Guidance of microswimmers by wall and flow: Thigmotaxis and rheotaxis of unsteady squirmers in two and three dimensions

The motion of micro-swimmers over a cavity in a micro-channel

This article combines the lattice Boltzmann method (LBM) with the squirmer model to investigate the motion of micro-swimmers in a channel-cavity system. The study analyses various influential factors, including the value of the squirmer-type factor (β), the swimming Reynolds number (Rep), the size of the cavity, initial position and particle size on the movement of micro-swimmers within the channel-cavity system. We simultaneously studied three types of squirmer models, Puller (β > 0), Pusher (β < 0), and Neutral (β = 0) swimmers. The findings reveal that the motion of micro-swimmers is determined by the value of β and Rep, which can be classified into six distinct motion modes. For Puller and Pusher, when the β value is constant, an increase in Rep will lead to transition in the motion mode. Moreover, the appropriate depth of cavity within the channel-cavity system plays a crucial role in capturing and separating Neutral swimmers. This study, for the first time, explores the effect of complex channel-cavity systems on the behaviour of micro-swimmers and highlights their separation and capture ability. These findings offer novel insights for the design and enhancement of micro-channel structures in achieving efficient separation and capture of micro-swimmers.

50-year History and perspective on biomechanics of swimming microorganisms: Part I. Individual behaviours

The paired review papers in Parts I and II describe the 50-year history of research on the biomechanics of swimming microorganisms and its prospects in the next 50 years: Part I explains the behaviour of individual microorganisms, and Part II explains collective behaviour. Since the discovery of microorganisms by van Leeuwenhoek in the 17th century, many natural scientists have been interested in their motility because it is directly associated with biological function. A research upsurge occurred in the 1970s, with the elucidation of swimming mechanisms among individual microorganisms and the theoretical derivation of swimming speeds. Various swimming strategies of three types of microorganisms, i.e. bacteria, ciliates and microalgae, are explained in this Part I. We show that some of the behaviours of microorganisms can be described by biomechanical equations and are to some extent predictable. Recent researches have revealed the behaviour of microorganisms in more complex environments and more realistic settings, which are also reviewed in the paper. Last, we provide future prospects for research on microbial behaviour.

Collective Behaviors of Active Matter Learning from Natural Taxes Across Scales

Taxis orientation is common in microorganisms, and it provides feasible strategies to operate active colloids as small-scale robots. Collective taxes involve numerous units that collectively perform taxis motion, whereby the collective cooperation between individuals enables the group to perform efficiently, adaptively, and robustly. Hence, analyzing and designing collectives is crucial for developing and advancing microswarm toward practical or clinical applications. In this review, natural taxis behaviors are categorized and synthetic microrobotic collectives are discussed as bio-inspired realizations, aiming at closing the gap between taxis strategies of living creatures and those of functional active microswarms. As collective behaviors emerge within a group, the global taxis to external stimuli guides the group to conduct overall tasks, whereas the local taxis between individuals induces synchronization and global patterns. By encoding the local orientations and programming the global stimuli, various paradigms can be introduced for coordinating and controlling such collective microrobots, from the viewpoints of fundamental science and practical applications. Therefore, by discussing the key points and difficulties associated with collective taxes of different paradigms, this review potentially offers insights into mimicking natural collective behaviors and constructing intelligent microrobotic systems for on-demand control and preassigned tasks.

Squirmer hydrodynamics near a periodic surface topography

The behaviour of microscopic swimmers has previously been explored near large-scale confining geometries and in the presence of very small-scale surface roughness. Here, we consider an intermediate case of how a simple microswimmer, the tangential spherical squirmer, behaves adjacent to singly and doubly periodic sinusoidal surface topographies that spatially oscillate with an amplitude that is an order of magnitude less than the swimmer size and wavelengths that are also within an order of magnitude of this scale. The nearest neighbour regularised Stokeslet method is used for numerical explorations after validating its accuracy for a spherical tangential squirmer that swims stably near a flat surface. The same squirmer is then introduced to different surface topographies. The key governing factor in the resulting swimming behaviour is the size of the squirmer relative to the surface topography wavelength. For instance, directional guidance is not observed when the squirmer is much larger, or much smaller, than the surface topography wavelength. In contrast, once the squirmer size is on the scale of the topography wavelength, limited guidance is possible, often with local capture in the topography troughs. However, complex dynamics can also emerge, especially when the initial configuration is not close to alignment along topography troughs or above topography crests. In contrast to sensitivity in alignment and topography wavelength, reductions in the amplitude of the surface topography or variations in the shape of the periodic surface topography do not have extensive impacts on the squirmer behaviour. Our findings more generally highlight that the numerical framework provides an essential basis to elucidate how swimmers may be guided by surface topography.

