Hydrodynamic interaction of microswimmers near a wall

Dynamics of a spheroidal squirmer interacting with a cylindrical obstacle

Microorganisms or man-made microswimmers swimming near obstacles have been investigated intensively owing to their importance in biology, physiology, and biomedical engineering. In this work, a direct-forcing fictitious domain method is employed to numerically investigate the interaction between a prolate microorganism (modeled as a squirmer) and a cylindrical obstacle. We report four distinct types of swimming trajectories-forward orbiting, backward orbiting, hovering, and scattering depending on swimmer's aspect ratio. The results illustrate that strong pushers prefer a forward orbit with a low obstacle curvature and a high aspect ratio, while a backward orbit is favored for small aspect ratios. But spheroidal pullers generally scatter off the obstacle. We observe a 'hovering' mode between the backward orbiting and scattering mode for both spherical and spheroidal pushers. Our findings highlight a transition in swimming modes influenced by the geometry and dipolarity of the microswimmer.

Sedimentation and structure of squirmer suspensions under gravity

The effect of gravity on the collective motion of living microswimmers, such as bacteria and micro-algae, is pivotal to unravel not only bio-convection patterns but also the settling of bacterial biofilms on solid surfaces. In this work, we investigate suspensions of microswimmers under the influence of a gravitational field and hydrodynamics, simulated via the dissipative particle dynamics (DPD) coarse-grained model. We first study the collective sedimentation of passive colloids and microswimmers of the puller and pusher types upon increasing the imposed gravitational field and compare them with previous results. Once sedimentation occurs, we observe that, as the gravitational field increases, the bottom layer undergoes a transition to an ordered state compatible with a hexagonal crystal. In comparison with passive colloids, both pullers and pushers easily rearrange at the bottom layer to anneal defects. Specifically, pullers are better than pushers in preserving the hexagonal order of the bottom mono-layer at high gravitational fields.

Numerical study of microorganisms swimming near a convex wall in a Giesekus fluid

The motion of microorganisms in complex fluids stands out as a prominent subject within fluid mechanics. In our study, we utilize the fictitious domain method to investigate the locomotion of squirmers along a convex wall in Giesekus viscoelastic fluids. This study examines the influence of fluid elasticity and wall curvature on squirmer particles, analyzing their movement patterns in detail. Near the convex wall, three distinct behavioral characteristics emerge: scattering, orbiting forward, and orbiting backward. The findings reveal that, compared with Newtonian fluids, squirmers exhibit a stronger tendency to be attracted toward the wall in viscoelastic fluids. This behavior is attributed to the elastic stress of the fluid, which generates a reverse torque on microbial particles, altering their movement direction and hindering their escape from the wall. Notably, as the wall curvature decreases, the likelihood of particles escaping diminishes.

A novel mechanism of microbial attachment: The flagellar pump of Giardia lamblia

The ability of microbes to attach to biological and inert substrates is a necessary prerequisite for colonization of new habitats. In contrast to well-characterized mechanisms that rely on specific or nonspecific chemical interactions between microbe and substrate, we describe here an effective hydrodynamic mechanism of attachment that relies on fluid flow generated by the microbe. The microbe Giardia lamblia, a flagellated protozoan parasite, naturally attaches to the microvilliated surface of the small intestine but is also capable of attaching indiscriminately to a wide range of natural and artificial substrates. By tracking fluorescent quantum dots, we demonstrate a persistent flow between the parasite and substrate generated by a pair of Giardia flagella. Using both experimental measures and computational modeling, we show that the negative pressure generated by this fluid flow is sufficient to generate the previously measured force of attachment. We further show that this dynamically generated negative pressure allows Giardia to attach to both solid and porous surfaces, thereby meeting the real-world demands of attachment to the microvilliated surface of intestinal cells. These findings provide experimental support for a hydrodynamic model of attachment that may be shared by other ciliated and flagellated microbes.

