Hydrodynamic surface interactions enable Escherichia coli to seek efficient routes to swim upstream

Collective dynamics of active dumbbells near a circular obstacle

In this article, we present the collective dynamics of active dumbbells in the presence of a static circular obstacle using Brownian dynamics simulation. The active dumbbells aggregate on the surface of a circular obstacle beyond a critical radius. The aggregation is non-uniform along the circumference, and the aggregate size increases with the activity (Pe) and the curvature radius (Ro). The dense aggregate of active dumbbells displays persistent rotational motion with a certain angular speed, which linearly increases with activity. Furthermore, we show a strong polar ordering of the active dumbbells within the aggregate. The polar ordering exhibits long-range correlation, with the correlation length corresponding to the aggregate size. Additionally, we show that the residence time of an active dumbbell on the obstacle surface increases rapidly with area fraction due to many-body interactions that lead to a slowdown of the rotational diffusion. This article further considers the dynamical behavior of a tracer particle in the solution of active dumbbells. Interestingly, the speed of the passive tracer particle displays a crossover from monotonically decreasing to increasing with the size of the tracer particle upon increasing the dumbbells' speed. Furthermore, the effective diffusion of the tracer particle displays non-monotonic behavior with the area fraction; the initial increase in diffusivity is followed by a decrease for a larger area fraction.

AI-aided geometric design of anti-infection catheters

Bacteria can swim upstream in a narrow tube and pose a clinical threat of urinary tract infection to patients implanted with catheters. Coatings and structured surfaces have been proposed to repel bacteria, but no such approach thoroughly addresses the contamination problem in catheters. Here, on the basis of the physical mechanism of upstream swimming, we propose a novel geometric design, optimized by an artificial intelligence model. Using Escherichia coli, we demonstrate the anti-infection mechanism in microfluidic experiments and evaluate the effectiveness of the design in three-dimensionally printed prototype catheters under clinical flow rates. Our catheter design shows that one to two orders of magnitude improved suppression of bacterial contamination at the upstream end, potentially prolonging the in-dwelling time for catheter use and reducing the overall risk of catheter-associated urinary tract infection.

Migration of surface-associated microbial communities in spaceflight habitats

Astronauts are spending longer periods locked up in ships or stations for scientific and exploration spatial missions. The International Space Station (ISS) has been inhabited continuously for more than 20 years and the duration of space stays by crews could lengthen with the objectives of human presence on the moon and Mars. If the environment of these space habitats is designed for the comfort of astronauts, it is also conducive to other forms of life such as embarked microorganisms. The latter, most often associated with surfaces in the form of biofilm, have been implicated in significant degradation of the functionality of pieces of equipment in space habitats. The most recent research suggests that microgravity could increase the persistence, resistance and virulence of pathogenic microorganisms detected in these communities, endangering the health of astronauts and potentially jeopardizing long-duration manned missions. In this review, we describe the mechanisms and dynamics of installation and propagation of these microbial communities associated with surfaces (spatial migration), as well as long-term processes of adaptation and evolution in these extreme environments (phenotypic and genetic migration), with special reference to human health. We also discuss the means of control envisaged to allow a lasting cohabitation between these vibrant microscopic passengers and the astronauts.

Characteristic features of self-avoiding active Brownian polymers under linear shear flow

We present Brownian dynamics simulation results of a flexible linear polymer with excluded-volume interactions under shear flow in the presence of active noise. The active noise strongly affects the polymer's conformational and dynamical properties, such as the stretching in the flow direction and compression in the gradient direction, shear-induced alignment, and shear viscosity. In the asymptotic limit of large activities and shear rates, the power-law scaling exponents of these quantities differ significantly from those of passive polymers. The chain's shear-induced stretching at a given shear rate is reduced by active noise, and it displays a non-monotonic behavior, where an initial polymer compression is followed by its stretching with increasing active force. The compression of the polymer in the gradient direction follows the relation ∼WiPe-3/4 as a function of the activity-dependent Weissenberg number WiPe, which differs from the scaling observed in passive systems ∼WiPe-1/2. The flow-induced alignment at large Péclet numbers Pe ≫ 1, where Pe is the Péclet number, and large shear rates WiPe ≫ 1 displays the scaling behavior WiPe-1/2, with an exponent differing from the passive value -1/3. Furthermore, the polymer's zero-shear viscosity displays a non-monotonic behavior, decreasing in an intermediate activity regime due to excluded-volume interactions and increasing again for large Pe. Shear thinning appears with increasing Weissenberg number with the power-laws WiPe-1/2 and WiPe-3/4 for passive and active polymers, respectively. In addition, our simulation results are compared with the results of an analytical approach, which predicts quantitatively similar behaviors for the various aforementioned physical quantities.

Bacteria in Fluid Flow

Bacteria thrive in environments rich in fluid flow, such as the gastrointestinal tract, bloodstream, aquatic systems, and the urinary tract. Despite the importance of flow, how flow affects bacterial life is underappreciated. In recent years, the combination of approaches from biology, physics, and engineering has led to a deeper understanding of how bacteria interact with flow. Here, we highlight the wide range of bacterial responses to flow, including changes in surface adhesion, motility, surface colonization, quorum sensing, virulence factor production, and gene expression. To emphasize the diversity of flow responses, we focus our review on how flow affects four ecologically distinct bacterial species: Escherichia coli, Staphylococcus aureus, Caulobacter crescentus, and Pseudomonas aeruginosa. Additionally, we present experimental approaches to precisely study bacteria in flow, discuss how only some flow responses are triggered by shear force, and provide perspective on flow-sensitive bacterial signaling.

Confined active matter in external fields

We analyze a dilute suspension of active particles confined between walls and subjected to fields that can modulate particle speed as well as orientation. Generally, the particle distribution is different in the bulk compared to near the walls. In the bulk, particles tend to accumulate in the regions of low speed, but in the presence of an orienting field normal to the walls, particles rotate to align with the field and accumulate in the field direction. At the walls, particles tend to accumulate pointing into the walls and thereby exert pressure on walls. But the presence of strong orienting fields can cause the particles to reorient away from the walls, and hence shows a possible mechanism for preventing contamination of surfaces. The pressure at the walls depends on the wall separation and the field strengths. This work demonstrates how multiple fields with different functionalities can be used to control active matter under confinement.

