Detention Times of Microswimmers Close to Surfaces: Influence of Hydrodynamic Interactions and Noise

Collective behavior of squirmers in thin films

Bacteria in biofilms form complex structures and can collectively migrate within mobile aggregates, which is referred to as swarming. This behavior is influenced by a combination of various factors, including morphological characteristics and propulsive forces of swimmers, their volume fraction within a confined environment, and hydrodynamic and steric interactions between them. In our study, we employ the squirmer model for microswimmers and the dissipative particle dynamics method for fluid modeling to investigate the collective motion of swimmers in thin films. The film thickness permits a free orientation of non-spherical squirmers, but constraints them to form a two-layered structure at maximum. Structural and dynamic properties of squirmer suspensions confined within the slit are analyzed for different volume fractions of swimmers, motility types (e.g., pusher, neutral squirmer, puller), and the presence of a rotlet dipolar flow field, which mimics the counter-rotating flow generated by flagellated bacteria. Different states are characterized, including a gas-like phase, swarming, and motility-induced phase separation, as a function of increasing volume fraction. Our study highlights the importance of an anisotropic swimmer shape, hydrodynamic interactions between squirmers, and their interaction with the walls for the emergence of different collective behaviors. Interestingly, the formation of collective structures may not be symmetric with respect to the two walls. Furthermore, the presence of a rotlet dipole significantly mitigates differences in the collective behavior between various swimmer types. These results contribute to a better understanding of the formation of bacterial biofilms and the emergence of collective states in confined active matter.

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}}.

How to steer active colloids up a vertical wall

An important challenge in active matter lies in harnessing useful global work from entities that produce work locally, e.g., via self-propulsion. We investigate here the active matter version of a classical capillary rise effect, by considering a non-phase separated sediment of self-propelled Janus colloids in contact with a vertical wall. We provide experimental evidence of an unexpected and dynamic adsorption layer at the wall. Additionally, we develop a complementary numerical model that recapitulates the experimental observations. We show that an adhesive and aligning wall enhances the pre-existing polarity heterogeneity within the bulk, enabling polar active particles to climb up a wall against gravity, effectively powering a global flux. Such steady-state flux has no equivalent in a passive wetting layer.

Dispersion of run-and-tumble microswimmers through disordered media

Understanding the transport properties of microorganisms and self-propelled particles in porous media has important implications for human health as well as microbial ecology. In free space, most microswimmers perform diffusive random walks as a result of the interplay of self-propulsion and orientation decorrelation mechanisms such as run-and-tumble dynamics or rotational diffusion. In an unstructured porous medium, collisions with the microstructure result in a decrease in the effective spatial diffusivity of the particles from its free-space value. Here, we analyze this problem for a simple model system consisting of noninteracting point particles performing run-and-tumble dynamics through a two-dimensional disordered medium composed of a random distribution of circular obstacles, in the absence of Brownian diffusion or hydrodynamic interactions. The particles are assumed to collide with the obstacles as hard spheres and subsequently slide on the obstacle surface with no frictional resistance while maintaining their orientation, until they either escape or tumble. We show that the variations in the long-time diffusivity can be described by a universal dimensionless hindrance function f(ϕ,Pe) of the obstacle area fraction ϕ and Péclet number Pe, or ratio of the swimmer run length to the obstacle size. We analytically derive an asymptotic expression for the hindrance function valid for dilute media (Peϕ≪1), and its extension to denser media is obtained using stochastic simulations. As we explain, the model is also easily generalized to describe dispersion in three dimensions.

Hydrodynamic Anisotropy of Depletion in Nonequilibrium

Active colloids in a bath of inert particles of smaller size cause anisotropic depletion. The active hydrodynamics of this nonequilibrium phenomenon, which is fundamentally different from its equilibrium counterpart and passive particles in an active bath, remains scarcely understood. Here we combine mesoscale hydrodynamic simulation as well as theoretical analysis to examine the physical origin for the active depletion around a self-propelled noninteractive colloid. Our results elucidate that the variable hydrodynamic effect critically governs the microstructure of the depletion zone. Three characteristic states of anisotropic depletion are identified, depending on the strength and stress of activity. This yields a state diagram of depletion in the two-parameter space, captured by developing a theoretical model with the continuum kinetic theory and leading to a mechanistic interpretation of the hydrodynamic anisotropy of depletion. Furthermore, we demonstrate that such depletion in nonequilibrium results in various clusters with ordered organization of squirmers, which follows a distinct principle contrary to that of the entropy scenario of depletion in equilibrium. The findings might be of immediate interest to tune the hydrodynamics-mediated anisotropic interactions and active nonequilibrium organizations in the self-propulsion systems.

