Janus Colloids Actively Rotating on the Surface of Water

Pair Interaction between Two Catalytically Active Colloids

Due to the intrinsically complex non-equilibrium behavior of the constituents of active matter systems, a comprehensive understanding of their collective properties is a challenge that requires systematic bottom-up characterization of the individual components and their interactions. For self-propelled particles, intrinsic complexity stems from the fact that the polar nature of the colloids necessitates that the interactions depend on positions and orientations of the particles, leading to a 2d - 1 dimensional configuration space for each particle, in d dimensions. Moreover, the interactions between such non-equilibrium colloids are generically non-reciprocal, which makes the characterization even more complex. Therefore, derivation of generic rules that enable us to predict the outcomes of individual encounters as well as the ensuing collective behavior will be an important step forward. While significant advances have been made on the theoretical front, such systematic experimental characterizations using simple artificial systems with measurable parameters are scarce. Here, two different contrasting types of colloidal microswimmers are studied, which move in opposite directions and show distinctly different interactions. To facilitate the extraction of parameters, an experimental platform is introduced in which these parameters are confined on a 1D track. Furthermore, a theoretical model for interparticle interactions near a substrate is developed, including both phoretic and hydrodynamic effects, which reproduces their behavior. For subsequent validation, the degrees of freedom are increased to 2D motion and resulting trajectories are predicted, finding remarkable agreement. These results may prove useful in characterizing the overall alignment behavior of interacting self-propelling active swimmer and may find direct applications in guiding the design of active-matter systems involving phoretic and hydrodynamic interactions.

3-D rotation tracking from 2-D images of spherical colloids with textured surfaces

Tracking the three-dimensional rotation of colloidal particles is essential to elucidate many open questions, e.g. concerning the contact interactions between particles under flow, or the way in which obstacles and neighboring particles affect self-propulsion in active suspensions. In order to achieve rotational tracking, optically anisotropic particles are required. We synthesise here rough spherical colloids that present randomly distributed fluorescent asperities and track their motion under different experimental conditions. Specifically, we propose a new algorithm based on a 3-D rotation registration, which enables us to track the 3-D rotation of our rough colloids at short time-scales, using time series of 2-D images acquired at high frame rates with a conventional wide-field microscope. The method is based on the image correlation between a reference image and rotated 3-D prospective images to identify the most likely angular displacements between frames. We first validate our approach against simulated data and then apply it to the cases of: particles flowing through a capillary, freely diffusing at solid-liquid and liquid-liquid interfaces, and self-propelling above a substrate. By demonstrating the applicability of our algorithm and sharing the code, we hope to encourage further investigations in the rotational dynamics of colloidal systems.

Evanescent field trapping and propulsion of Janus particles along optical nanofibers

Small composite objects, known as Janus particles, drive sustained scientific interest primarily targeted at biomedical applications, where such objects act as micro- or nanoscale actuators, carriers, or imaging agents. A major practical challenge is to develop effective methods for the manipulation of Janus particles. The available long-range methods mostly rely on chemical reactions or thermal gradients, therefore having limited precision and strong dependency on the content and properties of the carrier fluid. To tackle these limitations, we propose the manipulation of Janus particles (here, silica microspheres half-coated with gold) by optical forces in the evanescent field of an optical nanofiber. We find that Janus particles exhibit strong transverse localization on the nanofiber and much faster propulsion compared to all-dielectric particles of the same size. These results establish the effectiveness of near-field geometries for optical manipulation of composite particles, where new waveguide-based or plasmonic solutions could be envisaged.

Sorting of heterogeneous colloids by AC-dielectrophoretic forces in a microfluidic chip with asymmetric orifices

HYPOTHESIS

The synthesis of compositionally heterogeneous particles is central to the development of complex colloidal units for self-assembly and self-propulsion. Yet, as the complexity of particles grows, synthesis becomes more prone to "errors". We hypothesize that alternating-current dielectrophoretic forces can efficiently sort Janus particles, as a function of patch size and material, and colloidal dumbbells by size.

