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Flow patterns induced by the active forces that a single puller (A) or pusher (B) exerts on the surrounding fluid. The colors denote the amplitude of the flow that decreases at large distances, albeit only as a power law (red, largest, to blue, weakest). The arrows indicate the direction of the flow. Also shown for each swimmer are the location of the hydrodynamic center (white circle) and the direction of the self-propulsion velocity (white arrow). In both cases, the flow vanishes as expected at the center of the dipole.
Source publication
Unicellular living organisms, such as bacteria and algae, propel themselves through a medium via cyclic strokes involving the motion of cilia and flagella. Dense populations of such "active particles" or "swimmers" exhibit a rich collective behavior at large scales. Starting with a minimal physical model of a stroke-averaged swimmer in a fluid, we...
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... of anisotropic particles due to activity. For cytoskeletal filaments, the suppression arises from short-range interaction because of active cross-linkers (17,24). For swimmers in a fluid, this suppression originates from long- range hydrodynamic interactions, which are attractive at the head and tail of contractile swimmers as illustrated in Fig. 2. This sup- pression is absent in pushers, as in this case the hydrodynamic interaction enhances longitudinal ...
Citations
... Nematic interactions can induce instabilities, depending on the concentration of microswimmers and their swimming behavior. At low concentrations, the homogeneous and isotropic state for both pushers and pullers can be destabilized above a critical level of activity, leading to large-scale density fluctuations for pushers and orientational fluctuations at every scale for pullers (Baskaran and Marchetti, 2009). For pushers (pullers), bend (splay) fluctuations, where only the parallel (orthogonal) component of the wave vector contributes, dominate (Wang et al., 2018). ...
Magnetotactic bacteria are swimming microorganisms able to follow magnetic field lines with the help of an organelle called the magnetosome that is made of biomineralized magnetic crystals assembled in a chain. In combination with this ability, these bacteria perform active oxygen sensing to reach the oxic-anoxic transition zone, which is often located in the upper part of the sediment. From a physicist’s perspective, magnetotactic bacteria can be seen at the interface between bacterial active matter and magnetic colloids, which gives them unique properties at both the individual and collective levels. In crowded media and/or when they are submitted to external flows, their motion can be efficiently driven by magnetic fields, which leads to surprising effects. In this Colloquium, the different features of magnetotactic bacteria at are reviewed at every scale, from single cell to collective motion, from simple to complex environments, and by emphasizing the differences from other bacterial species or passive magnetic colloids. The Colloquium concludes with a discussion of perspectives on using magnetotactic bacteria in active magnetorheology.
... This subtlety is further confirmed by experimental measurements of flow fields around confined microswimmers 15 which show that these strongly depend on the details of the swimming mechanism, swimmer orientation, and nature of the confinement. In unbounded suspensions, the transition to active turbulence is driven by mutual reorientation due to the long-ranged dipolar flow fields of pusher microswimmers, decaying as r −2 , where r is the swimmer-swimmer separation 1,[23][24][25] . To leading order in r, the flow field at a point r due to a swimmer with orientation p placed at the origin reads ...
Self-propelled particles such as bacteria or algae swimming through a fluid are non-equilibrium systems where particle motility breaks microscopic detailed balance, often resulting in large-scale collective motion. Previous theoretical work has identified long-ranged hydrodynamic interactions as the driver of collective motion in unbounded suspensions of rear-actuated (“pusher”) microswimmers. In contrast, most experimental studies of collective motion in microswimmer suspensions have been carried out in restricted geometries where both the swimmers’ motion and their long-range flow fields become altered due to the proximity of a boundary. Here, we study numerically a minimal model of microswimmers in such a restricted geometry, where the particles move in the midplane between two no-slip walls. For pushers, we demonstrate collective motion with short-ranged order, in contrast with the long-ranged flows observed in unbounded systems. For front-actuated (“puller”) microswimmers, we discover a long-wavelength density instability resulting in the formation of dense microswimmer clusters. Both types of collective motion are fundamentally different from their previously studied counterparts in unbounded domains. Our results show that this difference is dictated by the geometrical restriction of the swimmers’ motion, while hydrodynamic screening due to the presence of a wall is subdominant in determining the suspension’s collective state.