Comparison of three-dimensional motion of bacteria with and without wall accumulation

A comparison of the movement characteristics between bacteria with and without wall accumulation could potentially elucidate the mechanisms of biofilm formation. However, authors of previous studies have mostly focused on the motion of bacteria that exhibit wall accumulation. Here, we applied digital holographic microscopy to compare the three-dimensional (3D) motions of two bacterial strains (Shewanella japonica UMDC19 and Shewanella sp. UMDC1): one exhibiting higher concentrations near the solid surfaces, and the other showing similar concentrations in near-wall and bulk regions. We found that the movement characteristics of the two strains are similar in the near-wall region but are distinct in the bulk region. Near the wall, both strains have small velocities and mostly perform subdiffusive motions. In the bulk, however, the bacteria exhibiting wall accumulation have significantly higher motility (including faster swimming speeds and longer movement trajectories) than the one showing no wall accumulation. Furthermore, we found that bacteria exhibiting wall accumulation slowly migrate from the bulk region to the near-wall region, and the hydrodynamic effect alone is insufficient to generate this migration speed. Future studies are required to test if the current findings apply to other bacterial species and strains.

Hydrodynamic interactions between squirmers near walls: far-field dynamics and near-field cluster stability

Confinement increases contacts between microswimmers in dilute suspensions and affects their interactions. In particular, boundaries have been shown experimentally to lead to the formation of clusters that would not occur in bulk fluids. To what extent does hydrodynamics govern these boundary-driven encounters between microswimmers? We consider theoretically the symmetric boundary-mediated encounters of model microswimmers under gravity through far-field interaction of a pair of weak squirmers, as well as the lubrication interactions occurring after contact between two or more squirmers. In the far field, the orientation of microswimmers is controlled by the wall and the squirming parameter. The presence of a second swimmer influences the orientation of the original squirmer, but for weak squirmers, most of the interaction occurs after contact. We thus analyse next the near-field reorientation of circular groups of squirmers. We show that a large number of swimmers and the presence of gravity can stabilize clusters of pullers, while the opposite is true for pushers; to be stable, clusters of pushers thus need to be governed by other interactions (e.g. phoretic). This simplified approach to the phenomenon of active clustering enables us to highlight the hydrodynamic contribution, which can be hard to isolate in experimental realizations.

Rectification of polymer translocation through nanopores by nonchiral and chiral active particles

We study translocation of a flexible polymer chain through a membrane pore under the influence of active forces and steric exclusion using Langevin dynamics simulations within a minimal two-dimensional model. The active forces on the polymer are imparted by nonchiral and chiral active particles that are introduced on one side or both sides of a rigid membrane positioned across the midline of a confining box. We show that the polymer can translocate through the pore to either side of the dividing membrane in the absence of external forcing. Translocation of the polymer to a given side of the membrane is driven (hindered) by an effective pulling (pushing) exerted by the active particles that are present on that side. The effective pulling results from accumulation of active particles around the polymer. This crowding effect signifies persistent motion of active particles causing prolonged detention times for them close to the confining walls and the polymer. The effective pushing that hinders the translocation, on the other hand, results from steric collisions that occur between the polymer and active particles. As a result of the competition between these effective forces, we find a transition between two rectified cis-to-trans and trans-to-cis translocation regimes. This transition is identified by a sharp peak in the average translocation time. The effects of active particles on the transition is studied by analyzing how the translocation peak is regulated by the activity (self-propulsion) strength of these particles, their area fraction, and chirality strength.

Settling mode of a bottom-heavy squirmer in a narrow vessel

The lattice Boltzmann-immersed boundary (IB-LB) method is used to numerically simulate the sedimentation motion of a single two-dimensional, bottom-heavy squirmer in a narrow vessel. The effects of the swimming Reynolds number Re_s = 0.1-3, eccentricity distance l = 0.15d-0.75d, and density ratio of squirmer to fluid γ = 1.1-2.0 on the settlement motion characteristics are investigated and analyzed. The results showed that four settling modes exist: vertical motion, unilateral oscillation, oscillation, and tilt. The bottom-heavy neutral squirmer and puller settle in the vessel during vertical motion when Re_s is 0.1-1.5. By increasing Re_s and swimming strength |β|, the bottom-heavy squirmer becomes more self-driven, shifting its settling mode from vertical motion to unilateral oscillation or oscillation. Increasing l or |β| does not affect the bottom-heavy neutral squirmer and puller's vertical settling mode but shifts the bottom-heavy pusher's settling mode from unilateral oscillation to oscillation or oscillation to unilateral oscillation. Similarly, altering γ or |β| has no impact on the eccentric neutral squirmer and puller's settling mode; however, pushers will switch from oscillation mode to attraction mode or from oscillation mode to tilt mode. Additionally, it was found that after the squirmer collided with the bottom wall, the bottom-heavy squirmer settled at the bottom of the vessel in a different state of motion.

Most probable path of an active Brownian particle

In this study, we investigate the transition path of a free active Brownian particle (ABP) on a two-dimensional plane between two given states. The extremum conditions for the most probable path connecting the two states are derived using the Onsager-Machlup integral and its variational principle. We provide explicit solutions to these extremum conditions and demonstrate their nonuniqueness through an analogy with the pendulum equation indicating possible multiple paths. The pendulum analogy is also employed to characterize the shape of the globally most probable path obtained by explicitly calculating the path probability for multiple solutions. We comprehensively examine a translation process of an ABP to the front as a prototypical example. Interestingly, the numerical and theoretical analyses reveal that the shape of the most probable path changes from an I to a U shape and to the ℓ shape with an increase in the transition process time. The Langevin simulation also confirms this shape transition. We also discuss further method applications for evaluating a transition path in rare events in active matter.