EXPERIMENTS

We prepared Janus particles with different patch size and material by physical vapor deposition and colloidal dumbbells via capillarity-assisted particle assembly. We then performed sorting experiments in a microfluidic chip comprising electrodes with asymmetric orifices, specifically exploiting the dielectric contrast between different portions of the particles or their size difference to steer them towards different outlets.

FINDINGS

We calculated that the DEP force for Janus particles may switch from positive to negative as a function of composition at a critical AC frequency, thus enabling sorting different particles crossing the electrodes' region. The predictions are confirmed by optical microscopy experiments. We also show that intact and "broken" dumbbells can be simply separated as they experience different DEP forces. The integration of multiple asymmetric orifices leads a larger zone with high field gradient to increase separation efficiency and makes it a promising tool to select precise particle populations, isolating fractions with narrowly distributed characteristics.

Multicompartment polymeric colloids from functional precursor Microgel: Synthesis in continuous process

Raspberry-like poly(oligoethylene methacrylate-b-N-vinylcaprolactam)/polystyrene (POEGMA-b-PVCL/PS) patchy particles (PPs) and complex colloidal particle clusters (CCPCs) were fabricated in two-, and one-step (cascade) flow process. Surfactant-free, photo-initiated reversible addition-fragmentation transfer (RAFT) precipitation polymerization (Photo-RPP) was used to develop internally cross-linked POEGMA-b-PVCL microgels with narrow size distribution. Resulting microgel particles were then used to stabilize styrene seed droplets in water, producing raspberry-like PPs. In the cascade process, different hydrophobicity between microgel and PS induced the self-assembly of the first formed raspberry particles that then polymerized continuously in a Pickering emulsion to form the CCPCs. The internal structure as well as the surface morphology of PPs and CCPCs were studied as a function of polymerization conditions such as flow rate/retention time (Rt), temperature and the amount of used cross-linker. By performing Photo-RPP in tubular flow reactor we were able to gained advantages over heat dissipation and homogeneous light distribution in relation to thermally-, and photo-initiated bulk polymerizations. Tubular reactor also enabled detailed studies over morphological evolution of formed particles as a function of flow rate/Rt.

Fitting an active Brownian particle's mean-squared displacement with improved parameter estimation

The active Brownian particle (ABP) model is widely used to describe the dynamics of active matter systems, such as Janus microswimmers. In particular, the analytical expression for an ABP's mean-squared displacement (MSD) is useful as it provides a means to describe the essential physics of a self-propelled, spherical Brownian particle. However, the truncated or "short-time" form of the MSD equation is typically fitted, which can lead to significant problems in parameter estimation. Furthermore, heteroscedasticity and the often statistically dependent observations of an ABP's MSD lead to a situation where standard ordinary least-squares regression leads to biased estimates and unreliable confidence intervals. Instead, we propose here to revert to always fitting the full expression of an ABP's MSD at short timescales, using bootstrapping to construct confidence intervals of the fitted parameters. Additionally, after comparison between different fitting strategies, we propose to extract the physical parameters of an ABP using its mean logarithmic squared displacement. These steps improve the estimation of an ABP's physical properties and provide more reliable confidence intervals, which are critical in the context of a growing interest in the interactions of microswimmers with confining boundaries and the influence on their motion.

Multimodal Bubble Microrobot Near an Air-Water Interface

The development of multifunctional and robust swimming microrobots working at the free air-liquid interface has encountered challenge as new manipulation strategies are needed to overcome the complicated interfacial restrictions. Here, flexible but reliable mechanisms are shown that achieve a remote-control bubble microrobot with multiple working modes and high maneuverability by the assistance of a soft air-liquid interface. This bubble microrobot is developed from a hollow Janus microsphere (JM) regulated by a magnetic field, which can implement switchable working modes like pusher, gripper, anchor, and sweeper. The collapse of the microbubble and the accompanying directional jet flow play a key role for functioning in these working modes, which is analogous to a "bubble tentacle." Using a simple gamepad, the orientation and the navigation of the bubble microrobot can be easily manipulated. In particular, a speed modulation method is found for the bubble microrobot, which uses vertical magnetic field to control the orientation of the JM and the direction of the bubble-induced jet flow without changing the fuel concentration. The findings demonstrate a substantial advance of the bubble microrobot specifically working at the air-liquid interface and depict some nonintuitive mechanisms that can help develop more complicated microswimmers.

