Unstable fronts and motile structures formed by microrollers

Abstract

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 ...

Brownian dynamics of confined suspensions of active microrollers

“…In this section, we perform Brownian Dynamics simulations of the fingering instability which was discovered in [7]. In that work, it was shown that suspensions of rollers (spherical particles) rotating parallel to a floor form narrow shock-like fronts which destabilize in the direction transverse to their motion.…”

“…2) is due to active motion: the flow field generated in front of a roller close to a wall lifts the neighboring particles upwards (see Fig. 1c in [7]). It is also interesting to note that, in both cases, P (h) is bi-modal when h g = 1.5a and tri-modal when h g = 6.1a.…”

“…The hematite is a canted anti-ferromagnet and thus provide the rollers with a small permanent magnetic moment |m| = 5 · 10 strong enough and the frequency low enough to overcome the viscous torque exerted by the surrounding fluid, the particles rotate synchronously with B at a rate ω. In our previous deterministic simulations of the fingering instability [7], we kept the particle angular velocity fixed at ω, and computed the torque required to maintain that specified rotation. However, qualitatively identical behavior is observed if the particles are driven by a constant torque instead, which can also be realized experimentally and is somewhat cheaper to simulate.…”

“…In a recent publication some of us performed simulations with thousands of colloidal particles to study a fingering hydrodynamic instability in a suspension of active rollers [7]. In a series of experiments, magnetic colloids roll above a floor with a specific angular frequency set by an external magnetic field.…”

“…For example, quasi-two-dimensional experiments use optical microscopy [1, 2] or light scattering techniques [3] to observe colloidal particles confined between microscopes slips. Synthetic active colloids are usually metallic [4,5] or have metallic components [6,7], making them much denser than the surrounding fluid and therefore prone to sediment towards the floor. Even neutrally buoyant active colloids are often advected toward the boundaries by the active flows [8].…”