Active Microswimmers Research Articles

Electrotaxis of Self-Propelling Artificial Swimmers in Microchannels.

Biological microswimmers alter their swimming trajectories to follow the direction of an applied electric field, exhibiting electrotaxis. We show that synthetic active droplet microswimmers also autonomously change swimming trajectories in microchannels, even undergoing "U-turns," in response to an electric field, mimicking electrotaxis. We exploit such electrotaxis, in the presence of an external flow, to robustly tune the swimming trajectory of active droplets between wall-adjacent, oscillatory, and channel centerline swimming. A general hydrodynamic model demonstrates that the electrotactic dynamics is governed by the electrical effects due to the swimmer's inherent surface charge, besides its motility, hydrodynamic wall interactions, and relative orientations of the electric field and imposed flow. Our study demonstrates a simple method for controlling active agents in complex geometries for microrobotic applications, like autonomous cargo delivery.

Machine learning assisted sorting of active microswimmers.

Active matter systems, being in a non-equilibrium state, exhibit complex behaviors, such as self-organization, giving rise to emergent phenomena. There are many examples of active particles with biological origins, including bacteria and spermatozoa, or with artificial origins, such as self-propelled swimmers and Janus particles. The ability to manipulate active particles is vital for their effective application, e.g., separating motile spermatozoa from nonmotile and dead ones, to increase fertilization chance. In this study, we proposed a mechanism-an apparatus-to sort and demix active particles based on their motility values (Péclet number). Initially, using Brownian simulations, we demonstrated the feasibility of sorting self-propelled particles. Following this, we employed machine learning methods, supplemented with data from comprehensive simulations that we conducted for this study, to model the complex behavior of active particles. This enabled us to sort them based on their Péclet number. Finally, we evaluated the performance of the developed models and showed their effectiveness in demixing and sorting the active particles. Our findings can find applications in various fields, including physics, biology, and biomedical science, where the sorting and manipulation of active particles play a pivotal role.

Deep learning and defocus imaging for determination of three-dimensional position and orientation of microscopic objects

We present a method to determine the three-dimensional position and orientation of microscopic, non-spherical objects in microfluidic and laboratory-on-a-chip systems observed through conventional optical microscopes. The method is based on the combination of the General Defocusing Particle Tracking technique [Barnkob et al., “General defocusing particle tracking,” Lab Chip 15, 3556–3560 (2015)] and deep learning. It requires minimal input from the user, is suitable for real-time applications, and can be applied to any microscopic object with an approximately ellipsoidal shape, such as unicellular swimming organisms, red blood cells, or spheroidal colloids. The main challenge is linked to the construction of suitable training datasets for the neural network. We provide a procedure generally valid for active microswimmers and discuss possible strategies for other types of objects. An implementation using the Visual Geometry Group convolutional neural network (VGG-16) is presented and tested on synthetic images with different backgrounds and noise levels. The same implementation is used to track the position and orientation of different specimens of the heterotrophic ciliate Euplotes Vannus in free-swimming motion. The measurements were performed with a 10 × objective over a depth of 800 μm with an average estimated uncertainty in the orientation angles of 9.0%.

Vortex Pattern Stabilization in Thin Films Resulting from Shear Thickening of Active Suspensions.

The need for structuring on micrometer scales is abundant, for example, in view of phononic applications. We here outline a novel approach based on the phenomenon of active turbulence on the mesoscale. As we demonstrate, a shear-thickening carrier fluid of active microswimmers intrinsically stabilizes regular vortex patterns of otherwise turbulent active suspensions. The fluid self-organizes into a periodically structured nonequilibrium state. Introducing additional passive particles of intermediate size leads to regular spatial organization of these objects. Our approach opens a new path toward functionalization through patterning of thin films and membranes.

Power-law intermittency in the gradient-induced self-propulsion of colloidal swimmers.

Active colloidal microswimmers serve as archetypical active fluid systems, and as models for biological swimmers. Here, by studying in detail their velocity traces, we find robust power-law intermittency with system-dependent exponential cut off. We model the intermittent motion by an interplay of the field gradient-dependent active force, which depends on a fluid gradient and is reduced when the swimmer moves, and the locally fluctuating hydrodynamic drag, that is set by the wetting properties of the substrate. The model closely describes the velocity distributions of two disparate swimmer systems: AC field activated and catalytic swimmers. The generality is highlighted by the collapse of all data in a single master curve, suggesting the applicability to further systems, both synthetic and biological.

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.