A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve.

Synthesis and Propulsion of Magnetic Dimers under Orthogonally Applied Electric and Magnetic Fields

Anisotropic particles have been widely used to make micro/nanomotors that convert chemical, ultrasonic, electrical, or magnetic energy into mechanical energy. The moving directions of most colloidal motors are, however, difficult to control. For example, asymmetric dimers with two lobes of different sizes, ζ-potential, or chemical composition have shown rich propulsion behaviors under alternating current (AC) electric fields due to unbalanced electrohydrodynamic flow. While they always propel in a direction perpendicular to the applied electric field, their moving directions along the substrate are hard to control, limiting their applications for cargo delivery. Inspired by two separate engine and steering wheel systems in automobiles, we use orthogonally applied AC electric field and direct current (DC) magnetic field to control the dimer's speed and direction independently. To this end, we first synthesize magnetic dimers by coating dopamine-functionalized nanoparticles on geometrically asymmetric polystyrene dimers. We further characterize their static and dynamic susceptibilities by measuring the hysteresis diagram and rotation speed experimentally and comparing them with theoretical predictions. The synthesized dimers align their long axes quickly with a planar DC magnetic field, allowing us to control the particles' orientation accurately. The propulsion speed of the dimers, on the other hand, is tunable by an AC electric field applied perpendicularly to the substrate. As a result, we can direct the particle's motion with predesigned trajectories of complex shapes. Our bulk-synthesis approach has the potential to make other types of magnetically anisotropic particles. And the combination of electric and magnetic fields will help pave the way for the assembly of magnetically anisotropic particles into complex structures.

Static and Dynamic Self-Assembly of Pearl-Like-Chains of Magnetic Colloids Confined at Fluid Interfaces

Magnetic colloids adsorbed at a fluid interface are unique model systems to understand self-assembly in confined environments, both in equilibrium and out of equilibrium, with important potential applications. In this work the pearl-chain-like self-assembled structures of superparamagnetic colloids confined to a fluid-fluid interface under static and time-dependent actuations are investigated. On the one hand, it is found that the structures generated by static fields transform as the tilt angle of the field with the interface is increased, from 2D crystals to separated pearl-chains in a process that occurs through a controllable and reversible zip-like thermally activated mechanism. On the other hand, the actuation with precessing fields about the axis perpendicular to the interface induces dynamic self-assembled structures with no counterpart in non-confined systems, generated by the interplay of averaged magnetic interactions, interfacial forces, and hydrodynamics. Finally, how these dynamic structures can be used as remotely activated roller conveyors, able to transport passive colloidal cargos at fluid interfaces and generate parallel viscous flows is shown. The latter can be used in the mixture of adsorbed molecules and the acceleration of surface-chemical reactions, overcoming diffusion limitations.

Active colloids orbiting giant vesicles

Living or artificial self-propelled colloidal particles show original dynamics when they interact with other objects like passive particles, interfaces or membranes. These active colloids can transport small cargos or can be guided by passive objects, performing simple tasks that could be implemented in more complex systems. Here, we present an experimental investigation at the single particle level of the interaction between isolated active colloids and giant unilamellar lipid vesicles. We observed a persistent orbital motion of the active particle around the vesicle, which is independent of both the particle and the vesicle sizes. Force and torque transfers between the active particle and the vesicle is also described. These results differ in many aspects from recent theoretical and experimental reports on active particles interacting with solid spheres or liquid drops, and may be relevant for the study of swimming particles interacting with cells in biology or with microplastics in environmental science.

Active spheres induce Marangoni flows that drive collective dynamics

For monolayers of chemically active particles at a fluid interface, collective dynamics is predicted to arise owing to activity-induced Marangoni flow even if the particles are not self-propelled. Here, we test this prediction by employing a monolayer of spherically symmetric active [Formula: see text] particles located at an oil-water interface with or without addition of a nonionic surfactant. Due to the spherical symmetry, an individual particle does not self-propel. However, the gradients produced by the photochemical fuel degradation give rise to long-ranged Marangoni flows. For the case in which surfactant is added to the system, we indeed observe the emergence of collective motion, with dynamics dependent on the particle coverage of the monolayer. The experimental observations are discussed within the framework of a simple theoretical mean-field model.

