We combine experiments, large scale simulations and continuum models to study the emergence of coherent structures in a suspension of magnetically driven microrollers sedimented near a floor. Collective hydrodynamic effects are predominant in this system, leading to strong density-velocity coupling. We characterize a uniform suspension and show that density waves propagate freely in all directions in a dispersive fashion. When sharp density gradients are introduced in the suspension, we observe the formation of a shock. Unlike Burgers' shock-like structures observed in other active and driven confined hydrodynamic systems, the shock front in our system has a well-defined finite width and moves rapidly compared to the mean suspension velocity. We introduce a continuum model demonstrating that the finite width of the front is due to far-field nonlocal hydrodynamic interactions and governed by a geometric parameter: the average particle height above the floor.
We derive a minimal continuum model to investigate the hydrodynamic mechanism behind the fingering instability recently discovered in a suspension of microrollers near a floor [Driscoll et al. Nature Physics, 2016]. Our model, consisting of two continuous lines of rotlets, exhibits a linear instability driven only by hydrodynamics interactions, and reproduces the lengthscale selection observed in large scale particle simulations and in experiments. By adjusting only one parameter, the distance between the two lines, our dispersion relation exhibits quantitative agreement with the simulations a…
Recent work has identified persistent cluster states which were shown to be assembled and held together by hydrodynamic interactions alone [Driscoll \textit{et al.} (2017) Nature Physics, 13(4), 375]. These states were seen in systems of colloidal microrollers; microrollers are colloidal particles which rotate about an axis parallel to the floor and generate strong, slowly decaying, advective flows. To understand these bound states, we study a simple, yet rich, model system of two microrollers. Here we show that pairs of microrollers can exhibit hydrodynamic bound states whose nature depends o…
We perform detailed computational and experimental measurements of the driven dynamics of a dense, uniform suspension of sedimented microrollers driven by a magnetic field rotating around an axis parallel to the floor. We develop a lubrication-corrected Brownian Dynamics method for dense suspensions of driven colloids sedimented above a bottom wall. The numerical method adds lubrication friction between nearby pairs of particles, as well as particles and the bottom wall, to a minimally-resolved model of the far-field hydrodynamic interactions. Our experiments combine fluorescent labeling with …
We develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently-observed fingering instability in an active suspension of colloidal rollers sedimented above a wall [M. Driscoll, B. Delmotte, M. Youssef, S. Sacanna, A. Donev and P. Chaikin, Nature Physics, 2016, doi:10.1038/nphys3970]. We present a stochastic Adams-Bashforth integrator for the equations of Brownian dynamics, which has the same cost as but is more accurate than the widely-used Euler-Maruyama scheme, and uses a random finite difference to capture the stochastic drift proportional to the…
It is known that obstacles can hydrodynamically trap bacteria and synthetic microswimmers in orbits, where the trapping time heavily depends on the swimmer flow field and noise is needed to escape the trap. Here, we use experiments and simulations to investigate the trapping of microrollers by obstacles. Microrollers are rotating particles close to a bottom surface, which have a prescribed propulsion direction imposed by an external rotating magnetic field. The flow field that drives their motion is quite different from previously studied swimmers. We found that the trapping time can be contro…
We investigate the collective transport properties of microscopic magnetic rollers that propel close to a surface due to a circularly polarized, rotating magnetic field. The applied field exerts a torque to the particles, which induces a net rolling motion close to a surface. The collective dynamics of the particles result from the balance between magnetic dipolar interactions and hydrodynamic ones. We show that, when hydrodynamics dominate, i.e. for high particle spinning, the collective mean velocity linearly increases with the particle density. In this regime we analyse the clustering kinet…
Condensation of objects into stable clusters occurs naturally in equilibrium and driven systems. It is commonly held that potential interactions, depletion forces, or sensing are the only mechanisms which can create long-lived compact structures. Here we show that persistent motile structures can form spontaneously from hydrodynamic interactions alone with no sensing or potential interactions. We study this structure formation in a system of colloidal rollers suspended and translating above a floor, using both experiments and large-scale 3D simulations. In this system, clusters originate from …
Evolution of a suspension drop entrained by Poiseuille flow is studied numerically at a low Reynolds number. A suspension drop is modelled by a cloud of many non-touching particles, initially randomly distributed inside a spherical volume of a viscous fluid which is identical to the host fluid outside the drop. Evolution of particle positions and velocities is evaluated by the accurate multipole method corrected for lubrication, implemented in the {\sc hydromultipole} numerical code. Deformation of the drop is shown to be smaller for a larger volume fraction. At high concentrations, hydrodynam…