Anomalous Cooling and Overcooling of Active Colloids

The phenomenon that a system at a hot temperature cools faster than at a warm temperature, referred to as the Mpemba effect, has recently been realized for trapped colloids. Here, we investigate the cooling and heating process of a self-propelled active colloid using numerical simulations and theoretical calculations with a model that can be directly tested in experiments. Upon cooling, activity induces a Mpemba effect and the active particle transiently escapes an effective temperature description. At the end of the cooling process the notion of temperature is recovered and the system can exhibit even smaller temperatures than its final temperature, a surprising phenomenon which we refer to as activity-induced overcooling.

Force Generation in Confined Active Fluids: The Role of Microstructure

We experimentally determine the force exerted by a bath of active particles onto a passive probe as a function of its distance to a wall and compare it to the measured averaged density distribution of active particles around the probe. Within the framework of an active stress, we demonstrate that both quantities are-up to a factor-directly related to each other. Our results are in excellent agreement with a minimal numerical model and confirm a general and system-independent relationship between the microstructure of active particles and transmitted forces.

The role of particle-electrode wall interactions in mobility of active Janus particles driven by electric fields

HYPOTHESIS

The interaction of active particles with walls can explain discrepancies between experiments and theory derived for particles in the bulk. For an electric field driven metallodielectric Janus particle (JP) adjacent to an electrode, interaction between the asymmetric particle and the partially screened electrode yields a net electrostatic force - termed self-dielectrophoresis (sDEP) - that competes with induced-charge electrophoresis (ICEP) to reverse particle direction.

EXPERIMENTS

The potential contribution of hydrodynamic flow to the reversal is evaluated by visualizing flow around a translating particle via micro-particle image velocimetry and chemically suppressing ICEP with poly(l-lysine)-g-poly(ethylene glycol) (PLL-PEG). Mobility of Polystyrene-Gold JPs is measured in KCl electrolytes of varying concentration and with a capacitive SiO₂ coating at the metallic JP surface or electrode. Results are compared with theory and numerical simulations accounting for electrode screening.

FINDINGS

PLL-PEG predominantly suppresses low-frequency mobility where propulsive electro-hydrodynamic jetting is observed; supporting the hypothesis of an electrostatic driving force at high frequencies. Simulations and theory show the magnitude, direction and frequency dispersion of JP mobility are obtained by superposition of ICEP and sDEP using the JP height and capacitance as fitting parameters. Wall proximity enhances ICEP and sDEP and manifests a secondary ICEP charge relaxation time dominating in the contact limit.

Gyrotactic cluster formation of bottom-heavy squirmers

Squirmers that are bottom-heavy experience a torque that aligns them along the vertical so that they swim upwards. In a suspension of many squirmers, they also interact hydrodynamically via flow fields that are initiated by their swimming motion and by gravity. Swimming under the combined action of flow field vorticity and gravitational torque is called gyrotaxis. Using the method of multi-particle collision dynamics, we perform hydrodynamic simulations of a many-squirmer system floating above the bottom surface. Due to gyrotaxis they exhibit pronounced cluster formation with increasing gravitational torque. The clusters are more volatile at low values but compactify to smaller clusters at larger torques. The mean distance between clusters is mainly controlled by the gravitational torque and not the global density. Furthermore, we observe that neutral squirmers form clusters more easily, whereas pullers require larger gravitational torques due to their additional force-dipole flow fields. We do not observe clustering for pusher squirmers. Adding a rotlet dipole to the squirmer flow field induces swirling clusters. At high gravitational strengths, the hydrodynamic interactions with the no-slip boundary create an additional vertical alignment for neutral squirmers, which also supports cluster formation.

Migration of active filaments under Poiseuille flow in a microcapillary tube

We present a comprehensive study of active filaments confined in a cylindrical channel under Poiseuille flow. The activity drives the filament towards the channel boundary, whereas external fluid flow migrates the filament away from the boundary. This migration further shifts towards the centre for higher flow strength. The migration behaviour of the filaments is presented in terms of the alignment order parameter that shows the alignment grows with shear and activity. Further, we have also addressed the role of length of filament on the migration behaviour, which suggests higher migration for larger filaments. Moreover, we discuss the polar ordering of filaments as a function of distance from the centre of channel that displays upstream motion near the boundary and downstream motion at the centre of the tube.

Oscillatory active microrheology of active suspensions

Using the method of Brownian dynamics, we investigate the dynamic properties of a 2d suspension of active disks at high Péclet numbers using active microrheology. In our simulations the tracer particle is driven either by a constant or an oscillatory external force. In the first case, we find that the mobility of the tracer initially appreciably decreases with the external force and then becomes approximately constant for larger forces. For an oscillatory driving force we find that the dynamic mobility shows a quite complex behavior-it displays a highly nonlinear behavior on both the amplitude and frequency of the driving force. In the range of forces studied, we do not observe a linear regime. This result is important because it reveals that a phenomenological description of tracer motion in active media in terms of a simple linear stochastic equation even with a memory-mobility kernel is not appropriate, in the general case.

