1and driven systems [2][3][4][5] . It is commonly held that potential interactions 6 , depletion forces 7 , or sensing 8 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 three-dimensional simulations. In this system, clusters originate from a previously unreported fingering instability, where fingers pinch o from an unstable front to form autonomous 'critters', whose size is selected by the height of the particles above the floor. These critters are a stable state of the system, move much faster than individual particles, and quickly respond to a changing drive. With speed and direction set by a rotating magnetic field, these active structures o er interesting possibilities for guided transport, flow generation, and mixing at the microscale.We have identified a new instability in one of the most basic systems of low-Reynolds-number (steady Stokes or overdamped) flow, a collection of spheres rotating near a wall. This system has been well studied analytically and numerically 9,10 , since it is considered a base model for understanding many microbial and colloidal flows. The instability visually resembles wet paint dripping down a wall or individual droplets sliding down a windshield 11 -examples of Rayleigh-Taylor instabilities 12 . However, in those and other clustering phenomena, what holds things together is surface tension or other forces deriving from an interaction potential.Here we use a model system to explore whether hydrodynamic interactions alone, without particle collisions, attractions or sense/response redirection, can lead to stable finite clusters.The experimental system consists of polymer colloids with radius a = 0.66 µm which have a small permanent magnetic moment (|m| ∼ 5 × 10 −16 A m −2 ) from an embedded haematite cube 13 (see schematic in Fig. 1a). Inter-particle magnetic interactions are small compared to thermal energy (< 0.1k B T ). A rotating magnetic field (B = B 0 cos(ωt)x + sin(ωt)ẑ ) with magnitude B 0 and frequency f = ω/2π is applied, causing all the particles to rotate about the y-axis at the same rate ω. The particles rotate synchronously with the field for ω < ω c , where ω c is the critical frequency above which the applied magnetic torque is not enough to balance the viscous torque on the particle (see Supplementary Section I for details of the rotation mechanism). In all of our experiments, ω < ω c . In contrast with recent experiments on Quincke rollers 14 , the rotation direction is prescribed and does not arise from the system dynamics.Hydrodynamics is the dominant inter-particle interaction in this system, which is distinctly different from many other systems of rotating magnetic particles, where dynamics is found to be a strong function of inter-particle ...

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally-resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. Key to the efficiency of the method is a technique for fast computation of the product of the blob-blob mobility matrix and a vector. For unbounded suspensions, we rely on existing analytical expressions for the Rotne-Prager-Yamakawa tensor combined with a fast multipole method (FMM) to obtain linear scaling in the number of particles. For suspensions sedimented against a single no-slip boundary, we use a direct summation on a Graphical Processing Unit (GPU), which gives quadratic asymptotic scaling with the number of particles. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently-developed rigid-body immersed boundary method ["An immersed boundary method for rigid

This contribution provides a general framework to use Lagrange multipliers for the simulation of low Reynolds number fiber dynamics based on Bead Models (BM). This formalism provides an efficient method to account for kinematic constraints. We illustrate, with several examples, to which extent the proposed formulation offers a flexible and versatile framework for the quantitative modeling of flexible fibers deformation and rotation in shear flow, the dynamics of actuated filaments and the propulsion of active swimmers. Furthermore, a new contact model called Gears Model is proposed and successfully tested. It avoids the use of numerical artifices such as repulsive forces between adjacent beads, a source of numerical difficulties in the temporal integration of previous Bead Models.

