Self-propelled Microswimmers Research Articles

Flow features induced by a rod-shaped microswimmer and its swimming efficiency: A two-dimensional numerical study

Abstract The swimming performance of rod-shaped microswimmers in a channel was numerically investigated using the two-dimensional lattice Boltzmann method (LBM). We considered variable-length squirmer rods, assembled from circular squirmer models with self-propulsion mechanisms, and analyzed the effects of the Reynolds number (Re), aspect ratio (ε), squirmer-type factor (β) and blockage ratio (κ) on swimming efficiency (η) and power expenditure (P). The results show no significant difference in power expenditure between pushers (microswimmers propelled from the tail) and pullers (microswimmers propelled from the head) at the low Reynolds numbers adopted in this study. However, the swimming efficiency of pushers surpasses that of pullers. Moreover, as the degree of channel blockage increases (i.e., κ increases), the squirmer rod consumes more energy while swimming, and its swimming efficiency also increases, which is clearly reflected when ε ≤ 3. Notably, squirmer rods with a larger aspect ratio ε and a β value approaching 0 can achieve high swimming efficiency with lower power expenditure. The advantages of self-propelled microswimmers are manifested when ε > 4 and β = ±1, where the squirmer rod consumes less energy than a passive rod driven by an external field. These findings underscore the potential for designing more efficient microswimmers by carefully considering the interactions between the microswimmer geometry, propulsion mechanism and fluid dynamic environment.

Optical tweezers for probing the interactions of ZnO and Ag nanoparticles with E. coli.

The antibacterial effect of nanoparticles is mainly studied on the ensembles of the bacteria. In contrast, the optical tweezer technique allows the investigation of similar effects on individual bacterium. E. coli is a self-propelled micro-swimmer and ATP-driven active microorganism. In this work, an optical tweezer is employed to examine the mechanical properties of E. coli incubated with ZnO and Ag nanoparticles (NP) in the growth medium. ZnO and Ag NP with a concentration of 10µg/ml were dispersed in growth medium during active log-growth phase of E. coli. This E. coli-NP incubation is further continued for 12h. The E. coli after incubation for 2h, 6h and 12h were separately studied by the optical tweezer for their mechanical property. The IR laser (λ = 975 nm; power = 100mW) was used for trapping the individual cells and estimated trapping force, trapping stiffness and corner frequency. The optical trapping force on E. coli incubated in nanoparticle suspension shows linear decreases with incubation time. This work brings the importance of optical trapping force measurement in probing the antibacterial stress due to nanoparticles on the individual bacterium.

Electroosmotic Self-Propelled Microswimmer With Magnetic Steering

Electroosmotic Self-Propelled Microswimmer With Magnetic Steering

Minimum entropy production by microswimmers with internal dissipation

The energy dissipation and entropy production by self-propelled microswimmers differ profoundly from passive particles pulled by external forces. The difference extends both to the shape of the flow around the swimmer, as well as to the internal dissipation of the propulsion mechanism. Here we derive a general theorem that provides an exact lower bound on the total, external and internal, dissipation by a microswimmer. The problems that can be solved include an active surface-propelled droplet, swimmers with an extended propulsive layer and swimmers with an effective internal dissipation. We apply the theorem to determine the swimmer shapes that minimize the total dissipation while keeping the volume constant. Our results show that the entropy production by active microswimmers is subject to different fundamental limits than the entropy production by externally driven particles.

Self-Propulsion of Two Contacting Bubbles Due to the Radiation Interaction Force.

In this paper, we consider a new bubble-based microswimmer composed of two contacting bubbles. Under the action of an acoustic field, both bubbles are oscillating, and locomotion of the two-bubble system is observed. A theory is developed that allows one to calculate the acoustic radiation interaction forces between two gas bubbles in an incompressible viscous liquid for any small separation distance between the bubbles. This theory is used to demonstrate that two acoustically excited bubbles can create a self-propelled microswimmer due to a nonzero net force experienced by the bubbles when they come in contact. Experimental evidence of the creation of such a swimmer and of its motion is provided.

