Turbulent fluid acceleration generates clusters of gyrotactic microorganisms

Anisotropic Mean Flow Enhancement and Anomalous Transport of Finite-Size Spherical Particles in Turbulent Flows

We investigate the influence of dispersed solid spherical particles on the largest scales of the turbulent Arnold-Beltrami-Childress (ABC) flow. The ABC flow is an ideal instance of a complex flow: it does not have solid boundaries, but possesses an inhomogeneous and three-dimensional mean shear. By tuning the parameters of the suspension, we show that particles modulate the largest scales of the flow toward an anisotropic, quasi-two-dimensional and more energetic state. In this regime, particles move along quasistraight trajectories and exhibit anomalous transport.

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.

Microswimmers in vortices: dynamics and trapping

Biological and artificial microswimmers often self-propel in external flows of vortical nature; relevant examples include algae in small-scale ocean eddies, spermatozoa in uterine peristaltic flows and bacteria in microfluidic devices. A recent experiment has shown that swimming bacteria in model vortices are expelled from the vortex all the way to a well-defined depletion zone (A. Sokolov and I. S. Aranson, Rapid expulsion of microswimmers by a vortical flow. Nat. Commun., 2016, 7, 11114). In this paper, we propose a theoretical model to investigate the dynamics of elongated microswimmers in elementary vortices, namely active particles in two- and three-dimensional rotlets. A deterministic model first reveals the existence of bounded orbits near the centre of the vortex and unbounded orbits elsewhere. We further discover a conserved quantity of motion that allows us to map the phase space according to the type of the orbit (bounded vs unbounded). We next introduce translational and rotational noise into the system. Using a Fokker-Planck formalism, we quantify the quality of trapping near the centre of the vortex by examining the probability of escape and the mean time of escape from the region of deterministically bounded orbits. We finally show how to use these findings to formulate a prediction for the radius of the depletion zone, which compares favourably with the experiments (A. Sokolov and I. S. Aranson, Rapid expulsion of microswimmers by a vortical flow. Nat. Commun., 2016, 7, 11114).

Investigating microscale patchiness of motile microbes under turbulence in a simulated convective mixed layer

Microbes play a primary role in aquatic ecosystems and biogeochemical cycles. Spatial patchiness is a critical factor underlying these activities, influencing biological productivity, nutrient cycling and dynamics across trophic levels. Incorporating spatial dynamics into microbial models is a long-standing challenge, particularly where small-scale turbulence is involved. Here, we combine a fully 3D direct numerical simulation of convective mixed layer turbulence, with an individual-based microbial model to test the key hypothesis that the coupling of gyrotactic motility and turbulence drives intense microscale patchiness. The fluid model simulates turbulent convection caused by heat loss through the fluid surface, for example during the night, during autumnal or winter cooling or during a cold-air outbreak. We find that under such conditions, turbulence-driven patchiness is depth-structured and requires high motility: Near the fluid surface, intense convective turbulence overpowers motility, homogenising motile and non-motile microbes approximately equally. At greater depth, in conditions analogous to a thermocline, highly motile microbes can be over twice as patch-concentrated as non-motile microbes, and can substantially amplify their swimming velocity by efficiently exploiting fast-moving packets of fluid. Our results substantiate the predictions of earlier studies, and demonstrate that turbulence-driven patchiness is not a ubiquitous consequence of motility but rather a delicate balance of motility and turbulent intensity.

Clustering of fast gyrotactic particles in low-Reynolds-number flow

Systems of particles in turbulent flows exhibit clustering where particles form patches in certain regions of space. Previous studies have shown that motile particles accumulate inside the vortices and in downwelling regions, while light and heavy non-motile particles accumulate inside and outside the vortices, respectively. While strong clustering is generated in regions of high vorticity, clustering of motile particles is still observed in fluid flows where vortices are short-lived. In this study, we investigate the clustering of fast swimming particles in a low-Reynolds-number turbulent flow and characterize the probability distributions of particle speed and acceleration and their influence on particle clustering. We simulate gyrotactic swimming particles in a cubic system with homogeneous and isotropic turbulent flow. Here, the swimming velocity explored is relatively faster than what has been explored in other reports. The fluid flow is produced by conducting a direct numerical simulation of the Navier-Stokes equation. In contrast with the previous results, our results show that swimming particles can accumulate outside the vortices, and clustering is dictated by the swimming number and is invariant with the stability number. We have also found that highly clustered particles are sufficiently characterized by their acceleration, where the increase in the acceleration frequency distribution of the most clustered particles suggests a direct influence of acceleration on clustering. Furthermore, the acceleration of the most clustered particles resides in acceleration values where a cross-over in the acceleration PDFs are observed, an indicator that particle acceleration generates clustering. Our findings on motile particles clustering can be applied to understanding the behavior of faster natural or artificial swimmers.