Research on sedimentation characteristics of squirmer in a power-law fluid

Sedimentation characteristics of a squirmer in a power-law fluid within a vertical channel are studied numerically using the two-dimensional lattice Boltzmann method. The effects of swimming type (- 5 ≤ β ≤ 5), self-propelling strength (0.5 ≤ α ≤ 1.1), power-law indexes (0.5 ≤ n ≤ 1.5), and the density ratio of the squirmer to the fluid (γ = 1.01, 1.5 and 2.3) on the sedimentation of the squirmer are analyzed. Four settlement patterns are identified: steady falling in the center, downward along the wall, oscillating with large amplitude and oscillating around the centerline. The squirmer in the channel exhibits more fluctuations in shear-thinning (n < 1) and Newtonian (n = 1) fluids compared to shear-thickening fluids (n > 1). Additionally, a puller (β > 0) settles faster than a pusher (β < 0) in shear-thinning and Newtonian fluids. Puller generates flow towards their head and away from their tail, exhibiting small amplitude oscillations. Pushers exhibit higher amplitude oscillations throughout the channel, creating flow towards their tail and away from their head. At lower γ, the fluctuation of the squirmer is less pronounced compared to higher γ.

Enhanced speed of microswimmers adjacent to a rough surface

Increased speed is not only the goal of human sports but also the aim we seek to achieve for artificial microswimmers. Microswimmers driven by various power mechanisms have shown unrivaled advantages in drug delivery and cancer therapy. Attaining high mobility with limited power has been a never-ending motive for researchers. We show the speed of squirmer-type microswimmers can be noticeably enhanced as they are released to move along the surface of a pillar array, which is constructed of multiple pillars of equal sizes and spacing. An additional pressure force arising from the significant low pressure between the swimmers and the surface is likely behind this enhancement. According to their polarity strengths, the speed of the microswimmers can be double or triple (or even more) compared with that in an unbounded environment. In particular, for systems requiring microswimmers moving along a complex path, the transport rate, instead of being slowed down, may be increased owing to the curvatures of the path constructed by the pillar arrays. We reveal two types of motion for microswimmers after increasing the pillar gap: free and forced oscillating. Our study sheds light on the hydrodynamic interactions between squirmer-type microswimmers and a rough wall.

Motility and pairwise interactions of chemically active droplets in one-dimensional confinement

Self-propelled droplets serve as ideal model systems to delve deeper into understanding the motion of biological microswimmers by simulating their motility. Biological microorganisms are renowned for showcasing a diverse array of dynamic swimming behaviors when confronted with physical constraints. This study aims to elucidate the impact of physical constraints on swimming characteristics of biological microorganisms. To achieve this, we present observations on the individual and pairwise behavior of micellar solubilized self-propelled 4-cyano-4'-pentyl-biphenyl (5CB) oil droplets in a square capillary channel filled with a surfactant trimethyl ammonium bromide aqueous solution. To explore the effect of the underlying Péclet number of the swimming droplets, the study is also performed in the presence of additives such as high molecular weight polymer polyethylene oxide and molecular solute glycerol. The capillary confinement restricts droplet to predominantly one-dimensional motion, albeit with noticeable differences in their motion across the three scenarios. Through a characterization of the chemical and hydrodynamic flow fields surrounding the droplets, we illustrate that the modification of the droplets' chemical field due to confinement varies significantly based on the underlying differences in the Péclet number in these cases. This alteration in the chemical field distribution notably affects the individual droplets' motion. Moreover, these distinct chemical field interactions between the droplets also lead to variations in their pairwise motion, ranging from behaviors like chasing to scattering.

Densitaxis: Active particle motion in density gradients

Organisms often swim through density-stratified fluids. Here, we investigate the dynamics of active particles swimming in fluid density gradients and report theoretical evidence of taxis as a result of these gradients (densitaxis). Specifically, we calculate the effect of density stratification on the dynamics of a force- and torque-free spherical squirmer and show that density gradients induce reorientation that tends to align swimming either parallel or normal to the gradient depending on the swimming gait. In particular, swimmers that propel by generating thrust in the front (pullers) rotate to swim parallel to gradients and hence display (positive or negative) densitaxis, while swimmers that propel by generating thrust in the back (pushers) rotate to swim normal to the gradients. This work could be useful to understand the motion of marine organisms in ocean or be leveraged to sort or organize a suspension of active particles by modulating density gradients.

