Modular approach to microswimming

Field-Driven Out-of-Equilibrium Collective Patterns for Swarm Micro-Robotics

Soft robotics has been rapidly advancing, offering significant improvements over traditional rigid robotic systems through the use of compliant materials that enhance adaptability and interaction with the environment. However, current approaches face critical challenges, including the reliance on complex "top-down" fabrication techniques and the difficulty of wireless powering and control at the microscale. Swarm robotics introduces a paradigm shift, leveraging collective dynamics to achieve cooperative and adaptable behaviors among multiple robotic units. Inspired by nature, this "bottom-up" approach enables swarm robots to execute task-specific reconfigurations, enhancing flexibility and robustness. Field-driven active colloids emerge as a promising platform for swarm microrobotics, capable of self-propulsion and self-organization into dynamic collective patterns under external field excitation and manipulation. These systems mimic biologically inspired swarm behaviors, such as flocking and vortex formation, providing a versatile foundation for designing innovative swarm microrobots. This review discusses the principles of electric and magnetic field-driven collective self-organization, focusing on the particle dynamics, the emergence of collective swarm patterns, and illustrative examples of functional swarm microrobots. It concludes with future perspectives on harnessing these systems for adaptive, scalable, and multifunctional microrobotic applications.

Metareview: a survey of active matter reviews

In the past years, the amount of research on active matter has grown extremely rapidly, a fact that is reflected in particular by the existence of more than 1000 reviews on this topic. Moreover, the field has become very diverse, ranging from theoretical studies of the statistical mechanics of active particles to applied work on medical applications of microrobots and from biological systems to artificial swimmers. This makes it very difficult to get an overview over the field as a whole. Here, we provide such an overview in the form of a metareview article that surveys the existing review articles and books on active matter. Thereby, this article provides a useful starting point for finding literature about a specific topic.

Weak Ion-Exchange Based Magnetic Swarm for Targeted Drug Delivery and Chemotherapy

Swimming microrobots that are actuated by multiple stimuli/fields display various intriguing collective behaviors, ranging from phase separation to clustering and giant number fluctuation; however, it is still chanllenging to achieve multiple responses and functionalities within one colloidal system to emulate high environmental adaptability and improved tasking capability of natural swarms. In this work, a weak ion-exchange based swarm is presented that can self-organize and reconfigure by chemical, light, and magnetic fields, showing living crystal, amorphous glass, liquid, chain, and wheel-like structures. By changing the frequency and strength of the rotating magnetic field, various well-controlled and fast transformations are obtained. Experiments show the high adaptability and functionality of the microrobot swarm in delivering drugs in confined spaces, such as narrow channels with turns or obstacles. The drug-carrying swarm exhibits excellent chemtherapy for Hela and CT26 cells due to the pH-enhanced drug release and locomotion. This reconfigurable microswarm provides a new platform for biomedical and environmental applications.

Electroosmotic flow spin tracers near chemical nano/micromotors

We report the first experimental observation of tracer spinning in place alongside chemically powered individual nano/micromotors. The torques are primarily generated by the electroosmotic flow on the motor surface. Such spinning is observed in various combinations of nano/micromotors and tracers of different shapes, sizes and chemical compositions.

Collective motion of Nafion-based micromotors in water

Ion exchange is one of the most interesting processes occurring at the interface between aqueous solutions and polymers, such as the well-known Nafion. If the exchanged ions have different diffusion coefficients, this interchange generates local electric fields which can be harnessed to drive fluid motion. In this work, we show how it is possible to design and fabricate self-propelling microswimmers based on Nafion, driven by ion-exchange, and fueled by innocuous salts. These Nafion micromotors are made using colloidal lithography by micro/nanostructuring Nafion in the form of asymmetric rods. These microswimmers exhibit fascinating collective motion in water driven by the interplay of their self-generated chemical/electric fields and their capability to pump matter nearby towards the collective motile structure. The pumping activity of the microswimmers induces the formation of growing mobile clusters, whose velocity increases with size. Such dynamic structures are able to trap nearby micro/nano-objects while purifying the liquid, which acts both as the transport media and as fuel. Such phenomenology opens the door to potential applications in water remediation that are currently under development.

