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.