Direct numerical simulations of a microswimmer in a viscoelastic fluid

This study presents the application of the smoothed profile (SP) method to perform direct numerical simulations for the motion of both passive and active "squirming" particles in Newtonian and viscoelastic fluids. We found that fluid elasticity has a significant impact on both the transient behavior and the steady-state velocity of the particles. Specifically, we observe that the swirling flow generated by the squirmer's surface velocity significantly enhances their swimming speed as the Weissenberg number increases, regardless of the swimming type. Furthermore, we find that pushers outperform pullers in Oldroyd-B fluids, suggesting that the speed of a squirmer depends on the swimmer type. To understand the physical origin of the phenomenon of swirling flow enhancing the swimming speed, we investigate the velocity field and polymer conformation around non-swirling and swirling neutral squirmers in viscoelastic fluids. Our investigation reveals that the velocity field around the neutral swirling squirmers exhibits pusher-like extensional flow characteristics, as well as an asymmetric polymer conformation distribution, which gives rise to this increased propulsion. This is confirmed by the investigation of the force on a fixed squirmer, which revealed that the polymer stress, particularly its diagonal components, plays a critical role in enhancing the swimming speed of swirling squirmers in viscoelastic fluids. Additionally, our results demonstrate that the maximum swimming speeds of swirling squirmers occur at an intermediate value of the fluid viscosity ratio for all swimmer types. These findings have important implications for understanding the behavior of particles and micro-organisms in complex fluids.

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.

The Hydrodynamics of a Rod-Shaped Squirmer near a Wall

The hydrodynamic characteristics of a rod-shaped squirmer swimming near a wall were studied numerically using the immersed boundary-lattice Boltzmann method in the swimming Reynolds number range of 0.1 ≤ Res ≤ 2.0, where the number of assembled squirmers was 2 ≤ i ≤ 4 and the distance between two adjacent assembled squirmers was 0.75 d ≤ s ≤ 1.5 d (d is the diameter of a single squirmer). The effect of Res, i and s on the swimming mode of the squirmer was explored. The results showed that there are four swimming modes after the first collision between the rod-shaped squirmer and the wall. There are also four swimming modes when Res changes from 0.1 to 2.0. Puller, pusher and neutral squirmers showed different swimming modes when i changed, and the effect degree of the flow at the previous moment on the squirmer’s motion was different for different values of i. The change in s only affected the trajectory of the squirmer without changing its motion mode. Puller, pusher and neutral squirmers showed different swimming modes and velocity changes when s changed.

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.

Hydrodynamics of chiral squirmers

Many microorganisms take a chiral path while swimming in an ambient fluid. In this paper we study the combined behavior of two chiral swimmers using the well-known squirmer model taking into account chiral asymmetries. In contrast to the simple squirmer model, which has an axisymmetric distribution of slip velocity, the chiral squirmer has additional asymmetries in the surface slip, which contribute to both translations and rotations of the motion. As a result, swimming trajectories can become helical and chiral asymmetries arise in the flow patterns. We study the swimming trajectories of a pair of chiral squirmers that interact hydrodynamically. This interaction can lead to attraction and repulsion, and in some cases even to bounded states where the swimmers continue to periodically orbit around a common average trajectory. Such bound states are a signature of the chiral nature of the swimmers. Our study could be relevant to the collective movements of ciliated microorganisms.

Interactions in active colloids

The past two decades have seen a remarkable progress in the development of synthetic colloidal agents which are capable of creating directed motion in an unbiased environment at the microscale. These self-propelling particles are often praised for their enormous potential to self-organize into dynamic nonequilibrium structures such as living clusters, synchronized super-rotor structures or self-propelling molecules featuring a complexity which is rarely found outside of the living world. However, the precise mechanisms underlying the formation and dynamics of many of these structures are still barely understood, which is likely to hinge on the gaps in our understanding of how active colloids interact. In particular, besides showing comparatively short-ranged interactions which are well known from passive colloids (Van der Waals, electrostatic etc), active colloids show novel hydrodynamic interactions as well as phoretic and substrate-mediated 'osmotic' cross-interactions which hinge on the action of the phoretic field gradients which are induced by the colloids on other colloids in the system. The present article discusses the complexity and the intriguing properties of these interactions which in general are long-ranged, non-instantaneous, non-pairwise and non-reciprocal and which may serve as key ingredients for the design of future nonequilibrium colloidal materials. Besides providing a brief overview on the state of the art of our understanding of these interactions a key aim of this review is to emphasize open key questions and corresponding open challenges.

