Hydrodynamically bound states of a pair of microrollers: A dynamical system insight

Abstract

Recent work has identified persistent cluster states which were shown to be assembled and held together by hydrodynamic interactions alone [Driscoll 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 on a dimensionless number, denoted B, that compares the relative strength of gravitational forces and external torques. Using a dynamical system framework, we characterize these various states in phase space and analyze the bifurcations of the system as B varies. In particular, we show that there is a critical value, B * , above which active flows can beat gravity and lead to stable motile orbiting, or "leapfrog", trajectories, reminiscent of the self-assembled motile structures, called "critters", observed by Driscoll et al. We identify the conditions for the emergence of these trajectories and study their basin of attraction. This work shows that a wide variety of stable bound states can be obtained with only two particles. Our results aid in understanding the mechanisms that lead to spontaneous self-assembly in hydrodynamic systems, such as microroller suspensions, as well as how to optimize these systems for particle transport. * blaise.delmotte@ladhyx.polytechnique.fr arXiv:1811.05168v4 [physics.flu-dyn]

Collective Motion of Quincke Rollers with Fully Resolved Hydrodynamics

“…First, as an evaluation of the SP method, we confirm that the speed of the single roller is in good agreement with lubrication theory [19,20], and that the flow field around the roller agrees with previous simulations that used a rotlet representation corrected by the Blake tensor [13,14,21,22] (see Supplementary Information). The advantage of the SP method is that it can accurately handle HIs between rollers.…”

“…6 (b). This flow field reproduces the results of the multiblob method with a rotlet corrected by the Blake tensor [14,21,22]. Here, we perform computations for a system that accounts for the effects between the upper and lower wall surfaces, which is slightly different from the system treated in the multiblob method.…”

Irreversible hydrodynamic trapping by surface rollers

“…1b [35]. Related hydrodynamic bound phenomena have been demonstrated using a pair of magnetically driven rollers [7,24]. In general, when a body rotates and translates simultaneously, a vortical flow field of finite size appears around the body.…”

A simple catch: thermal fluctuations enable hydrodynamic trapping of microrollers by obstacles

“…Additionally, in the microroller system, the orientation of propulsion does not diffuse, but is prescribed by a rotating field, and can therefore be externally controlled. These rotating particles generate strong flows, which can lead to a tunable and hydrodynamically-mediated attraction between adjacent microrollers [4,24,25]. Dense suspensions of microrollers give rise to interesting collective effects [4,[26][27][28], such as the formation of hydrodynamically stabilized motile clusters composed of microrollers [4].…”