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 widelyused Euler-Maruyama scheme, and uses a random finite difference to capture the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. We generate the Brownian increments using a Krylov method, and show that for particles confined to remain in the vicinity of a no-slip wall by gravity or active flows the number of iterations is independent of the number of particles.Our numerical experiments with active rollers show that the thermal fluctuations set the characteristic height of the colloids above the wall, both in the initial condition and the subsequent evolution dominated by active flows. The characteristic height in turn controls the timescale and wavelength for the development of the fingering instability.arXiv:1612.00474v3 [cond-mat.soft]

We present a new development of the force-coupling method (FCM) to address the accurate simulation of a large number of interacting micro-swimmers. Our approach is based on the squirmer model, which we adapt to the FCM framework, resulting in a method that is suitable for simulating semi-dilute squirmer suspensions. Other effects, such as steric interactions, can be readily considered with our model. We test our method by comparing the velocity field around a single squirmer and the pairwise interactions between two squirmers with exact solutions to the Stokes equations and results given by other numerical methods. We also illustrate our method's ability to describe spheroidal swimmer shapes and biologically-relevant time-dependent swimming gaits. We detail the numerical algorithm used to compute the hydrodynamic coupling between a large collection ($10^4-10 ^5$) of micro-swimmers. Using this methodology, we investigate the emergence of polar order in a suspension of squirmers and show that for large domains, both the steady-state polar order parameter and the growth rate of instability are independent of system size. These results demonstrate the effectiveness of our approach to achieve near continuum-level results, allowing for better comparison with experimental measurements while complementing and informing continuum models

Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we present an efficient computational method for the dynamic simulation of Brownian suspensions with fluctuating hydrodynamics that handles both computations and provides a similar approximation as Stokesian Dynamics for dilute and semidilute suspensions. This advancement relies on combining the fluctuating force-coupling method (FCM) with a new midpoint time-integration scheme we refer to as the drifter-corrector (DC). The DC resolves the drift term for fluctuating hydrodynamics-based methods at a minimal computational cost when constraints are imposed on the fluid flow to obtain the stresslet corrections to the particle hydrodynamic interactions. With the DC, this constraint need only be imposed once per time step, reducing the simulation cost to nearly that of a completely deterministic simulation. By performing a series of simulations, we show that the DC with fluctuating FCM is an effective and versatile approach as it reproduces both the equilibrium distribution and the evolution of particulate suspensions in periodic as well as bounded domains.In addition, we demonstrate that fluctuating FCM coupled with the DC provides an efficient and accurate method for large-scale dynamic simulation of colloidal dispersions and the study of processes such as colloidal gelation.

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 and collective motion in colloidal suspensions.

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. Large-scale structures can emerge naturally from the dynamics of driven and active systems [1]. These structures result from the collective, coherent motion of many * delmotte@courant.nyu.edu † mdriscoll@nyu.edu ‡ chaikin@nyu.edu § donev@courant.nyu.edu individual units, and although similar phenomena are seen in widely disparate systems [2][3][4], the interactions that result in collective and coherent motion strongly depend on the specifics of the system being considered. Colloidal suspensions, for example, are always in the Stokes (overdamped) limit due to their small scale. In this limit, the interactions between the colloidal particles are longranged and strongly depend on the presence of nearby boundaries. Despite the linearity of the equations for the fluid flow in the Stokes regime, elucidating the precise role of hydrodynamic interactions in confined or bounded systems is still an open and challenging problem.Under strong in-plane confinement, i.e. in a Hele-Shaw cell, active suspensions exhibit coherent motion at large scales and phase transitions to polar and ordered states. For example, recent experiments [5] and models [6][7][8][9][10][11] have shown that hydrodynamic and steric interactions lead to the emergence of collective motion and structure formation in the form of swirls and vortices [7,9], asters [7,9], or polarized density waves [6,7,12,13]. In addition to using motile particles, a background flow can also be used to drive a suspension, leading to a rich and diverse array of structure formation: long-ranged orientational correlations [14], density fluctuations at all scales [15], and the formation of Burgers-like shocks [7,12,16,17]. In all of these strongly-confined driven suspensions, despite the difference in propulsion mechanism/driving, the local flow field around a particle is always quasi-twodimensional (q2D) and can be modeled as a potential dipole [6,18,19]. Here we show that related but quite different structure formation can emerge from a fundamentally different system, with a different particle-induced flow field and a diffe...