Hydrodynamics of an odd active surfer in a chiral fluid

We theoretically and computationally study the low-Reynolds-number hydrodynamics of a linear active microswimmer surfing on a compressible thin fluid layer characterized by an odd viscosity. Since the underlying three-dimensional fluid is assumed to be very thin compared to any lateral size of the fluid layer, the model is effectively two-dimensional. In the limit of small odd viscosity compared to the even viscosities of the fluid layer, we obtain analytical expressions for the self-induced flow field, which includes non-reciprocal components due to the odd viscosity. On this basis, we fully analyze the behavior of a single linear swimmer, finding that it follows a circular path, the radius of which is, to leading order, inversely proportional to the magnitude of the odd viscosity. In addition, we show that a pair of swimmers exhibits a wealth of two-body dynamics that depends on the initial relative orientation angles as well as on the propulsion mechanism adopted by each swimmer. In particular, the pusher–pusher and pusher–puller-type swimmer pairs exhibit a generic spiral motion, while the puller–puller pair is found to either co-rotate in the steady state along a circular trajectory or exhibit a more complex chaotic behavior resulting from the interplay between hydrodynamic and steric interactions. Our theoretical predictions may pave the way toward a better understanding of active transport in active chiral fluids with odd viscosity, and may find potential applications in the quantitative microrheological characterization of odd-viscous fluids.

Data-Driven Discovery of Active Nematic Hydrodynamics

Active nematics can be modeled using phenomenological continuum theories that account for the dynamics of the nematic director and fluid velocity through partial differential equations (PDEs). While these models provide a statistical description of the experiments, the relevant terms in the PDEs and their parameters are usually identified indirectly. We adapt a recently developed method to automatically identify optimal continuum models for active nematics directly from spatiotemporal data, via sparse regression of the coarse-grained fields onto generic low order PDEs. After extensive benchmarking, we apply the method to experiments with microtubule-based active nematics, finding a surprisingly minimal description of the system. Our approach can be generalized to gain insights into active gels, microswimmers, and diverse other experimental active matter systems.

Autonomous Chiral Microswimmers with Self‐mixing Capabilities for Highly Efficient Enantioselective Synthesis

AbstractThe development of chiral catalysts plays a very important role in various areas of chemical science. Heterogeneous catalysts have the general advantage of allowing a more straightforward separation from the products. One specific case of heterogeneous catalysis is electrocatalysis, being potentially a green chemistry approach. However, a typical drawback is that the redox conversion of molecules occurs only at the electrode/electrolyte interface, and not in the bulk of the electrolyte. The second limitation is that the electrodes have to be physically connected to a power supply to induce the desired reactions. To circumvent these problems, we propose here a complementary approach by replacing macroscopic electrodes with an ensemble of self‐propelled redox active microswimmers. They move autonomously in solution while transforming simultaneously a prochiral starting compound into a specific enantiomer with a very high enantiomeric excess, accompanied by a significantly increased production rate of the favorite enantiomer.

Autonomous Chiral Microswimmers with Self-mixing Capabilities for Highly Efficient Enantioselective Synthesis.

The development of chiral catalysts plays a very important role in various areas of chemical science. Heterogeneous catalysts have the general advantage of allowing a more straightforward separation from the products. One specific case of heterogeneous catalysis is electrocatalysis, being potentially a green chemistry approach. However, a typical drawback is that the redox conversion of molecules occurs only at the electrode/electrolyte interface, and not in the bulk of the electrolyte. The second limitation is that the electrodes have to be physically connected to a power supply to induce the desired reactions. To circumvent these problems, we propose here a complementary approach by replacing macroscopic electrodes with an ensemble of self-propelled redox active microswimmers. They move autonomously in solution while transforming simultaneously a prochiral starting compound into a specific enantiomer with a very high enantiomeric excess, accompanied by a significantly increased production rate of the favorite enantiomer.

Role of cohesion in the flow of active particles through bottlenecks

We experimentally and numerically study the flow of programmable active particles (APs) with tunable cohesion strength through geometric constrictions. Similar to purely repulsive granular systems, we observe an exponential distribution of burst sizes and power-law-distributed clogging durations. Upon increasing cohesion between APs, we find a rather abrupt transition from an arch-dominated clogging regime to a cohesion-dominated regime where droplets form at the aperture of the bottleneck. In the arch-dominated regime the flow-rate only weakly depends on the cohesion strength. This suggests that cohesion must not necessarily decrease the group’s efficiency passing through geometric constrictions or pores. Such behavior is explained by “slippery” particle bonds which avoids the formation of a rigid particle network and thus prevents clogging. Overall, our results confirm the general applicability of the statistical framework of intermittent flow through bottlenecks developed for granular materials also in case of active microswimmers whose behavior is more complex than that of Brownian particles but which mimic the behavior of living systems.