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.

Non-monotonic speed-dependence of microswimmers on wall distance

While substrates naturally occur in most microswimmer experiments, their impact on the swimming performance is not well understood. In the present study, we functionalize substrates with polymer brushes of varying swelling properties, grafting densities and brush lengths to systematically modify and explore the substrate-swimmer interactions. Notably, the swimming speed does not monotonically change with brush thickness, but shows a distinct maximum at a certain intermediate thickness, which results from two counteracting factors: surface charge and surface roughness. The results show that the speed of thermophoretic microswimmers does not only depend on the particle properties but is also strongly influenced by the properties of the underlying substrate. This provides a route to control the speed of microswimmers via the underlying substrate, which could be applied in the future e.g. to design complex motility landscapes by patterning substrates with polymer brushes. It is expected that similar effects would occur for diffusio- and electrophoretic particles.

Self-Propelling Hybrid Gels Incorporating an Active Self-Assembled, Low-Molecular-Weight Gelator

Hybrid gel beads based on combining a low-molecular-weight gelator (LMWG) with a polymer gelator (PG) demonstrate an enhanced ability to self-propel in water, with the LMWG playing an active role. Hybrid gel beads were loaded with ethanol and shown to move in water owing to the Marangoni effect changes in surface tension caused by the expulsion of ethanol - smaller beads move farther and faster than larger beads. Flat shapes of the hybrid gel were cut using a "stamp" - circles moved the furthest, whereas stars showed more rotation on their own axes. Comparing hybrid LMWG/PG gel beads with PG-only beads demonstrated that the LMWG speeds up the beads, enhancing the rate of self-propulsion. Self-assembly of the LMWG into a "solid-like" network prevents its leaching from the gel. The LMWG also retains its own unique function - specifically, remediating methylene blue pollutant dye from basic water as a result of noncovalent interactions. The mobile hybrid beads accumulate this dye more effectively than PG-only beads. Self-propelling gel beads have potential applications in removal/delivery of active agents in environmental or biological settings. The ability of self-assembling LMWGs to enhance mobility and control removal/delivery suggests that adding them to self-propelling systems can add significant value.

High-order simulation scheme for active particles driven by stress boundary conditions

We study the dynamics and interactions of elliptic active particles in a two dimensional solvent. The particles are self-propelled through prescribing a fluid stress at one half of the fluid-particle boundary. The fluid is treated explicitly solving the Stokes equation through a discontinuous Galerkin scheme, which allows to simulate strictly incompressible fluids. We present numerical results for a single particle and give an outlook on how to treat suspensions of interacting active particles.

Vorticity Determines the Force on Bodies Immersed in Active Fluids

When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this motion to the density and current induced by-but far away from-the body. In general, the force is composed of two contributions: due to the strength of the dipolar field component and due to particles leaving the boundary, generating a nonvanishing vorticity of the polarization. We derive and numerically corroborate results for periodic systems, which are fundamentally different from unbounded systems with forces that scale with the area of the system. We demonstrate that vorticity is localized close to the body and to points at which the local curvature changes, enabling the rational design of particle shapes with desired propulsion properties.

Shaping the gradients driving phoretic micro-swimmers: influence of swimming speed, budget of carbonic acid and environment

pH gradient-driven modular micro-swimmers are investigated as a model for a large variety of quasi-two-dimensional chemi-phoretic self-propelled entities. Using three-channel micro-photometry, we obtain a precise large field mapping of pH at a spatial resolution of a few microns and a pH resolution of [Formula: see text] units for swimmers of different velocities propelling on two differently charged substrates. We model our results in terms of solutions of the three-dimensional advection-diffusion equation for a 1:1 electrolyte, i.e. carbonic acid, which is produced by ion exchange and consumed by equilibration with dissolved [Formula: see text]. We demonstrate the dependence of gradient shape and steepness on swimmer speed, diffusivity of chemicals, as well as the fuel budget. Moreover, we experimentally observe a subtle, but significant feedback of the swimmer's immediate environment in terms of a substrate charge-mediated solvent convection. We discuss our findings in view of different recent results from other micro-fluidic or active matter investigations. We anticipate that they are relevant for quantitative modelling and targeted applications of diffusio-phoretic flows in general and artificial micro-swimmers in particular.