Shear thickening is a widespread phenomenon in suspension flow that, despite sustained study, is still the subject of much debate. The longstanding view that shear thickening is due to hydrodynamic clusters has been challenged by recent theory and simulations suggesting that contact forces dominate, not only in discontinuous, but also in continuous shear thickening. Here, we settle this dispute using shear reversal experiments on micron-sized silica and latex colloidal particles to measure directly the hydrodynamic and contact force contributions to shear thickening. We find that contact force…
It is intuitive that the diffusivity of an isolated particle differs from those in a monodisperse suspension, in which hydrodynamic interactions between the particles are operative. Batchelor (1976,1983) calculated how hydrodynamic interactions influenced the diffusivity of a dilute suspension of spherical particles and Russel et al.(1991), and Brady (1994) treated non-dilute (higher particle volume fraction) suspensions. Although most particles lack perfect sphericity, little is known about the effects of hydrodynamic interactions on the diffusivity of spheroidal particles, which are the simp…
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…
We have shown [J.\ Fluid Mech.\ {\bf 592}, 447 (2007)] that swapping (reversing) trajectories in confined suspension flows prevent collisions between particles approaching each other in adjacent streamlines. Here we demonstrate that by inducing layering this hydrodynamic mechanism changes the microstructure of suspensions in a confined Couette flow. Layers occur either in the near-wall regions or span the whole channel width, depending on the strength of the swapping-trajectory effect. While our theory focuses on dilute suspensions, we postulate that this new hydrodynamic mechanism controls fo…
Self-organised structures in mixed active-passive suspensions due to hydrodynamic interactions
Capital Fund Management S.A.（资本基金管理公司）；Institut Pasteur, Université Paris Cité, CNRS UMR3738（巴斯德研究所，巴黎西岱大学，法国国家科学研究中心）；Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，巴黎文理研究大学，法国国家科学研究中心，索邦大学，巴黎西岱大学）；Department of Biomedical Engineering, Tohoku University（东北大学生物医学工程系）
We simulate with hydrodynamics a suspension of active disks squirming through a Newtonian fluid. We explore numerically the full range of squirmer area fractions from dilute to close packed and show that "motility induced phase separation" (MIPS), which was recently proposed to arise generically in active matter, and which has been seen in simulations of active Brownian disks, is strongly suppressed by hydrodynamic interactions. We give an argument for why this should be the case and support it with counterpart simulations of active Brownian disks in a parameter regime that provides a closer c…
Active bodies in viscous fluids interact hydrodynamically through self-generated flows. Here we study spontaneous aggregation induced by hydrodynamic flow in a suspension of stiff, apolar, active filaments. Lateral hydrodynamic attractions in extensile filaments lead, independent of volume fraction, to anisotropic aggregates which translate and rotate ballistically. Lateral hydrodynamic repulsion in contractile filaments lead, with increasing volume fractions, to microstructured states of asters, clusters, and incipient gels where, in each case, filament motion is diffusive. Our results demons…
Bacteria suspension exhibits a wide range of collective phenomena arising from interactions between individual cells. Here we show Serratia marcescens cells near an air-liquid interface spontaneously aggregate into dynamic clusters through surface-mediated hydrodynamic interactions. These long-lived clusters translate randomly and rotate in the counter-clockwise direction; they continuously evolve, merge with others and split into smaller ones. Measurements indicate that long-ranged hydrodynamic interactions have strong influences on cluster properties. Bacterial clusters change material and f…
Strongly confined active liquids are subject to unique hydrodynamic interactions due to momentum screening and lubricated friction by the confining walls. Using numerical simulations, we demonstrate that 2D dilute suspensions of fore-aft asymmetric polar swimmers in a Hele-Shaw geometry can exhibit a rich variety of novel phase behaviors depending on particle shape, including: coherent polarized density waves with global alignment, stationary asters, persistent counter-rotating vortices, density shocks and rarefaction waves. We also explain these phenomena using a linear stability analysis and…
The hydrodynamic interaction of two deformable vesicles in shear flow induces a net displacement, in most cases an increase of their distance in the transverse direction. The statistical average of these interactions leads to shear-induced diffusion in the suspension, both at the level of individual particles which experience a random walk made of successive interactions, and at the level of suspension where a non-linear down-gradient diffusion takes place, an important ingredient in the structuring of suspension flows. We make an experimental and computational study of the interaction of a pa…