... Whether this implies that the system reaches different steady states at long times is still an open question that we leave for future work. We also note that the density instability presented here is qualitatively similar to the instability reported by Baskaran & Marchetti (2009), as both are caused by the fluid's compressibility; in the case of Baskaran & Marchetti (2009), however, the compressibility arises as a result of an erroneous coarse-graining procedure, as discussed by Aranson (2022). ...
... Whether this implies that the system reaches different steady states at long times is still an open question that we leave for future work. We also note that the density instability presented here is qualitatively similar to the instability reported by Baskaran & Marchetti (2009), as both are caused by the fluid's compressibility; in the case of Baskaran & Marchetti (2009), however, the compressibility arises as a result of an erroneous coarse-graining procedure, as discussed by Aranson (2022). ...
A collection of microswimmers immersed in an incompressible fluid is characterised by strong interactions due to the long-range nature of the hydrodynamic fields generated by individual organisms. As a result, suspensions of rear-actuated ‘pusher’ swimmers such as bacteria exhibit a collective motion state often referred to as ‘bacterial turbulence’, characterised by large-scale chaotic flows. The onset of collective motion in pusher suspensions is classically understood within the framework of mean-field kinetic theories for dipolar swimmers. In bulk two and three dimensions, the theory predicts that the instability leading to bacterial turbulence is due to mutual swimmer reorientation and sets in at the largest length scale available to the suspension. Here, we construct a similar kinetic theory for the case of a dipolar microswimmer suspension restricted to a two-dimensional plane embedded in a three-dimensional incompressible fluid. This setting qualitatively mimics the effect of swimming close to a two-dimensional interface. We show that the in-plane flow fields are effectively compressible in spite of the incompressibility of the three-dimensional bulk fluid, and that microswimmers on average act as sources (pushers) or sinks (pullers). We analyse the stability of the homogeneous and isotropic state, and find two types of instability that are qualitatively different from the bulk, three-dimensional case: first, we show that the analogue of the orientational pusher instability leading to bacterial turbulence in bulk systems instead occurs at the smallest length scale available to the system. Second, an instability associated with density variations arises in puller suspensions as a generic consequence of the effective in-plane compressibility. Given these qualitative differences with respect to the standard bulk setting, we conclude that confinement can have a crucial role in determining the collective behaviour of microswimmer suspensions.
... is that small distortions to a uniformly aligned active nematic system grow through hydrodynamic feedback, fueled by active stresses [13]. When these distortions saturate, they create pairs of ± 1 2 defects, named according to their winding number. ...
This work is a unified study of stable and unstable steady states of 2D active nematic channel flow using the framework of Exact Coherent Structures (ECS). ECS are stationary, periodic, quasiperiodic, or traveling wave solutions of the governing equations that, together with their invariant manifolds, organize the dynamics of nonlinear continuum systems. We extend our earlier work on ECS in the preturbulent regime by performing a comprehensive study of stable and unstable ECS for a wide range of activity values spanning the preturbulent and turbulent regimes. In the weakly turbulent regime, we compute more than 200 unstable ECS that co-exist at a single set of parameters, and uncover the role of symmetries in organizing the phase space geometry. We provide conclusive numerical evidence that in the preturbulent regime, generic trajectories shadow a series of unstable ECS before settling onto an attractor. Finally, our studies hint at shadowing of quasiperiodic type ECS in the turbulent regime.
... At the individual level, the run-and-tumble motion exhibited by bacteria leads to thinking that those external forces push bacteria out of equilibrium. In active matter systems, such a mechanism has been shown to generate large density fluctuations 2,3 , and can also trigger several types of instabilities 4,5 . Once they are initially inoculated at a location in the petri dish device, bacteria aggregate into patterns of different sizes and textures, hence creating domains of high and small densities. ...
... Although the fluid constitutes the compact support upon which propagation of traveling wave structures is made possible 28,34 , the above mentioned-models did investigate its contribution to the evolution of chemotactic particles. In active suspensions, experimental evidence suggests that hydrodynamic interactions guide traveling bands of bacteria at finite speed [2][3][4]35 , emphasizing the role played by fluid flows on the transport of cells. Some of these studies were carried out either in a uniform fluid environment or in an incompressible Navier fluid. ...
