Microscopic Swimmer Research Articles

Universal Poisson statistics of a passive tracer diffusing in dilute active suspensions.

The statistics of a passive tracer immersed in a suspension of active particles (swimmers) is derived from first principles by considering a perturbative expansion of the tracer interaction with the microscopic swimmer field. To first order in the swimmer density, the tracer statistics is shown to be exactly represented by a spatial Poisson process combined with independent tracer-swimmer scattering events, rigorously reducing the multiparticle dynamics to two-body interactions. The Poisson representation is valid in any dimension, for arbitrary interaction forces and for a large class of swimmer dynamics. The framework not only allows for the systematic calculation of the tracer statistics in various dynamical regimes but highlights in particular surprising universal features that are independent of the swimmer dynamics such as a time-independent velocity distribution.

Hydrochemical interactions in dilute phoretic suspensions: From individual particle properties to collective organization

Janus phoretic colloids (JPs) self-propel as a result of self-generated chemical gradients and exhibit spontaneous nontrivial dynamics within phoretic suspensions, on length scales much larger than the microscopic swimmer size. Such collective dynamics arise from the competition of (i) the self-propulsion velocity of the particles, (ii) the attractive/repulsive chemically-mediated interactions between particles and (iii) the flow disturbance they introduce in the surrounding medium. These three ingredients are directly determined by the shape and physico-chemical properties of the colloids' surface. Owing to such link, we adapt a recent and popular kinetic model for dilute suspensions of chemically-active JPs where the particles' far-field hydrodynamic and chemical signatures are intrinsically linked and explicitly determined by the design properties. Using linear stability analysis, we show that self-propulsion can induce a wave-selective mechanism for certain particles' configurations consistent with experimental observations. Numerical simulations of the complete kinetic model are further performed to analyze the relative importance of chemical and hydrodynamic interactions in the nonlinear dynamics. Our results show that regular patterns in the particle density are promoted by chemical signaling but prevented by the strong fluid flows generated collectively by the polarized particles, regardless of their chemotactic or antichemotactic nature (i.e. for both puller and pusher swimmers).

Swimming with swirl in a viscoelastic fluid

Abstract

Stokes' second problem and reduction of inertia in active fluids

We study a generalized Navier-Stokes model describing the thin-film flows in non-dilute suspensions of ATP-driven microtubules or swimming bacteria that are enclosed by a moving ring-shaped container. Considering Stokes' second problem, which concerns the motion of an oscillating boundary, our numerical analysis predicts that a periodically rotating ring will oscillate at a higher frequency in an active fluid than in a passive fluid, due to an activity-induced reduction of the fluid inertia. In the case of a freely suspended fluid-container system that is isolated from external forces or torques, active fluid stresses can induce large fluctuations in the container's angular momentum if the confinement radius matches certain multiples of the intrinsic vortex size of the active suspension. This effect could be utilized to transform collective microscopic swimmer activity into macroscopic motion in optimally tuned geometries.

Memory effects in active particles with exponentially correlated propulsion.

The Ornstein-Uhlenbeck particle (OUP) model imagines a microscopic swimmer propelled by an active force which is correlated with itself on a finite time scale. Here we investigate the influence of external potentials on an ideal suspension of OUPs, in both one and two spatial dimensions, with particular attention paid to the pressure exerted on "confining walls." We employ a mathematical connection between the local density of OUPs and the statistics of their propulsion force to demonstrate the existence of an equation of state in one dimension. In higher dimensions we show that active particles generate a nonconservative force field in the surrounding medium. A simplified far-from-equilibrium model is proposed to account for OUP behavior in the vicinity of potentials. Building on this, we interpret simulations of OUPs in more complicated situations involving asymmetrical and spatially curved potentials, and characterize the resulting inhomogeneous stresses in terms of competing active length scales.

Can Magnetic Multilayers Propel Artificial Microswimmers Mimicking Sperm Cells?

We formulate and solve the equations governing the dynamics of a microscopic artificial swimmer composed of a head and of a tail made of a thin film of permanent magnetic material. This is a variant of the model swimmer proposed by Dreyfus et al. in 2005, whose tail is a filament obtained from the assembly of superparamagnetic beads. The swimmer is actuated by an oscillating magnetic field, and its geometry is inspired by that of sperm cells. Using values for the geometric and material parameters that are realistic for a magnetic multilayer, we show that the model swimmer can reach swimming speeds exceeding one body length per second, under reasonable values of the driving magnetic field. This provides a proof of principle for the viability of the concept. In addition, we discuss the possibility to steer the system along curved paths. Finally, we compare the propulsion mechanism (swimming “gait”) of our swimmer with that of sperm cells. The main difference between the two is that, contrary to its biological template, our artificial system does not rely on the propagation of bending waves along the tail, at least for the range of material and geometric parameters explored in this article.