We obtain hydrodynamic equations describing a fluid consisting of chiral molecules or a suspension of chiral particles in a Newtonian fluid. The stresses arising in a flowing chiral liquid have a component forbidden by symmetry in a Newtonian liquid. For example, a chiral liquid in a Poiseuille flow between parallel plates exerts forces on the plates, which are perpendicular to the flow. A generic flow results in spatial separation of particles of different chirality. Thus even a racemic suspension will exhibit chiral properties in a generic flow. A suspension of particles of random shape in a…
Since its development, Stokesian Dynamics has been a leading approach for the dynamic simulation of suspensions of particles at arbitrary concentrations with full hydrodynamic interactions. Although originally developed for the simulation of passive particle suspensions, the Stokesian Dynamics framework is equally well suited to the analysis and dynamic simulation of suspensions of active particles, as we elucidate here. We show how the reciprocal theorem can be used to formulate the exact dynamics for a suspension of arbitrary active particles and then show how the Stokesian Dynamics method p…
Confinement between two parallel surfaces is found, theoretically and experimentally, to drastically affect the hydrodynamic interaction between colloid particles, changing the sign of the coupling, its decay with distance and its concentration dependence. In particular, we show that three-body effects do not modify the coupling at large distances as would be expected from hydrodynamic screening.
Using a simple model of self-propelled particle, the effective shear viscosity of a dilute, spatially homogeneous suspension of active particles is studied. We use formulation of non-linear Fokker-Planck equation to drive a kinetic description, including the effect of external flow field, rotary diffusion, and particle-particle hydrodynamic interactions in two dimensions. Analytical expressions are obtained for the stress tensor at small Peclet numbers, in a simple shear flow, up to second order of volume fraction of the swimmers, which shows the explicit dependence of shear viscosity on the d…
The lack of detailed balance in active colloidal suspensions allows dissipation to determine stationary states. Here we show that slow viscous flow produced by polar or apolar active colloids near plane walls mediates attractive hydrodynamic forces that drive crystallization. Hydrodynamically mediated torques tend to destabilize the crystal but stability can be regained through critical amounts of bottom-heaviness or chiral activity. Numerical simulations show that crystallization is not nucleational, as in equilibrium, but is preceded by a spinodal-like instability. Harmonic excitations of th…
Near field hydrodynamic interactions are essential to determine many important emergent behaviors observed in active suspensions, but have not been successfully modeled so far. In this work we propose an effective model capable of efficiently capturing the essence of the near field hydrodynamic interactions, validated numerically by a pedagogic model system consisting of an E. coli and a spherical tracer. The proposed model effectively captures all the details of near field hydrodynamics through only a tensorial coefficient of resistance, which is fundamentally different from, and thus cannot …
We construct the hydrodynamic equations for {\em suspensions} of self-propelled particles (SPPs) with spontaneous orientational order, and make a number of striking, testable predictions:(i) SPP suspensions with the symmetry of a true {\em nematic} are {\em always} absolutely unstable at long wavelengths.(ii) SPP suspensions with {\em polar}, i.e., head-tail {\em asymmetric}, order support novel propagating modes at long wavelengths, coupling orientation, flow, and concentration. (iii) In a wavenumber regime accessible only in low Reynolds number systems such as bacteria, polar-ordered suspens…
We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective diffusion coefficients $D_T(ρ) / D_0$ and $D_C(ρ) / D_0$, where $D_0$ is the single-particle diffusion coefficient, as a function of the density of the colloids $ρ$. At low Schmidt numbers $Sc={\cal O}(1)$, we find that hydrodynamics has essentially no effect on the behaviour of $D_T(ρ)/D_0$. At larger $Sc$, $D_T(ρ)/D_0$ is enhanced at all densities, although the differences comp…
A universal characteristic of mesoscale turbulence in active suspensions is the emergence of a typical vortex length scale, distinctly different from the scale-invariance of turbulent high-Reynolds number flows. Collective length-scale selection has been observed in bacterial fluids, endothelial tissue and active colloides, yet the physical origins of this phenomenon remain elusive. Here, we systematically derive an effective fourth-order field theory from a generic microscopic model that allows us to predict the typical vortex size in microswimmer suspensions. Building on a self-consistent cl…
We present a computer simulation study on the crystal nucleation process in suspensions of hard spheres, fully taking into account the solvent hydrodynamics. If the dynamics of collodial crystallization were purely diffusive, the crystal nucleation rate densities would drop as the inverse of the solvent viscosity. However, we observe that the nucleation rate densities do not scale in this way, but are enhanced at high viscosities. This effect might explain the large discrepancy between the nuclation rate densities obtained by simulation and experiment that have reported in the literature so fa…