Active particles crossing sharp viscosity gradients

Active particles (living or synthetic) often move through inhomogeneous environments, such as gradients in light, heat or nutrient concentration, that can lead to directed motion (or taxis). Recent research has explored inhomogeneity in the rheological properties of a suspending fluid, in particular viscosity, as a mechanical (rather than biological) mechanism for taxis. Theoretical and experimental studies have shown that gradients in viscosity can lead to reorientation due to asymmetric viscous forces. In particular, recent experiments with Chlamydomonas Reinhardtii algae swimming across sharp viscosity gradients have observed that the microorganisms are redirected and scattered due to the viscosity change. Here we develop a simple theoretical model to explain these experiments. We model the swimmers as spherical squirmers and focus on small, but sharp, viscosity changes. We derive a law, analogous to Snell's law of refraction, that governs the orientation of active particles in the presence of a viscosity interface. Theoretical predictions show good agreement with experiments and provide a mechanistic understanding of the observed reorientation process.

Confinement, chaotic transport, and trapping of active swimmers in time-periodic flows

Microorganisms encounter complex unsteady flows, including algal blooms in marine settings, microbial infections in airways, and bioreactors for vaccine and biofuel production. Here, we study the transport of active swimmers in two-dimensional time-periodic flows using Langevin simulations and experiments with swimming bacteria. We find that long-term swimmer transport is controlled by two parameters, the pathlength of the unsteady flow and the normalized swimmer speed. The pathlength nonmonotonically controls swimmer dispersion dynamics, giving rise to three distinct dispersion regimes. Weak flows hinder swimmer transport by confining cells toward flow manifolds. As pathlength increases, chaotic transport along flow manifolds initiates, maximizing the number of unique flow cells traveled. Last, strong flows trap swimmers at the vortex core, suppressing dispersal. Experiments with Vibrio cholerae showed qualitative agreement with model dispersion patterns. Our results reveal that nontrivial chaotic transport can arise in simple unsteady flows and suggest a potentially optimal dispersal strategy for microswimmers in nature.

Motility Increases the Numbers and Durations of Cell-Surface Engagements for Escherichia coli Flowing near Poly(ethylene glycol)-Functionalized Surfaces

Bacteria are keenly sensitive to properties of the surfaces they contact, regulating their ability to form biofilms and initiate infections. This study examines how the presence of flagella, interactions between the cell body and the surface, or motility itself guides the dynamic contact between bacterial cells and a surface in flow, potentially enabling cells to sense physicochemical and mechanical properties of surfaces. This work focuses on a poly(ethylene glycol) biomaterial coating, which does not retain cells. In a comparison of four Escherichia coli strains with different flagellar expressions and motilities, cells with substantial run-and-tumble swimming motility exhibited increased flux to the interface (3 times the calculated transport-limited rate which adequately described the non-motile cells), greater proportions of cells engaging in dynamic nanometer-scale surface associations, extended times of contact with the surface, increased probability of return to the surface after escape and, as evidenced by slow velocities during near-surface travel, closer cellular approach. All these metrics, reported here as distributions of cell populations, point to a greater ability of motile cells, compared with nonmotile cells, to interact more closely, forcefully, and for greater periods of time with interfaces in flow. With contact durations of individual cells exceeding 10 s in the window of observation and trends suggesting further interactions beyond the field of view, the dynamic contact of individual cells may approach the minute timescales reported for mechanosensing and other cell recognition pathways. Thus, despite cell translation and the dynamic nature of contact, flow past a surface, even one rendered non-cell arresting by use of an engineered coating, may produce a subpopulation of cells already upregulating virulence factors before they arrest on a downstream surface and formally initiate biofilm formation.

Fluid Flow Induces Differential Detachment of Live and Dead Bacterial Cells from Nanostructured Surfaces

Nanotopographic surfaces are proven to be successful in killing bacterial cells upon contact. This non-chemical bactericidal property has paved an alternative way of fighting bacterial colonization and associated problems, especially the issue of bacteria evolving resistance against antibiotic and antiseptic agents. Recent advancements in nanotopographic bactericidal surfaces have made them suitable for many applications in medical and industrial sectors. The bactericidal effect of nanotopographic surfaces is classically studied under static conditions, but the actual potential applications do have fluid flow in them. In this study, we have studied how fluid flow can affect the adherence of bacterial cells on nanotopographic surfaces. Gram-positive and Gram-negative bacterial species were tested under varying fluid flow rates for their retention and viability after flow exposure. The total number of adherent cells for both species was reduced in the presence of flow, but there was no flowrate dependency. There was a significant reduction in the number of live cells remaining on nanotopographic surfaces with an increasing flowrate for both species. Conversely, we observed a flowrate-independent increase in the number of adherent dead cells. Our results indicated that the presence of flow differentially affected the adherent live and dead bacterial cells on nanotopographic surfaces. This could be because dead bacterial cells were physically pierced by the nano-features, whereas live cells adhered via physiochemical interactions with the surface. Therefore, fluid shear was insufficient to overcome adhesion forces between the surface and dead cells. Furthermore, hydrodynamic forces due to the flow can cause more planktonic and detached live cells to collide with nano-features on the surface, causing more cells to lyse. These results show that nanotopographic surfaces do not have self-cleaning ability as opposed to natural bactericidal nanotopographic surfaces, and nanotopographic surfaces tend to perform better under flow conditions. These findings are highly useful for developing and optimizing nanotopographic surfaces for medical and industrial applications.