Experimental investigation of preferential concentration in zooplankton swimming in turbulence

Turbulence can cause particles to accumulate within specific regions of the flow. One mechanism responsible for this phenomenon, called preferential concentration, consists in particle-fluid interactions yielding inhomogeneous spatial distribution of particles into clusters or depleted regions due to density difference or finite-size effects. In the case of living particles such as plankton, clustering may also originate from their motility or from their behavioral response to turbulent forcing. Preferential concentration of plankton has attracted much attention, because it is a key determinant of encounter rates and therefore relevant for a wide range of ecological processes. However, most studies have focused on microscopic cells, and consequently the case of larger organisms remains poorly studied. Here, we use high-performance particle tracking and three-dimensional Voronoï analysis to test for the emergence of clustering in the spatial distribution of calanoid copepods, the most important metazoans in the oceans in terms of biomass. We found that neither inertia nor motility resulted in significant departure from a random Poisson process over a range of turbulence intensity from very strong to moderate. However, we observed weak clustering in calm water, which may originate from hydrodynamic and olfactory interactions between organisms. Our results improve our understanding of fluid-particle interactions in the zooplankton and have important implications for the modeling of their encounter rates in turbulence.

Fluidic bacterial diodes rectify magnetotactic cell motility in porous environments

Directed motility enables swimming microbes to navigate their environment for resources via chemo-, photo-, and magneto-taxis. However, directed motility competes with fluid flow in porous microbial habitats, affecting biofilm formation and disease transmission. Despite this broad importance, a microscopic understanding of how directed motility impacts the transport of microswimmers in flows through constricted pores remains unknown. Through microfluidic experiments, we show that individual magnetotactic bacteria directed upstream through pores display three distinct regimes, whereby cells swim upstream, become trapped within a pore, or are advected downstream. These transport regimes are reminiscent of the electrical conductivity of a diode and are accurately predicted by a comprehensive Langevin model. The diode-like behavior persists at the pore scale in geometries of higher dimension, where disorder impacts conductivity at the sample scale by extending the trapping regime over a broader range of flow speeds. This work has implications for our understanding of the survival strategies of magnetotactic bacteria in sediments and for developing their use in drug delivery applications in vascular networks.

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.

Capturing Velocity Gradients and Particle Rotation Rates in Turbulence

Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics, which sensitively depends on the particle history. Here, we systematically develop a reduced-order model for the small-scale dynamics of turbulence, which captures the velocity gradient statistics along particle paths. An analysis of the resulting stochastic dynamical system allows pinpointing the emergence of non-Gaussian statistics and nontrivial temporal correlations of vorticity and strain, as previously reported from experiments and simulations. Based on these insights, we use our model to predict the orientational statistics of anisotropic particles in turbulence, enabling a host of modeling applications for complex particulate flows.

Harnessing random low Reynolds number flow for net migration

Random noise in low Reynolds number flow has rarely been used to obtain net migration of microscale objects. In this study, we numerically show that net migration of a microscale object can be extracted from random directional fluid forces in Stokes flow, by introducing deformability and inhomogeneous density into the object. We also developed a mathematical framework to describe the deformation-induced migration caused by noise. These results provide a basis for understanding the noise-induced migration of a microswimmer and are useful for harnessing energy from low Reynolds number flow.

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.

Bacterial scattering in microfluidic crystal flows reveals giant active Taylor-Aris dispersion

The natural habitats of planktonic and swimming microorganisms, from algae in the oceans to bacteria living in soil or intestines, are characterized by highly heterogeneous fluid flows. The complex interplay of flow-field topology, self-propulsion, and porous microstructure is essential to a wide range of biophysical and ecological processes, including marine oxygen production, remineralization of organic matter, and biofilm formation. Although much progress has been made in the understanding of microbial hydrodynamics and surface interactions over the last decade, the dispersion of active suspensions in complex flow environments still poses unsolved fundamental questions that preclude predictive models for microbial transport and spreading under realistic conditions. Here, we combine experiments and simulations to identify the key physical mechanisms and scaling laws governing the dispersal of swimming bacteria in idealized porous media flows. By tracing the scattering dynamics of swimming bacteria in microfluidic crystal lattices, we show that hydrodynamic gradients hinder transverse bacterial dispersion, thereby enhancing stream-wise dispersion [Formula: see text]-fold beyond canonical Taylor-Aris dispersion of passive Brownian particles. Our analysis further reveals that hydrodynamic cell reorientation and Lagrangian flow structure induce filamentous density patterns that depend upon the incident angle of the flow and disorder of the medium, in striking analogy to classical light-scattering experiments.

