Physics of Microswimmers - Single Particle Motion and Collective Behavior

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.Comment: 54 pages, 59 figures, review article, Reports of Progress in Physics (to appear

Three-Sphere Low Reynolds Number Swimmer with a Cargo Container

A recently introduced model for an autonomous swimmer at low Reynolds number that is comprised of three spheres connected by two arms is considered when one of the spheres has a large radius. The Stokes hydrodynamic flow associated with the swimming strokes and net motion of this system can be studied analytically using the Stokes Green's function of a point force in front of a sphere of arbitrary radius $R$ provided by Oseen. The swimming velocity is calculated, and shown to scale as $1/R^3$ with the radius of the sphere.Comment: 4 pages, 1 figur

Resilience and Controllability of Dynamic Collective Behaviors

The network paradigm is used to gain insight into the structural root causes of the resilience of consensus in dynamic collective behaviors, and to analyze the controllability of the swarm dynamics. Here we devise the dynamic signaling network which is the information transfer channel underpinning the swarm dynamics of the directed interagent connectivity based on a topological neighborhood of interactions. The study of the connectedness of the swarm signaling network reveals the profound relationship between group size and number of interacting neighbors, which is found to be in good agreement with field observations on flock of starlings [Ballerini et al. (2008) Proc. Natl. Acad. Sci. USA, 105: 1232]. Using a dynamical model, we generate dynamic collective behaviors enabling us to uncover that the swarm signaling network is a homogeneous clustered small-world network, thus facilitating emergent outcomes if connectedness is maintained. Resilience of the emergent consensus is tested by introducing exogenous environmental noise, which ultimately stresses how deeply intertwined are the swarm dynamics in the physical and network spaces. The availability of the signaling network allows us to analytically establish for the first time the number of driver agents necessary to fully control the swarm dynamics

Non-Equilibrium Strongly Hyperuniform Fluids of Circle Active Particles with Large Local Density Fluctuations

Disordered hyperuniform structures are an exotic state of matter having vanishing long-wavelength density fluctuations similar to perfect crystals but without long-range order. Although its importance in materials science has been brought to the fore in past decades, the rational design of experimentally realizable disordered strongly hyperuniform microstructures remains challenging. Here we find a new type of non-equilibrium fluid with strong hyperuniformity in two-dimensional systems of chiral active particles, where particles perform independent circular motions of the radius R with the same handedness. This new hyperuniform fluid features a special length scale, i.e., the diameter of the circular trajectory of particles, below which large density fluctuations are observed. By developing a dynamic mean-field theory, we show that the large local density fluctuations can be explained as a motility-induced microphase separation, while the Fickian diffusion at large length scales and local center-of-mass-conserved noises are responsible for the global hyperuniformity

Self-propelled rod-like swimmers near surfaces

Self-propelled microswimmers are biological organisms or synthetic objects that propel themselves through the surrounding fluid. Examples are sperm, various swimming bacteria such as Escherichia coli, the green alga Chlamydomonas reinhardtii and artificial bimetallic rods that catalyze chemical reactions in the surrounding hydrogen peroxide. Even though these swimmers differ in their size and driving mechanism, they can be classified as having pusher or puller polarity, which means that they are driven from the rear or the front, respectively. To study the differences in the dynamics of swimmers of different polarity, we develop a general model of rod-like swimmers and perform simulations in three dimensions, employing a particle-based mesoscopic simulation technique (multi-particle collision dynamics) for the hydrodynamic interactions. In the center of our interest are the interactions of swimmers with walls and with each other at higher densities. In the dilute case, we find that all polarities (pusher, puller and neutral) show surface adhesion, the strongest in the pusher case. For pushers, this adhesion originates from sterical alignment with the wall and hydrodynamic attraction towards the wall, making them swim closest to the wall. For pullers, we show that they swim at a slightly larger distance from the wall than pushers, and that they are inclined towards the wall by a hydrodynamic repulsion of their middle part, which also leads to strong surface adhesion. We also measure the attractive force between pusher and wall and compare it to the dipole model, which is a commonly used far-field approximation for the flow surrounding polar swimmers. Previous studies of self-propelled swimmers at high density were mostly performed in two dimensions or neglected either hydrodynamics or excluded-volume interactions. Using an efficient parallelization on GPU hardware, we are able to study the collective behavior of rods in three dimensions at various densities and driving forces, taking into account hydrodynamics and excluded-volume interactions. Our findings emphasize the importance of the polarity of swimmers: Neutrally propelled rods interact weakly via hydrodynamics, but display an isotropic-nematic phase transition at lower critical densities than passive rods. Pusher rods align parallel with each other and form medium sized motile clusters that can develop into flow defects such as jets and swirls. The clusters primarily swim close to the surfaces, where the rod concentration is highest. The surface aggregation decreases with increasing rod density. While polar order is apparent at short distances within the clusters, at longer scales the flow defects destroy the order. However, nematic order is found to be slightly positive at a system-wide scale for high-density systems, indicating that clusters can align with each other. The clusters in puller systems are radically different. At low rod densities several small non-motile hedgehog-like clusters are formed at the walls, merging into one giant, system-spanning cluster at high rod densities. These giant clusters usually include a large fraction of all rods in the system. While these are jamming clusters, they are not static but deform slowly. We conclude that the puller clusters are due to aster-like defects, which have been predicted for puller fluids, combined with excluded-volume interactions. A more specific model for sperm swimming is also being investigated. This model has been shown to display surface adhesion in the dilute solution and the capability to cluster and synchronize motion between two sperm. In multi-sperm simulations, we demonstrate the formation of small clusters by straight swimming sperm, but we find the interactions to be too weak for cluster formation among bent sperm. In order to strengthen interactions, we modify the sinusoidal beat pattern such that it displays an increasing amplitude towards the end of the tail. This indeed extends the time of two synchronized sperm swimming together, compared to the previous model

Collective motion of binary self-propelled particle mixtures

In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. We consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant magnitude. Within each species, the particles try to achieve polar alignment of their velocity vectors, whereas we analyze the cases of preferred polar, antiparallel, as well as perpendicular alignment between particles of different species. Our focus is on the effect that the interplay between the two species has on the threshold densities for the onset of collective motion and on the nature of the solutions above onset. For this purpose, we start from suitable Langevin equations in the particle picture, from which we derive mean field equations of the Fokker-Planck type and finally macroscopic continuum field equations. We perform particle simulations of the Langevin equations, linear stability analyses of the Fokker-Planck and macroscopic continuum equations, and we numerically solve the Fokker-Planck equations. Both, spatially homogeneous and inhomogeneous solutions are investigated, where the latter correspond to stripe-like flocks of collectively moving particles. In general, the interaction between the two species reduces the threshold density for the onset of collective motion of each species. However, this interaction also reduces the spatial organization in the stripe-like flocks. The most interesting behavior is found for the case of preferred perpendicular alignment between different species. There, a competition between polar and truly nematic orientational ordering of the velocity vectors takes place within each particle species. Finally, depending on the alignment rule for particles of different species and within certain ranges of particle densities, identical and inverted spatial density profiles can be found for the two particle species.Comment: 16 pages, 10 figure