Bacterial active matter

Bacteria are among the oldest and most abundant species on Earth. Bacteria successfully colonize diverse habitats and play a significant role in the oxygen, carbon, and nitrogen cycles. They also form human and animal microbiota and may become sources of pathogens and a cause of many infectious diseases. Suspensions of motile bacteria constitute one of the most studied examples of active matter: a broad class of non-equilibrium systems converting energy from the environment (e.g., chemical energy of the nutrient) into mechanical motion. Concentrated bacterial suspensions, often termed active fluids, exhibit complex collective behavior, such as large-scale turbulent-like motion (so-called bacterial turbulence) and swarming. The activity of bacteria also affects the effective viscosity and diffusivity of the suspension. This work reports on the progress in bacterial active matter from the physics viewpoint. It covers the key experimental results, provides a critical assessment of major theoretical approaches, and addresses the effects of visco-elasticity, liquid crystallinity, and external confinement on collective behavior in bacterial suspensions.

Environmental, Microbiological, and Immunological Features of Bacterial Biofilms Associated with Implanted Medical Devices

The spread of biofilms on medical implants represents one of the principal triggers of persistent and chronic infections in clinical settings, and it has been the subject of many studies in the past few years, with most of them focused on prosthetic joint infections. We review here recent works on biofilm formation and microbial colonization on a large variety of indwelling devices, ranging from heart valves and pacemakers to urological and breast implants and from biliary stents and endoscopic tubes to contact lenses and neurosurgical implants. We focus on bacterial abundance and distribution across different devices and body sites and on the role of environmental features, such as the presence of fluid flow and properties of the implant surface, as well as on the interplay between bacterial colonization and the response of the human immune system.

Micro-Nano Motors with Taxis Behavior: Principles, Designs, and Biomedical Applications

As a novel mobile nanodevice, micro-nano motors (MNMs) can convert the energy of the surrounding environment into mechanical motion. With this unique ability, they promise revolutionary potential in bio-applications including precise drug delivery, bio-sensing, and noninvasive surgery. Yet for practically reaching the target and fulfilling these tasks in dynamically changing bio-environment, environment adaptivity beyond propulsion is important yet challenging. MNMs with taxis behavior/autonomous target-seeking ability offer a desirable solution. These motors can adaptively move to the target location and complete the task. Thanks to the persistent efforts of researchers, tactic MNMs have shown automatic navigation to target under various energy fields, not only in static environments, but also in shear rheological conditions that simulate blood flow. Therefore, tactic motors with self-targeting capability lay a concrete foundation for targeted drug delivery, cell transplantation, and thrombus ablation. This review systematically presents the moving principle, design, and biological applications of tactic MNMs under different energy fields. Through in-depth analysis of state-of-art progress, the obstacles of the field and possible solutions are discussed. With the continuous innovation and breakthroughs of multi-disciplinary researchers, MNMs with taxis behavior are expected to provide a revolutionary solution for cancer and other major diseases in the biomedical field.

Diffusion of chiral active particles in a Poiseuille flow

We study the diffusive behavior of chiral active (self-propelled) Brownian particles in a two-dimensional microchannel with a Poiseuille flow. Using numerical simulations, we show that the behavior of the transport coefficients of particles, for example, the average velocity v and the effective diffusion coefficient D_{eff}, strongly depends on flow strength u_{0}, translational diffusion constant D_{0}, rotational diffusion rate D_{θ}, and chirality of the active particles Ω. It is demonstrated that the particles can exhibit upstream drift, resulting in a negative v, for the optimal parameter values of u_{0}, D_{θ}, and Ω. Interestingly, the direction of v can be controlled by tuning these parameters. We observe that for some optimal values of u_{0} and Ω, the chiral particles aggregate near a channel wall and the corresponding D_{eff} are enhanced. However, for the nonchiral particles (Ω=0), D_{eff} is suppressed by the presence of Poiseuille flow. It is expected that these findings have a great potential for developing microfluidic and lab-on-a-chip devices for separating the active particles.

On the cross-streamline lift of microswimmers in viscoelastic flows

The current work studies the dynamics of a microswimmer in pressure-driven flow of a weakly viscoelastic fluid. Employing a second-order fluid model, we show that a self-propelling swimmer experiences a viscoelastic swimming lift in addition to the well-known passive lift that arises from its resistance to shear flow. Using the reciprocal theorem, we evaluate analytical expressions for the swimming lift experienced by neutral and pusher/puller-type swimmers and show that they depend on the hydrodynamic signature associated with the swimming mechanism. We find that, in comparison to passive particles, the focusing of neutral swimmers towards the centerline can be significantly accelerated, while for force-dipole swimmers no net modification in cross-streamline migration occurs.

Migration of active filaments under Poiseuille flow in a microcapillary tube

We present a comprehensive study of active filaments confined in a cylindrical channel under Poiseuille flow. The activity drives the filament towards the channel boundary, whereas external fluid flow migrates the filament away from the boundary. This migration further shifts towards the centre for higher flow strength. The migration behaviour of the filaments is presented in terms of the alignment order parameter that shows the alignment grows with shear and activity. Further, we have also addressed the role of length of filament on the migration behaviour, which suggests higher migration for larger filaments. Moreover, we discuss the polar ordering of filaments as a function of distance from the centre of channel that displays upstream motion near the boundary and downstream motion at the centre of the tube.

Generating Shear Flows without Moving Parts by Thermo-osmosis in Heterogeneous Nanochannels

Shear flows play critical roles in biological systems and technological applications and are achieved experimentally using moving parts. However, when the system size is reduced to micro- and nanoscale, fabrication of moving parts becomes exceedingly challenging. We demonstrate that a heterogeneous nanochannel composed of two parallel walls with different wetting behaviors can generate shear flow without moving parts. Molecular dynamics simulations show that shear flows can be formed inside such a nanochannel under a temperature gradient. The physical origin is that thermo-osmosis velocities with different rates and directions can be tuned by wetting behaviors. Our analysis reveals that thermo-osmosis is governed by surface excess enthalpy and nanoscale interfacial hydrodynamics. This finding provides an efficient method of generating controllable shear flows at micro- and nanoscale confinement. It also demonstrates the feasibility of using fluids to drive micromechanical elements via shear torques generated by harvesting energy from temperature differences.