Accumulation of Tetrahymena pyriformis on Interfaces

The behavior of ciliates has been studied for many years through environmental biology and the ethology of microorganisms, and recent hydrodynamic studies of microswimmers have greatly advanced our understanding of the behavioral dynamics at the single-cell level. However, the association between single-cell dynamics captured by microscopic observation and pattern dynamics obtained by macroscopic observation is not always obvious. Hence, to bridge the gap between the two, there is a need for experimental results on swarming dynamics at the mesoscopic scale. In this study, we investigated the spatial population dynamics of the ciliate, Tetrahymena pyriformis, based on quantitative data analysis. We combined the image processing of 3D micrographs and machine learning to obtain the positional data of individual cells of T. pyriformis and examined their statistical properties based on spatio-temporal data. According to the 3D spatial distribution of cells and their temporal evolution, cells accumulated both on the solid wall at the bottom surface and underneath the air–liquid interface at the top. Furthermore, we quantitatively clarified the difference in accumulation levels between the bulk and the interface by creating a simple behavioral model that incorporated quantitative accumulation coefficients in its solution. The accumulation coefficients can be compared under different conditions and between different species.

Optimal navigation strategy of active Brownian particles in target-search problems

We investigate exploration patterns of a microswimmer, modeled as an active Brownian particle, searching for a target region located in a well of an energy landscape and separated from the initial position of the particle by high barriers. We find that the microswimmer can enhance its success rate in finding the target by tuning its activity and its persistence in response to features of the environment. The target-search patterns of active Brownian particles are counterintuitive and display characteristics robust to changes in the energy landscape. On the contrary, the transition rates and transition-path times are sensitive to the details of the specific energy landscape. In striking contrast to the passive case, the presence of additional local minima does not significantly slow down the active-target-search dynamics.

Rolling controls sperm navigation in response to the dynamic rheological properties of the environment

Mammalian sperm rolling around their longitudinal axes is a long-observed component of motility, but its function in the fertilization process, and more specifically in sperm migration within the female reproductive tract, remains elusive. While investigating bovine sperm motion under simple shear flow and in a quiescent microfluidic reservoir and developing theoretical and computational models, we found that rolling regulates sperm navigation in response to the rheological properties of the sperm environment. In other words, rolling enables a sperm to swim progressively even if the flagellum beats asymmetrically. Therefore, a rolling sperm swims stably along the nearby walls (wall-dependent navigation) and efficiently upstream under an external fluid flow (rheotaxis). By contrast, an increase in ambient viscosity and viscoelasticity suppresses rolling, consequently, non-rolling sperm are less susceptible to nearby walls and external fluid flow and swim in two-dimensional diffusive circular paths (surface exploration). This surface exploration mode of swimming is caused by the intrinsic asymmetry in flagellar beating such that the curvature of a sperm's circular path is proportional to the level of asymmetry. We found that the suppression of rolling is reversible and occurs in sperm with lower asymmetry in their beating pattern at higher ambient viscosity and viscoelasticity. Consequently, the rolling component of motility may function as a regulatory tool allowing sperm to navigate according to the rheological properties of the functional region within the female reproductive tract.

Enhanced diffusion of a tracer particle in a lattice model of a crowded active system

Living systems at the subcellular, cellular, and multicellular levels are often crowded systems that contain active particles. The active motion of these particles can also propel passive particles, which typically results in enhanced effective diffusion of the passive particles. Here we study the diffusion of a passive tracer particle in such a dense system of active crowders using a minimal lattice model incorporating particles pushing each other. We show that the model exhibits several regimes of motility and quantify the enhanced diffusion as a function of density and activity of the active crowders. Moreover, we demonstrate an interplay of tracer diffusion and clustering of active particles, which suppresses the enhanced diffusion. Simulations of mixtures of passive and active crowders show that a rather small fraction of active particles is sufficient for the observation of enhanced diffusion.

Squirming in a viscous fluid enclosed by a Brinkman medium

Cell motility plays important roles in a range of biological processes, such as reproduction and infections. Studies have hypothesized that the ulcer-causing bacterium Helicobacter pylori invades the gastric mucus layer lining the stomach by locally turning nearby gel into sol, thereby enhancing its locomotion through the biological barrier. In this work, we present a minimal theoretical model to investigate how heterogeneity created by a swimmer affects its own locomotion. As a generic locomotion model, we consider the swimming of a spherical squirmer in a purely viscous fluid pocket (representing the liquified or degelled region) surrounded by a Brinkman porous medium (representing the mucus gel). The use of the squirmer model enables an exact, analytical solution to this hydrodynamic problem. We obtain analytical expressions for the swimming speed, flow field, and power dissipation of the swimmer. Depending on the details of surface velocities and fluid properties, our results reveal the existence of a minimum threshold size of mucus gel that a swimmer needs to liquify in order to gain any enhancement in swimming speed. The threshold size can be as much as approximately 30% of the swimmer size. We contrast these predictions with results from previous models and highlight the significant role played by the details of surface actuations. In addition to their biological implications, these results could also inform the design of artificial microswimmers that can penetrate into biological gels for more effective drug delivery.