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…
Ordered phases emerged in active suspensions of polar swimmers are under long-wavelength hydrodynamic mediated instabilities. In this letter, we show that chemical molecules dissolved in aqueous suspensions, as an unavoidable part of most wet active systems, can mediate long-range interactions and subsequently stabilize the ordered phases. Chemoattractant in living suspensions and dissolved molecules producing phoretic forces in synthesized Janus suspensions are reminiscent of such molecules. Communication between swimmers through the gradients of such chemicals generated by individual swimmer…
We use a mesoscopic computer simulation method to study the interplay between hydrodynamic and Brownian fluctuations during steady-state sedimentation of hard sphere particles for Peclet numbers (Pe) ranging from 0.1 to 15. Even when the hydrodynamic interactions are an order of magnitude weaker than Brownian forces, they still induce backflow effects that dominate the reduction of the average sedimentation velocity with increasing particle packing fraction. Velocity fluctuations, on the other hand, begin to show nonequilibrium hydrodynamic character for Pe > 1
When particulate suspensions are sheared, perturbations in the shear flows around the rigid particles increase the local energy dissipation, so that the viscosity of the suspension is effectively higher than that of the solvent. For bulk (three-dimensional) fluids, understanding this viscosity enhancement is a classic problem in hydrodynamics that originated over a century ago with Einstein's study of a dilute suspension of spherical particles. \cite{Einstein1} In this paper, we investigate the analogous problem of the effective viscosity of a suspension of disks embedded in a two-dimensional …
We describe a new kind of self-propelling motion of bacteria based on the cooperative action of rotating flagella on the surface of bacteria. Describing the ensemble of rotating flagella in the framework of the hydrodynamics with spin the reciprocal theorem of Stokesian hydrodynamics is generalized accordingly. The velocity of the self-propulsion is expressed in terms of the characteristics of the vector field of flagella orientation and it is shown that unusually high velocities of \textit{Thiovulum majus} bacteria may be explained by the cooperative action of the rotating flagella. The expre…
Understanding the correlation between structure and rheology in colloidal suspensions is important as these suspensions are crucial in industrial applications. Moreover, colloids exhibit a wide range of structures under confinement that could considerably alter the viscosity. Here, we use a combination of experiments and simulations to elucidate how confinement induced structures alter the relative contributions of hydrodynamic and repulsive forces to produce up to a ten fold change in the viscosity. We use a custom built confocal rheoscope to image the particle configurations of a colloidal s…
We present a mesoscopic hydrodynamic description of the dynamics of colloidal suspensions. We consider the system as a gas of Brownian particles suspended in a Newtonian heat bath subjected to stationary non-equilibrium conditions imposed by a velocity field. Using results already obtained in previous studies in the field by means of a generalized Fokker-Planck equation, we obtain a set of coupled differential equations for the local diffusion current and the evolution of the total stress tensor. We find that the dynamic shear viscosity of the system contains contributions arising from the fin…
In this review article, we focus on collective motion in externally driven colloidal suspensions, as well as how these collective effects can be harnessed for use in microfluidic applications. We highlight the leading role of hydrodynamic interactions in the self-assembly, emergent behavior, transport, and mixing properties of colloidal suspensions. A special emphasis is given to recent numerical methods to simulate driven colloidal suspensions at large scales. In combination with experiments, they help us to understand emergent dynamics and to identify control parameters for both individual a…
Strong effects of the Faraday instability on suspensions of rodlike colloidal particles are reported through measurements of the critical acceleration and of the surface wave amplitude. We show that the transition to parametrically excited surface waves displays discontinuous and hysteretic features. This subcritical behaviour is attributed to the shear-thinning properties of our colloidal suspensions thanks to a phenomenological model based on rheological data under large amplitude oscillatory shear. Birefringence measurements provide direct evidence that Faraday waves induce local nematic or…
Active fluids comprise a variety of systems composed of elements immersed in a fluid environment which can convert some form of energy into directed motion; as such they are intrinsically out-of-equilibrium in the absence of any external forcing. A fundamental problem in the physics of active matter concerns the understanding of how the characteristics of the autonomous propulsion and agent-agent interactions determine the collective dynamics of the system. We study numerically suspensions of self-propelled diffusiophoretic colloids, in (quasi)-2d configurations, accounting for both dynamicall…