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.

A Review on the Some Issues of Multiphase Flow with Self-Driven Particles

Multiphase flow with self-driven particles is ubiquitous and complex. Exploring the flow properties has both important academic meaning and engineering value. This review emphasizes some recent studies on multiphase flow with self-driven particles: the hydrodynamic interactions between self-propelled/self-rotary particles and passive particles; the aggregation, phase separation and sedimentation of squirmers; the influence of rheological properties on its motion; and the kinematic characteristics of axisymmetric squirmers. Finally, some open problems, challenges, and future directions are highlighted.

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.

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.

Integrative Neuroscience of Paramecium, a "Swimming Neuron"

Paramecium is a unicellular organism that swims in fresh water by beating thousands of cilia. When it is stimulated (mechanically, chemically, optically, thermally…), it often swims backward then turns and swims forward again. This "avoiding reaction" is triggered by a calcium-based action potential. For this reason, some authors have called Paramecium a "swimming neuron." This review summarizes current knowledge about the physiological basis of behavior of Paramecium.

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.

Active motion of multiphase oil droplets: emergent dynamics of squirmers with evolving internal structure

Synthetic soft matter systems, when driven beyond equilibrium by active processes, offer the potential to achieve dynamical states and functions of a complexity found in living matter. Emulsions offer the basis of a simple yet versatile system for identification of the physicochemical principles underlying active soft matter, but how multiple internal phases within emulsion droplets (e.g., Janus morphologies) organize to impact emergent dynamics is not understood. Here, we create multiphase oil droplets with ultralow interfacial tensions but distinct viscosities, and drive them into motion in aqueous micellar solutions. Preferential solubilization of select components of the oil both drives the droplet motion and yields a progression of internal phase morphological states with distinct symmetries. We find the active droplets to exhibit five dynamical states during morphogenesis. By quantifying microscopic flow fields, we show that it is possible to map the diverse droplet behaviors to squirmer models of spherical microswimmers in Stokes flow, thus showing that multiphase droplets offer the basis of a versatile platform with which to study and engineer the hydrodynamics of microswimmers.

Symmetry breaking propulsion of magnetic microspheres in nonlinearly viscoelastic fluids

Microscale propulsion impacts a diverse array of fields ranging from biology and ecology to health applications, such as infection, fertility, drug delivery, and microsurgery. However, propulsion in such viscous drag-dominated fluid environments is highly constrained, with time-reversal and geometric symmetries ruling out entire classes of propulsion. Here, we report the spontaneous symmetry-breaking propulsion of rotating spherical microparticles within non-Newtonian fluids. While symmetry analysis suggests that propulsion is not possible along the fore-aft directions, we demonstrate the existence of two equal and opposite propulsion states along the sphere's rotation axis. We propose and experimentally corroborate a propulsion mechanism for these spherical microparticles, the simplest microswimmers to date, arising from nonlinear viscoelastic effects in rotating flows similar to the rod-climbing effect. Similar possibilities of spontaneous symmetry-breaking could be used to circumvent other restrictions on propulsion, revising notions of microrobotic design and control, drug delivery, microscale pumping, and locomotion of microorganisms.

A visibility-based approach to computing non-deterministic bouncing strategies

Inspired by motion patterns of some commercially available mobile robots, we investigate the power of robots that move forward in straight lines until colliding with an environment boundary, at which point they can rotate in place and move forward again; we visualize this as the robot “bouncing” off boundaries. We define bounce rules governing how the robot should reorient after reaching a boundary, such as reorienting relative to its heading prior to collision, or relative to the normal of the boundary. We then generate plans as sequences of rules, using the bounce visibility graph generated from a polygonal environment definition, while assuming we have unavoidable non-determinism in our actuation. Our planner can be queried to determine the feasibility of tasks such as reaching goal sets and patrolling (repeatedly visiting a sequence of goals). If the task is found feasible, the planner provides a sequence of non-deterministic interaction rules, which also provide information on how precisely the robot must execute the plan to succeed. We also show how to compute stable cyclic trajectories and use these to limit uncertainty in the robot’s position.

