Bimetallic Microswimmers Speed Up in Confining Channels

Motion control of chemically powered colloidal motors

Chemically powered colloidal motors can convert chemical energy into directional mechanical movement, making them promising for applications such as targeted drug delivery, environmental decontamination, and precision disease treatment. However, their self-propulsion is constantly disrupted by random Brownian motion, making precise control under low Reynolds number conditions highly challenging. This review provides a brief overview of the three main propulsion mechanisms of chemically powered colloidal motors. It also summarizes recent advances in motion control, including speed regulation and trajectory navigation. Finally, we discuss future directions for achieving more precise motion control. We hope this review will inspire further research on developing more effective and practical control strategies for colloidal motors.

Gating and tunable confinement of active colloids within patterned environments

Active colloidal particles typically exhibit a pronounced affinity for accumulating and being captured at boundaries. Here, we engineer long-range repulsive interactions between colloids that self-propel under an electric field and patterned obstacles. As a result of these interactions, particles turn away from obstacles and avoid accumulation. We show that by tuning the applied field frequency, we precisely and rapidly control the effective size of the obstacles and therefore modulate the particle approach distance. This feature allows us to achieve gating and tunable confinement of our active particles whereby they can access regions between obstacles depending on the applied field. Our work provides a versatile means to directly control confinement and organization, paving the way towards applications such as sorting particles based on motility or localizing active particles on demand.

Quantifying and understanding the tilt of a Pt Janus active colloid near solid walls

Active colloids powered by self-generated gradients are influenced by nearby solid boundaries, leading to their reorientation. In this study, the tilt angles (the angle between where an active colloid moves and where it faces) were measured to be 13.3° and -33.9° for 5 μm polystyrene microspheres half coated with 10 nm Pt caps moving in 5% H2O2 along the bottom and top glass wall, respectively, indicating that the colloids moved with their PS (forward) caps tilted slightly toward the wall. The speeds and tilt angles of Pt Janus colloids increased consistently with increasing H2O2 concentration (0.5 to 10 v/v%) and Pt cap thickness (5 to 50 nm). We propose that the tilt results from a balance between gravitational torque (caused by the Pt cap's weight) and chemical activity-induced torque (from self-generated chemical gradients), qualitatively supported by finite element simulations based on self-electrophoresis. Our findings are useful for understanding how chemically active colloids move in, and interact with, their environment.

Gout management using uricase and sodium citrate hollow mesoporous nanomotors

Uricase (UOx)-based gout treatments are generally limited due in part to the accumulation of H2O2 in an arthrosis environment characterized by a sluggish metabolism. Here we develop a self-cascade nanomotor with high efficiency toward simultaneous uric acid (UA) degradation and H2O2 elimination on the basis of UOx and sodium citrate loading in amine functionalized hollow mesoporous silica nanoparticles (AHMSNs). Due to the inherent asymmetry of AHMSNs, the developed nanomotors can be actuated by ionic diffusiophoresis induced by the enzymatic UA degradation, thus enlarging the diffusion range within the joint cavity. H2O2 generated during UA decomposition can be simultaneously eliminated by the loaded sodium citrate, resulting in a considerable improvement in mammalian cell viability. In vivo studies display powerful therapeutic effect in gouty models using this self-cascade nanomotor system. These results present the potential of nanomotors as active therapeutic agents for gout, providing a perspective on the application of enzyme-driven micro/nanomotors.

Swimming Modes of Bacteria Escaping from a Soft Confined Space

Navigating through soft and highly confined environments is crucial for bacteria moving within living organisms' tissues, yet this topic has been less explored. In our study, we experimentally harnessed the unique biconcave geometry of red blood cells (RBCs) to enable real-time visualization of swimming Escherichia coli interacting with soft RBCs. Our findings show that RBCs adhering to a rigid surface can enclose spaces comparable to the size of bacteria, effectively entrapping them. Remarkably, we found that bacteria can escape from this extremely confined space through three newly defined escape modes: Bundling, Unbundling, and Flipping, each mode relying on the specific states of bacterial flagella. A quantitative analysis uncovers significant differences among these modes in terms of scattering angle, escaping speed, and trapping duration. We used two methods to alter the rigidity and adhesion strength of RBCs, and we studied their effects on the detailed bacterial escape process. Our results contribute to the knowledge of bacterial migration in soft, confined spaces, thereby enhancing our understanding of similar processes in biological tissue environments.

Orbits, Spirals, and Trapped States: Dynamics of a Phoretic Janus Particle in a Radial Concentration Gradient

A long-standing goal in colloidal active matter is to understand how gradients in fuel concentration influence the motion of phoretic Janus particles. Here, we present a theoretical description of the motion of a spherical phoretic Janus particle in the presence of a radial gradient of the chemical solute driving self-propulsion. Radial gradients are a geometry relevant to many scenarios in active matter systems and naturally arise due to the presence of a point source or sink of fuel. We derive an analytical solution for the Janus particle's velocity and quantify the influence of the radial concentration gradient on the particle's trajectory. Compared to a phoretic Janus particle in a linear gradient in fuel concentration, we uncover a much richer set of dynamic behaviors including circular orbits and trapped stationary states. We identify the ratio of the phoretic mobilities between the two domains of the Janus particle as a central quantity in tuning their dynamics. Our results provide a path for developing optimum protocols for tuning the dynamics of phoretic Janus particles and mixing fluid at the microscale. In addition, this work suggests a method for quantifying the surface properties of phoretic Janus particles, which have proven to be challenging to probe experimentally.