This paper investigates a non-homogeneous two-dimensional model for reproducing chemotactic bacteria, immersed in a porous medium that experiences non-uniformly imposed flows. It is shown that independently of the form of the fluid velocity field, the compressible/incompressible nature of the fluid significantly shifts the Turing stability-instability transition line. In dry media, Gaussian perturbations travel faster than the hyperbolic secant ones, yet the latter exhibit better stability properties. The system becomes highly unstable under strong flows and high surface tension. Approximated solutions recovered by injecting Gaussian perturbations overgrow, in addition to triggering concentric breathing features that split the medium into high and low-density domains. Secant perturbations on the other hand scatter slowly and form patterns of non-uniformly distributed peaks for strong flows and high surface tension. These results emphasize that Gaussian perturbations strongly modulate the activity of bacteria, hence can be exploited to perform fast spreading in environments with changing properties. In this sense, Gaussian profiles are better candidates to explain quick bacterial responses to external factors. Secant-type approximated solutions slowly modulate the bacterial activity, hence are better alternatives to dive into weak bacterial progressions in heterogeneous media.
... [13,16,[27][28][29]. Continuum kinetic models of hydrodynamically interacting rodlike swimmers with prescribed stresses or forces were also developed [13,16,[30][31][32][33]. In Refs. ...
We explore a mechanism of the anomalous rheology of active suspensions by hydrodynamic simulations using model pusher swimmers. Our simulations demonstrate that hydrodynamic interactions under shear flow systematically orient swimmers along the extension direction, which is responsible for determining the global swimming states and the resulting significant viscosity reduction. The present results indicate the essential role of hydrodynamic interactions in the elementary processes controlling the rheological properties in active suspensions. Furthermore, such processes may be the substance of the previously proposed scenario for anomalous rheology based on the interplay between the rotational diffusivities and the external shear flow.
... The ABP model has been widely employed to obtain theoretical predictions [50][51][52] and still represents one of the more spread active matter models for its versatility and broad applicability [53][54][55][56][57][58]. Nevertheless, the more recent active Ornstein-Uhlenbeck particle (AOUP) model [59][60][61][62][63][64][65], to be regarded as a "sister/brother" [66] of the ABP model, is generally easier to handle and often conveniently used to achieve further theoretical progress. ...
We investigate how the competing presence of a nonuniform motility landscape and an external confining field affects the properties of active particles. We employ the active Ornstein-Uhlenbeck particle (AOUP) model with a periodic swim-velocity profile to derive analytical approximations for the steady-state probability distribution of position and velocity, encompassing both the Unified Colored Noise Approximation and the theory of potential-free active particles with spatially dependent swim velocity recently developed. We test the theory by confining an active particle in a harmonic trap, which gives rise to interesting properties, such as a transition from a unimodal to a bimodal (and, eventually multimodal) spatial density, induced by decreasing the spatial period of the self propulsion. Correspondingly, the velocity distribution shows pronounced deviations from the Gaussian shape, even displaying a bimodal profile in the high-motility regions. We thus show that the interplay of two relatively simple physical fields can be employed to generate complex emerging behavior.
... 5 A variety of micro-organisms, such as algae and bacteria, which are commonly found in nature, artificial motion devices, and micro-robots are active particles. Active particles are often accompanied by different remarkable collective behaviors, such as particles forming clusters of specific shapes, 6,7 presentation of vortex crystals, 8 accumulation of bacteria near the walls, 1 enhanced transport, 9,10 modification of rheological properties, 11,12 bioconvection, [13][14][15] phase separation, 16 and so on. Additionally, Berke et al. 17 demonstrated that swimming cells are reoriented in a direction parallel to the solid surface through hydrodynamic interactions with the solid surface, making them attracted to the nearest wall. ...