Rebound and scattering of motile Chlamydomonas algae in confined chambers

Motivated by recent experiments demonstrating that motile algae get trapped in draining foams, we study the trajectories of microorganisms confined in model foam channels (section of a Plateau border). We track single Chlamydomonas reinhardtii cells confined in a thin three-circle microfluidic chamber and show that their spatial distribution exhibits strong corner accumulation. Using empirical scattering laws observed in previous experiments (scattering with a constant scattering angle), we next develop a two-dimension geometrical model and compute the phase space of trapped and periodic trajectories of swimmers inside a three-circles billiard. We find that the majority of cell trajectories end up in a corner, providing a geometrical mechanism for corner accumulation. Incorporating the distribution of scattering angles observed in our experiments and including hydrodynamic interactions between the cells and the surfaces into the geometrical model enables us to reproduce the experimental probability density function of micro-swimmers in microfluidic chambers. Both our experiments and models demonstrate therefore that motility leads generically to trapping in complex geometries.

Escape dynamics of active particles in multistable potentials

Rare transitions between long-lived metastable states underlie a great variety of physical, chemical and biological processes. Our quantitative understanding of reactive mechanisms has been driven forward by the insights of transition state theory and in particular by Kramers' dynamical framework. Its predictions, however, do not apply to systems that feature non-conservative forces or correlated noise histories. An important class of such systems are active particles, prominent in both biology and nanotechnology. Here, we study the active escape dynamics of a silica nanoparticle trapped in a bistable potential. We introduce activity by applying an engineered stochastic force that emulates self-propulsion. Our experiments, supported by a theoretical analysis, reveal the existence of an optimal correlation time that maximises the transition rate. We discuss the origins of this active turnover, reminiscent of the much celebrated Kramers turnover. Our work establishes a versatile experimental platform to study single particle dynamics in non-equilibrium settings.

Statistics of pathogenic bacteria in the search of host cells

A crucial phase in the infection process, which remains poorly understood, is the localization of suitable host cells by bacteria. It is often assumed that chemotaxis plays a key role during this phase. Here, we report a quantitative study on how Salmonella Typhimurium search for T84 human colonic epithelial cells. Combining time-lapse microscopy and mathematical modeling, we show that bacteria can be described as chiral active particles with strong active speed fluctuations, which are of biological, as opposed to thermal, origin. We observe that there exists a giant range of inter-individual variability of the bacterial exploring capacity. Furthermore, we find Salmonella Typhimurium does not exhibit biased motion towards the cells and show that the search time statistics is consistent with a random search strategy. Our results indicate that in vitro localization of host cells, and also cell infection, are random processes, not involving chemotaxis, that strongly depend on bacterial motility parameters.

Active particles with polar alignment in ring-shaped confinement

We study steady-state properties of active, nonchiral and chiral Brownian particles with polar alignment and steric interactions confined within a ring-shaped confinement (annulus) in two dimensions. Exploring possible interplays between polar interparticle alignment, geometric confinement and the surface curvature, being incorporated here on minimal levels, we report a surface-population reversal effect, whereby active particles migrate from the outer concave boundary of the annulus to accumulate on its inner convex boundary. This contrasts the conventional picture, implying stronger accumulation of active particles on concave boundaries relative to the convex ones. The population reversal is caused by both particle alignment and surface curvature, disappearing when either of these factors is absent. We explore the ensuing consequences for the chirality-induced current and swim pressure of active particles and analyze possible roles of system parameters, such as the mean number density of particles and particle self-propulsion, chirality, and alignment strengths.

Confinement-induced alternating interactions between inclusions in an active fluid

In a system of colloidal inclusions suspended in an equilibrium bath of smaller particles, the particulate bath engenders effective, short-ranged, primarily attractive interactions between the inclusions, known as depletion interactions, that originate from the steric depletion of bath particles from the immediate vicinity of the inclusions. In a bath of active (self-propelled) particles, the nature of such bath-mediated interactions can qualitatively change from attraction to repulsion, and they become stronger in magnitude and range of action as compared with typical equilibrium depletion interactions, especially as the bath activity (particle self-propulsion) is increased. We study effective interactions mediated by a bath of active Brownian particles between two fixed, impenetrable, and disk-shaped inclusions in a planar (channel) confinement in two dimensions. Confinement is found to strongly influence the effective interaction between the inclusions, specifically by producing alternating interaction profiles with possible attractive and repulsive regions in sufficiently narrow channels. We study the dependence of the ensuing interactions on different system parameters and the orientational (parallel versus perpendicular) configuration of the inclusion pair relative to the channel walls. The confinement effects are largely regulated by the layering of active particles next to the surface boundaries, both of the inclusions and the channel walls that counteract one another in accumulating the active particles in their own proximities. In narrow channels, the combined effects due to the channel walls and the inclusions lead to peculiar structuring of active particles (reminiscent of wavelike interference patterns) within the channel.

