Phoretic and hydrodynamic interactions of weakly confined autophoretic particles

Emergent dynamics due to chemo-hydrodynamic self-interactions in active polymers

The field of synthetic active matter has, thus far, been led by efforts to create point-like, isolated (yet interacting) self-propelled objects (e.g. colloids, droplets, microrobots) and understanding their collective dynamics. The design of flexible, freely jointed active assemblies from autonomously powered sub-components remains a challenge. Here, we report freely-jointed active polymers created using self-propelled droplets as monomeric units. Our experiments reveal that the self-shaping chemo-hydrodynamic interactions between the monomeric droplets give rise to an emergent rigidity (the acquisition of a stereotypical asymmetric C-shape) and associated ballistic propulsion of the active polymers. The rigidity and propulsion of the chains vary systematically with their lengths. Using simulations of a minimal model, we establish that the emergent polymer dynamics are a generic consequence of quasi two-dimensional confinement and auto-repulsive trail-mediated chemical interactions between the freely jointed active droplets. Finally, we tune the interplay between the chemical and hydrodynamic fields to experimentally demonstrate oscillatory dynamics of the rigid polymer propulsion. Altogether, our work highlights the possible first steps towards synthetic self-morphic active matter.

Dynamic Clustering and Scaling Behavior of Active Particles under Confinement

A systematic investigation of the dynamic clustering behavior of active particles under confinement, including the effects of both particle density and active driving force, is presented based on a hybrid coarse-grained molecular dynamics simulation. First, a series of scaling laws are derived with power relationships for the dynamic clustering time as a function of both particle density and active driving force. Notably, the average number of clusters N¯ assembled from active particles in the simulation system exhibits a scaling relationship with clustering time t described by N¯∝t-m. Simultaneously, the scaling behavior of the average cluster size S¯ is characterized by S¯∝tm. Our findings reveal the presence of up to four distinct dynamic regions concerning clustering over time, with transitions contingent upon the particle density within the system. Furthermore, as the active driving force increases, the aggregation behavior also accelerates, while an increase in density of active particles induces alterations in the dynamic procession of the system.

Breaking action-reaction with active apolar colloids: emergent transport and velocity inversion

Artificial active particles are autonomous agents able to convert energy from the environment into net propulsion, breaking detailed balance and the action-reaction law, clear signatures of their out-of-equilibrium nature. Here we investigate the emergence of directed motion in clusters composed of passive and catalytically active apolar colloids. We use a light-induced chemophoretic flow to rapidly assemble hybrid self-propelling clusters composed of hematite particles and passive silica spheres. By increasing the size of the passive cargo, we observe a reversal in the transport direction of the pair. We explain this complex yet rich phenomenon using a theoretical model which accounts for the generated chemical field and its coupling with the surrounding medium. We exploit further our technique to build up more complex, chemically driven, architectures capable of carrying several passive or active species, that quickly assemble and disassemble under light control.

Hydrodynamic model of fish orientation in a channel flow

For over a century, scientists have sought to understand how fish orient against an incoming flow, even without visual and flow cues. Here, we elucidate a potential hydrodynamic mechanism of rheotaxis through the study of the bidirectional coupling between fish and the surrounding fluid. By modeling a fish as a vortex dipole in an infinite channel with an imposed background flow, we establish a planar dynamical system for the cross-stream coordinate and orientation. The system dynamics captures the existence of a critical flow speed for fish to successfully orient while performing cross-stream, periodic sweeping movements. Model predictions are examined in the context of experimental observations in the literature on the rheotactic behavior of fish deprived of visual and lateral line cues. The crucial role of bidirectional hydrodynamic interactions unveiled by this model points at an overlooked limitation of existing experimental paradigms to study rheotaxis in the laboratory.

One fascinating and perplexing fact about fish is that they tend to orient themselves and swim against the flow, rather than with it. This phenomenon is called rheotaxis, and it has countless examples, from salmon migrating upstream to lay their eggs to trout drift-foraging in a current. Yet, despite over a century of experimental studies, the mechanisms underlying rheotaxis remain poorly understood. There is general consensus that fish rely on water- and body-motion cues to vision, vestibular, tactile, and other senses. However, several questions remain unanswered, including how blind fish can perform rheotaxis or whether a passive hydrodynamic mechanism can support the phenomenon. One aspect that has been overlooked in studies of rheotaxis is the bidirectional hydrodynamic interaction between the fish and the surrounding flow, that is, how the presence of the fish alters the flow, which, in turn, affects the fish.

To address these open questions about rheotaxis, Porfiri, Zhang and Peterson wanted to develop a mathematical model of fish swimming, one that could help understand the passive hydrodynamic pathway that leads to swimming against a flow. Unlike experiments on live animals, a mathematical model offers the ability to remove cues to certain senses without interfering with animal behavior.

