Many swimming bacteria naturally inhabit confined environments, yet how confinement influences their swimming behaviors remains unclear. Here, we combine experiments, continuum modeling and particle-based simulations to investigate near-surface bacterial swimming in dilute suspensions under varying confinement. Confinement reduces near-surface accumulation and facilitates bacterial escape. These effects are quantitatively captured by models incorporating the force quadrupole, a higher-order hydrodynamic singularity, that generates a rotational flow reorienting bacteria away from surfaces. Under strong confinement, bacterial trajectories straighten due to the balancing torques exerted by opposing surfaces. These findings highlight the role of hydrodynamic quadrupole interactions in near-surface bacterial motility, with implications for microbial ecology, infection control, and industrial applications.
Although the motility of the flagellated bacteria, Escherichia coli, has been widely studied, the effect of viscosity on swimming speed remains controversial. The swimming mode of wild-type E.coli is often idealized as a "run-and- tumble" sequence in which periods of swimming at a constant speed are randomly interrupted by a sudden change of direction at a very low speed. Using a tracking microscope, we follow cells for extended periods of time in Newtonian liquids of varying viscosity, and find that the swimming behavior of a single cell can exhibit a variety of behaviors including run-and-tu…
We provide a detailed stochastic description of the swimming motion of an E.coli bacterium in two dimension, where we resolve tumble events in time. For this purpose, we set up two Langevin equations for the orientation angle and speed dynamics. Calculating moments, distribution and autocorrelation functions from both Langevin equations and matching them to the same quantities determined from data recorded in experiments, we infer the swimming parameters of E.coli . They are the tumble rate $λ$, the tumble time $r^{-1}$ , the swimming speed $v_0$ , the strength of speed fluctuations $σ$, the r…
The locomotion of swimming bacteria in simple Newtonian fluids can successfully be described within the framework of low Reynolds number hydrodynamics. The presence of polymers in biofluids generally increases the viscosity, which is expected to lead to slower swimming for a constant bacterial motor torque. Surprisingly, however, several experiments have shown that bacterial speeds increase in polymeric fluids, and there is no clear understanding why. Therefore we perform extensive coarse-grained simulations of a bacterium swimming in explicitly modeled solutions of macromolecular polymers of …
Bacteria in bulk fluids swim collectively and display fascinating emergent dynamics. Although bacterial collective swimming in three-dimensional (3D) geometries has been well studied, its counterpart in confined two-dimensional (2D) geometries relevant to natural habitats of bacteria is still poorly understood. Here, through carefully designed experiments on Escherichia coli in Hele-Shaw chambers, we show that a small change in the degree of confinement leads to a drastic change in bacterial collective swimming. While long-range nematic order emerges for bacteria that can cross during encounte…
Peritrichously-flagellated bacteria, such as Escherichia coli, self-propel in fluids by using specialised motors to rotate multiple helical filaments. The rotation of each motor is transmitted to a short flexible segment called the hook which in turn transmits it to a flagellar filament, enabling swimming of the whole cell. Since multiple motors are spatially distributed on the body of the organism, one would expect the propulsive forces from the filaments to push against each other leading to negligible swimming. We use a combination of computations and theory to show that the swimming of mul…
Bacterial contamination of biological conducts, catheters or water resources is a major threat to public health and can be amplified by the ability of bacteria to swim upstream. The mechanisms of this rheotaxis, the reorientation with respect to flow gradients, often in complex and confined environments, are still poorly understood. Here, we follow individual E. coli bacteria swimming at surfaces under shear flow with two complementary experimental assays, based on 3D Lagrangian tracking and fluorescent flagellar labelling and we develop a theoretical model for their rheotactic motion. Three t…
Swimming-limited aggregation of bacteria in liquid crystals
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), ESPCI Paris, PSL University, CNRS, Sorbonne University, and Paris Cité University（异质介质物理与力学实验室，巴黎高等物理化工学院，PSL大学，法国国家科学研究中心，索邦大学，巴黎西岱大学）；Laboratoire Gulliver, ESPCI Paris, PSL University, CNRS（高卢实验室，巴黎高等物理化工学院，PSL大学，法国国家科学研究中心）；Institut Universitaire de France (IUF)（法国高等研究院）；Institute of Physics, University of Amsterdam（阿姆斯特丹大学物理研究所）