Contact angle as a powerful tool in anisotropic colloid synthesis

Nucleation and growth is a technique widely used to prepare colloids, in which droplets are adsorbed onto substrate particles. Changing the contact angle of the substrates can greatly alter the morphology of the product particles. Here, we investigate the nucleation and growth of 3-methacryloxypropyltrimethoxysilane (MPTMS) both onto Stöber spheres and onto (cross-linked) MPTMS* spheres. The former results in 'snowman' particles with a cap-shaped MPTMS* compartment, and we show that their morphology is highly controllable via the MPTMS content in the reaction mixture. The contact angle of the MPTMS* compartment decreases with droplet diameter, suggesting that this wetting process is affected not only by surface tension but also by line tension. In contrast to Stöber spheres, MPTMS* substrate particles yield highly reproducible and tuneable 'engulfed-sphere' colloids with an internal reference axis (but a homogeneous mass distribution). These engulfed-sphere particles can be fully index-matched for confocal microscopy on account of their homogeneous refractive index. Suitable index-matching mixtures of polar and of low-polar media are presented, where cyclohexyl iodide (CHI) is introduced as a new medium for colloids of high refractive index. Finally, the index-matched engulfed-sphere colloids are self-assembled into (close-packed and long-range) plastic phases, and the particles' rotational diffusion inside the crystal phases is tracked via confocal microscopy.

Interfacial viscoelasticity and jamming of colloidal particles at fluid-fluid interfaces: a review

Colloidal particles can be adsorbed at fluid-fluid interfaces, a phenomenon frequently observed in particle-stabilized foams, Pickering emulsions, and bijels. Particles adsorbed at interfaces exhibit unique physical and chemical behaviors, which affect the mechanical properties of the interface. Therefore, interfacial colloidal particles are of interest in terms of both fundamental and applied research. In this paper, we review studies on the adsorption of colloidal particles at fluid-fluid interfaces, from both thermodynamic and mechanical points of view, and discuss the differences as compared with surfactants and polymers. The unique particle interactions induced by the interfaces as well as the particle dynamics including lateral diffusion and contact line relaxation will be presented. We focus on the rearrangement of the particles and the resultant interfacial viscoelasticity. Particular emphasis will be given to the effects of particle shape, size, and surface hydrophobicity on the interfacial particle assembly and the mechanical properties of the obtained particle layer. We will also summarize recent advances in interfacial jamming behavior caused by adsorption of particles at interfaces. The buckling and cracking behavior of particle layers will be discussed from a mechanical perspective. Finally, we suggest several potential directions for future research in this area.

Self-Propelled Janus Colloids in Shear Flow

To fully harness the potential of artificial active colloids, investigation of their response to various external stimuli including external flow is of great interest. Therefore, in this study, we perform experiments on SiO₂-Pt Janus particles suspended in an aqueous medium in a capillary subjected to different shear flow rates. Particles were propelled using varied H₂O₂ (fuel) concentrations. For a particular propulsion speed, with increasing shear flow, a continuous transition in the motion of active Janus particles (JPs) from the usual random active motion to preferential movement along the vorticity direction and then finally to migration along the flow was observed. This transition was accompanied by a significant decline in in-plane fluctuations of the particle trajectories. Another key observation is that the activity of JPs produces a delay in shear-induced rolling, which at moderate flow, allows the JPs to adopt a specific orientation, facilitating their migration along the vorticity direction. At higher flow rates, once shear flow overcomes the activity-induced resistance and initiates rolling, the probability of JPs adopting such preferred orientations reduces. Our analysis further revealed that these transitions are governed by a nondimensional quantity λ, which compares the relative strength of the shear-induced particle flow to the propulsion speed.

Particle Surface Roughness as a Design Tool for Colloidal Systems

Control over the surface roughness of colloidal particles offers exciting opportunities to tailor the properties and the processing of a broad range of soft matter systems. Moreover, identifying surface roughness as a design parameter reveals the possibility to connect seemingly distinct phenomena and materials via the role played by roughness effects. In this feature article, we concisely review some approaches to synthesize and characterize rough colloidal particles, with a focus on model spherical colloids. We then discuss the impact that surface roughness has on both the high-shear rheology of dense suspensions and the stabilization of Pickering emulsions. Commenting on developments of our own research, we aim to offer an original perspective for a property-oriented development of colloidal particles that transcends classical divisions between materials and processes toward innovative solutions.