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.

Motile Bacteria at Oil-Water Interfaces: Pseudomonas aeruginosa

Bacteria are important examples of active or self-propelled colloids. Because of their directed motion, they accumulate near interfaces. There, they can become trapped and swim adjacent to the interface via hydrodynamic interactions, or they can adsorb directly and swim in an adhered state with complex trajectories that differ from those in bulk in both form and spatiotemporal implications. We have adopted the monotrichous bacterium Pseudomonas aeruginosa PA01 as a model species and have studied its motion at oil-aqueous interfaces. We have identified conditions in which bacteria swim persistently without restructuring the interface, allowing detailed and prolonged study of their motion. In addition to characterizing the ensemble behavior of the bacteria, we have observed a gallery of distinct trajectories of individual swimmers on and near fluid interfaces. We attribute these diverse swimming behaviors to differing trapped states for the bacteria in the fluid interface. These trajectory types include Brownian diffusive paths for passive adsorbed bacteria, curvilinear trajectories including curly paths with radii of curvature larger than the cell body length, and rapid pirouette motions with radii of curvature comparable to the cell body length. Finally, we see interfacial visitors that come and go from the interfacial plane. We characterize these individual swimmer motions. This work may impact nutrient cycles for bacteria on or near interfaces in nature. This work will also have implications in microrobotics, as active colloids in general and bacteria in particular are used to carry cargo in this burgeoning field. Finally, these results have implications in engineering of active surfaces that exploit interfacially trapped self-propelled colloids.

Vortex formation of spherical self-propelled particles around a circular obstacle

A vortex is a common ratchet phenomenon in active systems. The spatial symmetry is usually broken by introducing asymmetric shapes or spontaneously by collective motion in the presence of hydrodynamic interactions or other alignment effects. Unexpectedly, we observe, by simulations, the formation of a vortex in the simplest model of a circular obstacle immersed in a bath of spherical self-propelled particles. No symmetry-breaking factors mentioned above are included in this model. The vortex forms only when the particle activity is high, i.e. large persistence. The obstacle size is also a key factor and the vortex only forms in a limited range of obstacle sizes. The sustainment of the vortex originates from the bias of the rotating particle cluster around the obstacle in accepting the incoming particles based on their propelling directions. Our results provide new understanding of and insights into the spontaneous symmetry-breaking and ratchet phenomena in active matter.

Active dipolar spheroids in shear flow and transverse field: Population splitting, cross-stream migration, and orientational pinning

We study the steady-state behavior of active, dipolar, Brownian spheroids in a planar channel subjected to an imposed Couette flow and an external transverse field, applied in the "downward" normal-to-flow direction. The field-induced torque on active spheroids (swimmers) is taken to be of magnetic form by assuming that they have a permanent magnetic dipole moment, pointing along their self-propulsion (swim) direction. Using a continuum approach, we show that a host of behaviors emerges over the parameter space spanned by the particle aspect ratio, self-propulsion and shear/field strengths, and the channel width. The cross-stream migration of the model swimmers is shown to involve a regime of linear response (quantified by a linear-response factor) in weak fields. For prolate swimmers, the weak-field behavior crosses over to a regime of full swimmer migration to the bottom half of the channel in strong fields. For oblate swimmers, a counterintuitive regime of reverse migration arises in intermediate fields, where a macroscopic fraction of swimmers reorient and swim to the top channel half at an acute "upward" angle relative to the field axis. The diverse behaviors reported here are analyzed based on the shear-induced population splitting (bimodality) of the swim orientation, giving two distinct, oppositely polarized, swimmer subpopulations (albeit very differently for prolate/oblate swimmers) in each channel half. In strong fields, swimmers of both types exhibit net upstream currents relative to the laboratory frame. The onsets of full migration and net upstream current depend on the aspect ratio, enabling efficient particle separation strategies in microfluidic setups.

Formation of stable and responsive collective states in suspensions of active colloids

Many animal species organise into disordered swarms, polarised flocks or swirls to protect from predators or optimise foraging. Previous studies suggest that such collective states are related to a critical point, which could explain their balance between robustness to noise and high responsiveness regarding external perturbations. Here we provide experimental evidence for this idea by investigating the stability of swirls formed by light-responsive active colloids which adjust their individual motion to positions and orientations of neighbours. Because their behaviour can be precisely tuned, controlled changes between different collective states can be achieved. During the transition between stable swirls and swarms we observe a maximum of the group's susceptibility indicating the vicinity of a critical point. Our results support the idea of system-independent organisation principles of collective states and provide useful strategies for the realisation of responsive yet stable ensembles in microrobotic systems.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Numerical simulations of self-diffusiophoretic colloids at fluid interfaces

The dynamics of active colloids is very sensitive to the presence of boundaries and interfaces which therefore can be used to control their motion. Here we analyze the dynamics of active colloids adsorbed at a fluid-fluid interface. By using a mesoscopic numerical approach which relies on an approximated numerical solution of the Navier-Stokes equation, we show that when adsorbed at a fluid interface, an active colloid experiences a net torque even in the absence of a viscosity contrast between the two adjacent fluids. In particular, we study the dependence of this torque on the contact angle of the colloid with the fluid-fluid interface and on its surface properties. We rationalize our results via an approximate approach which accounts for the appearance of a local friction coefficient. By providing insight into the dynamics of active colloids adsorbed at fluid interfaces, our results are relevant for two-dimensional self assembly and emulsion stabilization by means of active colloids.