Self-learning swimming of a three-disk microrobot in a viscous and stochastic environment using reinforcement learning

Artificial Intelligence (AI) is a novel and fascinating tool in the control of robots. In this study, using a reinforcement learning approach, we have trained an artificial three-disk microrobot in order to learn how to swim at low Reynolds number flow (Re≪1) like the behavior of young microorganisms. Here, as the first contribution, we introduced a discrete model of a novel microswimmer. As the second contribution, we demonstrated that, using the proposed intelligent method, the microswimmer will be able to not only escape the physical constraints of swimming in a viscous medium, but also find the best sequence of actuation to reach the target point in a stochastic environment. The proposed reinforcement learning strategy can be applied to any other type of self-propelled microswimmers consisting of disks and actuators, which swim with continuous state space in a perturbed environment. In the end, we investigated the effect of learning hyperparameters on the performance of the swimmer’s training, and showed that, in the current agent and environment, the optimal values for the discount factor γ and learning rate α are 0.7 and 0.001 respectively which should be properly set for other types of mechanisms and environments.

The control effort to steer self-propelled microswimmers depends on their morphology: comparing symmetric spherical versus asymmetric L-shaped particles.

Active goal-directed motion requires real-time adjustment of control signals depending on the system’s status, also known as control. The amount of information that needs to be processed depends on the desired motion and control, and on the system’s morphology. The morphology of the system may directly effectuate or support the desired motion. This morphology-based reduction to the neuronal ‘control effort’ can be quantified by a novel information-entropy-based approach. Here, we apply this novel measure of ‘control effort’ to active microswimmers of different morphology. Their motion is a combination of directed deterministic and stochastic motion. In spherical microswimmers, the active propulsion leads to linear velocities. Active propulsion of asymmetric L-shaped particles leads to circular or—on tilted substrates—directed motion. Thus, the difference in shape, i.e. the morphology of the particles, directly influence the motion. Here, we quantify how this morphology can be exploited by control schemes for the purpose of steering the particles towards targets. Using computer simulations, we found in both cases a significantly lower control effort for L-shaped particles. However, certain movements can only be achieved by spherical particles. This demonstrates that a suitably designed microswimmer’s morphology might be exploited to perform specific tasks.

Rechargeable self-assembled droplet microswimmers driven by surface phase transitions

The design of artificial microswimmers is often inspired by the strategies of natural microorganisms. Many of these creatures exploit the fact that elasticity breaks the time-reversal symmetry of motion at low Reynolds numbers, but this principle has been notably absent from model systems of active, self-propelled microswimmers. Here we introduce a class of microswimmers that spontaneously self-assembles and swims without using external forces, driven instead by surface phase transitions induced by temperature variations. The swimmers are made from alkane droplets dispersed in an aqueous surfactant solution, which start to self-propel on cooling, pushed by rapidly growing thin elastic tails. When heated, the same droplets recharge by retracting their tails, swimming for up to tens of minutes in each cycle. Thermal oscillations of approximately 5 °C induce the swimmers to harness heat from the environment and recharge multiple times. We develop a detailed elasto-hydrodynamic model of these processes and highlight the molecular mechanisms involved. The system offers a convenient platform for examining symmetry breaking in the motion of swimmers exploiting flagellar elasticity. The mild conditions and biocompatible media render these microswimmers potential probes for studying biological propulsion and interactions between artificial and biological swimmers. A class of synthetic microswimmers self-assembled from alkane oil drops in a surfactant solution offers a rechargeable platform for studying how microorganisms exploit flagellar elasticity to move around.

Controlled swarm motion of self-propelled microswimmers for energy saving

Swarm motion is an amazing collective behavior in nature for energy saving. Inspiring this natural phenomenon in microorganisms’ swimming, we have proposed a motion strategy for a swarm of microrobots to reduce their energy consumption during path tracking. The investigated microrobot is an artificial Self-Propelled Microswimmer (SPM) with high maneuverability at low Reynolds number flow (Re ≪ 1). In this study, we have demonstrated that forming a swarm behavior with minimum energy consumption requires the microswimmers to be close enough to each other, since at small distances the hydrodynamic interactions of microswimmers reduce their energy consumption. Moreover, we also showed that depending on the employed path-tracking control strategy, collective motion may lead to decrease or increase of the overall energy consumption. To save energy using swarm behavior, the microswimmers must be able to adapt their orientation according to the surrounding flow field which is induced by the other swimmers. Otherwise, the energy consumption due to the induced hydrodynamic forces and torques increases. Based on the conducted simulations, it has been shown that the proposed motion strategy minimizes the energy consumption of swarm microswimmers during path tracking.

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

.Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.Graphical abstract

Active Anion Delivery by Self-Propelled Microswimmers.

