Instability of a Drop in a Stably Stratified Liquid

Marangoni instabilities can emerge when a liquid interface is subjected to a concentration or temperature gradient. It is generally believed that for these instabilities bulk effects like buoyancy are negligible compared to interfacial forces, especially on small scales. Consequently, the effect of a stable stratification on the Marangoni instability has hitherto been ignored. Here, however, we show that they can matter. We report, for an immiscible drop immersed in a stably stratified ethanol-water mixture, a new type of oscillatory solutal Marangoni instability that is triggered once the stratification has reached a critical value. We experimentally explore the parameter space spanned by the stratification strength and the drop size and theoretically explain the observed crossover from levitating to bouncing by balancing the advection and diffusion around the drop. Finally, the effect of the stable stratification on the Marangoni instability is surprisingly strongly amplified in confined geometries, leading to an earlier onset.

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

We present a theory for the self-propulsion of symmetric, half-spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air-water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion-advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary conditions. We derive novel results for concentration profiles under constant flux boundary conditions and for the Nusselt number (the dimensionless ratio of total emitted flux and diffusive flux). Based on these results, we analyze the Marangoni boat for small Marangoni propulsion (low Peclet number) and show that two swimming regimes exist, a diffusive regime at low velocities and an advection-dominated regime at high swimmer velocities. We describe both the limit of large Marangoni propulsion (high Peclet number) and the effects from evaporation by approximative analytical theories. The swimming velocity is determined by force balance, and we obtain a general expression for the Marangoni forces, which comprises both direct Marangoni forces from the surface tension gradient along the air-water-swimmer contact line and Marangoni flow forces. We unravel whether the Marangoni flow contribution is exerting a forward or backward force during propulsion. Our main result is the relation between Peclet number and swimming velocity. Spontaneous symmetry breaking and, thus, swimming occur for a perfectly symmetrical swimmer above a critical Peclet number, which becomes small for large system sizes. We find a supercritical swimming bifurcation for a symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.

A hybrid camphor-camphene wax material for studies on self-propelled motion

A new material that combines the self-propelling properties of camphor with the malleability of camphene is reported. It has wax-like mechanical properties at room temperature and can be formed into required shapes. The speed of the self-propelled objects and the trajectory depend on the shape and camphor-camphene weight ratio.

Start of Micrometer-Sized Oil Droplet Motion through Generation of Surfactants

Self-propelled motion of micrometer-sized oil droplets in surfactant solution has drawn much attention as an example of nonlinear life-like dynamics under far-from-equilibrium conditions. The driving force of this motion is thought to be induced by Marangoni convection based on heterogeneity in the interfacial tension at the droplet surface. Here, to clarify the required conditions for the self-propelled motion of oil droplets, we have constructed a chemical system, where oil droplet motion is induced by the production of 1,2,3-triazole-containing surfactants through the Cu-catalyzed azide-alkyne cycloaddition reaction. From the results of the visualization and analysis of flow fields around the droplet, the motion of the droplets could be attributed to the formation of flow fields, which achieved sufficient strength caused by the in situ production of surfactants at the droplet surface.

A brief history of liquid computers

A substrate does not have to be solid to compute. It is possible to make a computer purely from a liquid. I demonstrate this using a variety of experimental prototypes where a liquid carries signals, actuates mechanical computing devices and hosts chemical reactions. We show hydraulic mathematical machines that compute functions based on mass transfer analogies. I discuss several prototypes of computing devices that employ fluid flows and jets. They are fluid mappers, where the fluid flow explores a geometrically constrained space to find an optimal way around, e.g. the shortest path in a maze, and fluid logic devices where fluid jet streams interact at the junctions of inlets and results of the computation are represented by fluid jets at selected outlets. Fluid mappers and fluidic logic devices compute continuously valued functions albeit discretized. There is also an opportunity to do discrete operation directly by representing information by droplets and liquid marbles (droplets coated by hydrophobic powder). There, computation is implemented at the sites, in time and space, where droplets collide one with another. The liquid computers mentioned above use liquid as signal carrier or actuator: the exact nature of the liquid is not that important. What is inside the liquid becomes crucial when reaction-diffusion liquid-phase computing devices come into play: there, the liquid hosts families of chemical species that interact with each other in a massive-parallel fashion. I shall illustrate a range of computational tasks, including computational geometry, implementable by excitation wave fronts in nonlinear active chemical medium. The overview will enable scientists and engineers to understand how vast is the variety of liquid computers and will inspire them to design their own experimental laboratory prototypes. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Self-propulsion of an active polar drop