Porfiri, Zhang and Peterson modeled a fish as a pair of vortices located infinitely close to each other, rotating in opposite directions with the same strength. The vortex pair could freely move through an infinitely long channel with an imposed background flow, devoid of all sensory information expect of that accessed through the lateral line. Analyzing the resulting system revealed that there is a critical speed for the background flow above which the fish successfully orients itself against the flow, resulting in rheotaxis. This critical speed depends on the width of the channel the fish is swimming in. Depriving the fish of sensory information received through the lateral line does not preclude rheotaxis, indicating that rheotaxis could emerge in a completely passive manner.

The finding that the critical speed for rheotaxis depends on channel width could improve the design of experiments studying the phenomenon, since this effect could confound experiments where fish are confined in narrow channels. In this vein, Porfiri, Zhang and Peterson’s model could assist biologists in designing experiments detailing the multisensory nature of rheotaxis. Evidence of the importance of bidirectional hydrodynamic interactions on fish orientation may also inform modeling research on fish behavior.

Enhanced diffusivity in microscopically reversible active matter

The physics of self-propelled objects at the nanoscale is a rapidly developing research field where recent experiments have focused on the motion of individual catalytic enzymes. Contrary to the experimental advancements, theoretical understanding of the possible self-propulsion mechanisms at these scales is limited. A particularly puzzling question concerns the origins of the reportedly high diffusivities of the individual enzymes. Here we start with the fundamental principle of microscopic reversibility (MR) of chemical reactions powering self-propulsion and demonstrate that MR can lead to an increase of the particle mobility and of the short- and long-time diffusion coefficients as compared to dynamics where MR is neglected. Furthermore, the derived diffusion coefficients are enhanced due to the action of an external force. These results can shed new light on interpretations of the measured diffusivities and help to test the relevance of MR for the active motion of individual nanoswimmers.

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.

Self-propulsion in 2D confinement: phoretic and hydrodynamic interactions

Chemically active Janus particles generate tangential concentration gradients along their surface for self-propulsion. Although this is well studied in unbounded domains, the analysis in biologically relevant environments such as confinement is scarce. In this work, we study the motion of a Janus sphere in weak confinement. The particle is placed at an arbitrary location, with arbitrary orientation between the two walls. Using the method of reflections, we study the effect of confining planar boundaries on the phoretic and hydrodynamic interactions, and their consequence on the Janus particle dynamics. The dynamical trajectories are analyzed using phase diagrams for different surface coverage of activity and solute-particle interactions. In addition to near wall states such as 'sliding' and 'hovering', we demonstrate that accounting for two planar boundaries reveals two new states: channel-spanning oscillations and damped oscillations around the centerline, which were characterized as 'scattering' or 'reflection' by earlier analyses on single wall interactions. Using phase-diagrams, we highlight the differences in inert-facing and active-facing Janus particles. We also compare the dynamics of Janus particles with squirmers for contrasting the chemical interactions with hydrodynamic effects. Insights from the current work suggest that biological and artificial swimmers sense their surroundings through long-ranged interactions, that can be modified by altering the surface properties.

Swimming droplets in 1D geometries: an active Bretherton problem

We investigate experimentally the behavior of self-propelled water-in-oil droplets, confined in capillaries of different square and circular cross-sections. The droplet's activity comes from the formation of swollen micelles at its interface. In straight capillaries the velocity of the droplet decreases with increasing confinement. However, at very high confinement, the velocity converges toward a non-zero value, so that even very long droplets swim. Stretched circular capillaries are used to explore even higher confinement. The lubrication layer around the droplet then takes a non-uniform thickness which constitutes a significant difference to usual flow-driven passive droplets. A neck forms at the rear of the droplet, deepens with increasing confinement, and eventually undergoes successive spontaneous splitting events for large enough confinement. Such observations stress the critical role of the activity of the droplet interface in the droplet's behavior under confinement. We then propose an analytical formulation by integrating the interface activity and the swollen micelle transport problem into the classical Bretherton approach. The model accounts for the convergence of the droplet's velocity to a finite value for large confinement, and for the non-classical shape of the lubrication layer. We further discuss on the saturation of the micelle concentration along the interface, which would explain the divergence of the lubrication layer thickness for long enough droplets, eventually leading to spontaneous droplet division.

Inferring non-equilibrium interactions from tracer response near confined active Janus particles

Chemically active Janus particles sustain non-equilibrium spatial variations in the chemical composition of the suspending solution; these induce hydrodynamic flow and (self-)motility of the particles. Direct mapping of these fields has so far proven to be too challenging. Therefore, indirect methods are needed, e.g., deconvolving the response of "tracer" particles to the activity-induced fields. Here, we study experimentally the response of silica particles, sedimented at a wall, to active Pt/silica Janus particles. The latter are either immobilized at the wall, with the symmetry axis perpendicular or parallel to the wall, or motile. The experiments reveal complex effective interactions that are dependent on the configuration and on the state of motion of the active particle. Within the framework of a coarse-grained model, the behavior of tracers near an immobilized Janus particle can be captured qualitatively once activity-induced osmotic flows on the wall are considered.