Self-propelled micro- and nanomachines are at the forefront of materials research, branching into applications in biomedical science and environmental remediation. Cationic frameworks enabling the collection and delivery of anionic species (A-) are highly required, due to the large variety of life-threatening pollutants, such as radioactive technetium and carcinogenic chromium, and medicines, such as dexamethasone derivatives with negative charges. However, such autonomous moving carriers for active transport of the anions have been barely discussed. A polymeric viologen (PV++)-consisting of electroactive bicationic subunits-is utilized in a tubular autonomous microswimmer to selectively deliver A- of different sizes and charge densities. The cargo loading is based on a facile anion exchange mechanism. The packed crystal structure of PV++ allows removal of an exceptionally high quantity of anions per one microswimmer (2.55 × 10-13 mol anions per microswimmer), a critical factor often neglected regarding the real-world application of microswimmers. Notably, there was virtually no leakage of anions during the delivery process or upon keeping the loaded microswimmers under ambient conditions for at least 4 months. Multiple release mechanisms, compatible with different environments, including electrochemical, photochemical, and a metathesis reaction, with high efficiencies up to 98% are introduced. Such functional autonomous micromachines provide great promise for the next generation of functional materials for biomedical and environmental applications.

Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: Implications for the hydrodynamics of an active microswimmer near an elastic interface.

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future for biomedical and technological applications. These microswimmers move autonomously through aqueous media, where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than those due to shear resistance. Bending can enhance (suppress) the velocities resulting from higher-order singularities whereas the shear related contribution decreases (increases) the velocities. Most prominently, we find that near an elastic interface of only energetic resistance toward shear deformation, such as that of an elastic capsule designed for drug delivery, a swimming bacterium undergoes rotation of the same sense as observed near a no-slip wall. In contrast to that, near an interface of only energetic resistance toward bending, such as that of a fluid vesicle or liposome, we find a reversed sense of rotation. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.

Supercapacitors in Motion: Autonomous Microswimmers for Natural-Resource Recovery.

An electroadsorption technique similar to the ultrafast charging mechanism in supercapacitors is utilized to remove metals with different sizes and hydrophilicities from contaminated water using self-propelled microswimmers. The swimmers carry graphite fibre or bismuth with a layered crystal structure providing high electrostatic double-layer capacitances. Unlike previous methods, this electrochemical technique does not only utilize the surface of the swimmers, but due to the interlayer spacing of the graphite and bismuth, it is able to store metals in ≈400 layers, allowing removal and recovery of >50 ppm lithium in only 5 min. A larger interlayer distance between bismuth sheets allows the removal of bigger cations (sodium and calcium), expanding the application of this method to a large variety of natural elements. Finally, magnetic navigation of charged swimmers to an oxygen-saturated media causes oxidation and thus immediate release of the metal ions from the swimmers.

Three-bead steering microswimmers

The self-propelled microswimmers have recently attracted considerable attention as model systems for biological cell migration as well as artificial micromachines. A simple and well-studied microswimmer model consists of three identical spherical beads joined by two springs in a linear fashion with active oscillatory forces being applied on the beads to generate self-propulsion. We have extended this linear microswimmer configuration to a triangular geometry where the three beads are connected by three identical springs in an equilateral triangular manner. The active forces acting on each spring can lead to autonomous steering motion; i.e., allowing the swimmer to move along arbitrary paths. We explore the microswimmer dynamics analytically and pinpoint its rich character depending on the nature of the active forces. The microswimmers can translate along a straight trajectory, rotate at a fixed location, as well as perform a simultaneous translation and rotation resulting in complex curved trajectories. The sinusoidal active forces on the three springs of the microswimmer contain naturally four operating parameters which are more than required for the steering motion. We identify the minimal operating parameters which are essential for the motion of the microswimmer along any given arbitrary trajectory. Therefore, along with providing insights into the mechanics of the complex motion of the natural and artificial microswimmers, the triangular three-bead microswimmer can be utilized as a model for targeted drug delivery systems and autonomous underwater vehicles where intricate trajectories are involved.

Theory for controlling individual self-propelled micro-swimmers by photon nudging I: directed transport

Photon nudging is a new experimental method which enables the force-free manipulation and localization of individual self-propelled artificial micro-swimmers in fluidic environments. It uses a weak laser to stochastically and adaptively turn on and off the swimmer's propulsion when the swimmer, through rotational diffusion, points towards or away from its target, respectively. This contribution presents a theoretical framework for the statistics of both 2D and 3D controls. The main results are: the on- and off-time distributions for the controlling laser, the arrival time statistics for the swimmer to reach a remote target, and how the experimentally accessible control parameters influence the control, e.g., the optimal acceptance angle for directed transport. The results are general in that they are independent of the propulsion or the actuation mechanisms. They provide a concrete physical picture for how a single artificial micro-swimmer could be navigated under thermal fluctuations-insights that could also be useful for understanding biological micro-swimmers.

