Active colloids are microscopic particles, which self-propel through viscous fluids by converting energy extracted from their environment into directed motion. We first explain how articial microswimmers move forward by generating near-surface flow fields via self-phoresis or the self-induced Marangoni effect. We then discuss generic features of the dynamics of single active colloids in bulk and in confinement, as well as in the presence of gravity, field gradients, and fluid flow. In the third part, we review the emergent collective behavior of active colloidal suspensions focussing on their structural and dynamic properties. After summarizing experimental observations, we give an overview on the progress in modeling collectively moving active colloids. While active Brownian particles are heavily used to study collective dynamics on large scales, more advanced methods are necessary to explore the importance of hydrodynamic and phoretic particle interactions. Finally, the relevant physical approaches to quantify the emergent collective behavior are presented.

We study the collective motion of confined spherical microswimmers such as active colloids which we model by so-called squirmers. To simulate hydrodynamic flow fields including thermal noise, we use the method of multiparticle collision dynamics. We demonstrate that hydrodynamic near fields acting between squirmers as well as between squirmers and bounding walls crucially determine their collective motion. In particular, with increasing density we observe a clear phase separation into a gaslike and cluster phase for neutral squirmers whereas strong pushers and pullers more gradually approach the hexagonal cluster state.

We study the three-dimensional dynamics of a spherical microswimmer in cylindrical Poiseuille flow which can be mapped onto a Hamiltonian system. Swinging and tumbling trajectories are identified. In 2D they are equivalent to oscillating and circling solutions of a mathematical pendulum. Hydrodynamic interactions between the swimmer and confining channel walls lead to dissipative dynamics and result in stable trajectories, different for pullers and pushers. We demonstrate this behavior in the dipole approximation of the swimmer and with simulations using the method of multi-particle collision dynamics.PACS numbers: 47.63. Gd, 47.63.mf, Microswimmers often have to respond to fluid flow and confining boundaries, like sperm cells in the Fallopian tubes [1] or pathogens in blood vessels [2]. Artificial microswimmers constructed with the vision to act as drugdeliverers in the human body [3] would have to swim in narrow channels like arteries. Two properties influence the swimming in microchannels. On the one hand, vortices in flow reorient the swimming direction of microorganisms. In simple shear flow, for example, microswimmers tumble due to a constant flow vorticity [4]. Vortices in Poiseuille flow in combination with bottom-heaviness due to gravitation lead to stable orientations of swimming algae cells [5]. On the other hand, microorganisms swimming near surfaces are trapped by hydrodynamic interactions [6] and ultimately escape with the help of rotational diffusion [10]. Finally, bacteria in Poiseuille flow show a net-upstream flux at the walls due to the interplay of confinement and flow vorticity [7,8]. All these examples show there is genuine interest in understanding generic features of microorganisms and artificial swimmers in Poiseuille flow.In this letter we demonstrate that the dynamics of a simple spherical microswimmer in a cylindrical Poiseuille flow can be mapped onto a conservative dynamical system with the Hamiltonian as a constant of motion. In analogy to the oscillating and circling solutions of a mathematical pendulum, we discuss in detail the swinging and tumbling motion of the microswimmer in 2D and generalize them to three dimensions. Hydrodynamic interactions with the channel wall treated in the dipole approximation introduce dissipation and the microswimmer assumes specific stable swimming trajectories depending on its type as puller or pusher.We first introduce the geometry. We consider a pointlike microswimmer that moves with a constant intrinsic swimming speed v 0 in a cylindrical microchannel where a Poiseuille flow is imposed. Using a cylindrical coordinate system (ρ, ϕ, z) with the coordinate basis (ρ,φ,ẑ), the flow is given by v f = v f (1 − ρ 2 /R 2 Ch )ẑ, where v f is the maximum flow speed in the center of the channel [ Fig. 1(a)]. In the absence of noise the equations of mo- tion for the swimmer position r and orientationê are given bywhereChφ is the flow vorticity. The swimmer orientationê = e ρρ + e ϕφ + e zẑ has the components e ρ = − cos Θ sin Ψ, e ϕ = sin Θ, e z = − cos Θ co...

After colliding with a surface, microswimmers reside there during the detention time. They accumulate and may form complex structures such as biofilms. We introduce a general framework to calculate the distribution of detention times using the method of first-passage times and study how rotational noise and hydrodynamic interactions influence the escape from a surface. We compare generic swimmer models to the simple active Brownian particle. While the respective detention times of source dipoles are smaller, the ones of pullers are larger by up to several orders of magnitude, and pushers show both trends. We apply our results to the more realistic squirmer model, for which we use lubrication theory, and validate them by simulations with multiparticle collision dynamics.

