We describe the consequences of time reversal invariance of the Stokes' equations for the hydrodynamic scattering of two low Reynolds number swimmers. For swimmers that are related to each other by a time reversal transformation this leads to the striking result that the angle between the two swimmers is preserved by the scattering. The result is illustrated for the particular case of a linked-sphere model swimmer. For more general pairs of swimmers, not related to each other by time reversal, we find hydrodynamic scattering can alter the angle between their trajectories by several tens of degrees. For two identical contractile swimmers this can lead to the formation of a bound state.
Here we introduce a two-dimensional (2D) low-Reynolds swimmer and discuss the motion of the swimmer both in noise-free and stochastic regimes. Three spheres, linked by extensible arms, in a plane form the triangle body of micro-swimmer. Expansion and contraction of two-stated linkers in appropriate order causes both translational and rotational movement of the swimmer. It is shown that the motion of the swimmer could be controlled from a rotor to a directed linear swimmer depend on the sequence of the linkers activities. A few amount of noise in the the rhythm of the cycles introduces an inter…
In their search for metabolic resources microbes swim through viscous environments that present physical anisotropies, including steric obstacles across a wide range of sizes. Hydrodynamic forces are known to significantly alter swimmer trajectories near flat and low-curvature surfaces. In this work, we imaged hundreds-of-thousands of high-curvature scattering interactions between swimming bacteria and micro-fabricated pillars with radii from ~1 to ~10 cell lengths. As a function of impact parameter, cell-pillar interactions produced distinct chiral distributions for scattering angle -- includ…
In the limit of zero Reynolds number (Re), swimmers propel themselves exploiting a series of non-reciprocal body motions. For an artificial swimmer, a proper selection of the power source is required to drive its motion, in cooperation with its geometric and mechanical properties. Although various external fields (magnetic, acoustic, optical, etc.) have been introduced, electric fields are rarely utilized to actuate such swimmers experimentally in unbounded space. Here we use uniform and static electric fields to demonstrate locomotion of a bi-flagellated sphere at low Re via Quincke rotation.…
We computationally studied the pair interactions and collective behavior of asymmetric, dumbbell swimmers over a range of intermediate Reynolds numbers and initial configurations. Depending on the initial positions and the Re, we found that two swimmers either repelled and swum away from one another or assembled one of four stable pairs: in-line and in-tandem, both parallel and anti-parallel. When in these stable pairs, swimmers were coordinated, swum together, and generated fluid flows as one. We compared the stable pairs' speeds, swim direction and fluid flows to those of the single swimmer.…
Metachronal swimming, the sequential beating of limbs with a small phase lag, is observed in many organisms at various scales, but has been studied mostly in the limits of high or low Reynolds numbers. Motivated by the swimming of brine shrimp, a mesoscale organism that operates at intermediate Reynolds numbers, we computationally studied a simple nonreciprocal 2D model that performs metachronal swimming. Our swimmer is composed of two pairs of paddles beating with a phase difference that are symmetrically attached to the sides of a flat body. We numerically solved the Navier-Stokes equations …
We computationally study the kinematics of a simple model reciprocal swimmer (asymmetric dumbbell) as a function of the Reynolds number (Re) and investigate how the onset and gradual increase of inertia impacts the swimming behavior: a reversal in the swim direction, flow directions, and the swim stroke. We divide the swim stroke into the expansion and compression of the two spheres and relate them to power and recovery strokes. We find that the switch in swim direction also corresponds to a switch in power and recovery strokes. We obtain expressions for the mean swimming velocity by collapsin…
Inspired by recent experiments using synthetic microswimmers to manipulate droplets, we investigate the low-Reynolds-number locomotion of a model swimmer (a spherical squirmer) encapsulated inside a droplet of comparable size in another viscous fluid. Meditated solely by hydrodynamic interactions, the encaged swimmer is seen to be able to propel the droplet, and in some situations both remain in a stable co-swimming state. The problem is tackled using both an exact analytical theory and a numerical implementation based on boundary element method, with a particular focus on the kinematics of th…
We describe experiments and simulations demonstrating the propulsion of a neutrally-buoyant swimmer that consists of a pair of spheres attached by a spring, immersed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There …
Swimming cells and microorganisms are a critical component of many biological processes. In order to better interpret experimental studies of low Reynolds number swimming, we combine experimental and numerical methods to perform an analysis of the flow-field around the swimming nematode Caenorhabditis elegans. We first use image processing and particle tracking velocimetry to extract the body shape, kinematics, and flow-fields around the nematode. We then construct a three-dimensional model using the experimental swimming kinematics and employ a boundary element method to simulate flow-fields,…
Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large w…
Hydrodynamic interactions are crucial for determining the cooperative behavior of microswimmers at low Reynolds numbers. Here we provide a comprehensive analysis of the scaling and strength of the interactions in the case of a pair of three-sphere swimmers with intrinsic elasticity. Both stroke-based and force-based microswimmers are analyzed using an analytic perturbative approach. Following a detailed analysis of the passive interactions, as well as active translations and rotations, we find that the mapping between the stroke-based and force-based swimmers is only possible in a low driving …
Effect of swimming mode on shielding of odor traces in turbulence
Machine Learning Genoa Center (MaLGa) & Department of Civil, Chemical and Environmental Engineering, University of Genoa（热那亚大学机器学习和环境工程学院）；Gran Sasso Science Institute (GSSI)（格兰萨索科学研究所）；INFN–Laboratori Nazionali del Gran Sasso（意大利国家核物理研究所格兰萨索国家实验室）