We investigate the self-propulsive motion of a drop containing an active polar field. The drop demonstrates spontaneous symmetry breaking from a uniform orientational order into a splay or bend instability depending on the types of active stress, namely, contractile or extensile, respectively. We develop an analytical theory of the mechanism of this instability, which has been observed only in numerical simulations. We show that both contractile and extensile active stresses result in the instability and self-propulsive motion. We also discuss asymmetry between contractile and extensile stresses and show that extensile active stress generates chaotic motion even under a simple model of the polarity field coupled with motion and deformation of the drop.

From hydrodynamic lubrication to many-body interactions in dense suspensions of active swimmers

We study how hydrodynamic interactions affect the collective behaviour of active particles suspended in a fluid at high concentrations, with particular attention to lubrication forces which appear when the particles are very close to one another. We compute exactly the limiting behaviour of the hydrodynamic interactions between two spherical (circular) active swimmers in very close proximity to one another in the general setting in both three and (two) dimensions. Combining this with far-field interactions, we develop a novel numerical scheme which allows us to study the collective behaviour of large numbers of active particles with accurate hydrodynamic interactions when close to one another. We study active swimmers whose intrinsic flow fields are characterised by force dipoles and quadrupoles. Using this scheme, we are able to show that lubrication forces when the particles are very close to each other can play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that when the swimmer force dipole is large, finite clusters and open gel-like clusters appear rather than complete phase separation. This suppression is due to near-field lubrication interactions. For swimmers with small force dipoles, we find surprisingly that a globally polar-ordered phase appears because near-field lubrication rather than long-range hydrodynamics dominates the alignment mechanism. Polar order is present for very large system sizes and is stable to fluctuations with a finite noise amplitude. We explain the emergence of polar order using a minimal model in which only the leading rotational effect of the near-field interaction is included. These phenomena are also reproduced in two dimensions.

Experimental Investigation of the Self-Propelled Motion of a Sodium Oleate Tablet and Boat at an Oil-Water Interface

The self-propelled behaviors of macroscopic inanimate objects at surfaces and interfaces are ubiquitous phenomena of fundamental interest in interface science. However, given the existence of a large variety of systems with their own inherent chemical properties, the kinematics of the self-propelled motion and the dynamics of the forces driving these systems often remain largely unknown. Here, we experimentally investigate the spontaneous motion of a sodium oleate tablet at a water-nitrobenzene interface, under nonequilibrium and global isothermal conditions, through measurements of the interfacial tension with the noninvasive, quasi-elastic laser scattering method. The sodium oleate tablet was self-propelled due to an imbalance in the interfacial tension induced by the inhomogeneous adsorption of oleate/oleic acid molecules. The kinetics of the self-propelled motion of a boat-shaped plastic sheet bearing sodium oleate tablets at a sodium oleate aqueous solution-nitrobenzene interface was also studied. The interfacial tension difference between the front and rear of the boat was quantitatively identified as the force pushing the boat forward, although the Marangoni flow due to the uneven distribution of the interfacial tension behind the boat tended to decelerate the motion.

