We propose a hydrodynamic model for a spheroidal microswimmer with two tangential surface velocity modes. This model is analytically solvable and reduces to Lighthill's and Blake's spherical squirmer model in the limit of equal major and minor semi-axes. Furthermore, we present an implementation of such a spheroidal squirmer by means of multiparticle collision dynamics simulations. We investigate its properties as well as the scattering of two spheroidal squirmers in a slit geometry. Thereby we find a stable fixed point, where two pullers swim cooperatively forming a wedge-like conformation with a small constant angle.
We analyse the effect of confining rigid and elastic boundaries on the motility of a model dipolar microswimmer. Flexible boundaries are deformed by the velocity field of the swimmer in such a way that the motility of both extensile and contractile swimmers is enhanced. The magnitude of the increase in swimming velocity is controlled by the ratio of the swimmer-advection and elastic timescales, and the dipole moment of the swimmer. We explain our results by considering swimming between inclined rigid boundaries.
Oscillatory flows are commonly experienced by swimming microorganisms in the environment, industrial applications and rheological investigations. We experimentally characterise the response of the alga {\it Dunaliella salina} to oscillatory shear flows, and report the surprising discovery that algal swimming trajectories orient perpendicular to the flow-shear plane. The ordering has the characteristics of a resonance in the driving parameter space. The behaviour is qualitatively reproduced by a simple model and simulations accounting for helical swimming, providing the mechanism for ordering a…
The hydrodynamic flow field generated by self-propelled active particles and swimming microorganisms is strongly altered by the presence of nearby boundaries in a viscous flow. Using a simple model three-linked sphere swimmer, we show that the swimming trajectories near a no-slip wall reveal various scenarios of motion depending on the initial orientation and the distance separating the swimmer from the wall. We find that the swimmer can either be trapped by the wall, completely escape, or perform an oscillatory gliding motion at a constant mean height above the wall. Using a far-field approxi…
Tunable asymmetric swimming in biflagellate microswimmers
University College London（伦敦大学学院）；Nantes Université, École Centrale Nantes, CNRS, LS2N（南特大学、中央理工南特学院、法国国家科学研究中心、LS2N）；Georgia Institute of Technology（佐治亚理工学院）；University of Oxford（牛津大学）；Living Systems Institute & Department of Mathematics and Statistics, University of Exeter（埃克塞特大学生命系统研究所与数学和统计系）
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 neutra…
Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and alga…
Microswimmers exhibit more diverse behavior in quasi-two dimensions than in three dimensions. Such behavior remains elusive due to the analytical difficulty of dealing with two parallel solid boundaries. The existence of additional obstacles in quasi-two dimensional systems further complicates the analysis. Combining experiments and hydrodynamic simulations, we investigate how the spatial dimension affects the interactions between microswimmers and obstacles. We fabricated microscopic pillars in quasi-two dimensions by etching glass coverslips and observed bacterial swimming among the pillars.…
External gradients can strongly influence the collective behavior of microswimmers. In this paper, we study the behavior of two hydrodynamically interacting self-propelled chiral swimmers, in the low-Reynolds number regime, under the influence of an external linear chemical gradient. We use the generalized squirmer model called the chiral squirmer, a spherically shaped body with an asymmetric surface slip velocity, to represent the swimmer. We find that the external gradient favors the attraction between the swimmers and, in some situations, leads to a bounded state in which the swimmers move …
Emergent swimming strategies of a smart three-bead swimmer
Institute for Theoretical Physics, TU Wien（维也纳工业大学理论物理研究所）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Institute of Computer Engineering, TU Wien（维也纳工业大学计算机工程研究所）；Allen Discovery Center, Tufts University（塔夫茨大学艾伦发现中心）
The locomotion of microorganisms and spermatozoa in complex viscoelastic fluids is of critical importance in many biological processes such as fertilization, infection, and biofilm formation. Depending on their propulsion mechanisms, microswimmers display various responses to a complex fluid environment: increasing or decreasing their swimming speed and efficiency, modifying their propulsion kinematics and swimming gaits, and experiencing different hydrodynamic interactions with their surroundings. In this article, we review the fundamental physics of locomotion of biological and synthetic mic…
Self-propulsion of cellular microswimmers generates flow signatures, commonly classified as pusher- and puller-type, which characterize hydrodynamic interactions with other cells or boundaries. Using experimentally measured beat patterns, we compute that flagellated alga and sperm oscillate between pusher and puller. Beyond a typical distance of 100 um from the swimmer, inertia attenuates oscillatory micro-flows. We show that hydrodynamic interactions between swimmers oscillate in time and are of similar magnitude as stochastic swimming fluctuations.
