Microorganisms living in microfluidic environments often form multi-species swarms, where they can leverage collective motions to achieve enhanced transport and spreading. Nevertheless, there is a general lack of physical understandings of the origins of the multiscale unstable dynamics observed within these systems. Here, we build a computational model to study binary suspensions of rear- and front-actuated microswimmers, or respectively the so-called "pusher" and "puller" particles, that have different populations and swimming speeds. We perform direct particle simulations to reveal that collective system dynamics are possible even in the scenario of an "activity-balanced" mixture, which produces near zero mean extra stress. We first construct a continuum kinetic model to describe the initial transient period when the system is near uniform isotropy and then perform linear stability analysis to reveal the system's finite-wavelength hydrodynamic instabilities, in contrast with the long-wavelength instabilities of pure pusher/puller suspensions. Then, we carry out slender-body discrete particle simulations to resolve both the short time instabilities and the the longtime dynamics, which feature non-trivial density fluctuations and spatially-correlated motions, distinct from those of single-species.
The ability of microswimmers to deploy optimal propulsion strategies is of paramount importance for their locomotory performance and survival at low Reynolds numbers. Although for perfectly spherical swimmers minimum dissipation requires a neutral type swimming, any departure from the spherical shape may lead the swimmer to adopt a new propulsion strategy, namely those of puller- or pusher-type swimming. In this study, by using the minimum dissipation theorem for microswimmers, we determine the flow field of an optimal nearly spherical swimmer, and show that indeed depending on the shape profi…
Suspensions of rear- and front-actuated microswimmers immersed in a fluid, known respectively as ``pushers'' and ``pullers'', display qualitatively different collective behaviours: beyond a characteristic density, pusher suspensions exhibit a hydrodynamic instability leading to collective motion known as active turbulence, a phenomenon which is absent for pullers. In this Letter, we describe the collective dynamics of a binary pusher--puller mixture using kinetic theory and large-scale particle-resolved simulations. We derive and verify an instability criterion, showing that the critical densi…
We use numerical simulations to address locomotion at zero Reynolds number in viscoelastic (Giesekus) fluids. The swimmers are assumed to be spherical, to self-propel using tangential surface deformation, and the computations are implemented using a finite element method. The emphasis of the study is on the change of the swimming kinematics, energetics, and flow disturbance from Newtonian to viscoelastic, and on the distinction between pusher and puller swimmers. In all cases, the viscoelastic swimming speed is below the Newtonian one, with a minimum obtained for intermediate values of the Wei…
We study the orientational and translational dynamics of spherical microswimmers trapped at fluid interfaces, in terms of the force dipole and source dipole components of their flow field. Using numerical simulations and analytical calculations, we show that the force dipole exerts a torque, orienting pushers parallel to the interface, and pullers in normal direction. The source dipole results in particle rotation only for a finite viscosity contrast between the two fluids, in agreement with previous studies. The superposition of these two contributions leads to an rotational dynamics with a s…
Interaction of motile microrganisms with a nearby solid substrate is a well studied phenomenon. However, the effects of hydrodynamic slippage on the substrate have received a little attention. In the present study, within the framework of the squirmer model, we impose a tangential velocity at the swimmer surface as a representation of the ciliatory propulsion and subsequently obtain exact solution of the Stokes equation based on a combined analytical-numerical approach. We illustrate how the near-wall swimming velocities are non-trivially altered by the interaction of wall slip and hydrodynami…
We present a hydrodynamic study of a monolayer of squirmer model microswimmers confined to a boundary by strong gravity using the simulation method of multi-particle collision dynamics. The squirmers interact with each other via their self-generated hydrodynamic flow fields and thereby form a variety of fascinating dynamic states when density and squirmer type are varied. Weak pushers, neutral squirmers, and pullers have an upright orientation. With their flow fields they push neighbors away and thereby form a hydrodynamic Wigner fluid at lower densities. Furthermore, states of fluctuating cha…
Active matter has been the object of huge amount of research in recent years for its important fundamental and applicative properties. In this paper we investigate active suspensions of micro-swimmers through direct numerical simulation, so that no approximation is made at the continuous level other than the numerical one. We consider both pusher and puller organisms, with a spherical or ellipsoidal shape. We analyse the velocity and the characteristic scales for an homogeneous two-dimensional suspension and the effective viscosity under shear. We bring evidences that the complex features disp…
In micro-swimmer suspensions locomotion necessarily generates fluid motion, and it is known that such flows can lead to collective behavior from unbiased swimming. We examine the complementary problem of how chemotaxis is affected by self-generated flows. A kinetic theory coupling run-and-tumble chemotaxis to the flows of collective swimming shows separate branches of chemotactic and hydrodynamic instabilities for isotropic suspensions, the first driving aggregation, the second producing increased orientational order in suspensions of "pushers" and maximal disorder in suspensions of "pullers".…