The behavior of flagellated bacteria swimming in non-Newtonian media remains an area with contradictory and conflicting results. We report on the behavior of wild-type and smooth-swimming E. coli in Newtonian, shear thinning and viscoelastic media, measuring their trajectories and swimming speed using a three dimensional real-time tracking microscope. We conclude that the speed enhancement in Methocel solution at higher concentration is due to shear-thinning and an analytical model is used to support our experimental result. We argue that shear-induced normal stresses reduce the wobbling behav…
Shewanella oneidensis MR-1 are facultative aerobic electroactive bacteria, with an appealing potential for sustainable energy production and bioremediation. They gather around air sources, forming aerotactic bands and biofilms. Though accumulation is crucial to technological exploitation, their collective behaviour remains poorly reported. Here we establish a comprehensive framework for the study of aerotaxis, unveiling a novel hybrid locomotion pattern. Despite having only one flagellum, MR-1 combine motility features of mono- and multiflagellate bacteria, alternating longitudinal fast and si…
We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system. Understanding chemotaxis quantitatively requires that one links the switching rate of the rotary system in a gradient of chemoattractant/repellant to experimental measures of the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model and show that the response of a population to the gradient is complex…
We present a simple model for bacteria like \emph{Escherichia coli} swimming near solid surfaces. It consists of two spheres of different radii connected by a dragless rod. The effect of the flagella is taken into account by imposing a force on the tail sphere and opposite torques exerted by the rod over the spheres. The hydrodynamic forces and torques on the spheres are computed by considering separately the interaction of a single sphere with the surface and with the flow produced by the other sphere. Numerically, we solve the linear system which contains the geometrical constraints and the …
We study the collective dynamics of elongated swimmers in a very thin fluid layer by devising long, filamentous, non-tumbling bacteria. The strong confinement induces weak nematic alignment upon collision, which, for large enough density of cells, gives rise to global nematic order. This homogeneous but fluctuating phase, observed on the largest experimentally-accessible scale of millimeters, exhibits the properties predicted by standard models for flocking such as the Vicsek-style model of polar particles with nematic alignment: true long-range nematic order and non-trivial giant number fluct…
We study catalytic Janus swimmers and Escherichia coli bacteria swimming in a two-dimensional colloidal crystal. The Janus swimmers orbit individual colloids and hop between colloids stochastically, with a hopping rate that varies inversely with fuel (hydrogen peroxide) concentration. At high fuel concentration, these orbits are stable for 100s of revolutions, and the orbital speed oscillates periodically as a result of hydrodynamic, and possibly also phoretic, interactions between the swimmer and the six neighbouring colloids. Motile E.~coli bacteria behave very differently in the same colloi…
Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and artificial environments. Here, we experimentally investigate sedimentation of passive particles in water containing various concentrations of the bacterium E. coli. Results show that the presence of living bacteria reduces the velocity of the sedimentation front even in the dilute regime, where the sedimentation velocity is expected to be independent of particle concentration. Bacteria increase the effective diffusion coefficient of the passive particles, which determines the width…
In a classic paper, Edward Purcell analysed the dynamics of flagellated bacterial swimmers and derived a geometrical relationship which optimizes the propulsion efficiency. Experimental measurements for wild-type bacterial species E. coli have revealed that they closely satisfy this geometric optimality. However, the dependence of the flagellar motor speed on the load and more generally the role of the torque-speed characteristics of the flagellar motor is not considered in Purcell's original analysis. Here we derive a tuned condition representing a match between the flagella geometry and the …
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.…
Flagellated bacteria exploiting helical propulsion are known to swim along circular trajectories near surfaces. Fluid dynamics predicts this circular motion to be clockwise (CW) above a rigid surface (when viewed from inside the fluid) and counter-clockwise (CCW) below a free surface. Recent experimental investigations showed that complex physicochemical processes at the nearby surface could lead to a change in the direction of rotation, both at solid surfaces absorbing slip-inducing polymers and interfaces covered with surfactants. Motivated by these results, we use a far-field hydrodynamic m…