Lattice Boltzmann study of chemically-driven self-propelled droplets

We numerically study the behavior of self-propelled liquid droplets whose motion is triggered by a Marangoni-like flow. This latter is generated by variations of surfactant concentration which affect the droplet surface tension promoting its motion. In the present paper a model for droplets with a third amphiphilic component is adopted. The dynamics is described by Navier-Stokes and convection-diffusion equations, solved by the lattice Boltzmann method coupled with finite-difference schemes. We focus on two cases. First, the study of self-propulsion of an isolated droplet is carried on and, then, the interaction of two self-propelled droplets is investigated. In both cases, when the surfactant migrates towards the interface, a quadrupolar vortex of the velocity field forms inside the droplet and causes the motion. A weaker dipolar field emerges instead when the surfactant is mainly diluted in the bulk. The dynamics of two interacting droplets is more complex and strongly depends on their reciprocal distance. If, in a head-on collision, droplets are close enough, the velocity field initially attracts them until a motionless steady state is achieved. If the droplets are vertically shifted, the hydrodynamic field leads to an initial reciprocal attraction followed by a scattering along opposite directions. This hydrodynamic interaction acts on a separation of some droplet radii otherwise it becomes negligible and droplets motion is only driven by the Marangoni effect. Finally, if one of the droplets is passive, this latter is generally advected by the fluid flow generated by the active one.

Flow of Deformable Droplets: Discontinuous Shear Thinning and Velocity Oscillations

We study the rheology of a suspension of soft deformable droplets subjected to a pressure-driven flow. Through computer simulations, we measure the apparent viscosity as a function of droplet concentration and pressure gradient, and provide evidence of a discontinuous shear thinning behavior, which occurs at a concentration-dependent value of the forcing. We further show that this response is associated with a nonequilibrium transition between a "hard" (or less deformable) phase, which is nearly jammed and flows very slowly, and a "soft" (or more deformable) phase, which flows much more easily. The soft phase is characterized by flow-induced time dependent shape deformations and internal currents, which are virtually absent in the hard phase. Close to the transition, we find sustained oscillations in both the droplet and fluid velocities. Polydisperse systems show similar phenomenology but with a smoother transition, and less regular oscillations.

Marangoni Effect-Driven Motion of Miniature Robots and Generation of Electricity on Water

The well-known Marangoni effect perfectly supports the dynamic mechanism of organic solvent-swollen gels on water. On this basis, we report a series of energy conversion processes of concentrated droplets of polyvinylidene fluoride/dimethyl formamide (PVDF/DMF) that can transfer chemical-free energy to kinetic energy to rapidly rotate itself on water. This droplet (22.2 mg) is capable to offer kinetic energy of 0.099 μJ to propel an artificial paper rocket of 31.8 mg to move over 560 cm on water at an initial velocity of 7.9 cm s^-1. As the droplet increases to 35.0 mg, a paper goldfish of 10.6 mg can be driven to swim longer at a higher initial velocity of 20 cm s^-1. The kinetic energy of the droplet can be further converted to electrical energy through an electromagnetic generator, in which as a 0.5 MΩ resistor is loaded, the peak output reaches 6.5 mV that corresponds to the power density of 0.293 μW kg^-1. We believe that this report would open up a promising avenue to exploit energies for applications in miniature robotics.

Anchoring-driven spontaneous rotations in active gel droplets

We study the dynamics of an active gel droplet with imposed orientational anchoring (normal or planar) at its surface. We find that if the activity is large enough droplets subject to strong anchoring spontaneously start to rotate, with the sense of rotation randomly selected by fluctuations. Contractile droplets rotate only for planar anchoring and extensile ones only for normal anchoring. This is because such a combination leads to a pair of stable elastic deformations which creates an active torque to power the rotation. Interestingly, under these conditions there is a conflict between the anchoring promoted thermodynamically and that favoured by activity. By tuning activity and anchoring strength, we find a wealth of qualitatively different droplet morphologies and spatiotemporal patterns, encompassing steady rotations, oscillations, and more irregular trajectories. The spontaneous rotations we observe are fundamentally different from previously reported instances of rotating defects in active fluids as they require the presence of strong enough anchoring and entail significant droplet shape deformations.

Swinging motion of active deformable particles in Poiseuille flow

Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.