Gyrotactic phytoplankton in laminar and turbulent flows: A dynamical systems approach

Gyrotactic algae are bottom heavy, motile cells whose swimming direction is determined by a balance between a buoyancy torque directing them upwards and fluid velocity gradients. Gyrotaxis has, in recent years, become a paradigmatic model for phytoplankton motility in flows. The essential attractiveness of this peculiar form of motility is the availability of a mechanistic description which, despite its simplicity, revealed predictive, rich in phenomenology, easily complemented to include the effects of shape, feedback on the fluid and stochasticity (e.g., in cell orientation). In this review we consider recent theoretical, numerical and experimental results to discuss how, depending on flow properties, gyrotaxis can produce inhomogeneous phytoplankton distributions on a wide range of scales, from millimeters to kilometers, in both laminar and turbulent flows. In particular, we focus on the phenomenon of gyrotactic trapping in nonlinear shear flows and in fractal clustering in turbulent flows. We shall demonstrate the usefulness of ideas and tools borrowed from dynamical systems theory in explaining and interpreting these phenomena.

Emergence of phytoplankton patchiness at small scales in mild turbulence

Phytoplankton often encounter turbulence in their habitat. As most toxic phytoplankton species are motile, resolving the interplay of motility and turbulence has fundamental repercussions on our understanding of their own ecology and of the entire ecosystems they inhabit. The spatial distribution of motile phytoplankton cells exhibits patchiness at distances of decimeter to millimeter scales for numerous species with different motility strategies. The explanation of this general phenomenon remains challenging. Furthermore, hydrodynamic cell-cell interactions, which grow more relevant as the density in the patches increases, have been so far ignored. Here, we combine particle simulations and continuum theory to study the emergence of patchiness in motile microorganisms in three dimensions. By addressing the combined effects of motility, cell-cell interaction, and turbulent flow conditions, we uncover a general mechanism: The coupling of cell-cell interactions to the turbulent dynamics favors the formation of dense patches. Identification of the important length and time scales, independent from the motility mode, allows us to elucidate a general physical mechanism underpinning the emergence of patchiness. Our results shed light on the dynamical characteristics necessary for the formation of patchiness and complement current efforts to unravel planktonic ecological interactions.

Evidence for ubiquitous preferential particle orientation in representative oceanic shear flows

In situ measurements were undertaken to characterize particle fields in undisturbed oceanic environments. Simultaneous, co-located depth profiles of particle fields and flow characteristics were recorded using a submersible holographic imaging system and an acoustic Doppler velocimeter, under different flow conditions and varying particle concentration loads, typical of those found in coastal oceans and lakes. Nearly one million particles with major axis lengths ranging from ∼14 μm to 11.6 mm, representing diverse shapes, sizes, and aspect ratios were characterized as part of this study. The particle field consisted of marine snow, detrital matter, and phytoplankton, including colonial diatoms, which sometimes formed "thin layers" of high particle abundance. Clear evidence of preferential alignment of particles was seen at all sampling stations, where the orientation probability density function (PDF) peaked at near horizontal angles and coincided with regions of low velocity shear and weak turbulent dissipation rates. Furthermore, PDF values increased with increasing particle aspect ratios, in excellent agreement with models of spheroidal particle motion in simple shear flows. To the best of our knowledge, although preferential particle orientation in the ocean has been reported in two prior cases, our findings represent the first comprehensive field study examining this phenomenon. Evidence of nonrandom particle alignment in aquatic systems has significant consequences to aquatic optics theory and remote sensing, where perfectly random particle orientation and thus isotropic symmetry in optical parameters is assumed. Ecologically, chain-forming phytoplankton may have evolved to form large aspect ratio chains as a strategy to optimize light harvesting.