Hydrodynamic interactions between swimming microorganisms in a linearly density stratified fluid

Oceans and lakes sustain intense biological activity due to the motion of marine organisms, which has significant ecological and environmental impacts. The motion of individual organisms and their interactions with each other play a significant role in the collective motion of swimming organisms. However, ubiquitous vertical density stratification in these aquatic environments significantly alters the swimmer interactions as compared to in a homogeneous fluid. Furthermore, organisms have sizes varying over a wide range which results in finite inertia. To this end, we numerically investigate the interactions between a pair of model swimming organisms in two configurations: (1) approaching each other and (2) moving side by side with finite inertia in a linearly density stratified fluid. We use the archetypal reduced-order squirmer model to numerically model the swimming organisms. We present trajectories and the contact times of interacting squirmer (puller & pusher) pairs for different Re in the range 1-50 and Ri in the range 0-10. Depending on the squirmer Re and Ri we observe that the squirmer interactions can be categorized as (i) pullers getting trapped in circular loops at high Re and low Ri, (ii) pullers escaping each other with separating angle decreasing with increasing stratification at low Re and high Ri, (iii) pushers sticking to each other after the collision and deflecting away from the collision plane for either low Re or high Ri, (iv) pushers escaping otherwise with an angle of separation increasing with stratification. Stratification also increases the contact time for squirmer pairs. The presented results can be useful to understand the mechanisms behind the accumulation of planktonic organisms in horizontal layers in a stratified environment such as oceans and lakes.

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.

Squirmer rods as elongated microswimmers: flow fields and confinement

Microswimmers or active elements, such as bacteria and active filaments, have an elongated shape, which determines their individual and collective dynamics. There is still a need to identify what role long-range hydrodynamic interactions play in their fascinating dynamic structure formation. We construct rods of different aspect ratios using several spherical squirmer model swimmers. With the help of the mesoscale simulation method of multi-particle collision dynamics we analyze the flow fields of these squirmer rods both in a bulk fluid and in Hele-Shaw geometries of different slab widths. Based on the hydrodynamic multipole expansion either for bulk or confinement between two parallel plates, we categorize the different multipole contributions of neutral as well as pusher-type squirmer rods. We demonstrate how confinement alters the radial decay of the flow fields for a given force or source multipole moment compared to the bulk fluid.

Partition of nanoswimmers between two immiscible phases: a soft and penetrable boundary

The behavior of run-and-tumble nanoswimmers which can self-propel in two immiscible liquids such as water-oil systems and are able to cross the interface is investigated by dissipative particle dynamics. At the steady-state, the partition ratio (φ) of nanoswimmers between the two immiscible liquids is obtained, and it depends on the active force (F_a), run time (τ), and swimmer-solvent interactions. The partition ratio φ is found to grow generally with increasing F_a²τ. At sufficiently large F_a, it is surprising to find that hydrophilic nanoswimmers prefer to stay in the oil phase rather than in the water phase. The partition ratio is also influenced by the hydrophobicity of swimmers in the oil phase. Two simple models are proposed to describe the partition ratio, including a near-equilibrium model and a kinetic model. Surface accumulation appearing at an impenetrable interface is also observed at the fluid-fluid interface for small F_a but it vanishes for sufficiently large F_a.

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.

Dynamics of a chiral swimmer sedimenting on a flat plate

Three-dimensional simulations with fully resolved hydrodynamics are performed to study the dynamics of a single squirmer with and without gravity to clarify its motion in the vicinity of a flat plate. In the absence of gravity and chirality, the usual dynamics of a squirmer near a wall are recovered. The introduction of chirality modifies the swimming motion of squirmers, adding a component of motion in the third direction. When sedimentation is considered, different dynamics emerge for different gravity strength regimes. In a moderate gravity regime, neutral squirmers and pullers eventually stop moving and reorient in a direction perpendicular to the plate; by contrast, pushers exhibit continuous motion in a tilted direction. In the strong gravity regime, all squirmers sediment and reorient perpendicular to the plate. In this study, chirality is introduced to model realistic microswimmers, and its crucial effects on the nature of squirmer trajectories, which change from straight to circular, are discussed.