Active Brownian motion of emulsion droplets: Coarsening dynamics at the interface and rotational diffusion

A micron-sized droplet of bromine water immersed in a surfactant-laden oil phase can swim (S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13 073021 (2011). The bromine reacts with the surfactant at the droplet interface and generates a surfactant mixture. It can spontaneously phase-separate due to solutocapillary Marangoni flow, which propels the droplet. We model the system by a diffusion-advection-reaction equation for the mixture order parameter at the interface including thermal noise and couple it to fluid flow. Going beyond previous work, we illustrate the coarsening dynamics of the surfactant mixture towards phase separation in the axisymmetric swimming state. Coarsening proceeds in two steps: an initially slow growth of domain size followed by a nearly ballistic regime. On larger time scales thermal fluctuations in the local surfactant composition initiates random changes in the swimming direction and the droplet performs a persistent random walk, as observed in experiments. Numerical solutions show that the rotational correlation time scales with the square of the inverse noise strength. We confirm this scaling by a perturbation theory for the fluctuations in the mixture order parameter and thereby identify the active emulsion droplet as an active Brownian particle.

Getting drowned in a swirl: Deformable bead-spring model microswimmers in external flow fields

Deformability is a central feature of many types of microswimmers, e.g., for artificially generated self-propelled droplets. Here, we analyze deformable bead-spring microswimmers in an externally imposed solvent flow field as simple theoretical model systems. We focus on their behavior in a circular swirl flow in two spatial dimensions. Linear (straight) two-bead swimmers are found to circle around the swirl with a slight drift to the outside with increasing activity. In contrast to that, we observe for triangular three-bead or squarelike four-bead swimmers a tendency of being drawn into the swirl and finally getting drowned, although a radial inward component is absent in the flow field. During one cycle around the swirl, the self-propulsion direction of an active triangular or squarelike swimmer remains almost constant, while their orbits become deformed exhibiting an "egglike" shape. Over time, the swirl flow induces slight net rotations of these swimmer types, which leads to net rotations of the egg-shaped orbits. Interestingly, in certain cases, the orbital rotation changes sense when the swimmer approaches the flow singularity. Our predictions can be verified in real-space experiments on artificial microswimmers.

Spontaneous motility of passive emulsion droplets in polar active gels

We study by computer simulations the dynamics of a droplet of passive, isotropic fluid, embedded in a polar active gel. The latter represents a fluid of active force dipoles, which exert either contractile or extensile stresses on their surroundings, modelling for instance a suspension of cytoskeletal filaments and molecular motors. When the polarisation of the active gel is anchored normal to the droplet at its surface, the nematic elasticity of the active gel drives the formation of a hedgehog defect; this defect then drives an active flow which propels the droplet forward. In an extensile gel, motility can occur even with tangential anchoring, which is compatible with a defect-free polarisation pattern. In this case, upon increasing activity the droplet first rotates uniformly, and then undergoes a discontinuous nonequilibrium transition into a translationally motile state, powered by bending deformations in the surrounding active medium.

Deformable microswimmer in a swirl: capturing and scattering dynamics

Inspired by the classical Kepler and Rutherford problem, we investigate an analogous setup in the context of active microswimmers: the behavior of a deformable microswimmer in a swirl flow. First, we identify new steady bound states in the swirl flow and analyze their stability. Second, we study the dynamics of a self-propelled swimmer heading towards the vortex center, and we observe the subsequent capturing and scattering dynamics. We distinguish between two major types of swimmers, those that tend to elongate perpendicularly to the propulsion direction and those that pursue a parallel elongation. While the first ones can get caught by the swirl, the second ones were always observed to be scattered, which proposes a promising escape strategy. This offers a route to design artificial microswimmers that show the desired behavior in complicated flow fields. It should be straightforward to verify our results in a corresponding quasi-two-dimensional experiment using self-propelled droplets on water surfaces.

Active crystals and their stability

A recently introduced active phase field crystal model describes the formation of ordered resting and traveling crystals in systems of self-propelled particles. Increasing the active drive, a resting crystal can be forced to perform collectively ordered migration as a single traveling object. We demonstrate here that these ordered migrating structures are linearly stable. In other words, during migration, the single-crystalline texture together with the globally ordered collective motion is preserved even on large length scales. Furthermore, we consider self-propelled particles on a substrate that are surrounded by a thin fluid film. We find that in this case the resulting hydrodynamic interactions can destabilize the order.