Fine balance of chemotactic and hydrodynamic torques: When microswimmers orbit a pillar just once

We study the detention statistics of self-propelling droplet microswimmers attaching to microfluidic pillars. These droplets show negative autochemotaxis: they shed a persistent repulsive trail of spent fuel that biases them to detach from pillars in a specific size range after orbiting them just once. We have designed a microfluidic assay recording microswimmers in pillar arrays of varying diameter, derived detention statistics via digital image analysis, and interpreted these statistics via the Langevin dynamics of an active Brownian particle model. By comparing data from orbits with and without residual chemical field, we can independently estimate quantities such as hydrodynamic and chemorepulsive torques, chemical coupling constants and diffusion coefficients, as well as their dependence on environmental factors such as wall curvature. This type of analysis is generalizable to many kinds of microswimmers.

Colloidal swimmers near curved and structured walls

We present systematic numerical simulations to understand the behavior of colloidal swimmers near a wall. We extend previous theoretical calculations based on lubrication theory to include walls with arbitrary curvature, and show how to extract from simulations a set of parameters crucial to accurately estimate the leading hydrodynamic contributions associated with the curvature of a wall. Our results show explicitly how introducing curvature to the wall not only affects the average incident angle the swimmer acquires when swimming near it, but it also leads to much broader angular distributions. This suggests an increasingly leading role of thermal fluctuations with curvature, which in turn results in significantly different motility of the swimmers. We also show how the backwards motion previously reported for pushers also extends to puller-like swimmers under the appropriate conditions. Finally, aiming at understanding the behavior of colloidal swimmers near a colloidal crystal, we also considered the case of a wall built from colloidal particles that are either free to rotate, representing a crystal held together by isotropic forces, or have their rotational degrees of freedom locked-in, representing a crystal held together by directional interactions. In both cases, we find that puller-like swimmers follow a stochastic run-and-tumble-like dynamics.

Enhanced propagation of motile bacteria on surfaces due to forward scattering

How motile bacteria move near a surface is a problem of fundamental biophysical interest and is key to the emergence of several phenomena of biological, ecological and medical relevance, including biofilm formation. Solid boundaries can strongly influence a cell's propulsion mechanism, thus leading many flagellated bacteria to describe long circular trajectories stably entrapped by the surface. Experimental studies on near-surface bacterial motility have, however, neglected the fact that real environments have typical microstructures varying on the scale of the cells' motion. Here, we show that micro-obstacles influence the propagation of peritrichously flagellated bacteria on a flat surface in a non-monotonic way. Instead of hindering it, an optimal, relatively low obstacle density can significantly enhance cells' propagation on surfaces due to individual forward-scattering events. This finding provides insight on the emerging dynamics of chiral active matter in complex environments and inspires possible routes to control microbial ecology in natural habitats.

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.

Oscillatory surface rheotaxis of swimming E. coli bacteria

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.

Hydrodynamic mobility reversal of squirmers near flat and curved surfaces

Self-propelled particles have been experimentally shown to orbit spherical obstacles and move along surfaces. Here, we theoretically and numerically investigate this behavior for a hydrodynamic squirmer interacting with spherical objects and flat walls using three different methods of approximately solving the Stokes equations: The method of reflections, which is accurate in the far field; lubrication theory, which describes the close-to-contact behavior; and a lattice Boltzmann solver that accurately accounts for near-field flows. The method of reflections predicts three distinct behaviors: orbiting/sliding, scattering, and hovering, with orbiting being favored for lower curvature as in the literature. Surprisingly, it also shows backward orbiting/sliding for sufficiently strong pushers, caused by fluid recirculation in the gap between the squirmer and the obstacle leading to strong forces opposing forward motion. Lubrication theory instead suggests that only hovering is a stable point for the dynamics. We therefore employ lattice Boltzmann to resolve this discrepancy and we qualitatively reproduce the richer far-field predictions. Our results thus provide insight into a possible mechanism of mobility reversal mediated solely through hydrodynamic interactions with a surface.

Collective dynamics in a monolayer of squirmers confined to a boundary by gravity

We present a hydrodynamic study of a monolayer of squirmer model microswimmers confined to a boundary by strong gravity using the simulation method of multi-particle collision dynamics. The squirmers interact with each other via their self-generated hydrodynamic flow fields and thereby form a variety of fascinating dynamic states when density and squirmer type are varied. Weak pushers, neutral squirmers, and pullers have an upright orientation. With their flow fields they push neighbors away and thereby form a hydrodynamic Wigner fluid at lower densities. Furthermore, states of fluctuating chains and trimers, of kissing, and at large densities a global cluster exist. Finally, pushers at all densities can tilt against the wall normal and their in-plane velocities align to show swarming. It turns into chaotic swarming for strong pushers at high densities. We characterize all these states quantitatively.