Thermodynamic Effects Are Essential for Surface Entrapment of Bacteria

The entrapment of bacteria near boundary surfaces is of biological and practical importance, yet the underlying physics is not well understood. We demonstrate that it is crucial to include a commonly neglected thermodynamic effect related to the spatial variation of hydrodynamic interactions, through a model that provides analytic explanation of bacterial entrapment in two dimensionless parameters: α_{1} the ratio of thermal energy to self-propulsion, and α_{2} an intrinsic shape factor. For α_{1} and α_{2} that match an Escherichia coli at room temperature, our model quantitatively reproduces existing experimental observations, including two key features that have not been previously resolved: The bacterial "nose-down" configuration, and the anticorrelation between the pitch angle and the wobbling angle. Furthermore, our model analytically predicts the existence of an entrapment zone in the parameter space defined by {α_{1},α_{2}}.

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

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

Chemical Micromotors Move Faster at Oil-Water Interfaces

Many real-world scenarios involve interfaces, particularly liquid-liquid interfaces, that can fundamentally alter the dynamics of colloids. This is poorly understood for chemically active colloids that release chemicals into their environment. We report here the surprising discovery that chemical micromotors─colloids that convert chemical fuels into self-propulsion─move significantly faster at an oil-water interface than on a glass substrate. Typical speed increases ranged from 3 to 6 times up to an order of magnitude and were observed for different types of chemical motors and interfaces made with different oils. Such speed increases are likely caused by faster chemical reactions at an oil-water interface than at a glass-water interface, but the exact mechanism remains unknown. Our results provide valuable insights into the complex interactions between chemical micromotors and their environments, which are important for applications in the human body or in the removal of organic pollutants from water. In addition, this study also suggests that chemical reactions occur faster at an oil-water interface and that micromotors can serve as a probe for such an effect.

Acoustically Powered Nano- and Microswimmers: From Individual to Collective Behavior

Micro- and nanoscopic particles that swim autonomously and self-assemble under the influence of chemical fuels and external fields show promise for realizing systems capable of carrying out large-scale, predetermined tasks. Different behaviors can be realized by tuning swimmer interactions at the individual level in a manner analogous to the emergent collective behavior of bacteria and mammalian cells. However, the limited toolbox of weak forces with which to drive these systems has made it difficult to achieve useful collective functions. Here, we review recent research on driving swimming and particle self-organization using acoustic fields, which offers capabilities complementary to those of the other methods used to power microswimmers. With either chemical or acoustic propulsion (or a combination of the two), understanding individual swimming mechanisms and the forces that arise between individual particles is a prerequisite to harnessing their interactions to realize collective phenomena and macroscopic functionality. We discuss here the ingredients necessary to drive the motion of microscopic particles using ultrasound, the theory that describes that behavior, and the gaps in our understanding. We then cover the combination of acoustically powered systems with other cross-compatible driving forces and the use of ultrasound in generating collective behavior. Finally, we highlight the demonstrated applications of acoustically powered microswimmers, and we offer a perspective on the state of the field, open questions, and opportunities. We hope that this review will serve as a guide to students beginning their work in this area and motivate others to consider research in microswimmers and acoustic fields.

Open Questions of Chemically Powered Nano- and Micromotors

Chemically powered nano- and micromotors are microscopic devices that convert chemical energy into motion. Interest in these motors has grown over the past 20 years because they exhibit interesting collective behaviors and have found potential uses in biomedical and environmental applications. Understanding how these motors operate both individually and collectively and how environments affect their operation is of both fundamental and applied significance. However, there are still significant gaps in our knowledge. This Perspective highlights several open questions regarding the propulsion mechanisms of, interactions among, and impact of confinements on nano- and micromotors driven by self-generated chemical gradients. These questions are based on my own experience as an experimentalist. For each open question, I describe the problem and its significance, analyze the status-quo, identify the bottleneck problem, and propose potential solutions. An underlying theme for these questions is the interplay among reaction kinetics, physicochemical distributions, and fluid flows. Unraveling this interplay requires careful measurements as well as a close collaboration between experimentalists and theoreticians/numerical experts. The interdisciplinary nature of these challenges suggests that their solutions could bring new revelations and opportunities across disciplines such as colloidal sciences, material sciences, soft matter physics, robotics, and beyond.

Active self-assembly of colloidal machines with passive rotational parts via coordination of phoresis and osmosis

The organization of microscopic objects into specific structures with movable parts is a prerequisite for building sophisticated micromachines with complex functions, as exemplified by their macroscopic counterparts. Here we report the self-assembly of active and passive colloids into micromachinery with passive rotational parts. Depending on the attachment of the active colloid to a substrate, which varies the degrees of free freedom of the assembly, colloidal machines with rich internal rotational dynamics are realized. Energetic analysis reveals that the energy efficiency increases with the degrees of freedom of the machine. The experimental results can be rationalized by the cooperation of phoretic interaction and osmotic flow encoded in the shape of the active colloid, which site-specifically binds and exerts a torque to passive colloids, supported by finite element calculations and mesoscale simulations. Our work offers a new design principle that utilizes nonequilibrium interfacial phenomena for spontaneous construction of multiple-component reconfigurable micromachinery.