The impact of rheotaxis and flow on the aggregation of organisms

Dispersed populations often need to organize into groups. Chemical attractants provide one means of directing individuals into an aggregate, but whether these structures emerge can depend on various factors, such as there being a sufficiently large population or the response to the attractant being sufficiently sensitive. In an aquatic environment, fluid flow may heavily impact on population distribution and many aquatic organisms adopt a rheotaxis response when exposed to a current, orienting and swimming according to the flow field. Consequently, flow-induced transport could be substantially different for the population members and any aggregating signal they secrete. With the aim of investigating how flows and rheotaxis responses impact on an aquatic population's ability to form and maintain an aggregated profile, we develop and analyse a mathematical model that incorporates these factors. Through a systematic analysis into the effect of introducing rheotactic behaviour under various forms of environmental flow, we demonstrate that each of flow and rheotaxis can act beneficially or detrimentally on the ability to form and maintain a cluster. Synthesizing these findings, we test a hypothesis that density-dependent rheotaxis may be optimal for group formation and maintenance, in which individuals increase their rheotactic effort as they approach an aggregated state.

Upcoming flow promotes the bundle formation of bacterial flagella

Flagellated bacteria swim by rotating a bundle of helical flagella and commonly explore the surrounding environment in a "run-and-tumble" motility mode. Here, we show that the upcoming flow could impact the bacterial run-and-tumble behavior by affecting the formation and dispersal of the flagellar bundle. Using a dual optical tweezers setup to trap individual bacteria, we characterized the effects of the imposed fluid flow and cell body rotation on the run-and-tumble behavior. We found that the two factors affect the behavior differently, with the imposed fluid flow increasing the running time and decreasing the tumbling time and the cell body rotation decreasing the tumbling time only. Using numerical simulations, we computed the flagellar bundling time as a function of flow velocity, which agrees well with our experimental observations. The mechanical effects we characterized here provide novel, to our knowledge, ingredients for further studies of bacterial chemotaxis in complex environments such as dynamic fluid environments.

Bacteria hinder large-scale transport and enhance small-scale mixing in time-periodic flows

Understanding mixing and transport of passive scalars in active fluids is important to many natural (e.g., algal blooms) and industrial (e.g., biofuel, vaccine production) processes. Here, we study the mixing of a passive scalar (dye) in dilute suspensions of swimming Escherichia coli in experiments using a two-dimensional (2D) time-periodic flow and in a simple simulation. Results show that the presence of bacteria hinders large-scale transport and reduces overall mixing rate. Stretching fields, calculated from experimentally measured velocity fields, show that bacterial activity attenuates fluid stretching and lowers flow chaoticity. Simulations suggest that this attenuation may be attributed to a transient accumulation of bacteria along regions of high stretching. Spatial power spectra and correlation functions of dye-concentration fields show that the transport of scalar variance across scales is also hindered by bacterial activity, resulting in an increase in average size and lifetime of structures. On the other hand, at small scales, activity seems to enhance local mixing. One piece of evidence is that the probability distribution of the spatial concentration gradients is nearly symmetric with a vanishing skewness. Overall, our results show that the coupling between activity and flow can lead to nontrivial effects on mixing and transport.

Engineered topographies and hydrodynamics in relation to biofouling control-a review

Biofouling, the unwanted growth of microorganisms on submerged surfaces, has appeared as a significant impediment for underwater structures, water vessels, and medical devices. For fixing the biofouling issue, modification of the submerged surface is being experimented as a non-toxic approach worldwide. This technique necessitated altering the surface topography and roughness and developing a surface with a nano- to micro-structured pattern. The main objective of this study is to review the recent advancements in surface modification and hydrodynamic analysis concerning biofouling control. This study described the occurrence of the biofouling process, techniques suitable for biofouling control, and current state of research advancements comprehensively. Different biofilms under various hydrodynamic conditions have also been outlined in this study. Scenarios of biomimetic surfaces and underwater super-hydrophobicity, locomotion of microorganisms, nano- and micro-hydrodynamics on various surfaces around microorganisms, and material stiffness were explained thoroughly. The review also documented the approaches to inhibit the initial settlement of microorganisms and prolong the subsequent biofilm formation process for patterned surfaces. Though it is well documented that biofouling can be controlled to various degrees with different nano- and micro-structured patterned surfaces, the understanding of the underlying mechanism is still imprecise. Therefore, this review strived to present the possibilities of implementing the patterned surfaces as a physical deterrent against the settlement of fouling organisms and developing an active microfluidic environment to inhibit the initial bacterial settlement process. In general, microtopography equivalent to that of bacterial cells influences attachment via hydrodynamics, topography-induced cell placement, and air-entrapment, whereas nanotopography influences physicochemical forces through macromolecular conditioning.

Lattice model for active flows in microchannels

We introduce a one-dimensional lattice model to study active particles in narrow channel connecting finite reservoirs. The model describes interacting run-and-tumble swimmers exerting pushing forces on neighboring particles, allowing the formation of long active clusters inside the channel. Our model is able to reproduce the emerging oscillatory dynamics observed in full molecular dynamics simulations of self-propelled bacteria [Paoluzzi et al., Phys. Rev. Lett. 115, 188303 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.188303] and allows us to extend in a simple way the analysis to a wide range of system parameters (box length, number of swimmers), taking into account different physical conditions (presence or absence of tumbling, different forms of the entrance probability into the channel). We find that the oscillatory behavior is suppressed for short channels length L<L^{*} and for high tumbling rates λ>λ^{*}, with threshold values L^{*} and λ^{*} which in general depend on physical parameters. Moreover, we find that oscillations persist by using different entrance probabilities, which, however, affect the oscillation properties and the filling dynamics of reservoirs.