We present a two dimensional model of hydrodynamic interaction between a circular swimmer and a circular post at low Reynolds number, using a point singularity description of the swimming activity. We derive a nonlinear dynamical system fully describing the motion and discuss the generic features of the phase portrait and typical trajectories for a variety of squirmer modes. Contractile swimmers exhibit stable bound orbits arising from the contrasting nature of monopolar and dipolar squirmer modes, which are robust with respect to swimmer size and the inclusion of higher squirmer modes. The be…
We present a theory for the self-propulsion of symmetric, half spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air-water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion-advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary cond…
The drag anisotropy of slender filaments is a critical physical property allowing swimming in low-Reynolds number flows, and without it linear translation is impossible. Here we show that, in contrast, net rotation can occur under isotropic drag. We first demonstrate this result formally by considering the consequences of the force- and torque-free conditions on swimming bodies and we then illustrate it with two examples (a simple swimmers made of three rods and a model bacterium with two helical flagellar filaments). Our results highlight the different role of hydrodynamic forces in generatin…
We study the effect of inhomogeneous environments on the swimming direction of the microalgae \textit{Chlamydomonas Reinhardtii} (CR) in the presence of a light stimulus. Positive or negative phototaxis describe the ability of microorganisms to bias their swimming towards or away from a light source. Here we consider microswimmers with negative phototaxis in a microfluidic device with a microfabricated square lattice of pillars as obstacles. We measured a mean deflection of microswimmers that shows an interesting nonlinear dependence on the direction of the guiding light beam with respect to t…
Hydrodynamic interaction strongly influences the collective behavior of the microswimmers. With this work, we study the behavior of two hydrodynamically interacting self-propelled chiral swimmers in the low Reynolds number regime, considering both the near and far-field interactions. We use the chiral squirmer model, a spherically shaped body with non-axisymmetric surface slip velocity, which generalizes the well-known squirmer model. We calculate the lubrication force between the swimmers when they are very close to each other. By varying the slip coefficients and the initial configuration of…
We use a three-bead-spring model to investigate the dynamics of bi-flagellate micro-swimmers near a surface. While the primary dynamics and scattering are governed by geometric-dependent direct contact, the fluid flows generated by the swimmer locomotion are important in orienting it toward or away from the surface. Flagellar noise and in particular cell spinning about the main axis help a surface-trapped swimmer escape, whereas the time a swimmer spends at the surface depends on the incident angle. The dynamics results from a nuanced interplay of direct collisions, hydrodynamics, noise and th…
We use boundary element simulations to study the interaction of model microswimmers with a neutrally buoyant spherical particle. The ratio of the size of the particle to that of the swimmer is varied from $R^\mathrm{P} / R^\mathrm{S} \ll 1$, corresponding to swimmer--tracer scattering, to $R^\mathrm{P} / R^\mathrm{S} \gg 1$, approximately equivalent to the swimmer interacting with a fixed, flat surface. We find that details of the swimmer and particle trajectories vary for different swimmers. However, the overall characteristics of the scattering event fall into two regimes, depending on the r…
Both natural and artificial small-scale swimmers may often self-propel in environments subject to complex geometrical constraints. While most past theoretical work on low-Reynolds number locomotion addressed idealised geometrical situations, not much is known on the motion of swimmers in heterogeneous environments. As a first theoretical model, we investigate numerically the behaviour of a single spherical micro-swimmer located in an infinite, periodic body-centred cubic lattice consisting of rigid inert spheres of the same size as the swimmer. Running a large number of simulations we uncover …
Swimming cells often have to self-propel through fluids displaying non-Newtonian rheology. While past theoretical work seems to indicate that stresses arising from complex fluids should systematically hinder low-Reynolds number locomotion, experimental observations suggest that locomotion enhancement is possible. In this paper we propose a physical mechanism for locomotion enhancement of microscopic swimmers in a complex fluid. It is based on the fact that micro-structured fluids will generically phase-separate near surfaces, leading to the presence of low-viscosity layers which promote slip a…
The design of artificial microswimmers is often inspired by the strategies of natural microorganisms. Many of these creatures exploit the fact that elasticity breaks the time-reversal symmetry of motion at low Reynolds numbers, but this principle has been notably absent from model systems of active, self-propelled microswimmers. Here we introduce a class of microswimmer that spontaneously self-assembles and swims without using external forces, driven instead by surface phase transitions induced by temperature variations. The swimmers are made from alkane droplets dispersed in aqueous surfactan…
Helical propulsion is used by many microorganisms to swim in viscous-dominated environments. Their swimming dynamics are relatively well understood, but detailed study of the flow fields and actuation mechanisms are still needed to realize wall effects and hydrodynamic interactions. In this letter, we describe the development of an autonomous swimming robot with a helical tail that operates in the Stokes regime. The device uses a battery-based power system with a miniature motor that imposes a rotational speed to a helical tail. The speed, direction, and activation are controlled electronicall…
We study synchronization in bulk suspensions of spherical microswimmers with chiral trajectories using large scale numerics. The model is generic. It corresponds to the lowest order solution of a general model for self-propulsion at low Reynolds numbers, consisting of a nonaxisymmetric rotating source dipole. We show that both purely circular and helical swimmers can spontaneously synchronize their rotation. The synchronized state corresponds to velocity alignment with high orientational order in both the polar and azimuthal directions. Finally, we consider a racemic mixture of helical swimmer…