A Versatile Method for Synthesis of Light-Activated, Magnet-Steerable Organic–Inorganic Hybrid Active Colloids

The immense potential of active colloids in practical applications and fundamental research calls for an efficient method to synthesize active colloids of high uniformity. Herein, a facile method is reported to synthesize uniform organic–inorganic hybrid active colloids based on the wetting effect of polystyrene (PS) with photoresponsive inorganic nanoparticles in a tetrahydrofuran/water mixture. The results show that a range of dimer active colloids can be produced by using different inorganic components, such as AgCl, ZnO, TiO2, and Fe2O3 nanoparticles. Moreover, the strategy provides a simple way to prepare dual-drive active colloids by a rational selection of the starting organic materials, such as magnetic PS particles that result in light and magnet dual-drive active colloids. The motions of these active colloids are quantified, and well-controlled movements are demonstrated.

Steering Micromotors via Reprogrammable Optoelectronic Paths

Steering micromotors is important for using them in practical applications and as model systems for active matter. This functionality often requires magnetic materials in the micromotor, taxis behavior of the micromotor, or the use of specifically designed physical boundaries. Here, we develop an optoelectronic strategy that steers micromotors with programmable light patterns. In this strategy, light illumination turns hydrogenated amorphous silicon conductive, generating local electric field maxima at the edge of the light pattern that attracts micromotors via positive dielectrophoresis. As an example, metallo-dielectric Janus microspheres that self-propelled under alternating current electric fields were steered by static light patterns along customized paths and through complex microstructures. Their long-term directionality was also rectified by ratchet-shaped light patterns. Furthermore, dynamic light patterns that varied in space and time enabled more advanced motion controls such as multiple motion modes, parallel control of multiple micromotors, and the collection and transport of motor swarms. This optoelectronic steering strategy is highly versatile and compatible with a variety of micromotors, and thus it possesses the potential for their programmable control in complex environments.

Squirmer hydrodynamics near a periodic surface topography

The behaviour of microscopic swimmers has previously been explored near large-scale confining geometries and in the presence of very small-scale surface roughness. Here, we consider an intermediate case of how a simple microswimmer, the tangential spherical squirmer, behaves adjacent to singly and doubly periodic sinusoidal surface topographies that spatially oscillate with an amplitude that is an order of magnitude less than the swimmer size and wavelengths that are also within an order of magnitude of this scale. The nearest neighbour regularised Stokeslet method is used for numerical explorations after validating its accuracy for a spherical tangential squirmer that swims stably near a flat surface. The same squirmer is then introduced to different surface topographies. The key governing factor in the resulting swimming behaviour is the size of the squirmer relative to the surface topography wavelength. For instance, directional guidance is not observed when the squirmer is much larger, or much smaller, than the surface topography wavelength. In contrast, once the squirmer size is on the scale of the topography wavelength, limited guidance is possible, often with local capture in the topography troughs. However, complex dynamics can also emerge, especially when the initial configuration is not close to alignment along topography troughs or above topography crests. In contrast to sensitivity in alignment and topography wavelength, reductions in the amplitude of the surface topography or variations in the shape of the periodic surface topography do not have extensive impacts on the squirmer behaviour. Our findings more generally highlight that the numerical framework provides an essential basis to elucidate how swimmers may be guided by surface topography.

Controlled propulsion of micro/nanomotors: operational mechanisms, motion manipulation and potential biomedical applications

Inspired by natural mobile microorganisms, researchers have developed micro/nanomotors (MNMs) that can autonomously move by transducing different kinds of energies into kinetic energy. The rapid development of MNMs has created tremendous opportunities for biomedical fields including diagnostics, therapeutics, and theranostics. Although the great progress has been made in MNM research, at a fundamental level, the accepted propulsion mechanisms are still a controversial matter. In practical applications such as precision nanomedicine, the precise control of the motion, including the speed and directionality, of MNMs is also important, which makes advanced motion manipulation desirable. Very recently, diverse MNMs with different propulsion strategies, morphologies, sizes, porosities and chemical structures have been fabricated and applied for various uses. Herein, we thoroughly summarize the physical principles behind propulsion strategies, as well as the recent advances in motion manipulation methods and relevant biomedical applications of these MNMs. The current challenges in MNM research are also discussed. We hope this review can provide a bird's eye overview of the MNM research and inspire researchers to create novel and more powerful MNMs.

Confined Motion: Motility of Active Microparticles in Cell-Sized Lipid Vesicles

Active materials can transduce external energy into kinetic energy at the nano and micron length scales. This unique feature has sparked much research, which ranges from achieving fundamental understanding of their motility to the assessment of potential applications. Traditionally, motility is studied as a function of internal features such as particle topology, while external parameters such as energy source are assessed mainly in bulk. However, in real-life applications, confinement plays a crucial role in determining the type of motion active particles can adapt. This feature has been however surprisingly underexplored experimentally. Here, we showcase a tunable experimental platform to gain an insight into the dynamics of active particles in environments with restricted 3D topology. Particularly, we examined the autonomous motion of coacervate micromotors confined in giant unilamellar vesicles (GUVs) spanning 10–50 μm in diameter and varied parameters including fuel and micromotor concentration. We observed anomalous diffusion upon confinement, leading to decreased motility, which was more pronounced in smaller compartments. The results indicate that the theoretically predicted hydrodynamic effect dominates the motion mechanism within this platform. Our study provides a versatile approach to understand the behavior of active matter under controlled, compartmentalized conditions.