Ion-exchange enabled synthetic swarm

Active matters are out-of-equilibrium systems that convert energy from the environment to mechanical motion. Non-reciprocal interaction between active matters may lead to collective intelligence beyond the capability of individuals. In nature, such emergent behaviours are ubiquitously observed in animal colonies, giving these species remarkable adaptive capability. In artificial systems, however, the emergence of non-trivial collective intelligent dynamics remains undiscovered. Here we show that a simple ion-exchange reaction can couple self-propelled ZnO nanorods and sulfonated polystyrene microbeads together. Chemical communication is established that enhances the reactivity and motion of both nanorods and the microbeads, resulting in the formation of an active swarm of nanorod-microbead complexes. We demonstrate that the swarm is capable of macroscopic phase segregation and intelligent consensus decision-making.

Active Assembly of Spheroidal Photocatalytic BiVO4 Microswimmers

We create single-component photocatalytic bismuth vanadate (BiVO₄) microswimmers with a spheroidal shape that move individually upon irradiation without any asymmetrization step. These particles form active assemblies which we investigate combining an experimental approach with numerical simulations and analytical calculations. We systematically explore the speed and assembly of the swimmers into clusters of up to four particles and find excellent agreement between experiment and theory, which helps us to understand motion patterns and speed trends. Moreover, different batches of particles can be functionalized separately, making them ideal candidates to fulfill a multitude of tasks, such as sensing or environmental remediation. To exemplify this, we coat our swimmers with silica (SiO₂) and selectively couple some of their modules to fluorophores in a way which does not inhibit self-propulsion. The present work establishes spheroidal BiVO₄ microswimmers as a versatile platform to design multifunctional microswimmers.

Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere

The main goal of the current work was to study the coupled mechanism of thermophoretic transportation and mixed convection flow around the surface of the sphere. To analyze the characteristics of heat and fluid flow in the presence of thermophoretic transportation, a mathematical model in terms of non-linear coupled partial differential equations obeying the laws of conservation was formulated. Moreover, the mathematical model of the proposed phenomena was approximated by implementing the finite difference scheme and boundary value problem of fourth order code BVP4C built-in scheme. The novelty point of this paper is that the primitive variable formulation is introduced to transform the system of partial differential equations into a primitive form to make the line of the algorithm smooth. Secondly, the term thermophoretic transportation in the mass equation is introduced in the mass equation and thus the effect of thermophoretic transportation can be calculated at different positions of the sphere. Basically, in this study, some favorite positions around the sphere were located, where the velocity field, temperature distribution, mass concentration, skin friction, and rate of heat transfer can be calculated simultaneously without any separation in flow around the surface of the sphere.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

A practical guide to active colloids: choosing synthetic model systems for soft matter physics research

Synthetic active colloids that harvest energy stored in the environment and swim autonomously are a popular model system for active matter. This emerging field of research sits at the intersection of materials chemistry, soft matter physics, and engineering, and thus cross-talk among researchers from different backgrounds becomes critical yet difficult. To facilitate this interdisciplinary communication, and to help soft matter physicists with choosing the best model system for their research, we here present a tutorial review article that describes, in appropriate detail, six experimental systems of active colloids commonly found in the physics literature. For each type, we introduce their background, material synthesis and operating mechanisms and notable studies from the soft matter community, and comment on their respective advantages and limitations. In addition, the main features of each type of active colloid are summarized into two useful tables. As materials chemists and engineers, we intend for this article to serve as a practical guide, so those who are not familiar with the experimental aspects of active colloids can make more informed decisions and maximize their creativity.