Wetting of a solid surface by active matter

A lattice model is used to study repulsive active particles at a planar surface. A rejection-free Kinetic Monte Carlo method is employed to characterize the wetting behaviour. The model predicts a motility-induced phase separation of active particles, and the bulk coexistence of dense liquid-like and dilute vapour-like steady states is determined. An "ensemble", with a varying number of particles, analogous to a grand canonical ensemble in equilibrium, is introduced. The formation and growth of the liquid film between the solid surface and the vapour phase is investigated. At constant activity, as the system is brought towards coexistence from the vapour side, the thickness of the adsorbed film exhibits a divergent behaviour regardless of the activity. This suggests a complete wetting scenario along the full coexistence curve.

The impact of geometrical confinement in a slab on the behavior of tracer particles near active glucose oxidase micropump

Patches of surface-immobilized and catalytically active enzyme, immersed into a solution with the corresponding substrate, induce flow in the solution. Such systems are currently investigated as a promising direction in the development of self-powered micropumps that could operate autonomously within microfluidic devices. Here, we investigate the influence of confinement, within a slab of height H, on the response exhibited by silica tracer particles sedimented near a chemically active glucose oxidase patch which is immersed into a glucose solution of very low ionic strength. Irrespective of the value H, within the range explored in this study, a region depleted of tracers forms around the patch. When H is not much larger than the radius of the patch, the rate of growth of the depletion zone depends on H; somewhat surprisingly, this dependence is influenced by the glucose concentration. The results are discussed within the context of a simple model for a chemically active patch.

Chemically Active Particles: From One to Few on the Way to Many

Chemically active particles suspended in a liquid solution can achieve self-motility by locally changing the chemical composition of the solution via catalytic reactions at their surfaces. They operate intrinsically out of equilibrium, continuously extracting free energy from the environment to power the dissipative self-motility. The effective interactions involving active particles are, in general, nonreciprocal and anisotropic, even if the particles have simple shapes (e.g., Janus spheres). Accordingly, for chemically active particles a very rich behavior of collective motion and self-assembly may be expected to emerge, including phenomena such as microphase separation in the form of kinetically stable, finite-sized aggregates. Here, I succinctly review a number of recent experimental studies that demonstrate the self-assembly of structures, involving chemically active Janus particles, which exhibit various patterns of motion. These examples illustrate concepts such as "motors made out of motors" (as suggestively named by Fischer [Fischer, P. Nat. Phys. 2018, 14, 1072]). The dynamics of assembly and structure formation observed in these systems can provide benchmark, in-depth testing of the current understanding of motion and effective interactions produced by chemical activity. Finally, one notes that these significant achievements are likely just the beginning of the field. Recently reported particles endowed with time-dependent chemical activity or switchable reaction mechanisms open the way for exciting developments, such as periodic reshaping of self-assembled structures based on man-made internal clocks.

Exact Phoretic Interaction of Two Chemically Active Particles

We study the nonequilibrium interaction of two isotropic chemically active particles taking into account the exact near-field chemical interactions as well as hydrodynamic interactions. We identify regions in the parameter space wherein the dynamical system describing the two particles can have a fixed point-a phenomenon that cannot be captured under the far-field approximation. We find that, due to near-field effects, the particles may reach a stable equilibrium at a nonzero gap size or make a complex that can dissociate in the presence of sufficiently strong noise. We explicitly show that the near-field effects originate from a self-generated neighbor-reflected chemical gradient, similar to interactions of a self-propelling phoretic particle and a flat substrate.

Review: Interactions of Active Colloids with Passive Tracers

Collective phenomena existing universally in both biological systems and artificial active matter are increasingly attracting interest. The interactions can be grouped into active-active and active-passive ones, where the reports on the purely active system are still clearly dominating. Despite the growing interest, summarizing works for active-passive interactions in artificial active matter are still missing. For that reason, we start this review with a general introduction, followed by a short spotlight on theoretical works and then an extensive overview of experimental realizations. We classify the cases according to the active colloids’ mechanisms of motion and discuss the principles of the interactions. A few key applications of the active-passive interaction of current interest are also highlighted (such as cargo transport, flow field mapping, assembly of structures). We expect that this review will help the fundamental understanding and inspire further studies on active matter.

Which interactions dominate in active colloids?

Despite mounting evidence that the same gradients, which active colloids use for swimming, induce important cross-interactions (phoretic interactions), they are still ignored in most many-body descriptions, perhaps to avoid complexity and a zoo of unknown parameters. Here we derive a simple model, which reduces phoretic far-field interactions to a pair-interaction whose strength is mainly controlled by one genuine parameter (swimming speed). The model suggests that phoretic interactions are generically important for autophoretic colloids (unless effective screening of the phoretic fields is strong) and should dominate over hydrodynamic interactions for the typical case of half-coating and moderately nonuniform surface mobilities. Unlike standard minimal models, but in accordance with canonical experiments, our model generically predicts dynamic clustering in active colloids at a low density. This suggests that dynamic clustering can emerge from the interplay of screened phoretic attractions and active diffusion.