Abstract.We study the dynamics of a prolate spheroidal microswimmer in Poiseuille flow for different flow geometries. When moving between two parallel plates or in a cylindrical microchannel, the swimmer performs either periodic swinging or periodic tumbling motion. Although the trajectories of spherical and elongated swimmers are qualitatively similar, the swinging and tumbling frequency strongly depends on the aspect ratio of the swimmer. In channels with reduced symmetry the swimmers perform quasiperiodic motion which we demonstrate explicitly for swimming in a channel with elliptical cross-section.

A striking feature of the collective behavior of spherical microswimmers is that for sufficiently strong self-propulsion they phase-separate into a dense cluster coexisting with a low-density disordered surrounding. Extending our previous work, we use the squirmer as a model swimmer and the particle-based simulation method of multi-particle collision dynamics to explore the influence of hydrodynamics on their phase behavior in a quasi-two-dimensional geometry. The coarsening dynamics towards the phase-separated state is diffusive in an intermediate time regime followed by a final ballistic compactification of the dense cluster. We determine the binodal lines in a phase diagram of Péclet number versus density. Interestingly, the gas binodals are shifted to smaller densities for increasing mean density or dense-cluster size, which we explain using a recently introduced pressure balance [S. C. Takatori, et al., Phys. Rev. Lett. 2014, 113, 028103] extended by a hydrodynamic contribution. Furthermore, we find that for pushers and pullers the binodal line is shifted to larger Péclet numbers compared to neutral squirmers. Finally, when lowering the Péclet number, the dense phase transforms from a hexagonal "solid" to a disordered "fluid" state.

The locomotion of swimming bacteria in simple Newtonian fluids can successfully be described within the framework of low Reynolds number hydrodynamics [1]. The presence of polymers in biofluids generally increases the viscosity, which is expected to lead to slower swimming for a constant bacterial motor torque. Surprisingly, however, several experiments have shown that bacterial speeds increase in polymeric fluids [2][3][4][5], and there is no clear understanding why. Therefore we perform extensive coarse-grained simulations of a bacterium swimming in explicitly modeled solutions of macromolecular polymers of different lengths and densities. We observe an increase of up to 60% in swimming speed with polymer density and demonstrate that this is due to a depletion of polymers in the vicinity of the bacterium leading to an effective slip. However this in itself cannot predict the large increase in swimming velocity: coupling to the chirality of the bacterial flagellum is also necessary.Microorganisms typically move through complex biological environments which contain high-molecular weight polymeric material. Prominent examples include the extracellular matrix, mucosal barriers and polymer-aggregated marine snow [6,7]. Many explanations have been proposed to describe the increase in speed of bacteria in such polymeric fluids, including viscoelastic effects [5], local shear thinning [4], local shear-induced viscosity gradients [8], polymer depletion [9] or modelling the polymers as a gel-forming network [3,10] or a porous medium [11]. Experiments do not, however, yet have the resolution to distinguish between the different theories. Therefore there is a vital role for detailed numerical models that will allow us to understand motion through biologically relevant but rheologically complex, fluids. Drawing on ideas from simulations of polymer hydrodynamics [12] and of bacterial locomotion in Newtonian fluids (see for example ) we simulate a bacterium moving in suspensions of different polymer density (Figure 1 and Supplementary Movie 1). Hence we reproduce, and explain, the enhanced swimming speed.Swimming bacteria such as Pseudomponas aeruginosa, Helicobacter pylori or Eschericia coli rotate helical flagella attached to their cell body to create a thrust force which moves them forwards [1]. Inspired by the biological swimmers we employ a model bacterium consisting of an elongated cell body of length 2b and width 2a connected to a stiff helical flagellum of radius R (Fig. 1a). Our swimmer is driven by applying a constant motor torque T to the flagellum and an opposing torque −T to the body (Fig. 1b). This results in the body rotating with angular velocity Ω, and the counter-rotating flagellum with angular velocity ω (Fig. 1a) which drives the model cell to swim forwards at an average speed V .The fluid consists of a Newtonian background fluid at viscosity η 0 and temperature T modelled by multiparticle collision dynamics (MPCD, see Methods). This is coupled to an ensemble of coarse-grained polymers that are modelled as...

Bacterial contamination of biological channels, catheters or water resources is a major threat to public health, which can be amplified by the ability of bacteria to swim upstream. The mechanisms of this ‘rheotaxis’, the reorientation with respect to flow gradients, are still poorly understood. Here, we follow individual E. coli bacteria swimming at surfaces under shear flow using 3D Lagrangian tracking and fluorescent flagellar labelling. Three transitions are identified with increasing shear rate: Above a first critical shear rate, bacteria shift to swimming upstream. After a second threshold, we report the discovery of an oscillatory rheotaxis. Beyond a third transition, we further observe coexistence of rheotaxis along the positive and negative vorticity directions. A theoretical analysis explains these rheotaxis regimes and predicts the corresponding critical shear rates. Our results shed light on bacterial transport and reveal strategies for contamination prevention, rheotactic cell sorting, and microswimmer navigation in complex flow environments.