Activity-induced interactions and cooperation of artificial microswimmers in one-dimensional environments

Cooperative motion in biological microswimmers is crucial for their survival as it facilitates adhesion to surfaces, formation of hierarchical colonies, efficient motion, and enhanced access to nutrients. Here, we confine synthetic, catalytic microswimmers along one-dimensional paths and demonstrate that they too show a variety of cooperative behaviours. We find that their speed increases with the number of swimmers, and that the activity induces a preferred distance between swimmers. Using a minimal model, we ascribe this behavior to an effective activity-induced potential that stems from a competition between chemical and hydrodynamic coupling. These interactions further induce active self-assembly into trains where swimmers move at a well-separated, stable distance with respect to each other, as well as compact chains that can elongate, break-up, become immobilized and remobilized. We identify the crucial role that environment morphology and swimmer directionality play on these highly dynamic chain behaviors. These activity-induced interactions open the door toward exploiting cooperation for increasing the efficiency of microswimmer motion, with temporal and spatial control, thereby enabling them to perform intricate tasks inside complex environments.

Biological microswimmers such as bacteria show collective motion that is made possible by an intricate interplay of sensing and signaling. Ketzetzi et al. reproduce this phenomenon in a catalytic system undergoing, for instance, cooperative speed-ups and dynamic reconfiguration of microswimmer chains.

Upstream Rheotaxis of Catalytic Janus Spheres

Fluid flow is ubiquitous in many environments that form habitats for microorganisms. Therefore, it is not surprising that both biological and artificial microswimmers show responses to flows that are determined by the interplay of chemical and physical factors. In particular, to deepen the understanding of how different systems respond to flows, it is crucial to comprehend the influence played by swimming pattern. The tendency of organisms to navigate up or down the flow is termed rheotaxis. Early theoretical studies predicted a positive rheotactic response for puller-type spherical Janus micromotors. However, recent experimental studies have focused on pusher-type Janus particles, finding that they exhibit cross-stream migration in externally applied flows. To study the response to the flow of swimmers with a qualitatively different flow pattern, we introduce Cu@SiO₂ micromotors that swim toward their catalytic cap. On the basis of experimental observations, and supported by flow field calculations using a model for self-electrophoresis, we hypothesize that they behave effectively as a puller-type system. We investigate the effect of externally imposed flow on these spherically symmetrical Cu@SiO₂ active Janus colloids, and we indeed observe a steady upstream directional response. Through a simple squirmer model for a puller, we recover the major experimental observations. Additionally, the model predicts a "jumping" behavior for puller-type micromotors at high flow speeds. Performing additional experiments at high flow speeds, we capture this phenomenon, in which the particles "roll" with their swimming axes aligned to the shear plane, in addition to being dragged downstream by the fluid flow.

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.

A Practical Guide to Analyzing and Reporting the Movement of Nanoscale Swimmers

The recent invention of nanoswimmers-synthetic, powered objects with characteristic lengths in the range of 10-500 nm-has sparked widespread interest among scientists and the general public. As more researchers from different backgrounds enter the field, the study of nanoswimmers offers new opportunities but also significant experimental and theoretical challenges. In particular, the accurate characterization of nanoswimmers is often hindered by strong Brownian motion, convective effects, and the lack of a clear way to visualize them. When coupled with improper experimental designs and imprecise practices in data analysis, these issues can translate to results and conclusions that are inconsistent and poorly reproducible. This Perspective follows the course of a typical nanoswimmer investigation from synthesis through to applications and offers suggestions for best practices in reporting experimental details, recording videos, plotting trajectories, calculating and analyzing mobility, eliminating drift, and performing control experiments, in order to improve the reliability of the reported results.

Collective Entrainment and Confinement Amplify Transport by Schooling Microswimmers

Microswimmers can serve as cargo carriers that move deep inside complex flow networks. When a school collectively entrains the surrounding fluid, their transport capacity can be enhanced. This effect is quantified with good agreement between experiments with self-propelled droplets and a confined Brinkman squirmer model. The volume of liquid entrained can be much larger than the droplet itself, amplifying the effective cargo capacity over an order of magnitude, even for dilute schools. Hence, biological and engineered swimmers can efficiently transport materials into confined environments.

An effective and efficient model of the near-field hydrodynamic interactions for active suspensions of bacteria

Active suspensions of microswimmers demonstrate novel emergent behaviors (self-organizations, active turbulence, etc.) on macroscopic length scales. For such systems with, minimally, thousands of microswimmers, direct numerical simulations of the hydrodynamic interactions are computationally infeasible, and reduced models are needed. We demonstrated that existing models are not satisfactory in describing the hydrodynamic interactions for microswimmers in close proximity with even qualitatively erroneous predictions, indicating a pressing need for an adequate model. We propose a model that is both physically effective and computationally efficient in describing such hydrodynamics. The main novelty of our model is the description of hydrodynamic interactions through a resistance tensor, as opposed to an effective steric interaction in existing models.

Near-field hydrodynamic interactions in active fluids are essential to determine many important emergent behaviors observed, but have not been successfully modeled so far. In this work, we propose an effective model capturing the essence of the near-field hydrodynamic interactions through a tensorial coefficient of resistance, validated numerically by a pedagogic model system consisting of an Escherichia coli bacterium and a passive sphere. In a critical test case that studies the scattering angle of the bacterium–sphere pair dynamics, we prove that the near-field hydrodynamics can make a qualitative difference even for this simple two-body system: Calculations based on the proposed model reveal a region in parameter space where the bacterium is trapped by the passive sphere, a phenomenon that is regularly observed in experiments but cannot be explained by any existing model. In the end, we demonstrate that our model also leads to efficient simulation of active fluids with tens of thousands of bacteria, sufficiently large for investigations of many emergent behaviors.