Brownian Diffusion of Individual Janus Nanoparticles at Water/Oil Interfaces

Janus nanoparticles could exhibit a higher interfacial activity and adsorb stronger to fluid interfaces than homogeneous nanoparticles of similar sizes. However, little is known about the interfacial diffusion of Janus nanoparticles and how it compares to that of homogeneous ones. Here, we employed fluorescence correlation spectroscopy to study the lateral diffusion of ligand-grafted Janus nanoparticles adsorbed at water/oil interfaces. We found that the diffusion was significantly slower than that of homogeneous nanoparticles. We carried out dissipative particle dynamic simulations to study the mechanism of interfacial slowdown. Good agreement between experimental and simulation results has been obtained only provided that the flexibility of ligands grafted on the nanoparticle surface was taken into account. The polymeric ligands were deformed and oriented at an interface so that the effective radius of Janus nanoparticles is larger than the nominal one obtained by measuring the diffusion in bulk solution. These findings highlight further the critical importance of the ligands grafted on Janus nanoparticles for applications involving nanoparticle adsorption at an interface, such as oil recovery or two-dimensional self-assembly.

Self-Propulsion of Janus Particles near a Brush-Functionalized Substrate

Thermophoresis is a common mechanism that can drive autonomous motion of Janus particles under the right environment. Despite recent efforts to investigate the mechanism underlying the self-propulsion of thermophoretic particles, the interaction of particles with the substrate underneath the particle has remained unclear. In this work, we explore the impact of poly(N-isopropylacrylamide) (PNIPAM)-functionalized substrate with various chain lengths on the active motion of a single polystyrene particle half-coated with gold (Au-PS). We show how the modification of the substrate with polymer brushes enhances the particle velocity, where brush chain length plays a significant role as well. The results demonstrate the intrinsic dependence of particle velocity on the flow boundary condition and the thermo-osmotic slip at the interface.

Motile Bacteria at Oil-Water Interfaces: Pseudomonas aeruginosa

Bacteria are important examples of active or self-propelled colloids. Because of their directed motion, they accumulate near interfaces. There, they can become trapped and swim adjacent to the interface via hydrodynamic interactions, or they can adsorb directly and swim in an adhered state with complex trajectories that differ from those in bulk in both form and spatiotemporal implications. We have adopted the monotrichous bacterium Pseudomonas aeruginosa PA01 as a model species and have studied its motion at oil-aqueous interfaces. We have identified conditions in which bacteria swim persistently without restructuring the interface, allowing detailed and prolonged study of their motion. In addition to characterizing the ensemble behavior of the bacteria, we have observed a gallery of distinct trajectories of individual swimmers on and near fluid interfaces. We attribute these diverse swimming behaviors to differing trapped states for the bacteria in the fluid interface. These trajectory types include Brownian diffusive paths for passive adsorbed bacteria, curvilinear trajectories including curly paths with radii of curvature larger than the cell body length, and rapid pirouette motions with radii of curvature comparable to the cell body length. Finally, we see interfacial visitors that come and go from the interfacial plane. We characterize these individual swimmer motions. This work may impact nutrient cycles for bacteria on or near interfaces in nature. This work will also have implications in microrobotics, as active colloids in general and bacteria in particular are used to carry cargo in this burgeoning field. Finally, these results have implications in engineering of active surfaces that exploit interfacially trapped self-propelled colloids.

