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Concentrated suspensions of swimming microorganisms and other forms of active matter are known to display complex, self-organized spatiotemporal patterns on scales that are large compared with those of the individual motile units. Despite intensive experimental and theoretical study, it has remained unclear the extent to which the hydrodynamic flows generated by swimming cells, rather than purely steric interactions between them, drive the self-organization. Here we use the recent discovery of a spiral-vortex state in confined suspensions of Bacillus subtilis to study this issue in detail. Those experiments showed that if the radius of confinement in a thin cylindrical chamber is below a critical value, the suspension will spontaneously form a steady single-vortex state encircled by a counter-rotating cell boundary layer, with spiral cell orientation within the vortex. Left unclear, however, was the flagellar orientation, and hence the cell swimming direction, within the spiral vortex. Here, using a fast simulation method that captures oriented cell–cell and cell–fluid interactions in a minimal model of discrete particle systems, we predict the striking, counterintuitive result that in the presence of collectively generated fluid motion, the cells within the spiral vortex actually swim upstream against those flows. This prediction is then confirmed by the experiments reported here, which include measurements of flagella bundle orientation and cell tracking in the self-organized state. These results highlight the complex interplay between cell orientation and hydrodynamic flows in concentrated suspensions of microorganisms.

We study the effect of turbulence on marine life by performing numerical simulations of motile micro-organisms, modelled as prolate spheroids, in isotropic homogeneous turbulence. We show that the clustering and patchiness observed in laminar flows, linear shear and vortex flows, are significantly reduced in a three-dimensional turbulent flow mainly because of the complex topology; elongated micro-organisms show some level of clustering in the case of swimmers without any preferential alignment whereas spherical swimmers remain uniformly distributed. Micro-organisms with one preferential swimming direction (e.g. gyrotaxis) still show significant clustering if spherical in shape, whereas prolate swimmers remain more uniformly distributed. Due to their large sensitivity to the local shear, these elongated swimmers react more slowly to the action of vorticity and gravity and therefore do not have time to accumulate in a turbulent flow. These results show how purely hydrodynamic effects can alter the ecology of micro-organisms that can vary their shape and their preferential orientation.

Suspensions of swimming micro-organisms are known to undergo intricate collective dynamics as a result of hydrodynamic and collision interactions. Micro-swimmers, such as bacteria and micro-algae, naturally live and have evolved in complex habitats that include impurities, obstacles and interfaces. To elucidate their dynamics in a heterogeneous environment, we consider a continuum theory where the the micro-swimmers are embedded in a Brinkman wet porous medium, which models viscous flow with an additional resistance or friction due to the presence of smaller stationary obstacles. The conservation equation for the swimmer configurations includes advection and rotation by the immersing fluid, and is coupled to the viscous Brinkman fluid flow with an active stress due to the swimmers' motion in it. Resistance alters individual swimmer locomotion and the way it disturbs the surrounding fluid, and thus it alters its hydrodynamic interactions with others and and such affects collective dynamics.The entropy analysis and the linear stability analysis of the system of equations both reveal that resistance delays and hinders the onset and development of the collective swimming instabilities, and can completely suppress it if sufficiently large. Simulations of the full nonlinear system confirm these. We contrast the results with previous theoretical studies on micro-swimmers in homogeneous viscous flow, and discuss relevant experimental realizations.

Micro-swimmer locomotion in heterogeneous media is increasingly relevant in biological physics due to the prevalence of microorganisms in complex environments. A model for such porous media is the Brinkman fluid which accounts for a sparse matrix of stationary obstacles via a linear resistance term in the momentum equation. We investigate two models for the locomotion and the flow field generated by a swimmer in such a medium. First, we analyze a dumbbell swimmer composed of two spring-connected spheres and driven by a flagellar force and derive its exact swimming velocity as a function of the Brinkman medium resistance, showing that the swimmer monotonically slows down as the medium drag monotonically increases. In the limit of no resistance the model reduces to the classical Stokes dipole swimmer, while finite resistance introduces hydrodynamic screening that attenuates long-range interactions. Additionally, we derive an analytical expression for the far-field flow generated by a Brinkmanlet force-dipole, which can be used for propulsive point-dipole swimmer models. Remarkably, this approximation reproduces the dumbbell swimmer's flow field in the far-field regime with high accuracy. These results provide new analytical tools for understanding locomotion in complex fluids and offer foundational insights for future studies on collective behavior in active and passive suspensions within porous or structured environments.