Active colloids under geometrical constraints in viscoelastic media

We study the behavior of active particles (APs) moving in a viscoelastic fluid in the presence of geometrical confinements. Upon approaching a flat wall, we find that APs slow down due to compression of the enclosed viscoelastic fluid. In addition, they receive a viscoelastic torque leading to sudden orientational changes and departure from walls. Based on these observations, we develop a numerical model which can also be applied to other geometries and yields good agreement with experimental data. Our results demonstrate, that APs are able to move through complex geometrical structures more effectively when suspended in a viscoelastic compared to a Newtonian fluid.

Bio-inspired Acousto-magnetic Microswarm Robots with Upstream Motility

The ability to propel against flows, i.e., to perform positive rheotaxis, can provide exciting opportunities for applications in targeted therapeutics and non-invasive surgery. To date, no biocompatible technologies exist for navigating microparticles upstream when they are in a background fluid flow. Inspired by many naturally- occurring microswimmers such as bacteria, spermatozoa, and plankton that utilize the non-slip boundary conditions of the wall to exhibit upstream propulsion, here, we report on the design and characterization of self-assembled microswarms that can execute upstream motility in a combination of external acoustic and magnetic fields. Both acoustic and magnetic fields are safe to humans, non-invasive, can penetrate deeply into the human body, and are well-developed in clinical settings. The combination of both fields can overcome the limitations encountered by single actuation methods. The design criteria of the acoustically-induced reaction force of the microswarms, which is needed to perform rolling-type motion, are discussed. We show quantitative agreement between experimental data and our model that captures the rolling behaviour. The upstream capability provides a design strategy for delivering small drug molecules to hard-to-reach sites and represents a fundamental step toward the realization of micro- and nanosystem-navigation against the blood flow.

Confined Bubble-Propelled Microswimmers in Capillaries: Wall Effect, Fuel Deprivation, and Exhaust Product Excess

Self-propelled autonomous nano/microswimmers are at the forefront of materials science. These swimmers are expected to operate in highly confined environments, such as between the grains of soil or in the capillaries of the human organism. To date, little attention is paid to the problem that in such a confined environment the fuel powering catalytic nano/microswimmers can be exhausted quickly and the space can be polluted with the product of the catalytic reaction. In addition, the motion of the nano/microswimmers may be influenced by the confinement. These issues are addressed here, showing the influence of the size of the capillary and length of the micromotor on the motion and the influence of the depletion of the fuel and excess of the exhaust products. Theoretical modeling is provided as well to bring further insight into the observations. This article shows challenges that these systems face and stimulates research to overcome them.

Rod separation by sawtooth channel

By applying entropic barriers, we present a rod separation mechanism that induces the movement of rods of different sizes in the opposite directions. This mechanism is based on the combination of the saw-tooth channel, a static force, and an oscillating driving force. The asymmetric shape of the channel and the elongated shape of the rod causesa complicated interaction effect between the rods and the channel walls which reduces the accessible configuration space for the rods and leads to entropic free-energy effects.

Self-Diffusiophoresis of Slender Catalytic Colloids

We consider the self-diffusiophoresis of axisymmetric particles using a continuum description where the interfacial chemical reaction is modeled by first-order kinetics with a prescribed axisymmetric distribution of rate-constant magnitude. We employ the standard macroscale framework where the interaction of solute molecules with the particle boundary is represented by diffusio-osmotic slip. The dimensionless problem governing the solute transport involves two parameters (the particle slenderness ϵ and the Damköhler number Da) as well as two arbitrary functions which describe the axial distributions of the particle shape and rate-constant magnitude. The resulting particle speed is determined throughout the solution of the accompanying problem governing the flow about the force-free particle. Motivated by experimental configurations, we employ slender-body theory to investigate the asymptotic limit ϵ ≪ 1. In doing so, we seek algebraically accurate approximations where the asymptotic error is smaller than a positive power of ϵ. The resulting approximations are thus significantly more useful than those obtained in the conventional manner, where the asymptotic expansion is carried out in inverse powers of ln ϵ. The price for that utility is that two linear integral equations need to be solved: one governing the axial solute-sink distribution and the other governing the axial distribution of Stokeslets. When restricting the analysis to spheroidal particles, no need arises to solve for the Stokeslet distribution. The integral equation governing the solute-sink distribution is then solved using a numerical finite-difference scheme. This solution is supplemented by a large-Da asymptotic analysis, wherein a subtle nonuniformity necessitates a careful treatment of the regions near the particle ends. The simple approximations thereby obtained are in excellent agreement with the numerical solution.

Shape- and Material-Dependent Self-Propulsion of Photocatalytic Active Colloids, Interfacial Effects, and Dynamic Interparticle Interactions

Active colloids powered by self-generated, local chemical concentration gradients exhibit dynamics that are a function of the particles' morphology and material properties. These characteristics also govern how the active colloids interact with surfaces, including other particles and nearby walls. Thus, by targeted design, the dynamic behavior, on average, can be engineered, despite a lack of "external" control such as an applied magnetic field. This allows for the development of new applications and the investigation of novel effects that arise when self-propelled active colloids have complex shapes and material composition. Here, we explore some of our recent work on this topic including the dynamics and interactions of photoactivated, self-propelled colloids with such multifaceted properties. We also delve into some special cases, such as a new variety of active particle-particle interaction that we recently developed, in which direct contact between the active colloids is forbidden, and the direction of propulsion for pairs of particles is correlated. The unifying theme of the work highlighted herein is the relationship between the physical, chemical, and material properties of active colloids and their motive behavior, the understanding of which opens up a wide range of new possibilities as we move toward the ultimate goal of realizing functional, man-made micro- and nanomachinery.