We simulated the sedimentation of two self-propelled particles in a two-dimensional (2D) vertical channel using the lattice Boltzmann method. A 2D squirmer model was employed to simulate the microswimmers, and five typical locomotive modes were obtained for a single squirmer, namely central steady sedimentation, near-wall steady motion, wall-attracted oscillation, large-amplitude oscillation, and small-amplitude oscillation. The locomotive modes of two squirmers are obtained by combinations of different locomotive modes of a single squirmer. It was found that the motion of two squirmers was much more complex than that of a single squirmer, and this complex locomotive mode could be explained by the pressure distribution of the two squirmers. Moreover, we performed a comprehensive analysis of the obtained locomotive modes and determined that the angle at which the two squirmers separated from each other and swimming speed were crucial, which may be the reason for the different locomotive modes of the squirmers that switch from each other.
... In contrast, inspection of active turbulent patterns found with microtubule-kinesin mixtures in the presence of polyethylene-glycol (which causes adsorption to the oil-water interface [5,26]) shows that the density of active material is significantly inhomogeneous. While a linear stability analysis shows that in extensile gels, such as a microtubule-kinesin mixture, the onset of spontaneous flow depends on orientational bend fluctuations and density fluctuations should be irrelevant [27], active turbulence is a highly non-linear phenomenon and the relevance of density inhomogeneities to its physics remains unclear. Additionally, passive colloidal particles aggregate in active nematics [28], through a mechanism reminiscent of path coalescence [29,30] or fluctuationdominated phase ordering [31]. ...
... With respect to conventional models for active gels, which only consider the velocity field and Q tensor, our theory also allows for the time evolution of the active matter density φ. Previous work has shown by a linear stability analysis that density fluctuations are irrelevant for the physics of the "generic instability" of active gels [27], which stands for the transition between the passive (quiescent) and the active (spontaneously flowing) phase. It has however remained unclear what their role is deep in the active phase, where nonlinearities are important; shedding light on this issue has been the focus of our current work. ...
We report numerical results for the hydrodynamics of inhomogeneous lyotropic and extensile active nematic gels. By simulating the coupled Cahn-Hilliard, Navier-Stokes and Beris-Edwards equation for the evolution of the density, flow and orientational order of an active nematic, we ask whether density variations are important to determine its emergent physics. As in constant-density active gels, we find that increasing either activity or nematic tendency (e.g., overall active matter density) triggers a transition between an isotropic passive phase and an active nematic one. We show that density inhomogeneities are important in the latter phase, where we find three types of possible dynamical regimes. First, we observe regular patterns with defects and vortices: these exist close to the passive-active transition. Second, for larger activity, or deeper in the nematic phase, we find active turbulence, as in constant-density active gels, but with exceedingly large density variation. In the third regime, which is unique to inhomogeneous active nematics and occurs for large nematic tendency and intermediate activity, we observe spontaneous microphase separation into active and passive domains. The microphase separated regime is notable in view of the absence of an explicit demixing term in the underlying free energy which we use, and we provide a theoretical analysis based on the common tangent construction which explains its existence. We hope this regime can be probed experimentally in the future.
... In order to understand and rationalize the experimental observations, a considerable theoretical effort has been devoted to develop continuous, coarse-grained descriptions of dense active suspensions [17][18][19][20]. More recently, simple models with a reduced number of parameters have been introduced [12, 21-25], and compared with experimental results [12,[26][27][28]. ...
... In order to understand and rationalize the experimental observations, a considerable theoretical effort has been devoted to develop continuous, coarse-grained descriptions of dense active suspensions [17][18][19][20]. More recently, simple models with a reduced number of parameters have been introduced [12,[21][22][23][24][25], and compared with experimental results [12,[26][27][28]. ...
We report the numerical evidence of a new state of active turbulence in confined domains. By means of extensive numerical simulations of the Toner-Tu-Swift-Hohenberg model for dense bacterial suspensions in circular geometry, we discover the formation a stable, ordered state in which the angular momentum symmetry is broken. This is achieved by self-organization of a turbulent-like flow into a single, giant vortex of the size of the domain. The giant vortex is surrounded by an annular region close to the boundary, characterized by small-scale, radial vorticity streaks. The average radial velocity profile of the vortex is found to be in agreement with a simple analytical prediction. We also provide an estimate of the temporal and spatial scales of a suitable experimental setup comparable with our numerical findings.