Bioinspired reorientation strategies for application in micro/nanorobotic control

Engineers have recently been inspired by swimming methodologies of microorganisms in creating micro-/nanorobots for biomedical applications. Future medicine may be revolutionized by the application of these small machines in diagnosing, monitoring, and treating diseases. Studies over the past decade have often concentrated on propulsion generation. However, there are many other challenges to address before the practical use of robots at the micro-/nanoscale. The control and reorientation ability of such robots remain as some of these challenges. This paper reviews the strategies of swimming microorganisms for reorientation, including tumbling, reverse and flick, direction control of helical-path swimmers, by speed modulation, using complex flagella, and the help of mastigonemes. Then, inspired by direction change in microorganisms, methods for orientation control for microrobots and possible directions for future studies are discussed. Further, the effects of solid boundaries on the swimming trajectories of microorganisms and microrobots are examined. In addition to propulsion systems for artificial microswimmers, swimming microorganisms are promising sources of control methodologies at the micro-/nanoscale.

Biofilms at interfaces: microbial distribution in floating films

Cellular motility is a key function guiding microbial adhesion to interfaces, which is the first step in the formation of biofilms. The close association of biofilms and bioremediation has prompted extensive research aimed at comprehending the physics of microbial locomotion near interfaces. We study the dynamics and statistics of microorganisms in a 'floating biofilm', i.e., a confinement with an air-liquid interface on one side and a liquid-liquid interface on the other. We use a very general mathematical model, based on a multipole representation and probabilistic simulations, to ascertain the spatial distribution of microorganisms in films of different viscosities. Our results reveal that microorganisms can be distributed symmetrically or asymmetrically across the height of the film, depending on their morphology and the ratio of the film's viscosity to that of the fluid substrate. Long-flagellated, elongated bacteria exhibit stable swimming parallel to the liquid-liquid interface when the bacterial film is less viscous than the underlying fluid. Bacteria with shorter flagella on the other hand, swim away from the liquid-liquid interface and accumulate at the free surface. We also analyze microorganism dynamics in a flowing film and show how a microorganism's ability to resist 'flow-induced-erosion' from interfaces is affected by its elongation and mode of propulsion. Our study generalizes past efforts on understanding microorganism dynamics under confinement by interfaces and provides key insights on biofilm initiation at liquid-liquid interfaces.

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.

Direct-forcing fictitious domain method for simulating non-Brownian active particles

We present a direct-forcing fictitious domain method for simulating non-Brownian squirmer particles with both the hydrodynamic interactions and collisions being fully resolved. In this method, we solve the particle motion by distributing collocation points inside the particle interior domain that overlay upon a fixed Eulerian mesh. The fluid motions, including those of the "fictitious fluids" being extended into the particle, are solved on the entire computation domain. Pseudo-body forces are used to enforce the fictitious fluids to follow the particle movement. A direct-forcing approach is employed to map physical variables between the overlaid meshes, which does not require additional iterations to achieve convergence. We perform a series of numerical studies at both small and finite Reynolds numbers. First, accuracy of the algorithm is examined in studying benchmark problems of a free-swimming squirmer and two side-by-side squirmers. Then we investigate statistic properties of the quasi-two-dimensional collective dynamics for a monolayer of squirmer particles that are confined on a surface immersed in a bulk flow. Finally, we explore the physical mechanisms of how a freely moving short cylinder interacts with a monolayer of active particles, and find out that the cylinder movement is dominated by collision. We demonstrate that a more directional migration of cylinder can be resultant from an inhomogeneous distribution of active particles around the cylinder that has an anisotropic shape.

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.