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.

The inhibition of concentrated active baths

Passive tracers in the active bath express fascinating behaviors. However, most studies are restricted to dilute active baths. Here, we use 2D simulation of suspensions consisting of active Brownian particles and a passive disk-shaped tracer to investigate tracers' diffusive behaviors in a wide range of volume fractions. Due to the competition between the thermal noise and collisions with active particles, tracers express a first transition from the normal diffusion to the superdiffusion at a short time scale and recur to normal diffusion at a long time scale. At a low volume fraction, infrequent active collisions retard the first transition of smaller tracers. At a high volume fraction, active particles with high activity aggregating around tracers induce a bimodal probability distribution function of tracer displacements during superdiffusion. Considering the enhancement of diffusion, the non-dimensional enhanced diffusivity increases asymptotically with the Peclet number. The asymptotic line gives an upper limit of non-dimensional enhanced diffusivity of tracers. Cases with lower enhanced diffusion have a high volume fraction and a low active velocity that indicates the inhibition of concentrated active baths. With the high negentropic work of these cases, the inhibition is explained as the change of the configuration of active baths for introducing tracers.

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.

The mesoscopic collective motion of self-propelling active particle suspension confined in two-dimensional micro-channel

The mesoscopic collective motion of self-propelling active particle suspension confined in high aspect ratio two-dimensional micro-channel is numerically studied through coupled [Formula: see text] equation by considering background thermal fluctuation, inter-particle interaction, self-propulsion and micro-channel confinement. Both the self-propulsion and micro-channel confinement are the factors driving the system away from equilibrium and sustaining heterogeneous motion. In such system, the propulsion induced particle accumulation around the channel walls is a universal phenomenon with spatial heterogeneity, where large fraction of particles are caged inside the accumulated cluster with local oscillation coexisting with few fast propelling particles in the center region. Although the formation mechanism of the induced accumulation is well studied, post the cluster formation, how the cluster evolves and its dynamical properties is rarely discussed. Based on the merits of [Formula: see text] equation, the dynamical evolution of induced accumulation is revealed by particle trajectories. It is found that the induced accumulation can be dissociated through the slow re-orientation process of few jammed particles. By using the idea of force chain network, how the transverse confinement couples the transverse displacement with the longitudinal displacement is evidenced. It is further verified by the statistical measurement of correlation probability between transverse and longitudinal displacements. The suppressed displacements in both directions is the origin leading to the slow dynamics of cluster evolution. Temporally, within the orientational relaxation time, this system exhibits non-trivial anomalous diffusion under the competition between the counter effects of self-propulsion (enhanced diffusion) and micro-channel confinement (suppressed diffusion). Additionally, by considering the orientational coupling, the deep hysteresis of accumulation has been found even for very weak orientational coupling strength.

Metachronal Swimming with Rigid Arms near Boundaries

Various organisms such as crustaceans use their appendages for locomotion. If they are close to a confining boundary then viscous as opposed to inertial effects can play a central role in governing the dynamics. To study the minimal ingredients needed for swimming without inertia, we built an experimental system featuring a robot equipped with a pair of rigid slender arms with negligible inertia. Our results show that directing the arms to oscillate about the same time-averaged orientation produces no net displacement of the robot each cycle, regardless of any phase delay between the oscillating arms. The robot is able to swim if the arms oscillate asynchronously around distinct orientations. The measured displacement over time matches well with a mathematical model based on slender-body theory for Stokes flow. Near a confining boundary, the robot with no net displacement every cycle showed similar behavior, while the swimming robot increased in speed closer to the boundary.

Relating Rheotaxis and Hydrodynamic Actuation using Asymmetric Gold-Platinum Phoretic Rods

We explore the behavior of micron-scale autophoretic Janus (Au/Pt) rods, having various Au/Pt length ratios, swimming near a wall in an imposed background flow. We find that their ability to robustly orient and move upstream, i.e., to rheotax, depends strongly on the Au/Pt ratio, which is easily tunable in synthesis. Numerical simulations of swimming rods actuated by a surface slip show a similar rheotactic tunability when varying the location of the surface slip versus surface drag. The slip location determines whether swimmers are pushers (rear actuated), pullers (front actuated), or in between. Our simulations and modeling show that pullers rheotax most robustly due to their larger tilt angle to the wall, which makes them responsive to flow gradients. Thus, rheotactic response infers the nature of difficult to measure flow fields of an active particle, establishes its dependence on swimmer type, and shows how Janus rods can be tuned for flow responsiveness.