Near-wall rheotaxis of the ciliate Tetrahymena induced by the kinesthetic sensing of cilia

To survive in harsh environments, single-celled microorganisms autonomously respond to external stimuli, such as light, heat, and flow. Here, we elucidate the flow response of Tetrahymena, a well-known single-celled freshwater microorganism. Tetrahymena moves upstream against an external flow via a behavior called rheotaxis. While micrometer-sized particles are swept away downstream in a viscous flow, what dynamics underlie the rheotaxis of the ciliate? Our experiments reveal that Tetrahymena slides along walls during upstream movement, which indicates that the cells receive rotational torque from shear flow to control cell orientation. To evaluate the effects of the shear torque and propelling speed, we perform a numerical simulation with a hydrodynamic model swimmer adopting cilia dynamics in a shear flow. The swimmer orientations converge to an upstream alignment, and the swimmer slides upstream along a boundary wall. The results suggest that Tetrahymena automatically responds to shear flow by performing rheotaxis using cilia-stalling mechanics.

Driving a Microswimmer with Wall-Induced Flow

Active walls such as cilia and bacteria carpets generate background flows that can influence the trajectories of microswimmers moving nearby. Recent advances in artificial magnetic cilia carpets offer the potentiality to use a similar wall-generated background flow to steer bio-hybrid microrobots. In this paper, we provide some ground theoretical and numerical work assessing the viability of this novel means of swimmer guidance by setting up a simple model of a spherical swimmer in an oscillatory flow and analysing it from the control theory viewpoint. We show a property of local controllability around the reference free trajectories and investigate the bang-bang structure of the control for time-optimal trajectories, with an estimation of the minimal time for suitable objectives. By direct simulation, we have demonstrated that the wall actuation can improve the wall-following transport by nearly 50%, which can be interpreted by synchronous flow structure. Although an open-loop control with a periodic bang-bang actuation loses some robustness and effectiveness, a feedback control is found to improve its robustness and effective transport, even with hydrodynamic wall-swimmer interactions. The results shed light on the potentialities of flow control and open the way to future experiments on swimmer guidance.

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.

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.

Axisymmetric spheroidal squirmers and self-diffusiophoretic particles

We study, by means of an exact analytical solution, the motion of a spheroidal, axisymmetric squirmer in an unbounded fluid, as well as the low Reynolds number hydrodynamic flow associated to it. In contrast to the case of a spherical squirmer-for which, e.g. the velocity of the squirmer and the magnitude of the stresslet associated with the flow induced by the squirmer are respectively determined by the amplitudes of the first two slip ('squirming') modes-for the spheroidal squirmer each squirming mode either contributes to the velocity, or contributes to the stresslet. The results are straightforwardly extended to the self-phoresis of axisymmetric, spheroidal, chemically active particles in the case when the phoretic slip approximation holds.

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.

Boundary behaviours of Leishmania mexicana: A hydrodynamic simulation study

It is well established that the parasites of the genus Leishmania exhibit complex surface interactions with the sandfly vector midgut epithelium, but no prior study has considered the details of their hydrodynamics. Here, the boundary behaviours of motile Leishmania mexicana promastigotes are explored in a computational study using the boundary element method, with a model flagellar beating pattern that has been identified from digital videomicroscopy. In particular a simple flagellar kinematics is observed and quantified using image processing and mode identification techniques, suggesting a simple mechanical driver for the Leishmania beat. Phase plane analysis and long-time simulation of a range of Leishmania swimming scenarios demonstrate an absence of stable boundary motility for an idealised model promastigote, with behaviours ranging from boundary capture to deflection into the bulk both with and without surface forces between the swimmer and the boundary. Indeed, the inclusion of a short-range repulsive surface force results in the deflection of all surface-bound promastigotes, suggesting that the documented surface detachment of infective metacyclic promastigotes may be the result of their particular morphology and simple hydrodynamics. Further, simulation elucidates a remarkable morphology-dependent hydrodynamic mechanism of boundary approach, hypothesised to be the cause of the well-established phenomenon of tip-first epithelial attachment of Leishmania promastigotes to the sandfly vector midgut.