Bacteria can chemotactically migrate up attractant gradients by controlling run-and-tumble motility patterns. In addition to this well-known chemotactic behaviour, several soil and marine bacterial species perform chemokinesis: they adjust their swimming speed according to the local concentration of chemoeffector, with higher speed at higher concentration. A field of attractant then induces a spatially varying swimming speed, which results in a drift towards lower attractant concentrations -- contrary to the drift created by chemotaxis. Here, to explore the biological benefits of chemokinesis …
The run and tumble motions of a swimming bacterium are well characterized by two stochastic variables: the speed $v(t)$ and the change of direction or deflection \mbox{$x(t)=\cosφ(t)$}, where $φ(t)$ is the turning angle at time $t$. Recently, we have introduced [Soft Matter {\bf 13}, 3385 (2017)] a single stochastic model for the deflection $x(t)$ of an {\sl E. coli} bacterium performing both types of movement in isotropic media without taxis, based on available experimental data. In this work we introduce Langevin equations for the variables $(v,x)$, which for particular values of a control p…
In this work we introduce a stochastic model to describe directional changes in the movement of swimming bacteria. We use the probability density function (PDF) of turn angles, measured on tumbling wild-type {\it E. coli}, to build a Langevin equation for the deflection of the bacterial body swimming in isotropic media. We have solved this equation analytically by means of the Green function method and shown that three parameters are sufficient to describe the movement: the characteristic time, the steady-state solution and the control parameter. We conclude that the tumble motion, which is ma…
The natural habitats of microorganisms in the human microbiome and ocean and soil ecosystems are full of colloids and macromolecules, which impart non-Newtonian flow properties drastically affecting the locomotion of swimming microorganisms. Although the low-Reynolds-number hydrodynamics of the swimming of flagellated bacteria in simple Newtonian fluids has been well developed, our understanding of bacterial motility in complex non-Newtonian fluids is still primitive. Even after six decades of research, fundamental questions about the nature and origin of bacterial motility enhancement in poly…
Controlling and suppressing bacterial accumulation at solid surfaces is essential for preventing biofilm formation and biofouling. Whereas various chemical surface treatments are known to reduce cell accumulation and attachment, the role of complex surface geometries remains less well understood. Here, we report experiments and simulations that explore the effects of locally varying boundary curvature on the scattering and accumulation dynamics of swimming Escherichia coli bacteria in quasi-two-dimensional microfluidic channels. Our experimental and numerical results show that a concave period…
Concentrated suspensions of swimming microorganisms and other forms of active matter are known to display complex, self-organized spatio-temporal patterns on scales large compared to those of the individual motile units. Despite intensive experimental and theoretical study, it has remained unclear the extent to which the hydrodynamic flows generated by swimming cells, rather than purely steric interactions between them, drive the self-organization. Here we utilize the recent discovery of a spiral-vortex state in confined suspensions of \textit{B. subtilis} to study this issue in detail. Those …
Magnetotactic swimmers tend to align along magnetic field lines against stochastic reorientations. We show that the swimming strategy, e.g. active Brownian motion versus run-and-tumble dynamics, strongly affects the orientation statistics. The latter can exhibit a velocity condensation whereby the alignment probability density diverges. As a consequence, we find that the swimming strategy affects the nature of the phase transition to collective motion, indicating that Lévy run-and-tumble walks can outperform active Brownian processes as strategies to trigger collective behavior.
The near-surface swimming patterns of bacteria are strongly determined by the hydrodynamic interactions between bacteria and the surface, which trap bacteria in smooth circular trajectories that lead to inefficient surface exploration. Here, we show by combining experiments and a data-driven mathematical model that surface exploration of enterohemorrhagic Escherichia coli (EHEC) -- a pathogenic strain of E. coli causing serious illnesses such as bloody diarrhea -- results from a complex interplay between motility and transient surface adhesion events. These events allow EHEC to break the smoot…
External control of the swimming speed of `active particles' can be used to self assemble designer structures in situ on the micrometer to millimeter scale. We demonstrate such reconfigurable templated active self assembly in a fluid environment using light powered strains of Escherichia coli. The physics and biology controlling the sharpness and formation speed of patterns is investigated using a bespoke fast-responding strain.