Dynamics of groups of magnetically driven artificial microswimmers

Magnetically driven artificial microswimmers have the potential to revolutionize many biomedical technologies, such as minimally invasive microsurgery, microparticle manipulation, and localized drug delivery. However, many of these applications will require the controlled dynamics of teams of these microrobots with minimal feedback. In this work, we study the motion and fluid dynamics produced by groups of artificial microswimmers driven by a torque induced through a uniform, rotating magnetic field. Through Stokesian dynamics simulations, we show that the swimmer motion produces a rotational velocity field in the plane orthogonal to the direction of the magnetic field's rotation, which causes two interacting swimmers to move in circular trajectories in this plane around a common center. The resulting overall motion is on a helical trajectory for the swimmers. We compare the highly rotational velocity field of the fluid to the velocity field generated by a rotlet, the point-torque singularity of Stokes flows, showing that this is a reasonable approximation on the time average. Finally, we study the motion of larger groups of swimmers, and we show that these groups tend to move coherently, especially when swimmer magnetizations are uniform. This coherence is achieved because the group center remains almost constant in the plane orthogonal to the net motion of the swimmers. The results in the paper will prove useful for controlling the ensemble dynamics of small collections of magnetic swimmers.

Hydrodynamic Interaction Enhances Colonization of Sinking Nutrient Sources by Motile Microorganisms

In this study, we document hydrodynamics-mediated trapping of microorganisms around a moving spherical nutrient source such as a settling marine snow aggregate. There exists a range of size and excess density of the nutrient source, and motility and morphology of the microorganism under which hydrodynamic interactions enable the passive capture of approaching microorganisms onto a moving nutrient source. We simulate trajectories of chemotactic and non-chemotactic bacteria encountering a sinking marine snow particle effusing soluble nutrients. We calculate the average nutrient concentration to which the bacteria are exposed, under regimes of strong and weak hydrodynamic trapping. We find that hydrodynamic trapping can significantly amplify (by ≈40%) the nutrient exposure of bacteria, both chemotactic and non-chemotactic. The subtle interactions between hydrodynamic and chemotactic effects reveal non-trivial variations in this “hydrodynamic amplification,” as a function of relevant biophysical parameters. Our study provides a consistent description of how microorganism motility, fluid flow and nutrient distribution affect foraging by marine microbes, and the formation of biofilms on spherical nutrient sources under the influence of fluid flow.

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.

From hydrodynamic lubrication to many-body interactions in dense suspensions of active swimmers

We study how hydrodynamic interactions affect the collective behaviour of active particles suspended in a fluid at high concentrations, with particular attention to lubrication forces which appear when the particles are very close to one another. We compute exactly the limiting behaviour of the hydrodynamic interactions between two spherical (circular) active swimmers in very close proximity to one another in the general setting in both three and (two) dimensions. Combining this with far-field interactions, we develop a novel numerical scheme which allows us to study the collective behaviour of large numbers of active particles with accurate hydrodynamic interactions when close to one another. We study active swimmers whose intrinsic flow fields are characterised by force dipoles and quadrupoles. Using this scheme, we are able to show that lubrication forces when the particles are very close to each other can play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that when the swimmer force dipole is large, finite clusters and open gel-like clusters appear rather than complete phase separation. This suppression is due to near-field lubrication interactions. For swimmers with small force dipoles, we find surprisingly that a globally polar-ordered phase appears because near-field lubrication rather than long-range hydrodynamics dominates the alignment mechanism. Polar order is present for very large system sizes and is stable to fluctuations with a finite noise amplitude. We explain the emergence of polar order using a minimal model in which only the leading rotational effect of the near-field interaction is included. These phenomena are also reproduced in two dimensions.

Maximum in density heterogeneities of active swimmers

Suspensions of unicellular microswimmers such as flagellated bacteria or motile algae can exhibit spontaneous density heterogeneities at large enough concentrations. We introduce a novel model for biological microswimmers that creates the flow field of the corresponding microswimmers, and takes into account the shape anisotropy of the swimmer's body and stroke-averaged flagella. By employing multiparticle collision dynamics, we directly couple the swimmer's dynamics to the fluid's. We characterize the nonequilibrium phase diagram, as the filling fraction and Péclet number are varied, and find density heterogeneities in the distribution of both pullers and pushers, due to hydrodynamic instabilities. We find a maximum degree of clustering at intermediate filling fractions and at large Péclet numbers resulting from a competition of hydrodynamic and steric interactions between the swimmers. We develop an analytical theory that supports these results. This maximum might represent an optimum for the microorganisms' colonization of their environment.

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.