Collective forces in scalar active matter

Large-scale collective behavior in suspensions of active particles can be understood from the balance of statistical forces emerging beyond the direct microscopic particle interactions. Here we review some aspects of the collective forces that can arise in suspensions of self-propelled active Brownian particles: wall forces under confinement, interfacial forces, and forces on immersed bodies mediated by the suspension. Even for non-aligning active particles, these forces are intimately related to a non-uniform polarization of particle orientations induced by walls and bodies, or inhomogeneous density profiles. We conclude by pointing out future directions and promising areas for the application of collective forces in synthetic active matter, as well as their role in living active matter.

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.

Analysis of the Vertical Driving Performance of Multiple Connected Pipe-Climbing Microrobots with Magnetic Wheels

In this study, we analyzed the vertical driving performance of multiple connected magnetic wheel-driven microrobots when moving up and down a small cylinder that simulated a pipe. The dynamics of pipe climbing by the magnetic wheel-driven microrobot were analyzed considering the magnetic attraction force and slip; a vertical climbing simulator was developed considering the hoop force and external force from the adjacent microrobots to determine the magnetic attraction force required for multiple connected microrobot pipe climbing. A prototype of an independent vertical climbing microrobot, 5 mm long, 9 mm wide, and 6.5 mm high, and prototypes of 10 microrobots were manufactured to evaluate the vertical driving performance. The usefulness was verified by showing that three driving microrobots can move seven non-driving microrobots comprising 60% of their own weight up and down along a small cylinder.

Comparing Models of Lateral Station-Keeping for Pitching Hydrofoils

Fish must maneuver laterally to maintain their position in schools or near solid boundaries. Unsteady hydrodynamic models, such as the Theodorsen and Garrick models, predict forces on tethered oscillating hydrofoils aligned with the incoming flow. How well these models predict forces when bio-inspired hydrofoils are free to move laterally or when angled relative to the incoming flow is unclear. We tested the ability of five linear models to predict a small lateral adjustment made by a hydrofoil undergoing biased pitch oscillations. We compared the models to water channel tests in which air bushings gave a rigid pitching hydrofoil lateral freedom. What we found is that even with no fitted coefficients, linear models predict some features of the lateral response, particularly high frequency features like the amplitude and phase of passive heave oscillations. To predict low frequency features of the response, such as overshoot and settling time, we needed a semiempirical model based on tethered force measurements. Our results suggest that fish and fish-inspired vehicles could use linear models for some aspects of lateral station-keeping, but would need nonlinear or semiempirical wake models for more advanced maneuvers.

Dynamics of Binary Active Clusters Driven by Ion-Exchange Particles

We present a framework to quantitatively predict the linear and rotational directed motion of synthetic modular microswimmers. To this end, we study binary dimers and characterize their approach motion as effective interactions within a minimal model. We apply this framework to the assembly of small aggregates composed of a cationic ion-exchange particle with up to five passive particles or anionic ion-exchange particles at dilute conditions. Particles sediment and move close to a substrate, above which the ion-exchange particles generate flow. This flow mediates long-range attractions leading to a slow collapse during which long-lived clusters of a few particles assemble. The effective interactions between unlike particles break Newton's third law. Depending on their symmetry, assemblies thus can become linear or circle swimmers, or remain inert (no directed motion).

Colloidal electro-phoresis in the presence of symmetric and asymmetric electro-osmotic flow

We characterize the electro-phoretic motion of charged sphere suspensions in the presence of substantial electro-osmotic flow using a recently introduced small angle super-heterodyne dynamic light scattering instrument (ISASH-LDV). Operation in integral mode gives access to the particle velocity distribution over the complete cell cross-section. Obtained Doppler spectra are evaluated for electro-phoretic mobility, wall electro-osmotic mobility and particle diffusion coefficient. Simultaneous measurements of differing electro-osmotic mobilities leading to asymmetric solvent flow are demonstrated in a custom made electro-kinetic cell fitting standard microscopy slides as exchangeable sidewalls. The scope and range of our approach are discussed demonstrating the possibility of an internal calibration standard and using the simultaneously measured electro-kinetic mobilities in the interpretation of a microfluidic pumping experiment involving an inhomogeneous electric field and a complex solvent flow pattern.