Confined 1D Propulsion of Metallodielectric Janus Micromotors on Microelectrodes under Alternating Current Electric Fields

There is mounting interest in synthetic microswimmers ("micromotors") as microrobots as well as a model system for the study of active matters, and spatial navigation is critical for their success. Current navigational technologies mostly rely on magnetic steering or guiding with physical boundaries, yet limitations with these strategies are plenty. Inspired by an earlier work with magnetic domains on a garnet film as predefined tracks, we present an interdigitated microelectrodes (IDE) system where, upon the application of AC electric fields, metallodielectric (e.g., SiO₂-Ti) Janus particles are hydrodynamically confined and electrokinetically propelled in one dimension along the electrode center lines with tunable speeds. In addition, comoving micromotors moved in single files, while those moving in opposite directions primarily reoriented and moved past each other. At high particle densities, turbulence-like aggregates formed as many-body interactions became complicated. Furthermore, a micromotor made U-turns when approaching an electrode closure, while it gradually slowed down at the electrode opening and was collected in large piles. Labyrinth patterns made of serpentine chains of Janus particles emerged by modifying the electrode configuration. Most of these observations can be qualitatively understood by a combination of electroosmotic flows pointing inward to the electrodes, and asymmetric electrical polarization of the Janus particles under an AC electric field. Emerging from these observations is a strategy that not only powers and confines micromotors on prefabricated tracks in a contactless, on-demand manner, but is also capable of concentrating active particles at predefined locations. These features could prove useful for designing tunable tracks that steer synthetic microrobots, as well as to enable the study of single file diffusion, active turbulence, and other collective behaviors of active matters.

Dynamics near planar walls for various model self-phoretic particles

For chemically active particles suspended in a liquid solution and moving by self-phoresis, the dynamics near chemically inert, planar walls is studied theoretically by employing various choices for the activity function, i.e., the spatial distribution of the sites where various chemical reactions take place. We focus on the case of solutions composed of electrically neutral species. This analysis extends previous studies of the case that the chemical activity can be modeled effectively as the release of a "product" molecular species from parts of the surface of the particle by accounting for annihilation of the product molecules by chemical reactions, either on the rest of the surface of the particle or in the volume of the surrounding solution. We show that, for the models considered here, the emergence of "sliding" and "hovering" wall-bound states is a generic, robust feature. However, the details of these states, such as the range of parameters within which they occur, depend on the specific model for the activity function. Additionally, in certain cases there is a reversal of the direction of the motion compared to the one observed if the particle is far away from the wall. We have also studied the changes of the dynamics induced by a direct interaction between the particle and the wall by including a short-ranged repulsive component to the interaction in addition to the steric one (a procedure often employed in numerical simulations of active colloids). Upon increasing the strength of this additional component, while keeping its range fixed, significant qualitative changes occur in the phase portraits of the dynamics near the wall: for sufficiently strong short-ranged repulsion, the sliding steady states of the dynamics are transformed into hovering states. Furthermore, our studies provide evidence for an additional "oscillatory" wall-bound steady state of motion for chemically active particles due to a strong, short-ranged, and direct repulsion. This kind of particle translates along the wall at a distance from it which oscillates between a minimum and a maximum.

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.

Diffusion of colloidal rods in corrugated channels

In many natural and artificial devices diffusive transport takes place in confined geometries with corrugated boundaries. Such boundaries cause both entropic and hydrodynamic effects, which have been studied only for the case of spherical particles. Here we experimentally investigate the diffusion of particles of elongated shape confined in a corrugated quasi-two-dimensional channel. The elongated shape causes complex excluded-volume interactions between particles and channel walls which reduce the accessible configuration space and lead to novel entropic free-energy effects. The extra rotational degree of freedom also gives rise to a complex diffusivity matrix that depends on both the particle location and its orientation. We further show how to extend the standard Fick-Jacobs theory to incorporate combined hydrodynamic and entropic effects, so as, for instance, to accurately predict experimentally measured mean first passage times along the channel. Our approach can be used as a generic method to describe translational diffusion of anisotropic particles in corrugated channels.

Effective Interactions between Chemically Active Colloids and Interfaces

Chemically active colloids can achieve force- and torque-free motility ("self-propulsion") via the promotion, on their surface, of catalytic chemical reactions involving the surrounding solution. Such systems are valuable both from a theoretical perspective, serving as paradigms for nonequilibrium processes, as well as from an application viewpoint, according to which active colloids are envisioned to play the role of carriers ("engines") in novel lab-on-a-chip devices. The motion of such colloids is intrinsically connected with a "chemical field", i.e., the distribution near the colloid of the number densities of the various chemical species present in the solution, and with the hydrodynamic flow of the solution around the particle. In most of the envisioned applications, and in virtually all reported experimental studies, the active colloids operate under spatial confinement (e.g., within a microfluidic channel, a drop, a free-standing liquid film, etc.). In such cases, the chemical field and the hydrodynamic flow associated with an active colloid are influenced by any nearby confining surfaces, and these disturbances couple back to the particle. Thus, an effective interaction with the spatial confinement arises. Consequently, the particle is endowed with means to perceive and to respond to its environment. Understanding these effective interactions, finding the key parameters which control them, and designing particles with desired, preconfigured responses to given environments, require interdisciplinary approaches which synergistically integrate methods and knowledge from physics, chemistry, engineering, and materials science. Here we review how, via simple models of chemical activity and self-phoretic motion, progress has recently been made in understanding the basic physical principles behind the complex behaviors exhibited by active particles near interfaces. First, we consider the occurrence of "interface-bounded" steady states of chemically active colloids near simple, nonresponsive interfaces. Examples include particles "sliding" along, or "hovering" above, a hard planar wall while inducing hydrodynamic flow of the solution. These states lay the foundations for concepts like the guidance of particles by the topography of the wall. We continue to discuss responsive interfaces: a suitable chemical patterning of a planar wall allows one to bring the particles into states of motion which are spatially localized (e.g., within chemical stripes or along chemical steps). These occur due to the wall responding to the activity-induced chemical gradients by generating osmotic flows, which encode the surface-chemistry of the wall. Finally, we discuss how, via activity-induced Marangoni stresses, long-ranged effective interactions emerge from the strong hydrodynamic response of fluid interfaces. These examples highlight how in this context a desired behavior can be potentially selected by tuning suitable parameters (e.g., the phoretic mobility of the particle, or the strength of the Marangoni stress at an interface). This can be accomplished via a judicious design of the surface chemistry of the particle and of the boundary, or by the choice of the chemical reaction in solution.