We explore theoretically the complex dynamics and emergent behaviors of spinning spheres immersed in viscous fluid. The particles are coupled to each other via the fluid in which they are suspended: Each particle disturbs the surrounding fluid with a rotlet field and that fluid flow affects the motion of the other particles. We notice the emergence of intricate periodic or chaotic trajectories that depend on the rotors initial position and separation. The point-rotor motions confined to a plane bear similarities to the classic 2D point-vortex dynamics. Our analyses highlight the complexity of the interaction between just a few rotors and suggest richer behavior in denser populations. We discuss how the model gives insight into more complex systems and suggest possible extensions for future theoretical studies.

We use numerical simulations to systematically investigate the vesicle dynamics in two-dimensional (2D) Taylor-Green vortex flow in the absence of inertial forces. Vesicles are highly deformable membranes encapsulating an incompressible fluid and they serve as numerical and experimental proxies for biological cells such as red blood cells. Vesicle dynamics has been studied in free-space/bounded shear, Poiseuille and Taylor-Couette flows in 2D and 3D. Taylor-Green vortex are characterized with even more complicated properties than those flows such as non-uniform flow line curvature, shear gradient. We study the effects of two parameters on the vesicle dynamics: the ratio of the interior fluid viscosity to that of the exterior one and the ratio of the shear forces on the vesicle to the membrane stiffness (characterized by the capillary number). Vesicle deformability nonlinearly depends on these parameters. Although the study is in 2D, our findings contribute to the wide spectrum of intriguing vesicle dynamics: vesicles migrate inwards and eventually rotate at the vortex center if they are sufficiently deformable. If not so, they migrate away from the vortex center and travel across the periodic arrays of vortices.

Micro-swimmers such as bacteria perform random walks known as run-and-tumbles to move up chemo-attractant gradients and as a result aggregate with others. It is also known that such micro-swimmers can self-organize into macroscopic patterns due to interactions with neighboring cells through the fluidic environment they live in. While the pattern formation resulting from chemotactic and hydrodynamic interactions separately and together have been previously investigated, the effect of the anisotropy in the tumbles of micro-swimmers has been unexplored. Here we show through linear analysis and full nonlinear simulations that the slight anisotropy in the individual swimmer tumbles can alter the collective pattern formation in non-trivial ways. We show that tumbling anisotropy diminishes the magnitude of the chemotactic aggregates but may result in more such aggregation peaks.

We use a three-bead-spring model to investigate the dynamics of bi-flagellate micro-swimmers near a surface. While the primary dynamics and scattering are governed by geometric-dependent direct contact, the fluid flows generated by the swimmer locomotion are important in orienting it toward or away from the surface. Flagellar noise and in particular cell spinning about the main axis help a surface-trapped swimmer escape, whereas the time a swimmer spends at the surface depends on the incident angle. The dynamics results from a nuanced interplay of direct collisions, hydrodynamics, noise and the swimmer geometry. We show that to correctly capture the dynamics of a biflagellate swimmer, minimal models need to resolve the shape asymmetry.

We explore theoretically the complex dynamics and emergent behaviors of spinning spheres immersed in viscous fluid. The particles are coupled to each-other via the fluid in which they are suspended: each particle disturbs the surrounding fluid with a rotlet field and that fluid flow affects the motion of the other particles. We notice the emergence of intricate periodic or chaotic trajectories that depend on the rotors initial position and separation. The point-rotor motions confined to a plane bear similarities the classic 2D point-vortex dynamics. Our analyses highlight the complexity of the interaction between just a few rotors and suggest richer behavior in denser populations. We discuss how the model gives insight into more complex systems and suggest possible extensions for future theoretical studies.

We study, numerically, the collective dynamics of self-rotating nonaligning particles by considering a monolayer of spheres driven by constant clockwise or counterclockwise torques. We show that hydrodynamic interactions alter the emergence of large-scale dynamical patterns compared to those observed in dry systems. In dilute suspensions, the flow stirred by the rotors induces clustering of opposite-spin rotors, while at higher densities same-spin rotors phase separate. Above a critical rotor density, dynamic hexagonal crystals form. Our findings underscore the importance of inclusion of the many-body, long-range hydrodynamic interactions in predicting the phase behavior of active particles.