Tracer trajectories and displacement due to a micro-swimmer near a surface

We study tracer particle transport due to flows created by a self-propelled micro-swimmer, such as a swimming bacterium, alga or a microscopic artificial swimmer. Recent theoretical work has shown that as a swimmer moves in the fluid bulk along an infinite straight path, tracer particles far from its path perform closed loops, whereas those close to the swimmer are entrained by its motion. However, in biologically and technologically important cases tracer transport is significantly altered for swimmers that move in a run-and-tumble fashion with a finite persistence length, and/or in the presence of a free surface or a solid boundary. Here we present a systematic analytical and numerical study exploring the resultant regimes and their crossovers. Our focus is on describing qualitative features of the tracer particle transport and developing quantitative tools for its analysis. Our work is a step towards understanding the ecological effects of flows created by swimming organisms, such as enhanced fluid mixing and biofilm formation.

Effect of defect location on the swimming speed of a microscopic artificial swimmer: A numerical study

The main objective of this work is to explore the effect of defect location on the swimming speed of a microscopic artificial swimmer. The swimmer consists of an artificial filament composed of super-paramagnetic beads connected by elastic linkers and is modeled with a worm-like-chain configuration. To simulate the swimming motion of the filament, a load particle is attached at one end of the filament. The Rotne-Prager approximation is used to evaluate the hydrodynamic interactions between the filament and the fluid. To validate the numerical code, we first simulated the swimming motion of the filament without defect (‘without defect’ means the bending stiffness of the filament is uniform along its length). Next, we simulated the swimming motion of defective filament by setting zero for the bending stiffness value at a particular bead location. We observed that when the location of defect is on the load side of the filament, the swimming velocity is less than that of the defect-less filament, and vice versa. The effect of defect is more significant when it is located on the load side of the filament (The difference between the swimming velocity of defective and defect-less filament amounts to 38%) than when it is on the free end side (The difference is only 7% ). We also observed that at a certain sperm number the swimming direction is reversed when the defect is located very close to the load particle.

Self-Propelled Microswimmer Actuated by Stimuli-Sensitive Bilayered Hydrogel.

Using computational modeling, we design a microscopic swimmer made of a bilayered responsive hydrogel capable of swimming in a viscous fluid when actuated by a periodically applied stimulus. The gel has an X-shaped geometry and two bonded layers, one of which is responsive to environmental changes and the other which is passive. When the stimulus is turned on, the responsive layer swells and causes the swimmer to deform. We demonstrate that when such stimulus-induced deformations occur periodically the gel swimmer effectively propels forward through the fluid. We show that the swimming speed depends on the relative stiffness of the two gel layers composing the swimmer, and we determine the optimal stiffness ratio that maximizes the swimming speed.

Effective swimming strategies in low Reynolds number flows

The optimal strategy for a microscopic swimmer to migrate across a linear shear flow is discussed. The two cases, in which the swimmer is located at large distance, and in the proximity of a solid wall, are taken into account. It is shown that migration can be achieved by means of a combination of sailing through the flow and swimming, where the swimming strokes are induced by the external flow without need of internal energy sources or external drives. The structural dynamics required for the swimmer to move in the desired direction is discussed and two simple models, based respectively on the presence of an elastic structure, and on an orientation dependent friction, to control the deformations induced by the external flow, are analyzed. In all cases, the deformation sequence is a generalization of the tank-treading motion regimes observed in vesicles in shear flows. Analytic expressions for the migration velocity as a function of the deformation pattern and amplitude are provided. The effects of thermal fluctuations on propulsion have been discussed and the possibility that noise be exploited to overcome the limitations imposed on the microswimmer by the scallop theorem have been discussed.

Numerical study of a microscopic artificial swimmer

We present a detailed numerical study of a microscopic artificial swimmer realized recently by Dreyfus in experiments [Dreyfus, Nature 437, 862 (2005)]. It consists of an elastic filament composed of superparamagnetic particles that are linked together by DNA strands. Attached to a load particle, the resulting swimmer is actuated by an oscillating external magnetic field so that it performs a nonreciprocal motion in order to move forward. We model the superparamagnetic filament by a bead-spring configuration that resists bending like a rigid rod and whose beads experience friction with the surrounding fluid and hydrodynamic interactions with each other. We show that, aside from finite-size effects, its dynamics is governed by the dimensionless sperm number, the magnitude of the magnetic field, and the angular amplitude of the field's oscillating direction. Then we study the mean velocity and the efficiency of the swimmer as a function of these parameters and the size of the load particle. In particular, we clarify that the real velocity of the swimmer is influenced by two main factors, namely the shape of the beating filament (determined by the sperm number and the magnetic-field strength) and the oscillation frequency. Furthermore, the load size influences the performance of the swimmer and has to be chosen as a compromise between the largest swimming velocity and the best efficiency. Finally, we demonstrate that the direction of the swimming velocity changes in a symmetry-breaking transition when the angular amplitude of the field's oscillating direction is increased, in agreement with experiments.