Pt-SiO2 Janus Particles and the Water/Oil Interface: A Competition between Motility and Thermodynamics

Various aspects of the behavior of Janus particles near liquid/liquid interfaces have been studied through different experimental and theoretical realizations, but the effect of motility on the behavior of Janus particles near liquid/liquid interfaces has not been investigated, yet. Here, we demonstrate the ability to engineer the behavior of highly interfacial active Janus particles near a water/oil interface by introducing motility to the system. Passive, i.e., nonmotile, platinum-capped 8 μm silica (Pt-SiO₂) Janus particles exhibit a strong tendency to attach to water/oil interfaces with the Pt-cap facing the oil and the SiO₂ side facing the water phase. In contrast, we show that active, i.e., motile, 8 μm Pt-SiO₂ Janus particles approach the interface, orient in a sideways fashion with the Janus boundary perpendicular to the interface, and then swim in the vicinity of the interface similar to observations reported near solid/liquid interfaces. Active Pt-SiO₂ Janus particles near the water/oil interface show motility as a result of adding H₂O₂ to the particle solution. The decomposition of H₂O₂ into O₂ and H₂O creates a nonuniform gradient of O₂ around the particle that hydrodynamically interacts with the water/decalin boundary. The interaction enables rotation of the particle within the swimming plane that is parallel to the interface but restricts rotation in and out of the swimming plane, thereby preventing adsorption to the liquid/liquid interface.

Influence of cap weight on the motion of a Janus particle very near a wall

The dynamics of anisotropic nano- to micro scale colloidal particles in confined environments, either near neighboring particles or boundaries, is relevant to a wide range of applications. We utilized Brownian dynamics simulations to predict the translational and rotational fluctuations of a Janus sphere with a cap of nonmatching density near a boundary. The presence of the cap significantly impacted the rotational dynamics of the particle as a consequence of gravitational torque at experimentally relevant conditions. Gravitational torque dominated stochastic torque for a particle >1 μm in diameter and with a 20-nm-thick gold cap. Janus particles at these conditions sampled mostly cap-down or "quenched" orientations. Although the results summarized herein showed that particles of smaller diameter (<1 μm) with a thin gold coating (<5 nm) behave similarly to an isotropic particle, small increases in either particle diameter or coating thickness quenched the polar rotation of the particle. Histogram landscapes of the separation distance from the boundary and orientation observations of particles with larger diameters or thicker gold coatings were mostly populated with quenched configurations. Finally, the histogram landscapes were inverted to obtain the potential energy landscapes, providing a road map for experimental data to be interpreted.

Dynamics of a ratchet gear powered by an active granular bath

Recent experiments show universal features of ratchet gear dynamics that are powered by different types of active baths. We investigate further for the case of a ratchet gear in a bath of self-propelling granular rods (SPRs). The resulting angular velocity was found to follow a nonmonotonic dependence to the SPR concentration similar to the observation from other active bath systems. This behavior is caused by the interplay of the momentum transfer of the SPRs in the trapping regions of the gear and the mean velocity of the SPRs inside the bath. For all SPR concentrations, we found that the angular velocity is proportional to the product of the number of SPRs pushing the gear and the SPRs mean velocity.

Guidance of active particles at liquid-liquid interfaces near surfaces

Artificial microswimmers have the potential for applications in many fields, ranging from targeted cargo delivery and mobile sensing to environmental remediation. In many of these applications, the artificial swimmers will operate in complex media necessarily involving liquid-liquid interfaces. Here, we experimentally study the motion of chemically powered phoretic active colloids close to liquid-liquid interfaces while swimming next to a solid substrate. In a system involving this complex geometry, we find that the active particles have an alignment interaction with both the neighbouring solid and liquid interfaces, allowing for a robust guiding mechanism along the liquid interface. We compare with minimal active Brownian simulations to show that these phoretically active particles stay along the interfaces for much longer times and lengths than expected for standard active Brownian particles. We also track the propulsion speeds of these particles and find a reduced speed close to the liquid-liquid interface. We report an interesting non-linear dependence of this reduction on the particle's bulk speed.