Bactericidal efficiency of micro- and nanostructured surfaces: a critical perspective

Micro/nanostructured surfaces (MNSS) have shown the ability to inactivate bacterial cells by physical means. An enormous amount of research has been conducted in this area over the past decade. Here, we review the various surface factors that affect the bactericidal efficiency. For example, surface hydrophobicity of the substrate has been accepted to be influential on the bactericidal effect of the surface, but a review of the literature suggests that the influence of hydrophobicity differs with the bacterial species. Also, various bacterial viability quantification methods on MNSS are critically reviewed for their suitability for the purpose, and limitations of currently used protocols are discussed. Presently used static bacterial viability assays do not represent the conditions of which those surfaces could be applied. Such application conditions do have overlaying fluid flow, and bacterial behaviours are drastically different under flow conditions compared to under static conditions. Hence, it is proposed that the bactericidal effect should be assessed under relevant fluid flow conditions with factors such as shear stress and flowrate given due significance. This review will provide a range of opportunities for future research in design and engineering of micro/nanostructured surfaces with varying experimental conditions.

Sorting and Extraction of Self-Propelled Chiral Particles by Polarized Wall Currents

The dynamics of self-propelled particles with curved trajectories is investigated. Two modes are observed, a bulk mode with a quasicircular motion and a surface mode with the particles following the walls. The surface mode is the only mode of ballistic transport and the particle current is polar and depends on the particles' chirality. We show that a robust sorting and extraction occurs when the particles explore a domain with two exit gates collecting selectively the particles circling left and right. With a counterslope, the extraction rate is found to increase while the sorting error is reduced.

Chirality-induced bacterial rheotaxis in bulk shear flows

Interaction of swimming bacteria with flows controls their ability to explore complex environments, crucial to many societal and environmental challenges and relevant for microfluidic applications such as cell sorting. Combining experimental, numerical, and theoretical analysis, we present a comprehensive study of the transport of motile bacteria in shear flows. Experimentally, we obtain with high accuracy and, for a large range of flow rates, the spatially resolved velocity and orientation distributions. They are in excellent agreement with the simulations of a kinematic model accounting for stochastic and microhydrodynamic properties and, in particular, the flagella chirality. Theoretical analysis reveals the scaling laws behind the average rheotactic velocity at moderate shear rates using a chirality parameter and explains the reorientation dynamics leading to saturation at large shear rates from the marginal stability of a fixed point. Our findings constitute a full understanding of the physical mechanisms and relevant parameters of bacteria bulk rheotaxis.

Confined Bubble-Propelled Microswimmers in Capillaries: Wall Effect, Fuel Deprivation, and Exhaust Product Excess

Self-propelled autonomous nano/microswimmers are at the forefront of materials science. These swimmers are expected to operate in highly confined environments, such as between the grains of soil or in the capillaries of the human organism. To date, little attention is paid to the problem that in such a confined environment the fuel powering catalytic nano/microswimmers can be exhausted quickly and the space can be polluted with the product of the catalytic reaction. In addition, the motion of the nano/microswimmers may be influenced by the confinement. These issues are addressed here, showing the influence of the size of the capillary and length of the micromotor on the motion and the influence of the depletion of the fuel and excess of the exhaust products. Theoretical modeling is provided as well to bring further insight into the observations. This article shows challenges that these systems face and stimulates research to overcome them.

Motile Bacteria at Oil-Water Interfaces: Pseudomonas aeruginosa

Bacteria are important examples of active or self-propelled colloids. Because of their directed motion, they accumulate near interfaces. There, they can become trapped and swim adjacent to the interface via hydrodynamic interactions, or they can adsorb directly and swim in an adhered state with complex trajectories that differ from those in bulk in both form and spatiotemporal implications. We have adopted the monotrichous bacterium Pseudomonas aeruginosa PA01 as a model species and have studied its motion at oil-aqueous interfaces. We have identified conditions in which bacteria swim persistently without restructuring the interface, allowing detailed and prolonged study of their motion. In addition to characterizing the ensemble behavior of the bacteria, we have observed a gallery of distinct trajectories of individual swimmers on and near fluid interfaces. We attribute these diverse swimming behaviors to differing trapped states for the bacteria in the fluid interface. These trajectory types include Brownian diffusive paths for passive adsorbed bacteria, curvilinear trajectories including curly paths with radii of curvature larger than the cell body length, and rapid pirouette motions with radii of curvature comparable to the cell body length. Finally, we see interfacial visitors that come and go from the interfacial plane. We characterize these individual swimmer motions. This work may impact nutrient cycles for bacteria on or near interfaces in nature. This work will also have implications in microrobotics, as active colloids in general and bacteria in particular are used to carry cargo in this burgeoning field. Finally, these results have implications in engineering of active surfaces that exploit interfacially trapped self-propelled colloids.

Active dipolar spheroids in shear flow and transverse field: Population splitting, cross-stream migration, and orientational pinning

We study the steady-state behavior of active, dipolar, Brownian spheroids in a planar channel subjected to an imposed Couette flow and an external transverse field, applied in the "downward" normal-to-flow direction. The field-induced torque on active spheroids (swimmers) is taken to be of magnetic form by assuming that they have a permanent magnetic dipole moment, pointing along their self-propulsion (swim) direction. Using a continuum approach, we show that a host of behaviors emerges over the parameter space spanned by the particle aspect ratio, self-propulsion and shear/field strengths, and the channel width. The cross-stream migration of the model swimmers is shown to involve a regime of linear response (quantified by a linear-response factor) in weak fields. For prolate swimmers, the weak-field behavior crosses over to a regime of full swimmer migration to the bottom half of the channel in strong fields. For oblate swimmers, a counterintuitive regime of reverse migration arises in intermediate fields, where a macroscopic fraction of swimmers reorient and swim to the top channel half at an acute "upward" angle relative to the field axis. The diverse behaviors reported here are analyzed based on the shear-induced population splitting (bimodality) of the swim orientation, giving two distinct, oppositely polarized, swimmer subpopulations (albeit very differently for prolate/oblate swimmers) in each channel half. In strong fields, swimmers of both types exhibit net upstream currents relative to the laboratory frame. The onsets of full migration and net upstream current depend on the aspect ratio, enabling efficient particle separation strategies in microfluidic setups.

