Swimming trajectories of a three-sphere microswimmer near a wall

Propulsion of a three-sphere microrobot in a porous medium

Microorganisms and synthetic microswimmers often encounter complex environments consisting of networks of obstacles embedded into viscous fluids. Such settings include biological media, such as mucus with filamentous networks, as well as environmental scenarios, including wet soil and aquifers. A fundamental question in studying their locomotion is how the impermeability of these porous media impacts their propulsion performance compared with the case of that in a purely viscous fluid. Previous studies showed that the additional resistance due to the embedded obstacles leads to an enhanced propulsion of different types of swimmers, including undulatory swimmers, helical swimmers, and squirmers. In this paper, we employ a canonical three-sphere swimmer model to probe the impact of propulsion in porous media. The Brinkman equation is utilized to model a sparse network of stationary obstacles embedded into an incompressible Newtonian liquid. We present both a far-field theory and numerical simulations to characterize the propulsion performance of the swimmer in such porous media. In contrast to enhanced propulsion observed in other swimmer models, our results reveal that both the propulsion speed and efficiency of the three-sphere swimmer are largely reduced by the impermeability of the porous medium. We attribute the substantial reduction in propulsion performance to the screened hydrodynamic interactions among the spheres due to the more rapid spatial decays of flows in Brinkman media. These results highlight how enhanced or hindered propulsion in porous media is largely dependent on individual propulsion mechanisms. The specific example and physical insights provided here may guide the design of synthetic microswimmers for effective locomotion in porous media in their potential biological and environmental applications.

Analytical approach to chiral active systems: suppressed phase separation of interacting Brownian circle swimmers

We consider chirality in active systems by exemplarily studying the phase behavior of planar systems of interacting Brownian circle swimmers with a spherical shape. For this purpose, we derive a predictive field theory that is able to describe the collective dynamics of circle swimmers. The theory yields a mapping between circle swimmers and noncircling active Brownian particles and predicts that the angular propulsion of the particles leads to a suppression of their motility-induced phase separation, being in line with recent simulation results. In addition, the theory provides analytical expressions for the spinodal corresponding to the onset of motility-induced phase separation and the associated critical point as well as for their dependence on the angular propulsion of the circle swimmers. We confirm our findings by Brownian dynamics simulations. The agreement between results from theory and simulations is found to be good.

Collective dynamics of active circle-swimming Lennard- Jones particles

We report a numerical study on collective dynamics of self-propelling and circle-swimming Lennard- Jones (LJ) particles in two dimensions using Brownian dynamics simulations. We investigate the combined role of attraction,...

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.

Dynamic Modeling and Optimal Control of a Novel Microswimmer with Gimbal Based Disks

We have introduced a new low-Reynolds-number microrobot with high 3D maneuverability. Our novel proposed microrobot has a higher rank of the controllability matrix with respect to the previous microswimmers which makes it capable of performing complex motions in space. In this study, governing equations of the microswimmer’s motion have been derived and simulated. Subsequently, we have proposed a cascade optimal control technique to control the swimmer trajectory. In the proposed control scheme, the actuation is provided in a way that an exponential stability on the system trajectory error as well as minimum fluctuations of control signals are achieved.

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.

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.

Hydrodynamic effects on the motility of crawling eukaryotic cells

Eukaryotic cell motility is crucial during development, wound healing, the immune response, and cancer metastasis. Some eukaryotic cells can swim, but cells more commonly adhere to and crawl along the extracellular matrix. We study the relationship between hydrodynamics and adhesion that describe whether a cell is swimming, crawling, or combining these motions. Our simple model of a cell, based on the three-sphere swimmer, is capable of both swimming and crawling. As cell-matrix adhesion strength increases, the influence of hydrodynamics on migration diminishes. Cells with significant adhesion can crawl with speeds much larger than their nonadherent, swimming counterparts. We predict that, while most eukaryotic cells are in the strong-adhesion limit, increasing environment viscosity or decreasing cell-matrix adhesion could lead to significant hydrodynamic effects even in crawling cells. Signatures of hydrodynamic effects include a dependence of cell speed on the presence of a nearby substrate or interactions between noncontacting cells. These signatures will be suppressed at large adhesion strengths, but even strongly adherent cells will generate relevant fluid flows that will advect nearby passive particles and swimmers.

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.

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.

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.