We utilize a generalized Irving-Kirkwood procedure to derive the hydrodynamic equations of an active matter suspension with internal structure and driven by internal torque. The internal structure and torque of the active Brownian particles give rise to a balance law for internal angular momentum density, making the hydrodynamic description a polar theory of continuum mechanics. We derive exact microscopic expressions for the stress tensor, couple stress tensor, internal energy density, and heat flux vector. Unlike passive matter, the symmetry of the stress tensor is broken explicitly due to a…
Colloidal shear thickening presents a significant challenge because the macroscopic rheology becomes increasingly controlled by the microscopic details of short ranged particle interactions in the shear thickening regime. Our measurements here of the first normal stress difference over a wide range of particle volume fraction elucidate the relative contributions from hydrodynamic lubrication and frictional contact forces, which have been debated. At moderate volume fractions we find $N_1<0$, consistent with hydrodynamic models, however at higher volume fractions and shear stresses these models…
Recent experiments report that slowly-sheared noncolloidal particle suspensions can exhibit unexpected rate($ω$)-dependent complex viscosities in oscillatory shear, despite a constant relative viscosity in steady shear. Using a minimal hydrodynamic model, we show that a weak interparticle attraction reproduces this behavior. At volume fractions $ϕ=20\sim50$%, the complex viscosities in both experiments and simulations display power-law reductions in shear, with a $ϕ$-dependent exponent maximum at $ϕ=40$%, resulting from the interplay between hydrodynamic, collision and adhesive interactions. F…
We have studied the correlated Brownian motion of micron-sized particles suspended in water and confined between two plates. The hydrodynamic interaction between the particles exhibits three anomalies. (i) The transverse coupling is negative, i.e., particles exert "anti-drag" on one another when moving perpendicular to their connecting line. (ii) The interaction decays with inter-particle distance r as 1/r^2, faster than in unconfined suspensions but slower than near a single wall. (iii) At large distances the pair interaction is independent of concentration within the experimental accuracy. T…
The dynamics of an adhesive two-dimensional vesicle doublet under various flow conditions is investigated numerically using a high-order, adaptive-in-time boundary integral method. In a quiescent flow, two nearby vesicles move slowly towards each other under the adhesive potential, pushing out fluid between them to form a vesicle doublet at equilibrium. A lubrication analysis on such draining of a thin film gives the dependencies of draining time on adhesion strength and separation distance that are in good agreement with numerical results. In a planar extensional flow we find a stable vesicle…
We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and used to analyse colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We fur…
Flowing blood displays a phenomenon called margination, in which leukocytes and platelets are preferentially found near blood vessel walls, while erythrocytes are depleted from these regions. Here margination is investigated using direct hydrodynamic simulations of a binary suspension of stiff (s) and floppy (f) capsules, as well as a stochastic model that incorporates the key particle transport mechanisms in suspensions -- wall-induced hydrodynamic migration and shear-induced pair collisions. The stochastic model allows the relative importance of these two mechanisms to be directly evaluated …
We derive the hydrodynamic equations of motion for a fluid of active particles described by under- damped Langevin equations that reduce to the Active-Brownian-Particle model, in the overdamped limit. The contraction into the hydrodynamic description is performed by locally averaging the par- ticle dynamics with the non-equilibrium many-particle probability density, whose formal expression is found in the physically relevant limit of high-friction through a multiple-time-scale analysis. This approach permits to identify the conditions under which self-propulsion can be subsumed into the fluid …
Hydrodynamic interactions between particles confined in a liquid-filled linear channel are known to be screened beyond a distance comparable to the channel width. Using a simple analytical theory and lattice-Boltzmann simulations, we show that the hydrodynamic screening is qualitatively modified when the time-dependent response and finite compressibility of the host liquid are taken into account. Diffusive compression modes in the confined liquid cause the particles to have velocity correlations of unbounded range, whose amplitude decays with time only as $t^{-3/2}$.
We study the role of hydrodynamic interactions in the collective behaviour of collections of microscopic active particles suspended in a fluid. We introduce a novel calculational framework that allows us to separate the different contributions to their collective dynamics from hydrodynamic interactions on different length scales. Hence we are able to systematically show that lubrication forces when the particles are very close to each other play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that motility-induced phase separation i…