Theory for controlling individual self-propelled micro-swimmers by photon nudging II: confinement.

Photon nudging allows the manipulation and confinement of individual self-propelled micro-swimmers in 2D and 3D environments using feedback controls. Presented in this second part of a two-part contribution are theoretical models that afford the characterization for the positioning distribution associated with active localization. A derivation for the optimal nudging speed and acceptance angle is given for minimal placement uncertainty. The analytical solutions allow for a discussion on the physical underpinning that underlies controllability and optimality.

Dynamical density functional theory for circle swimmers

The majority of studies on self-propelled particles and microswimmers concentrates on objects that do not feature a deterministic bending of their trajectory. However, perfect axial symmetry is hardly found in reality, and shape-asymmetric active microswimmers tend to show a persistent curvature of their trajectories. Consequently, we here present a particle-scale statistical approach to circle-swimmer suspensions in terms of a dynamical density functional theory. It is based on a minimal microswimmer model and, particularly, includes hydrodynamic interactions between the swimmers. After deriving the theory, we numerically investigate a planar example situation of confining the swimmers in a circularly symmetric potential trap. There, we find that increasing curvature of the swimming trajectories can reverse the qualitative effect of active drive. More precisely, with increasing curvature, the swimmers less effectively push outwards against the confinement, but instead form high-density patches in the center of the trap. We conclude that the circular motion of the individual swimmers has a localizing effect, also in the presence of hydrodynamic interactions. Parts of our results could be confirmed experimentally, for instance, using suspensions of L-shaped circle swimmers of different aspect ratio.

Role of Correlations in the Collective Behavior of Microswimmer Suspensions.

In this Letter, we study the collective behavior of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedentedly large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is nonperturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers and reveal its nontrivial density dependence. The theory is in quantitative agreement with the lattice Boltzmann simulations and captures the asymmetry between pusher and puller swimmers below the transition to turbulence.

Active Particles in Complex and Crowded Environments

Differently from passive Brownian particles, active particles, also known as self-propelled Brownian particles or microswimmers and nanoswimmers, are capable of taking up energy from their environment and converting it into directed motion. Because of this constant flow of energy, their behavior can only be explained and understood within the framework of nonequilibrium physics. In the biological realm, many cells perform directed motion, for example, as a way to browse for nutrients or to avoid toxins. Inspired by these motile microorganisms, researchers have been developing artificial particles that feature similar swimming behaviors based on different mechanisms; these manmade micro- and nanomachines hold a great potential as autonomous agents for healthcare, sustainability, and security applications. With a focus on the basic physical features of the interactions of self-propelled Brownian particles with a crowded and complex environment, this comprehensive review will put the reader at the very forefront of the field, providing a guided tour through its basic principles, the development of artificial self-propelling micro- and nanoparticles, and their application to the study of nonequilibrium phenomena, as well as the open challenges that the field is currently facing.

Diffusion of Bacterial Cells in Porous Media

The chemotaxis signal transduction network regulates the biased random walk of many bacteria in favorable directions and away from harmful ones through modulating the frequency of directional reorientations. In mutants of diverse bacteria lacking the chemotaxis response, migration in classic motility agar, which constitutes a fluid-filled porous medium, is compromised; straight-swimming cells unable to tumble become trapped within the agar matrix. Spontaneous mutations that restore spreading have been previously observed in the enteric bacterium Escherichia coli, and recent work in other bacterial species has isolated and quantified different classes of nonchemotacting mutants exhibiting the same spreading phenotype. We present a theoretical description of bacterial diffusion in a porous medium—the natural habitat for many cell types—which elucidates how diverse modifications of the motility apparatus resulting in a nonzero tumbling frequency allows for unjamming of otherwise straight-swimming cells at internal boundaries and leads to net migration. A unique result of our analysis is increasing diffusive spread with increasing tumbling frequency in the small pore limit, consistent with earlier experimental observations but not captured by previous models. Our theoretical results, combined with a simple model of bacterial diffusion and growth in agar, are compared with our experimental measurements of swim ring expansion as a function of time, demonstrating good quantitative agreement. Our results suggest that the details of the cellular tumbling process may be adapted to enable bacteria to propagate efficiently through complex environments. For engineered, self-propelled microswimmers that navigate via alternating straight runs and changes in direction, these results suggest an optimal reorientation strategy for efficient migration in a porous environment with a given microarchitecture.