We present the results of hydrodynamic simulations using the method of multi-particle collision dynamics for a system of squirmer microswimmers moving under the influence of gravity at low Reynolds numbers. In addition, the squirmers are bottom-heavy so that they experience a torque which aligns them along the vertical. The squirmers interact hydrodynamically by the flow fields of a stokeslet and rotlet, which are initiated by the acting gravitational force and torque, respectively, and by their own flow fields. By varying the ratio of swimming to bulk sedimentation velocity and the torque, we…
Active colloids self-organise to a variety of collective states, ranging from highly motile 'molecules' to complex 3D structures. Using large-scale simulations, we show that hydrodynamic interactions, together with a gravity-like aligning field, lead to tunable self-assembly of active colloidal spheres near a surface. The observed structures depend on the hydrodynamic characteristics: particles driven at the front, pullers, form small chiral spinners consisting of two or three particles, whereas those driven at the rear, pushers, assemble to large dynamic aggregates. The rotational motion of t…
We study the coupled hydrodynamics between a motile slender microswimmer and a deformable interface that separates two Newtonian fluid regions. From the disturbance field generated by the swimming motion, we quantitatively characterize the interface deformation and the manner in which the coupling modifies the microswimmer translation itself. We treat the role of the swimmer type (pushers and pullers), size and model an interface that can deform due to both surface tension and bending elasticity. Our analysis reveals a strong dependence of the hydrodynamics on the swimmer orientation and posit…
Many eukaryotic cells undergo frequent shape changes (described as amoeboid motion) that enable them to move forward. We investigate the effect of confinement on a minimal model of amoeboid swimmer. Complex pictures emerge: (i) The swimmer's nature (i.e., either pusher or puller) can be modified by confinement, thus suggesting that this is not an intrinsic property of the swimmer. This swimming nature transition stems from intricate internal degrees of freedom of membrane deformation. (ii) The swimming speed might increase with increasing confinement before decreasing again for stronger confin…
We study the collective motion of confined spherical microswimmers such as active colloids which we model by so-called squirmers. To simulate hydrodynamic flow fields including thermal noise, we use the method of multi-particle collision dynamics. We demonstrate that hydrodynamic near fields acting between squirmers as well as squirmers and bounding walls crucially determine their collective motion. In particular, with increasing density we observe a clear phase separation into a gas-like and cluster phase for neutral squirmers whereas strong pushers and pullers more gradually approach the hex…
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Brandeis University（布兰迪斯大学）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；TU Dresden（德累斯顿工业大学）
Three-dimensional simulations with fully resolved hydrodynamics are performed to study the dynamics of a single squirmer under gravity, in order to clarify its motion in the vicinity of a flat plate. Different dynamics emerge for different gravity strengths. In a moderate gravity regime, neutral squirmers and pullers eventually stop moving and reorient in a direction perpendicular to the plate; pushers, instead, exhibit continuous motion in a tilted direction. In the strong gravity regime, all types of squirmers sediment and reorient perpendicularly to the plate. In this study, the chirality i…
Microorganisms can preferentially orient and move along gradients of a chemo-attractant (i.e., chemotax) while colonies of many microorganisms can collectively undergo complex dynamics in response to chemo-attractants that they themselves produce. For colonies or groups of micro-swimmers we investigate how an "auto-chemotactic" response that should lead to swimmer aggregation is affected by the non-trivial fluid flows that are generated by collective swimming. For this, we consider chemotaxis models based upon a hydrodynamic theory of motile suspensions that are fully coupled to chemo-attracta…
The breakup of a fluid jet into droplets has long fascinated natural scientists, with early research dating back to the 19th century. Infinitesimal perturbations to a jet grow because of surface tension, which eventually leads to breakup of the jet into droplets (Rayleigh-Plateau instability). Although this classical phenomenon has long been studied, it is not clear how it is modified when the fluid is replaced by an active fluid. In this study, we investigate instabilities of a jet of an active fluid. The active fluid is modelled by a suspension of microswimmers that propel themselves by gene…
We investigate the dynamics of a dilute suspension of hydrodynamically interacting motile or immotile stress-generating swimmers or particles as they invade a surrounding viscous fluid. Colonies of aligned pusher particles are shown to elongate in the direction of particle orientation and undergo a cascade of transverse concentration instabilities, governed at small times by an equation which also describes the Saffman-Taylor instability in a Hele-Shaw cell, or Rayleigh-Taylor instability in two-dimensional flow through a porous medium. Thin sheets of aligned pusher particles are always unstab…
Active particles, which interact hydrodynamically, display a remarkable variety of emergent collective phenomena. We use squirmers to model spherical microswimmers and explore the collective behavior of thousands of them under the influence of strong gravity using the method of multi-particle collision dynamics for simulating fluid flow. The sedimentation profile depends on the ratio of swimming to sedimentation velocity as well as on the squirmer type. It shows close packed squirmer layers at the bottom and a highly dynamic region with exponential density dependence towards the top. The mean …