Zooplankton can actively adjust their motility to turbulent flow

Calanoid copepods are among the most abundant metazoans in the ocean and constitute a vital trophic link within marine food webs. They possess relatively narrow swimming capabilities, yet are capable of significant self-locomotion under strong hydrodynamic conditions. Here we provide evidence for an active adaptation that allows these small organisms to adjust their motility in response to background flow. We track simultaneously and in three dimensions the motion of flow tracers and planktonic copepods swimming freely at several intensities of quasi-homogeneous, isotropic turbulence. We show that copepods synchronize the frequency of their relocation jumps with the frequency of small-scale turbulence by performing frequent relocation jumps of low amplitude that seem unrelated to localized hydrodynamic signals. We develop a model of plankton motion in turbulence that shows excellent quantitative agreement with our measurements when turbulence is significant. We find that, compared with passive tracers, active motion enhances the diffusion of organisms at low turbulence intensity whereas it dampens diffusion at higher turbulence levels. The existence of frequent jumps in a motion that is otherwise dominated by turbulent transport allows for the possibility of active locomotion and hence to transition from being passively advected to being capable of controlling diffusion. This behavioral response provides zooplankton with the capability to retain the benefits of self-locomotion despite turbulence advection and may help these organisms to actively control their distribution in dynamic environments. Our study reveals an active adaptation that carries strong fitness advantages and provides a realistic model of plankton motion in turbulence.

Modeling of active swimmer suspensions and their interactions with the environment

In this article, we review mathematical models used to study the behaviour of suspensions of micro-swimmers and the accompanying biophysical phenomena, with specific focus on stimulus response. The methods discussed encompass a range of interactions exhibited by the micro-swimmers; including passive hydrodynamic (gyrotaxis) and gravitational (gravitaxis) effects, and active responses to chemical cues (chemotaxis) and light intensities (phototaxis). We introduce the simplest models first, and then build towards more sophisticated recent developments, in the process, identifying the limitations of the former and the new results obtained by the latter. We comment on the accuracy/validity of the models adopted, based on the agreement between theoretical results and experimental observations. We conclude by identifying some of the open problems and associated challenges faced by researchers in the realm of active suspensions.

Ontogenetic changes in larval swimming and orientation of pre-competent sea urchin Arbacia punctulata in turbulence

Many marine organisms have complex life histories, having sessile adults and relying on the planktonic larvae for dispersal. Larvae swim and disperse in a complex fluid environment and the effect of ambient flow on larval behavior could in turn impact their survival and transport. However, to date, most studies on larvae–flow interactions have focused on competent larvae near settlement. We examined the importance of flow on early larval stages by studying how local flow and ontogeny influence swimming behavior in pre-competent larval sea urchins, Arbacia punctulata. We exposed larval urchins to grid-stirred turbulence and recorded their behavior at two stages (4- and 6-armed plutei) in three turbulence regimes. Using particle image velocimetry to quantify and subtract local flow, we tested the hypothesis that larvae respond to turbulence by increasing swimming speed, and that the increase varies with ontogeny. Swimming speed increased with turbulence for both 4- and 6-armed larvae, but their responses differed in terms of vertical swimming velocity. 4-Armed larvae swam most strongly upward in the unforced flow regime, while 6-armed larvae swam most strongly upward in weakly forced flow. Increased turbulence intensity also decreased the relative time that larvae spent in their typical upright orientation. 6-Armed larvae were tilted more frequently in turbulence compared with 4-armed larvae. This observation suggests that as larvae increase in size and add pairs of arms, they are more likely to be passively re-oriented by moving water, rather than being stabilized (by mechanisms associated with increased mass), potentially leading to differential transport. The positive relationship between swimming speed and larval orientation angle suggests that there was also an active response to tilting in turbulence. Our results highlight the importance of turbulence to planktonic larvae, not just during settlement but also in earlier stages through morphology–flow interactions.

Highlighted Article: Pre-competent, 6-armed larval urchins swim faster and are less stable in experimental turbulent flow than younger 4-armed larvae, suggesting a potential age/morphology-driven differential transport mechanism in ambient flow conditions.

Advection by ocean currents modifies phytoplankton size structure

Advection by ocean currents modifies phytoplankton size structure at small scales (1-10 cm) by aggregating cells in different regions of the flow depending on their size. This effect is caused by the inertia of the cells relative to the displaced fluid. It is considered that, at larger scales (greater than or equal to 1 km), biological processes regulate the heterogeneity in size structure. Here, we provide observational evidence of heterogeneity in phytoplankton size structure driven by ocean currents at relatively large scales (1-10 km). Our results reveal changes in the phytoplankton size distribution associated with the coastal circulation patterns. A numerical model that incorporates the inertial properties of phytoplankton confirms the role of advection on the distribution of phytoplankton according to their size except in areas with enhanced nutrient inputs where phytoplankton dynamics is ruled by other processes. The observed preferential concentration mechanism has important ecological consequences that range from the phytoplankton level to the whole ecosystem.