Effective squirmer models for self-phoretic chemically active spherical colloids

Various aspects of self-motility of chemically active colloids in Newtonian fluids can be captured by simple models for their chemical activity plus a phoretic-slip hydrodynamic boundary condition on their surface. For particles of simple shapes (e.g., spheres) --as employed in many experimental studies-- which move at very low Reynolds numbers in an unbounded fluid, such models of chemically active particles effectively map onto the well studied so-called hydrodynamic squirmers (S. Michelin and E. Lauga, J. Fluid Mech. 747, 572 (2014)). Accordingly, intuitively appealing analogies of "pusher/puller/neutral" squirmers arise naturally. Within the framework of self-diffusiophoresis we illustrate the above-mentioned mapping and the corresponding flows in an unbounded fluid for a number of choices of the activity function (i.e., the spatial distribution and the type of chemical reactions across the surface of the particle). We use the central collision of two active particles as a simple, paradigmatic case for demonstrating that in the presence of other particles or boundaries the behavior of chemically active colloids may be qualitatively different, even in the far field, from the one exhibited by the corresponding "effective squirmer", obtained from the mapping in an unbounded fluid. This emphasizes that understanding the collective behavior and the dynamics under geometrical confinement of chemically active particles necessarily requires to explicitly account for the dependence of the hydrodynamic interactions on the distribution of chemical species resulting from the activity of the particles.

A fast and powerful swimming microrobot with a serrated tail enhanced propulsion interface

We demonstrate the use of a swimming microrobot with a serrated tail in the propulsion region to enhance reaction interfaces. A 3D printed tail with multiple catalytic channels and nanointerfaces could reinforce the microrobot, allowing it to reach swimming speeds of ∼1 mm s-1 and enabling it to transport objects with a weight 6500 times that of itself. This research represents a new concept in swimming microrobot design and is expected to benefit a wide range of engineering fields.

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.

Two Forces Are Better than One: Combining Chemical and Acoustic Propulsion for Enhanced Micromotor Functionality

Engines and motors are everywhere in the modern world, but it is a challenge to make them work if they are very small. On the micron length scale, inertial forces are weak and conventional motor designs involving, e.g., pistons, jets, or flywheels cease to function. Biological motors work by a different principle, using catalysis to convert chemical to mechanical energy on the nanometer length scale. To do this, they must apply force continuously against their viscous surroundings, and because of their small size, their movement is "jittery" because of the random shoves and turns they experience from molecules in their surroundings. The first synthetic catalytic motors, discovered about 15 years ago, were bimetallic Pt-Au microrods that swim in fluids through self-electrophoresis, a mechanism that is apparently not used by biological catalytic nanomotors. Despite the difference in propulsion mechanisms, catalytic microswimmers are subject to the same external forces as natural swimmers such as bacteria. Therefore, they follow similar scaling laws, are subject to Brownian forces, and exhibit a rich array of biomimetic emergent behavior (e.g., chemotaxis, rheotaxis, schooling, and predator-prey behavior). It was later discovered, quite by accident, that the same metallic microrods undergo rapid autonomous movement in acoustic fields, converting excitation energy in the frequency (MHz) and power range (up to several W/cm²) that is commonly used for ultrasonic imaging into axial movement. Because the acoustic propulsion mechanism is fuel-free, it can operate in media that have been inaccessible to chemically powered motors, such as the interior of living cells. The power levels used are intermediate between those of ultrasonic diagnostic imaging and therapy, so the translation of basic research on microswimmers into biomedical applications, including in vivo diagnostics and drug delivery, is possible. Acoustic and chemical propulsion are applied independently to microswimmers, so by modulating the acoustic power one can achieve microswimmer functionalities that are not accessible with the individual propulsion mechanisms. These include motion of particles forward and backward with switching between chemical and acoustic propulsion, the assembly/disassembly equilibrium of particle swarms and colloidal molecules, and controllable upstream or downstream propulsion in a flowing fluid. This Account relates our current understanding of the chemical and acoustic propulsion mechanisms, and describes how their combination can be particularly powerful for imparting enhanced functionality to micromotors.

Flexible Guidance of Microengines by Dynamic Topographical Pathways in Ferrofluids

In this work, we demonstrate a simple, versatile, and real-time motion guidance strategy for artificial microengines and motile microorganisms in a ferrofluid by dynamic topographical pathways (DTPs), which are assembled from superparamagnetic nanoparticles in response to external magnetic field ( H). In this general strategy, the DTPs can exert anisotropic resistance forces on autonomously moving microengines and thus regulate their orientation. As the DTPs with different directions and lengths can be reversibly and swiftly assembled in response to the applied H, the microengines in the ferrofluid can be guided on demand with controlled motion directions and trajectories, including circular, elliptical, straight-line, semi-sine, and sinusoidal trajectories. The as-demonstrated control strategy obviates reliance on the customized responses of micromotors and applies to autonomously propelling agents swimming both in bulk and near substrate walls. Furthermore, the microengines (or motile microorganisms) in a ferrofluid can be considered as an integrated system, and it may inspire the development of intelligent systems with cooperative functions for biomedical and environmental applications.

State diagram of a three-sphere microswimmer in a channel

Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that the resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.