One of the hallmarks of active matter is its rich nonlinear dynamics and instabilities. Recent numerical simulations of phototactic algae showed that a thin jet of swimmers, obtained from hydrodynamic focusing inside a Poiseuille flow, was unstable to longitudinal perturbations with swimmers dynamically clustering (Jibuti et al., Phys. Rev. E, 90, 2014). As a simple starting point to understand these instabilities, we consider in this paper an initially homogeneous one-dimensional line of aligned swimmers moving along the same direction, and characterise its instability using both a continuum …
After colliding with a surface, microswimmers reside there during the detention time. They accumulate and may form complex structures such as biofilms. We introduce a general framework to calculate the distribution of detention times using the method of first-passage times and study how rotational noise and hydrodynamic interactions influence the escape from a surface. We compare generic swimmer models to the simple active Brownian particle. While the respective detention times of source dipoles are smaller, the ones of pullers are larger by up to several orders of magnitude, and pushers show …
In this Letter, we study the collective behaviour of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedently large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is non-perturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers …
In this paper we systematically derive a fourth-order continuum theory capable of reproducing mesoscale turbulence in a three-dimensional suspension of microswimmers. We start from overdamped Langevin equations for a generic microscopic model (pushers or pullers), which include hydrodynamic interactions on both, small length scales (polar alignment of neighboring swimmers) and large length scales, where the solvent flow interacts with the order parameter field. The flow field is determined via the Stokes equation supplemented by an ansatz for the stress tensor. In addition to hydrodynamic inte…
Similarly to their biological counterparts, suspensions of chemically-active autophoretic swimmers exhibit nontrivial dynamics involving self-organization processes as a result of inter-particle interactions. Using a kinetic model for a dilute suspension of autochemotactic Janus particles, we analyse the effect of a confined pressure-driven flow on these collective behaviours and the impact of chemotactic aggregation on the effective viscosity of the active fluid. Four dynamic regimes are identified when increasing the strength of the imposed pressure-driven flow, each associated with a differ…
We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is a coupled Vicsek-Stokes system. The Vicsek model describes self-propelled agents interacting through alignment. It provides a phenomenological description of hydrodynamic interactions between agents at high density. Stokes equations describe a low Reynolds number fluid. These two dynamics are coupled by the interaction between the agents and the fluid. The fluid contributes to rotating the particles through Jeffery's equation. Particle self-propulsion induces a force dipole on the fluid. After coarse-…
Various aspects of self-motility of chemically active colloids in Newtonian fluids can be captured by simple models for their chemical activity plus a phoretic slip hydrodynamic boundary condition on their surface. For particles of simple shapes (e.g., spheres) -- as employed in many experimental studies -- which move at very low Reynolds numbers in an unbounded fluid, such models of chemically active particles effectively map onto the well studied so-called hydrodynamic squirmers [S. Michelin and E. Lauga, J. Fluid Mech. \textbf{747}, 572 (2014)]. Accordingly, intuitively appealing analogies …
The incessant swimming motion of microbes in dense suspensions can give rise to striking collective motions and coherent structures. However, theoretical investigations of these structures typically utilize either computationally demanding numerical simulations, or simplified continuum models. Here we analytically investigate the collective dynamics of a dense array of steady, spherical squirmers. We first calculate the forces and torques acting on two closely-separated squirmers, through solving the Stokes equations to second-order in the ratio of mean spacing to squirmer radius. This lubrica…
Janus phoretic colloids (JPs) self-propel as a result of self-generated chemical gradients and exhibit spontaneous nontrivial dynamics within phoretic suspensions, on length scales much larger than the microscopic swimmer size. Such collective dynamics arise from the competition of (i) the self-propulsion velocity of the particles, (ii) the attractive/repulsive chemically-mediated interactions between particles and (iii) the flow disturbance they introduce in the surrounding medium. These three ingredients are directly determined by the shape and physico-chemical properties of the colloids' su…
We perform hydrodynamic simulations using the method of multi-particle collision dynamics and a theoretical analysis to study a single squirmer microswimmer at high Péclet number, which moves in a low Reynolds number fluid and under gravity. The relevant parameters are the ratio $α$ of swimming to bulk sedimentation velocity and the squirmer type $β$. The combination of self-propulsion, gravitational force, hydrodynamic interactions with the wall, and thermal noise leads to a surprisingly diverse behavior. At $α> 1$ we observe cruising states, while for $α<1$ the squirmer resides close to the …
Suspended colloidal particles interacting chemically with a solute are able to self-propel by autophoretic motion when they are asymmetrically patterned (Janus colloids). Here we demonstrate that the chemical anisotropy is not a necessary condition to achieve locomotion. The non linear interplay between surface osmotic flows and solute advection can produce spontaneous, and self-sustained motion of isotropic particles. We solve, for a spherical particle, the classical nonlinear autophoretic theoretical framework at arbitrary Péclet number. For a given set of material parameters, there exists a…