Scale-dependent colocalization in a population of gyrotactic swimmers

We study the small scale clustering of gyrotactic swimmers transported by a turbulent flow, when the intrinsic variability of the swimming parameters within the population is considered. By means of extensive numerical simulations, we find that the variety of the population introduces a characteristic scale R^{*} in its spatial distribution. At scales smaller than R^{*} the swimmers are homogeneously distributed, while at larger scales an inhomogeneous distribution is observed with a fractal dimension close to what observed for a monodisperse population characterized by mean parameters. The scale R^{*} depends on the dispersion of the population and it is found to scale linearly with the standard deviation both for a bimodal and for a Gaussian distribution. Our numerical results, which extend recent findings for a monodisperse population, indicate that in principle it is possible to observe small scale, fractal clustering in a laboratory experiment with gyrotactic cells.

Lagrangian model of copepod dynamics: Clustering by escape jumps in turbulence

Planktonic copepods are small crustaceans that have the ability to swim by quick powerful jumps. Such an aptness is used to escape from high shear regions, which may be caused either by flow perturbations, produced by a large predator (i.e., fish larvae), or by the inherent highly turbulent dynamics of the ocean. Through a combined experimental and numerical study, we investigate the impact of jumping behavior on the small-scale patchiness of copepods in a turbulent environment. Recorded velocity tracks of copepods displaying escape response jumps in still water are here used to define and tune a Lagrangian copepod (LC) model. The model is further employed to simulate the behavior of thousands of copepods in a fully developed hydrodynamic turbulent flow obtained by direct numerical simulation of the Navier-Stokes equations. First, we show that the LC velocity statistics is in qualitative agreement with available experimental observations of copepods in turbulence. Second, we quantify the clustering of LC, via the fractal dimension D_{2}. We show that D_{2} can be as low as ∼2.3 and that it critically depends on the shear-rate sensitivity of the proposed LC model, in particular it exhibits a minimum in a narrow range of shear-rate values. We further investigate the effect of jump intensity, jump orientation, and geometrical aspect ratio of the copepods on the small-scale spatial distribution. At last, possible ecological implications of the observed clustering on encounter rates and mating success are discussed.

Photofocusing: Light and flow of phototactic microswimmer suspension

We explore in this paper the phenomenon of photofocusing: a coupling between flow vorticity and biased swimming of microalgae toward a light source that produces a focusing of the microswimmer suspension. We combine experiments that investigate the stationary state of this phenomenon as well as the transition regime with analytical and numerical modeling. We show that the experimentally observed scalings on the width of the focalized region and the establishment length as a function of the flow velocity are well described by a simple theoretical model.

Centripetal focusing of gyrotactic phytoplankton

A suspension of gyrotactic microalgae Chlamydomonas augustae swimming in a cylindrical water vessel in solid-body rotation is studied. Our experiments show that swimming algae form an aggregate around the axis of rotation, whose intensity increases with the rotation speed. We explain this phenomenon by the centripetal orientation of the swimming direction towards the axis of rotation. This centripetal focusing is contrasted by diffusive fluxes due to stochastic reorientation of the cells. The competition of the two effects lead to a stationary distribution, which we analytically derive from a refined mathematical model of gyrotactic swimmers. The temporal evolution of the cell distribution, obtained via numerical simulations of the stochastic model, is in quantitative agreement with the experimental measurements in the range of parameters explored.

Preferential Sampling and Small-Scale Clustering of Gyrotactic Microswimmers in Turbulence

Recent studies show that spherical motile microorganisms in turbulence subject to gravitational torques gather in down-welling regions of the turbulent flow. By analyzing a statistical model we analytically compute how shape affects the dynamics, preferential sampling, and small-scale spatial clustering. We find that oblong organisms may spend more time in up-welling regions of the flow, and that all organisms are biased to regions of positive fluid-velocity gradients in the upward direction. We analyze small-scale spatial clustering and find that oblong particles may either cluster more or less than spherical ones, depending on the strength of the gravitational torques.