Behavior of active filaments near solid-boundary under linear shear flow

The steady-state behavior of a dilute suspension of self-propelled filaments confined between planar walls subjected to Couette-flow is reported herein. The effect of hydrodynamics has been taken into account using a mesoscale simulation approach. We present a detailed analysis of positional and angular probability distributions of filaments with varying propulsive force and shear-flow. The distribution of the centre-of-mass of the filament shows adsorption near the surfaces, which diminishes with the flow. The excess density of filaments decreases with Weissenberg number as Wi-β with an exponent β ≈ 0.8, in the intermediate shear range (1 < Wi < 30). The angular orientational moment also decreases near the wall as Wi-δ with δ ≈ 1/5; the variation in orientational moment near the wall is relatively slower than the bulk. It shows a strong dependence on the propulsive force near the wall, with variation on force as Pe-1/3 for large Pe ≥ 1. The active filament shows orientational preference with flow near the surfaces, which splits into upstream and downstream swimming. The population splitting from a unimodal (propulsive force dominated regime) to bimodal phase (shear dominated regime) is identified in the parameter space of propulsive force and shear flow.

Hydrodynamic self-assembly of active colloids: chiral spinners and dynamic crystals

Active colloids self-organise into a variety of collective states, ranging from highly motile "molecules" to complex 2D structures. Using large-scale simulations, we show that hydrodynamic interactions, together with a gravity-like aligning field, lead to tunable self-assembly of active colloidal spheres near a surface. The observed structures depend on the hydrodynamic characteristics: particles driven at the front, pullers, form small chiral spinners consisting of two or three particles, whereas those driven at the rear, pushers, assemble into large dynamic aggregates. The rotational motion of the puller spinners, arises from spontaneous breaking of the internal chirality. Our results show that the fluid flow mediates chiral transfer between neighbouring spinners. Finally we show that the chirality of the individual spinners controls the topology of the self-assembly in solution: homochiral samples assemble into a hexagonally symmetric 2D crystal lattice while racemic mixtures show reduced hexatic order with diffusion-like dynamics.

Stokes velocity generated by a point force in various geometries

In this short review, we visualize the fluid velocity generated by a point force close to a plane free surface or a plane rigid wall. We present separately contributions from all the multipoles which form the corresponding classical systems of images. Such graphical images might be useful in the theoretical and numerical modeling of the dynamics of micro-objects moving close to an interface.

Combined influence of hydrodynamics and chemotaxis in the distribution of microorganisms around spherical nutrient sources

We study how the interaction between hydrodynamics and chemotaxis affects the colonization of nutrient sources by microorganisms. We use an individual-based model and perform probabilistic simulations to ascertain the impact of important environmental and motility characteristics on the spatial distribution of microorganisms around a spherical nutrient source. In general, we unveil four distinct regimes based on the distribution of the microorganisms: (i) strong surface colonization, (ii) rotary-diffusion-induced "off-surface" accumulation, (iii) a depletion zone in the spatial distribution, and (iv) no appreciable aggregation, with their occurrence being contingent on the relative strengths of hydrodynamic and chemotactic effects. More specifically, we show that the extent of surface colonization first increases, then reaches a plateau, and finally decreases as the nutrient availability is increased. We also show that surface colonization reduces monotonically as the mean run length of the chemotactic microorganisms increases. Our study provides insight into the interplay of two important mechanisms governing microorganism behavior near nutrient sources, isolates each of their effects, and thus offers greater predictability of this nontrivial phenomenon.

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.

Active fluids at circular boundaries: swim pressure and anomalous droplet ripening

We investigate the swim pressure exerted by non-chiral and chiral active particles on convex or concave circular boundaries. Active particles are modeled as non-interacting and non-aligning self-propelled Brownian particles. The convex and concave circular boundaries are used to model a fixed inclusion immersed in an active bath and a cavity (or container) enclosing the active particles, respectively. We first present a detailed analysis of the role of convex versus concave boundary curvature and of the chirality of active particles in their spatial distribution, chirality-induced currents, and the swim pressure they exert on the bounding surfaces. The results will then be used to predict the mechanical equilibria of suspended fluid enclosures (generically referred to as 'droplets') in a bulk with active particles being present either inside the bulk fluid or within the suspended droplets. We show that, while droplets containing active particles behave in accordance with standard capillary paradigms when suspended in a normal bulk, those containing a normal fluid exhibit anomalous behaviors when suspended in an active bulk. In the latter case, the excess swim pressure results in non-monotonic dependence of the inside droplet pressure on the droplet radius; hence, revealing an anomalous regime of behavior beyond a threshold radius, in which the inside droplet pressure increases upon increasing the droplet size. Furthermore, for two interconnected droplets, mechanical equilibrium can occur also when the droplets have different sizes. We thus identify a regime of anomalous droplet ripening, where two unequal-sized droplets can reach a final state of equal size upon interconnection, in stark contrast with the standard Ostwald ripening phenomenon, implying shrinkage of the smaller droplet in favor of the larger one.