Surface fluctuating hydrodynamics methods for the drift-diffusion dynamics of particles and microstructures within curved fluid interfaces

We introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial hydrodynamic coupling, traction coupling with the surrounding bulk fluid, and thermal fluctuations. For fluid-structure interactions, we introduce Immersed Boundary Methods (IBM) and related Stochastic Eulerian-Lagrangian Methods (SELM) for curved surfaces. We use these approaches to investigate the statistics of surface fluctuating hydrodynamics and microstructures. For velocity autocorrelations, we find characteristic power-law scalings τ−1, τ−2, and plateaus can emerge. This depends on the physical regime associated with the geometry, surface viscosity, and bulk viscosity. This differs from the characteristic τ−3/2 scaling for bulk three dimensional fluids. We develop theory explaining these observed power-laws associated with time-scales for dissipation within the fluid interface and coupling to the surrounding fluid. We then use our introduced methods to investigate a few example systems and roles of hydrodynamic coupling and thermal fluctuations including for the kinetics of passive particles and active microswimmers in curved fluid interfaces.

Mediated interactions between rigid inclusions in two-dimensional elastic or fluid films.

Interactions between rigid inclusions in continuous three-dimensional linearly elastic solids and low-Reynolds-number viscous fluids have largely been quantified in the past. Prime example systems are given by functionalized elastic composite materials or fluid colloidal suspensions. Here, we address the significantly less frequently studied situation of rigid inclusions in two-dimensional elastic or low-Reynolds-number fluid films. We concentrate on the situation in which disklike inclusions remain well separated from each other and do not get into contact. Specifically, we demonstrate and explain that the logarithmic divergence of the associated Green's function is removed in the absence of net external forces on the inclusions, in line with physical intuition. For instance, this situation applies when only pairwise mutual interactions between the inclusions prevail. Our results will support, for example, investigations on membranes functionalized by appropriate inclusions, both of technical or biological origin, or the dynamics of active microswimmers in appropriately prepared thin films.

Chemical design of self-propelled Janus droplets

Chemical design of self-propelled Janus droplets

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.

Microswimmer Combing: Controlling Interfacial Dynamics for Open-Surface Multifunctional Screening of Small Animals.

Image-based screening of multicellular model organisms is critical for both investigating fundamental biology and drug development. Current microfluidic techniques for high-throughput manipulation of small model organisms, although useful, are generally complicated to operate, which impedes their widespread adoption by biology laboratories. To address this challenge, this paper presents an ultrasimple and yet effective approach, "microswimmer combing," to rapidly isolate live small animals on an open-surface array. This approach exploits a dynamic contact line-combing mechanism designed to handle highly active microswimmers. The isolation method is robust, and the device operation is simple for users without a priori experience. The versatile open-surface device enables multiple screening applications, including high-resolution imaging of multicellular organisms, on-demand mutant selection, and multiplexed chemical screening. The simplicity and versatility of this method provide broad access to high-throughput experimentation for biologists and open up new opportunities to study active microswimmers by different scientific communities.

Lagrangian mechanics of active systems

We present a multi-scale modeling and simulation framework for low-Reynolds number hydrodynamics of shape-changing immersed objects, e.g., biological microswimmers and active surfaces. The key idea is to consider principal shape changes as generalized coordinates and define conjugate generalized hydrodynamic friction forces. Conveniently, the corresponding generalized friction coefficients can be pre-computed and subsequently reused to solve dynamic equations of motion fast. This framework extends Lagrangian mechanics of dissipative systems to active surfaces and active microswimmers, whose shape dynamics is driven by internal forces. As an application case, we predict in-phase and anti-phase synchronization in pairs of cilia for an experimentally measured cilia beat pattern.Graphic

Minimum Dissipation Theorem for Microswimmers.

We derive a theorem for the lower bound on the energy dissipation rate by a rigid surface-driven active microswimmer of arbitrary shape in a fluid at a low Reynolds number. We show that, for any swimmer, the minimum dissipation at a given velocity can be expressed in terms of the resistance tensors of two passive bodies of the same shape with a no-slip and perfect-slip boundary. To achieve the absolute minimum dissipation, the optimal swimmer needs a surface velocity profile that corresponds to the flow around the perfect-slip body, and a propulsive force density that corresponds to the no-slip body. Using this theorem, we propose an alternative definition of the energetic efficiency of microswimmers that, unlike the commonly used Lighthill efficiency, can never exceed unity. We validate the theory by calculating the efficiency limits of spheroidal swimmers.

Surface anchoring controls orientation of a microswimmer in nematic liquid crystal

Microscopic swimmers, both living and synthetic, often dwell in anisotropic viscoelastic environments. The most representative realization of such an environment is water-soluble liquid crystals. Here, we study how the local orientation order of liquid crystal affects the motion of a prototypical elliptical microswimmer. In the framework of well-validated Beris-Edwards model, we show that the microswimmer’s shape and its surface anchoring strength affect the swimming direction and can lead to reorientation transition. Furthermore, there exists a critical surface anchoring strength for non-spherical bacteria-like microswimmers, such that swimming occurs perpendicular in a sub-critical case and parallel in super-critical case. Finally, we demonstrate that for large propulsion speeds active microswimmers generate topological defects in the bulk of the liquid crystal. We show that the location of these defects elucidates how a microswimmer chooses its swimming direction. Our results can guide experimental works on control of bacteria transport in complex anisotropic environments.

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