Growth of microorganisms in an interfacially driven space bioreactor analog

Fluid bioreactors in microgravity environments may utilize alternative methods of containment and mixing. The ring-sheared drop (RSD) is a containerless mixing device which functions in microgravity using surface tension for containment and mixes through interfacially-driven flow. To assess the feasibility of using interfacially driven flow devices, such as the RSD, as bioreactors, Escherichia coli growth and recombinant protein expression were analyzed in a ground-based analog of the RSD called the knife edge surface viscometer (KEV). Results demonstrated that the KEV can facilitate the growth of E. coli and that growth rate increases logarithmically with increasing knife edge rotation rate, similar to the standard growth method on Earth (orbital shaker). Furthermore, the KEV was shown to be viable for supporting recombinant protein expression in E. coli at levels comparable to those achieved using standard growth methods.

E. coli "super-contaminates" narrow ducts fostered by broad run-time distribution

One notable feature of bacterial motion is their ability to swim upstream along corners and crevices, by leveraging hydrodynamic interactions. This motion through anatomic ducts or medical devices might be at the origin of serious infections. However, it remains unclear how bacteria can maintain persistent upstream motion while exhibiting run-and-tumble dynamics. Here, we demonstrate that Escherichia coli can travel upstream in microfluidic devices over distances of 15 mm in times as short as 15 min. Using a stochastic model relating the run times to the time that bacteria spend on surfaces, we quantitatively reproduce the evolution of the contamination profiles when considering a broad distribution of run times. The experimental data cannot be reproduced using the usually accepted exponential distribution of run times. Our study demonstrates that the run-and-tumble statistics determine macroscopic bacterial transport properties. This effect, which we name "super-contamination," could explain the fast onset of some life-threatening medical emergencies.

Relating Rheotaxis and Hydrodynamic Actuation using Asymmetric Gold-Platinum Phoretic Rods

We explore the behavior of micron-scale autophoretic Janus (Au/Pt) rods, having various Au/Pt length ratios, swimming near a wall in an imposed background flow. We find that their ability to robustly orient and move upstream, i.e., to rheotax, depends strongly on the Au/Pt ratio, which is easily tunable in synthesis. Numerical simulations of swimming rods actuated by a surface slip show a similar rheotactic tunability when varying the location of the surface slip versus surface drag. The slip location determines whether swimmers are pushers (rear actuated), pullers (front actuated), or in between. Our simulations and modeling show that pullers rheotax most robustly due to their larger tilt angle to the wall, which makes them responsive to flow gradients. Thus, rheotactic response infers the nature of difficult to measure flow fields of an active particle, establishes its dependence on swimmer type, and shows how Janus rods can be tuned for flow responsiveness.

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.

Not Just Going with the Flow: The Effects of Fluid Flow on Bacteria and Plankton

Microorganisms often live in habitats characterized by fluid flow, from lakes and oceans to soil and the human body. Bacteria and plankton experience a broad range of flows, from the chaotic motion characteristic of turbulence to smooth flows at boundaries and in confined environments. Flow creates forces and torques that affect the movement, behavior, and spatial distribution of microorganisms and shapes the chemical landscape on which they rely for nutrient acquisition and communication. Methodological advances and closer interactions between physicists and biologists have begun to reveal the importance of flow-microorganism interactions and the adaptations of microorganisms to flow. Here we review selected examples of such interactions from bacteria, phytoplankton, larvae, and zooplankton. We hope that this article will serve as a blueprint for a more in-depth consideration of the effects of flow in the biology of microorganisms and that this discussion will stimulate further multidisciplinary effort in understanding this important component of microorganism habitats.

Oscillatory surface rheotaxis of swimming E. coli bacteria

Bacterial contamination of biological channels, catheters or water resources is a major threat to public health, which can be amplified by the ability of bacteria to swim upstream. The mechanisms of this 'rheotaxis', the reorientation with respect to flow gradients, are still poorly understood. Here, we follow individual E. coli bacteria swimming at surfaces under shear flow using 3D Lagrangian tracking and fluorescent flagellar labelling. Three transitions are identified with increasing shear rate: Above a first critical shear rate, bacteria shift to swimming upstream. After a second threshold, we report the discovery of an oscillatory rheotaxis. Beyond a third transition, we further observe coexistence of rheotaxis along the positive and negative vorticity directions. A theoretical analysis explains these rheotaxis regimes and predicts the corresponding critical shear rates. Our results shed light on bacterial transport and reveal strategies for contamination prevention, rheotactic cell sorting, and microswimmer navigation in complex flow environments.

Fight the flow: the role of shear in artificial rheotaxis for individual and collective motion

To navigate in complex fluid environments, swimming organisms like fish or bacteria often reorient their bodies antiparallel or against the flow, more commonly known as rheotaxis. This reorientation motion enables the organisms to migrate against the fluid flow, as observed in salmon swimming upstream to spawn. Rheotaxis can also be realized in artificial microswimmers - self-propelled particles that mimic swimming microorganisms. Here we study experimentally and by computer simulations the rheotaxis of self-propelled gold-platinum nanorods in microfluidic channels. We observed two distinct modes of artificial rheotaxis: a high shear domain near the bottom wall of the microfluidic channel and a low shear regime in the corners. Reduced fluid drag in the corners promotes the formation of many particle aggregates that rheotax collectively. Our study provides insight into the biomimetic functionality of artificial self-propelled nanorods for dynamic self-assembly and the delivery of payloads to targeted locations.