Re-entrant bimodality in spheroidal chiral swimmers in shear flow

We use a continuum model to report on the behavior of a dilute suspension of chiral swimmers subject to externally imposed shear in a planar channel. Swimmer orientation in response to the imposed shear can be characterized by two distinct phases of behavior, corresponding to unimodal or bimodal distribution functions for swimmer orientation along the channel. These phases indicate the occurrence (or not) of a population splitting phenomenon changing the swimming direction of a macroscopic fraction of active particles to the exact opposite of that dictated by the imposed flow. We present a detailed quantitative analysis elucidating the complexities added to the population splitting behavior of swimmers when they are chiral. In particular, the transition from unimodal to bimodal and vice versa are shown to display a re-entrant behavior across the parameter space spanned by varying the chiral angular speed. We also present the notable effects of particle aspect ratio and self-propulsion speed on system phase behavior and discuss potential implications of our results in applications such as swimmer separation/sorting.

Simulating squirmers with multiparticle collision dynamics

Multiparticle collision dynamics is a modern coarse-grained simulation technique to treat the hydrodynamics of Newtonian fluids by solving the Navier-Stokes equations. Naturally, it also includes thermal noise. Initially it has been applied extensively to spherical colloids or bead-spring polymers immersed in a fluid. Here, we review and discuss the use of multiparticle collision dynamics for studying the motion of spherical model microswimmers called squirmers moving in viscous fluids.

Clustering of Magnetic Swimmers in a Poiseuille Flow

We investigate the collective behavior of magnetic swimmers, which are suspended in a Poiseuille flow and placed under an external magnetic field, using analytical techniques and Brownian dynamics simulations. We find that the interplay between intrinsic activity, external alignment, and magnetic dipole-dipole interactions leads to longitudinal structure formation. Our work sheds light on a recent experimental observation of a clustering instability in this system.

Hydrodynamic interaction of a self-propelling particle with a wall : Comparison between an active Janus particle and a squirmer model

Using lattice Boltzmann simulations we study the hydrodynamics of an active spherical particle near a no-slip wall. We develop a computational model for an active Janus particle, by considering different and independent mobilities on the two hemispheres and compare the behaviour to a standard squirmer model. We show that the topology of the far-field hydrodynamic nature of the active Janus particle is similar to the standard squirmer model, but in the near-field the hydrodynamics differ. In order to study how the near-field effects affect the interaction between the particle and a flat wall, we compare the behaviour of a Janus swimmer and a squirmer near a no-slip surface via extensive numerical simulations. Our results show generally a good agreement between these two models, but they reveal some key differences especially with low magnitudes of the squirming parameter [Formula: see text]. Notably the affinity of the particles to be trapped at a surface is increased for the active Janus particles when compared to standard squirmers. Finally, we find that when the particle is trapped on the surface, the velocity parallel to the surface exceeds the bulk swimming speed and scales linearly with [Formula: see text].

Simple mechanosense and response of cilia motion reveal the intrinsic habits of ciliates

Single-celled microorganisms are important in ecosystems, and their behaviors impact the Earth’s environments. To survive in harsh environments, these organisms frequently act as though exercising discretion. How do they achieve such intelligent behaviors? In this work, we focused on the accumulation of ciliates on solid/fluid interfaces, where they can obtain sufficient nutrients and a stable environment. This phenomenon is not described in the standard hydrodynamics of microswimmers. Our experiment and simulation revealed that simple principles, the anisotropic shape of the cell and the mechanosensing nature of cilia, induce the accumulation of ciliates on solid/fluid interfaces. The contribution of our work is that a simple response of the cellular apparatus and fluid dynamics explain the apparently clever behavior of ciliates.

An important habit of ciliates, namely, their behavioral preference for walls, is revealed through experiments and hydrodynamic simulations. A simple mechanical response of individual ciliary beating (i.e., the beating is stalled by the cilium contacting a wall) can solely determine the sliding motion of the ciliate along the wall and result in a wall-preferring behavior. Considering ciliate ethology, this mechanosensing system is likely an advantage in the single cell’s ability to locate nutrition. In other words, ciliates can skillfully use both the sliding motion to feed on a surface and the traveling motion in bulk water to locate new surfaces according to the single “swimming” mission.