In this letter we propose a kinematic model to show how collisions with a surface and rotational Brownian motion give rise to the accumulation of micro-swimmers near a surface. In this model, an elongated microswimmer invariably travels parallel to the surface after hitting it from any incident angle. It then swims away from the surface after some time, facilitated by rotational Brownian motion. Simulations based on this model reproduce the density distributions measured for the small bacteria E. coli and Caulobacter crescentus, as well as for the much larger bull spermatozoa swimming in confi…
A body immersed in a highly viscous fluid can locomote by drawing in and expelling fluid through pores at its surface. We consider this mechanism of jet propulsion without inertia in the case of spheroidal bodies, and derive both the swimming velocity and the hydrodynamic efficiency. Elementary examples are presented, and exact axisymmetric solutions for spherical, prolate spheroidal, and oblate spheroidal body shapes are provided. In each case, entirely and partially porous (i.e. jetting) surfaces are considered, and the optimal jetting flow profiles at the surface for maximizing the hydrodyn…
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Brandeis University（布兰迪斯大学）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；TU Dresden（德累斯顿工业大学）
We perform hydrodynamic simulations using the method of multi-particle collision dynamics and a theoretical analysis to study a single squirmer microswimmer at high Péclet number, which moves in a low Reynolds number fluid and under gravity. The relevant parameters are the ratio $α$ of swimming to bulk sedimentation velocity and the squirmer type $β$. The combination of self-propulsion, gravitational force, hydrodynamic interactions with the wall, and thermal noise leads to a surprisingly diverse behavior. At $α> 1$ we observe cruising states, while for $α<1$ the squirmer resides close to the …
Modeling bacterial flow field with regularized singularities
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家实验室）；Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院）
Hydrodynamic interactions in systems comprised of self-propelled particles, such as swimming microorganisms, and passive tracers have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force/counter-force based lattice-Boltzmann (LB) algorithm [J. de Graaf~\textit{et al.}, J. Chem. Phys.~\textbf{144}, 134106 (2016)] in order to validate its ability to cap…
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…
Motivated by recent experiments, we consider the hydrodynamic capture of a microswimmer near a stationary spherical obstacle. Simulations of model equations show that a swimmer approaching a small spherical colloid is simply scattered. In contrast, when the colloid is larger than a critical size it acts as a passive trap: the swimmer is hydrodynamically captured along closed trajectories and endlessly orbits around the colloidal sphere. In order to gain physical insight into this hydrodynamic scattering problem, we address it analytically. We provide expressions for the critical trapping radiu…
The journey of mammalian spermatozoa in nature is well-known to be reliant on their individual motility. Often swimming in crowded microenvironments, the progress of any single swimmer is likely dependent on their interactions with other nearby swimmers. Whilst the complex dynamics of lone spermatozoa have been well-studied, the detailed effects of hydrodynamic interactions between neighbors remain unclear, with inherent nonlinearity in the governing hydrodynamics and potential dependence on the details of swimmer morphology. In this study we will attempt to elucidate the pairwise swimming beh…
Interactions between swimming cells and surfaces are essential to many microbiological processes, from bacterial biofilm formation to human fertilization. However, in spite of their fundamental importance, relatively little is known about the physical mechanisms that govern the scattering of flagellated or ciliated cells from solid surfaces. A more detailed understanding of these interactions promises not only new biological insights into structure and dynamics of flagella and cilia, but may also lead to new microfluidic techniques for controlling cell motility and microbial locomotion, with p…