Behavior of active filaments near solid-boundary under linear shear flow

The steady-state behavior of a dilute suspension of self-propelled filaments confined between planar walls subjected to Couette-flow is reported herein. The effect of hydrodynamics has been taken into account using a mesoscale simulation approach. We present a detailed analysis of positional and angular probability distributions of filaments with varying propulsive force and shear-flow. The distribution of the centre-of-mass of the filament shows adsorption near the surfaces, which diminishes with the flow. The excess density of filaments decreases with Weissenberg number as Wi-β with an exponent β ≈ 0.8, in the intermediate shear range (1 < Wi < 30). The angular orientational moment also decreases near the wall as Wi-δ with δ ≈ 1/5; the variation in orientational moment near the wall is relatively slower than the bulk. It shows a strong dependence on the propulsive force near the wall, with variation on force as Pe-1/3 for large Pe ≥ 1. The active filament shows orientational preference with flow near the surfaces, which splits into upstream and downstream swimming. The population splitting from a unimodal (propulsive force dominated regime) to bimodal phase (shear dominated regime) is identified in the parameter space of propulsive force and shear flow.

Nanopillared Surfaces Disrupt Pseudomonas aeruginosa Mechanoresponsive Upstream Motility

Pseudomonas aeruginosa is an opportunistic, multidrug-resistant, human pathogen that forms biofilms in environments with fluid flow, such as the lungs of cystic fibrosis patients, industrial pipelines, and medical devices. P. aeruginosa twitches upstream on surfaces by the cyclic extension and retraction of its mechanoresponsive type IV pili motility appendages. The prevention of upstream motility, host invasion, and infectious biofilm formation in fluid flow systems remains an unmet challenge. Here, we describe the design and application of scalable nanopillared surface structures fabricated using nanoimprint lithography that reduce upstream motility and colonization by P. aeruginosa. We used flow channels to induce shear stress typically found in catheter tubes and microscopy analysis to investigate the impact of nanopillared surfaces with different packing fractions on upstream motility trajectory, displacement, velocity, and surface attachment. We found that densely packed, subcellular nanopillared surfaces, with pillar periodicities ranging from 200 to 600 nm and widths ranging from 70 to 215 nm, inhibit the mechanoresponsive upstream motility and surface attachment. This bacteria-nanostructured surface interface effect allows us to tailor surfaces with specific nanopillared geometries for disrupting cell motility and attachment in fluid flow systems.

Profile analysis of C. elegans rheotaxis behavior using a microfluidic device

The directed motility of organisms in response to fluid velocity, which is called rheotaxis, is important in the life cycle of C. elegans, enabling them to navigate their environment and maintain their positions in the presence of adverse flow. Thus, to study the mechanism underlying rheotaxis behavior and reveal information on parasitic diseases, the profile analysis of the rheotaxis response in worm populations with high resolution in well-defined fluid environments is highly desirable. In this work, we presented a rapid and robust microfluidic approach to quantitatively analyze the rheotaxis behavior of worms in response to velocity. The flow-based microfluidic chip contained six helical spline microchannels for generating six flow streams with different flow velocities. Since the worms loaded in the chip would swim upstream into channels, the distribution of the worms in response to the different flow velocities was successfully monitored for the quantitative analysis of their rheotaxis behavior using this microfluidic chip. The results indicated that the rate range of around 50 μm s-1 was the most favorable flow velocity for the wild-type worms. Further, we analyzed ASH neuron-blocked worms and found that the functionally defective ASH neurons inhibited their sensitivity to flow rate. In addition, the rheotaxis analysis of the mutant worms indicated that TRP mechanosensory channels and serotonin signals also play a regulatory role in the rheotaxis response of these worms. Thus, our microfluidic method provides a useful platform to study the rheotaxis behaviors in C. elegans and can be further applied for anti-parasitic drug tests.

Confined Flow: Consequences and Implications for Bacteria and Biofilms

Bacteria overwhelmingly live in geometrically confined habitats that feature small pores or cavities, narrow channels, or nearby interfaces. Fluid flows through these confined habitats are ubiquitous in both natural and artificial environments colonized by bacteria. Moreover, these flows occur on time and length scales comparable to those associated with motility of bacteria and with the formation and growth of biofilms, which are surface-associated communities that house the vast majority of bacteria to protect them from host and environmental stresses. This review describes the emerging understanding of how flow near surfaces and within channels and pores alters physical processes that control how bacteria disperse, attach to surfaces, and form biofilms. This understanding will inform the development and deployment of technologies for drug delivery, water treatment, and antifouling coatings and guide the structuring of bacterial consortia for production of chemicals and pharmaceuticals.

Re-entrant bimodality in spheroidal chiral swimmers in shear flow

We use a continuum model to report on the behavior of a dilute suspension of chiral swimmers subject to externally imposed shear in a planar channel. Swimmer orientation in response to the imposed shear can be characterized by two distinct phases of behavior, corresponding to unimodal or bimodal distribution functions for swimmer orientation along the channel. These phases indicate the occurrence (or not) of a population splitting phenomenon changing the swimming direction of a macroscopic fraction of active particles to the exact opposite of that dictated by the imposed flow. We present a detailed quantitative analysis elucidating the complexities added to the population splitting behavior of swimmers when they are chiral. In particular, the transition from unimodal to bimodal and vice versa are shown to display a re-entrant behavior across the parameter space spanned by varying the chiral angular speed. We also present the notable effects of particle aspect ratio and self-propulsion speed on system phase behavior and discuss potential implications of our results in applications such as swimmer separation/sorting.

Magnetotaxis Enables Magnetotactic Bacteria to Navigate in Flow

Magnetotactic bacteria (MTB) play an important role in Earth's biogeochemical cycles by transporting minerals in aquatic ecosystems, and have shown promise for controlled transport of microscale objects in flow conditions. However, how MTB traverse complex flow environments is not clear. Here, using microfluidics and high-speed imaging, it is revealed that magnetotaxis enables directed motion of Magnetospirillum magneticum over long distances in flow velocities ranging from 2 to 1260 µm s^-1 , corresponding to shear rates ranging from 0.2 to 142 s^-1 -a range relevant to both aquatic environments and biomedical applications. The ability of MTB to overcome a current is influenced by the flow, the magnetic field, and their relative orientation. MTB can overcome 2.3-fold higher flow velocities when directed to swim perpendicular to the flow as compared to upstream, as the latter orientation induces higher drag. The results indicate a threshold drag of 9.5 pN, corresponding to a flow velocity of 550 µm s^-1 , where magnetotaxis enables MTB to overcome counterdirectional flow. These findings bring new insights into the interactions of MTB with complex flow environments relevant to aquatic ecosystems, while suggesting opportunities for in vivo applications of MTB in microbiorobotics and targeted drug delivery.