Getting drowned in a swirl: Deformable bead-spring model microswimmers in external flow fields

Deformability is a central feature of many types of microswimmers, e.g., for artificially generated self-propelled droplets. Here, we analyze deformable bead-spring microswimmers in an externally imposed solvent flow field as simple theoretical model systems. We focus on their behavior in a circular swirl flow in two spatial dimensions. Linear (straight) two-bead swimmers are found to circle around the swirl with a slight drift to the outside with increasing activity. In contrast to that, we observe for triangular three-bead or squarelike four-bead swimmers a tendency of being drawn into the swirl and finally getting drowned, although a radial inward component is absent in the flow field. During one cycle around the swirl, the self-propulsion direction of an active triangular or squarelike swimmer remains almost constant, while their orbits become deformed exhibiting an "egglike" shape. Over time, the swirl flow induces slight net rotations of these swimmer types, which leads to net rotations of the egg-shaped orbits. Interestingly, in certain cases, the orbital rotation changes sense when the swimmer approaches the flow singularity. Our predictions can be verified in real-space experiments on artificial microswimmers.

Inhomogeneous distribution of Chlamydomonas in a cylindrical container with a bubble plume

Swimming microalgae show various taxes, such as phototaxis and gravitaxis, which sometimes result in the formation of a cell-rich layer or a patch in a suspension. Despite intensive studies on the effects of shear flow and turbulence on the inhomogeneous distribution of microalgae, the effect of a bubble plume has remained unclear. In this study, we used Chlamydomonas as model microalgae, and investigated the spatial distribution of cells in a cylindrical container with a bubble plume. The results illustrate that cells become inhomogeneously distributed in the suspension due to their motility and photo-responses. A vortical ring distribution was observed below the free surface when the bubble flow rate was sufficiently small. We performed a scaling analysis on the length scale of the vortical ring, which captured the main features of the experimental results. These findings are important in understanding transport phenomena in a microalgae suspension with a bubble plume.

Summary: A substantially inhomogeneous distribution of micro algae was developed in suspension with a bubble plume. A vortical ring and vertical layers of cells were observed when the cells displayed phototaxis and motility.

Phytoplankton's motion in turbulent ocean

We study the influence of turbulence on upward motion of phytoplankton. Interaction with the flow is described by the Pedley-Kessler model considering spherical microorganisms. We find a range of parameters when the upward drift is only weakly perturbed or when turbulence completely randomizes the drift direction. When the perturbation is small, the drift is either determined by the local vorticity or is Gaussian. We find a range of parameters where the phytoplankton interaction with the flow can be described consistently as diffusion of orientation in effective potential. By solving the corresponding Fokker-Planck equation we find exponential steady-state distribution of phytoplankton's propulsion orientation. We further identify the range of parameters where phytoplankton's drift velocity with respect to the flow is determined uniquely by its position. In this case, one can describe phytoplankton's motion by a smooth flow and phytoplankton concentrates on fractal. We find fractal dimensions and demonstrate that phytoplankton forms vertical stripes in space with a nonisotropic pair-correlation function of concentration increased in the vertical direction. The probability density function of the distance between two particles obeys power law with the negative exponent given by the ratio of integrals of the turbulent energy spectrum. We find the regime of strong clustering where the exponent is of order one so that turbulence increases the rate of collisions by a large factor. The predictions hold for Navier-Stokes turbulence and stand for testing.

Clustering of vertically constrained passive particles in homogeneous isotropic turbulence

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of the fluid slab in which the particles can move. This allows us to analyze the statistical features of the system over a wide range of conditions going from a fully 3D incompressible flow (corresponding to the case of no confinement) to the extremely confined case corresponding to a two-dimensional slice. The background 3D turbulent velocity field is evolved by means of fully resolved direct numerical simulations. Whenever some level of vertical confinement is present, the particle trajectories deviate from that of fluid tracers and the particles experience an effectively compressible velocity field. Here, we have quantified the compressibility, the preferential concentration of the particles, and the correlation dimension by changing the strength of the restoring force. The main result is that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale η, that maximizes the clustering of the particles.

Interfacial mechanisms in active emulsions

Active emulsions, i.e., emulsions whose droplets perform self-propelled motion, are of tremendous interest for mimicking collective phenomena in biological populations such as phytoplankton and bacterial colonies, but also for experimentally studying rheology, pattern formation, and phase transitions in systems far from thermal equilibrium. For fuelling such systems, molecular processes involving the surfactants which stabilize the emulsions are a straightforward concept. We outline and compare two different types of reactions, one which chemically modifies the surfactant molecules, the other which transfers them into a different colloidal state. While in the first case symmetry breaking follows a standard linear instability, the second case turns out to be more complex. Depending on the dissolution pathway, there is either an intrinsically nonlinear instability, or no symmetry breaking at all (and hence no locomotion).