Active particles in noninertial frames: How to self-propel on a carousel

Typically the motion of self-propelled active particles is described in a quiescent environment establishing an inertial frame of reference. Here we assume that friction, self-propulsion, and fluctuations occur relative to a noninertial frame and thereby the active Brownian motion model is generalized to noninertial frames. First, analytical solutions are presented for the overdamped case, both for linear swimmers and for circle swimmers. For a frame rotating with constant angular velocity ("carousel"), the resulting noise-free trajectories in the static laboratory frame are trochoids if these are circles in the rotating frame. For systems governed by inertia, such as vibrated granulates or active complex plasmas, centrifugal and Coriolis forces become relevant. For both linear and circling self-propulsion, these forces lead to out-spiraling trajectories which for long times approach a spira mirabilis. This implies that a self-propelled particle will typically leave a rotating carousel. A navigation strategy is proposed to avoid this expulsion, by adjusting the self-propulsion direction at will. For a particle, initially quiescent in the rotating frame, it is shown that this strategy only works if the initial distance to the rotation center is smaller than a critical radius R_{c} which scales with the self-propulsion velocity. Possible experiments to verify the theoretical predictions are discussed.

Transition from Linear to Circular Motion in Active Spherical-Cap Colloids

Nonspherical self-propelling colloidal particles offer many possibilities for creating a variety of active motions. In this work, we report on the transition from linear to circular motion of active spherical-cap particles near a substrate. Self-propulsion is induced by self-diffusiophoresis by catalytic decomposition of hydrogen peroxide (H₂O₂) on one side of the particle. Asymmetric distribution of reaction products combined with the asymmetric shape of the particle gives rise to two types of motions depending upon the relative orientation of the particle with respect to the underlying substrate. At a low concentration of H₂O₂, linear active motion is observed, whereas increasing the H₂O₂ concentration leads to persistent circular motion. However, the speed of self-propulsion is nearly independent of the size of the particle. The study demonstrates the use of nonspherical particles to create linear and circular motion by varying the fuel concentration.

A Review of Micromotors in Confinements: Pores, Channels, Grooves, Steps, Interfaces, Chains, and Swimming in the Bulk

One of the recent frontiers of nanotechnology research involves machines that operate at nano- and microscales, also known as nano/micromotors. Their potential applications in biomedicine, environmental sciences and engineering, military and defense industries, self-assembly, and many other areas have fueled an intense interest in this topic over the last 15 years. Despite deepened understanding of their propulsion mechanisms, we are still in the early days of exploring the dynamics of micromotors in complex and more realistic environments. Confinements, as a typical example of complex environments, are extremely relevant to the applications of micromotors, which are expected to travel in mucus gels, blood vessels, reproductive and digestive tracts, microfluidic chips, and capillary tubes. In this review, we summarize and critically examine recent studies (mostly experimental ones) of micromotor dynamics in confinements in 3D (spheres and porous network, channels, grooves, steps, and obstacles), 2D (liquid-liquid, liquid-solid, and liquid-air interfaces), and 1D (chains). In addition, studies of micromotors moving in the bulk solution and the usefulness of acoustic levitation is discussed. At the end of this article, we summarize how confinements can affect micromotors and offer our insights on future research directions. This review article is relevant to readers who are interested in the interactions of materials with interfaces and structures at the microscale and helpful for the design of smart and multifunctional materials for various applications.

Surface swimmers, harnessing the interface to self-propel

In the study of microscopic flows, self-propulsion has been particularly topical in recent years, with the rise of miniature artificial swimmers as a new tool for flow control, low Reynolds number mixing, micromanipulation or even drug delivery. It is possible to take advantage of interfacial physics to propel these microrobots, as demonstrated by recent experiments using the proximity of an interface, or the interface itself, to generate propulsion at low Reynolds number. This paper discusses how a nearby interface can provide the symmetry breaking necessary for propulsion. An overview of recent experiments illustrates how forces at the interface can be used to generate locomotion. Surface swimmers ranging from the microscopic scale to typically the capillary length are covered. Two systems are then discussed in greater detail. The first is composed of floating ferromagnetic spheres that assemble through capillarity into swimming structures. Two previously studied configurations, triangular and collinear, are discussed and contrasted. A new interpretation for the triangular swimmer is presented. Then, the non-monotonic influence of surface tension and viscosity is evidenced in the collinear case. Finally, a new system is introduced. It is a magnetically powered, centimeter-sized piece that swims similarly to water striders.