Adiabatic elimination of inertia of the stochastic microswimmer driven by α-stable noise

We consider a microswimmer that moves in two dimensions at a constant speed and changes the direction of its motion due to a torque consisting of a constant and a fluctuating component. The latter will be modeled by a symmetric Lévy-stable (α-stable) noise. The purpose is to develop a kinetic approach to eliminate the angular component of the dynamics to find a coarse-grained description in the coordinate space. By defining the joint probability density function of the position and of the orientation of the particle through the Fokker-Planck equation, we derive transport equations for the position-dependent marginal density, the particle's mean velocity, and the velocity's variance. At time scales larger than the relaxation time of the torque τ_{ϕ}, the two higher moments follow the marginal density and can be adiabatically eliminated. As a result, a closed equation for the marginal density follows. This equation, which gives a coarse-grained description of the microswimmer's positions at time scales t≫τ_{ϕ}, is a diffusion equation with a constant diffusion coefficient depending on the properties of the noise. Hence, the long-time dynamics of a microswimmer can be described as a normal, diffusive, Brownian motion with Gaussian increments.

Cross-stream migration of active particles

For natural microswimmers, the interplay of swimming activity and external flow can promote robust directed motion, for example, propulsion against (upstream rheotaxis) or perpendicular to the direction of flow. These effects are generally attributed to their complex body shapes and flagellar beat patterns. Using catalytic Janus particles as a model experimental system, we report on a strong directional response that occurs for spherical active particles in a channel flow. The particles align their propulsion axes to be nearly perpendicular to both the direction of flow and the normal vector of a nearby bounding surface. We develop a deterministic theoretical model of spherical microswimmers near a planar wall that captures the experimental observations. We show how the directional response emerges from the interplay of shear flow and near-surface swimming activity. Finally, adding the effect of thermal noise, we obtain probability distributions for the swimmer orientation that semiquantitatively agree with the experimental distributions.

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

The motions of an unsteady circular-disk squirmer and a spherical squirmer have been investigated in the presence of a no-slip infinite wall and a background shear flow in order to clarify the similarities and differences between two- and three-dimensional motions. Despite the similar bifurcation structure of the dynamical system, the stability of the fixed points differs due to the Hamiltonian structure of the disk squirmer. Once the unsteady oscillating surface velocity profile is considered, the disk squirmer can behave in a chaotic manner and cease to be confined in a near-wall region. In contrast, in an unsteady spherical squirmer, the dynamics is well attracted by a stable fixed point. Additional wall contact interactions lead to stable fixed points for the disk squirmer, and, in turn, the surface entrapment of the disk squirmer can be stabilized, regardless of the existence of the background flow. Finally, we consider spherical motion under a background flow. The separated time scales of the surface entrapment (thigmotaxis) and the turning toward the flow direction (rheotaxis) enable us to reduce the dynamics to two-dimensional phase space, and simple weather-vane mechanics can predict squirmer rheotaxis. The analogous structure of the phase plane with the wall contact in two and three dimensions implies that the two-dimensional disk swimmer successfully captures the nonlinear interactions, and thus two-dimensional approximation could be useful in designing microfluidic devices for the guidance of microswimmers and for clarifying the locomotions in a complex geometry.

Intermediate scattering function of an anisotropic Brownian circle swimmer

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 wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.

Population splitting of rodlike swimmers in Couette flow

We present a quantitative analysis on the response of a dilute active suspension of self-propelled rods (swimmers) in a planar channel subjected to an imposed shear flow. To best capture the salient features of the shear-induced effects, we consider the case of an imposed Couette flow, providing a constant shear rate across the channel. We argue that the steady-state behavior of swimmers can be understood in the light of a population splitting phenomenon, occurring as the shear rate exceeds a certain threshold, initiating the reversal of the swimming direction for a finite fraction of swimmers from down- to upstream or vice versa, depending on the swimmer position within the channel. Swimmers thus split into two distinct, statistically significant and oppositely swimming majority and minority populations. The onset of population splitting translates into a transition from a self-propulsion-dominated regime to a shear-dominated regime, corresponding to a unimodal-to-bimodal change in the probability distribution function of the swimmer orientation. We present a phase diagram in terms of the swim and flow Péclet numbers showing the separation of these two regimes by a discontinuous transition line. Our results shed further light on the behavior of swimmers in a shear flow and provide an explanation for the previously reported non-monotonic behavior of the mean, near-wall, parallel-to-flow orientation of swimmers with increasing shear strength.

Geometric control of active collective motion

Recent experimental studies have shown that confinement can profoundly affect self-organization in semi-dilute active suspensions, leading to striking features such as the formation of steady and spontaneous vortices in circular domains and the emergence of unidirectional pumping motions in periodic racetrack geometries. Motivated by these findings, we analyze the two-dimensional dynamics in confined suspensions of active self-propelled swimmers using a mean-field kinetic theory where conservation equations for the particle configurations are coupled to the forced Navier-Stokes equations for the self-generated fluid flow. In circular domains, a systematic exploration of the parameter space casts light on three distinct states: equilibrium with no flow, stable vortex, and chaotic motion, and the transitions between these are explained and predicted quantitatively using a linearized theory. In periodic racetracks, similar transitions from equilibrium to net pumping to traveling waves to chaos are observed in agreement with experimental observations and are also explained theoretically. Our results underscore the subtle effects of geometry on the morphology and dynamics of emerging patterns in active suspensions and pave the way for the control of active collective motion in microfluidic devices.

Diffusion of active chiral particles

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v[over ̂] at time t, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.