A growing body of work aims at designing and testing micron-scale synthetic swimmers. One method, inspired by the locomotion of flagellated bacteria, consists of applying a rotating magnetic field to a rigid, helically-shaped, propeller attached to a magnetic head. When the resulting device, termed an artificial bacteria flagellum, is aligned perpendicularly to the applied field, the helix rotates and the swimmer moves forward. Experimental investigation of artificial bacteria flagella shows that at low frequency of the applied field, the axis of the helix does not align perpendicularly to the…
We study the transport of bacteria in a porous media modeled by a square channel containing one cylindrical obstacle via molecular dynamics simulations coupled to a lattice Boltzmann fluid. Our bacteria model is a rod-shaped rigid body which is propelled by a force-free mechanism. To account for the behavior of living bacteria, the model also incorporates a run-and-tumble process. The model bacteria are capable of hydrodynamically interacting with both of the channel walls and the obstacle. This enables the bacteria to get reoriented when experiencing a shear-flow. We demonstrate that this mod…
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）
Motivated by bacterial transport through porous media, here we study the swimming of an actuated, flexible helical filament in both three-dimensional free space and within a cylindrical tube whose diameter is much smaller than the length of the helix. The filament, at rest, has a native helical shape modeled after the geometry of a typical bacterial flagellar bundle. The finite length filament is a free swimmer, and is driven by an applied torque as well as a counter-torque (of equal strength and opposite direction) that represents a virtual cell body. We use a regularized Stokeslet framework …
Peritrichous bacteria such as Escherichia coli swim in viscous fluids by forming a helical bundle of flagellar filaments. The filaments are spatially distributed around the cell body to which they are connected via a flexible hook. To understand how the swimming direction of the cell is determined, we theoretically investigate the elastohydrodynamic motility problem of a multi-flagellated bacterium. Specifically, we consider a spherical cell body with a number N of flagella which are initially symmetrically arranged in a plane in order to provide an equilibrium state. We analytically solve the…
Dense suspensions of swimming bacteria are known to exhibit collective behaviour arising from the interplay of steric and hydrodynamic interactions. Unconfined suspensions exhibit transient, recurring vortices and jets, whereas those confinedin circular domains may exhibit order in the form of a spiral vortex. Here we show that confinement into a long and narrow macroscopic `racetrack' geometry stabilises bacterial motion to form a steady unidirectional circulation. This motion is reproduced in simulations of discrete swimmers that reveal the crucial role that bacteria-driven fluid flows play …
The presence of a nearby boundary is likely to be important in the life cycle and evolution of motile flagellate bacteria. This has led many authors to employ numerical simulations to model near-surface bacterial motion and compute hydrodynamic boundary effects. A common choice has been the method of images for regularized Stokeslets (MIRS); however, the method requires discretization sizes and regularization parameters that are not specified by any theory. To determine appropriate regularization parameters for given discretization choices in MIRS, we conducted dynamically similar macroscopic …
University of Pennsylvania（宾夕法尼亚大学）；National Institute for Mathematical Sciences（韩国数学科学国立研究所）；Chung-Ang University（中央大学）；University of Cincinnati（辛辛那提大学）
Interactions between swimming bacteria have led to remarkable experimentally observable macroscopic properties such as the reduction of the effective viscosity, enhanced mixing, and diffusion. In this work, we study an individual based model for a suspension of interacting point dipoles representing bacteria in order to gain greater insight into the physical mechanisms responsible for the drastic reduction in the effective viscosity. In particular, asymptotic analysis is carried out on the corresponding kinetic equation governing the distribution of bacteria orientations. This allows one to de…
Controlling the swimming behavior of bacteria is crucial, for example, to prevent contamination of ducts and catheters. We show the bacteria modeled by deformable microswimmers can accumulate in flows through straight microchannels either in their center or on previously unknown attractors near the channel walls. We predict a novel resonance effect for semiflexible microswimmers in flows through wavy microchannels. As a result, microswimmers can be deflected in a controlled manner so that they swim in modulated channels distributed over the channel cross-section rather than localized near the …
Bacterial processes ranging from gene expression to motility and biofilm formation are constantly challenged by internal and external noise. While the importance of stochastic fluctuations has been appreciated for chemotaxis, it is currently believed that deterministic long-range fluid dynamical effects govern cell-cell and cell-surface scattering - the elementary events that lead to swarming and collective swimming in active suspensions and to the formation of biofilms. Here, we report the first direct measurements of the bacterial flow field generated by individual swimming Escherichia coli …
Due to their morphology, the dynamics of bacteria suspended in media can exhibit complex behaviors. In the presence of a shear, swimming bacteria experience a drift perpendicular to the shear plane. This drift, termed rheotaxis, is studied here semi-analytically, numerically and experimentally. We find the dependency of bacterial orientation and bacterial speed on the shear rate, in the presence of rotational diffusion. This enables us to show that the drift speed of bacteria perpendicular to the shear is predominantly due to bacterial propulsion, and not rheotactic forces. Comparing the drift…
This fluid dynamics video presents three-dimensional kinetic simulations of the dynamics in suspensions of oxytactic bacteria confined in thin liquid film surrounded by air. At the initial time, the bacterial concentration is uniform and isotropic, and there is no oxygen inside the film. The spatio-temporal dynamics of the oxygen and bacterial concentration are analyzed. For small film thicknesses, there is a weak migration of bacteria to the boundaries, and the oxygen concentration is high inside the film as a result of diffusion; both bacterial and oxygen concentrations quickly reach steady …
The induced diffusion of tracers in a bacterial suspension is studied theoretically and experimentally at low bacterial concentrations. Considering the swimmer-tracer hydrodynamic interactions at low-Reynolds number and using a kinetic theory approach, it is shown that the induced diffusion coefficient is proportional to the swimmer concentration, their mean velocity and a coefficient $β$, as observed experimentally. The coefficient $β$ scales as the tracer-swimmer cross section times the mean square displacement produced by single scatterings. The displacements depend on the swimmer propulsio…