Phase coexistence in a monolayer of active particles induced by Marangoni flows

Thermally or chemically active colloids generate thermodynamic gradients in the solution in which they are immersed and thereby induce hydrodynamic flows that affect their dynamical evolution. Here we study a mean-field model for the many-body dynamics of a monolayer of spherically symmetric active particles located at a fluid-fluid interface. Due to the spherical symmetry, the particles do not self-propel. Instead, the dynamics is driven by the long-ranged Marangoni flows, due to the response of the interface to the activity of the particles, which compete with the direct interaction between particles. We demonstrate analytically that, in spite of the intrinsic out-of-equilibrium character of the system, the monolayer evolves to a "pseudoequilibrium" state, in which the Marangoni flows force the coexistence of the thermodynamic phases associated to the direct interaction. In particular, we study the most interesting case of a r-3 soft repulsion that models electrostatic or magnetic interparticle forces. For a sufficiently large average density, two-dimensional phase transitions (freezing from liquid to hexatic, and melting from solid to hexatic) should be observable in a radially stratified, "onion-like" structure within the monolayer. Furthermore, the analysis allows us to conclude that, while the activity may be too weak to allow direct detection of such induced Marangoni flows, it is relevant as a collective effect in the emergence of the experimentally observable spatial structure of phase coexistences noted above. Finally, the relevance of these results for potential experimental realizations is critically discussed.

Local Measurement of Janus Particle Cap Thickness

Janus particles have anisotropy in surface chemistry or composition that will effect dynamics and interactions with neighboring surfaces. One specific type of Janus particle is that consisting of a native micrometer-scale particle with a cap of gold, platinum, or another metal deposited with a typical thicknesses of ∼10 nm. A key characteristic of metal-capped Janus particles prepared with glancing angle deposition is the cap thickness. The nominal thickness is usually assumed to be uniform across the cap for modeling or interpretation of data, but the vapor deposition fabrication process likely does not produce such a cap because of the particle's curvature. These nonuniformities in the cap thickness may have a profound impact on Janus particle dynamics at equilibrium and in response to external fields. Herein, we summarize an experimental technique that utilizes focused ion beam slicing, image analysis, and results for the direct and local measure of cap thickness for 5 μm polystyrene spheres with a gold cap of nominal thicknesses of 10 or 20 nm. We found the cap varied in thickness continuously along the perimeter of the particle and also that the deposition rate, varying between 0.5 and 2.0 Å/s, did not significantly alter the way in which the thickness varied. These data support the hypothesis that cap thickness of a Janus sphere will vary across the gold surface contour, while demonstrating a feasible route for direct measurement of Janus particle cap thickness.

Cargo carrying bacteria at interfaces

The displacements of ensembles of colloids at the interface between oil and suspensions of the bacterium Pseudomonas aeruginosa PA14ΔpelA indicate enhanced colloid mobilities and apparently diffusive motion driven by interactions with the bacteria. However, inspection of individual trajectories of ∼500 particles reveals prolonged, directed displacements inconsistent with purely hydrodynamic interactions between swimming bacteria and colloids. Analysis of the properties of colloid paths indicates trajectories can be sorted into four distinct categories, including diffusive, persistent, curly, and mixed trajectory types. Non-diffusive trajectories are the norm, comprising 2/3 of the observed trajectories. Imaging of colloids in the interface reveals anisotropic assemblies formed by colloids decorated with one or more adhered bacteria that drive the colloids along these paths. The trajectories and enhanced transport result from individual colloids being moved as cargo by these adhered bacteria. The implications of these structures and open questions for interfacial transport are discussed and related to the active colloid literature.

Autophoretic motion in three dimensions

Janus particles with the ability to move phoretically in self-generated chemical concentration gradients are model systems for active matter. Their motion typically consists of straight paths with rotational diffusion being the dominant reorientation mechanism. In this paper, we show theoretically that by a suitable surface coverage of both activity and mobility, translational and rotational motion can be induced arbitrarily in three dimensions. The resulting trajectories are in general helical, and their pitch and radius can be controlled by adjusting the angle between the translational and angular velocity. Building on the classical mathematical framework for axisymmetric self-phoretic motion under fixed-flux chemical boundary conditions, we first show how to calculate the most general three-dimensional motion for an arbitrary surface coverage of a spherical particle. After illustrating our results on surface distributions, we next introduce a simple intuitive patch model to serve as a guide for designing arbitrary phoretic spheres.