Collective Dynamics in a Binary Mixture of Hydrodynamically Coupled Microrotors

Abstract

We study numerically the collective dynamics of self-rotating non-aligning particles by considering a monolayer of spheres driven by constant clockwise or counterclockwise torques. We show that hydrodynamic interactions alter the emergence of large-scale dynamical patterns compared to those observed in dry systems. In dilute suspensions, the flow stirred by the rotors induces clustering of opposite-spin rotors, while at higher densities same-spin rotors phase separate. Above a critical rotor density, dynamic hexagonal crystals form. Our findings underscore the importance of inclusion of the many-body, long-range hydrodynamic interactions in predicting the phase behavior of active particles.PACS numbers: 47.57. 47.63.mf, 83.10.Tv, 64.75.Xc Systems of motile and interacting units can exhibit non-equilibrium phenomena such as self-organization and directed motion at large scales [1]. Theoretical studies of active matter report clustering [2], phase separations [3][4][5] and rotating structures [6]. Some of these phenomena have been observed in experiments of bacterial suspensions [7] or chemically-activated motile colloids [8].The collective motion of translating units such as bacteria has received much interest [1]. On the other hand, little is known about spinning units, partly because such systems were realized experimentally only recently. Active rotation of particles can be achieved using external forcing such as rotating magnetic fields [9,10], uniform electric fields (the Quincke rotation effect) [11] or chemical reactions [12]. Self-assembly from polymers by motile bacteria can create micro-rotors [13]. In biological systems, the dancing volvox [14], uniflagellar algae C. reinhardtii [15] and bacteria T. majus [16] exhibit rotorlike behaviors. Rising interest in rotor systems generated theoretical studies exploring rotor pair dynamics [17,18], non-equilibrium structure formation [19], dynamics at interfaces [20,21], rheology of suspensions [22,23], and phase separation driven by active rotation [24,25].Models of the collective behavior of active matter often neglect particle motion due to the flow stirred by the other particles [4,5,24,26], tacitly assuming that the observed phase behavior of the "dry" system would persist in a system with fluid motion. However in the viscosity-dominated world of colloidal-size particles, hydrodynamic interaction generates a long-range correlation, which can play an important role in the self-organization in many-body systems [27][28][29]. For example, in the studies of micro-swimmers, it was found that the hydrodynamic interactions determine the collective motion of squirmers (self-propelled spheres with no aligning interaction) [30] and the recently observed self-organization of bacteria into a macro-scale bidirectional vortex when confined inside a drop [31] can only be explained by accounting for the fluid-mediated interactions [32]. It is the hydrodynamic interactions that cause two point rotors spinning in the opposite direction to translate [18] or undergo complex...

Dynamics of inert spheres in active suspensions of micro-rotors

“…In a collection of rotors, the flow stirred by each particle drags the other particles. The particles positions and rotations evolve as [33] …”

“…For pairwise interactions, the corrections to the fluid flow are O(1/r 7 ) as calculated in [33], but for multi-body interactions and in periodic domains these change [38].…”

“…Self-organization in rotor suspensions have been analyzed mostly computationally [29][30][31][32][33], though not all studies consider the effects of the immersing liquid on the rotor motions.…”

Brownian dynamics of confined suspensions of active microrollers

“…In a previous work we consider many body simulations of arbitrary shaped passive or active colloids near a planar wall using a rigid multiblob method [14], however, we did not discuss how to include Brownian motion. Recently, Singh and Adhikari [11] have used a Galerkin boundary integral representation for active spheres [15] to study the crystallization of a two-dimensional rotating suspension of spheres near a boundary; similar crystal behavior has been observed in experiments with bacteria and synthetic active colloids [6,16], as well in simulations of unconfined rotating spheres [17,18]. These studies neglect all Brownian motion because their magnitude is estimated to be small compared with the active forces.…”

Targeted assembly and synchronization of self-spinning microgears

“…Colloidal spinners provide a platform to explore active spinning matter and test theoretical predictions [34][35][36][37][38][39] , although the competition in our system of long-range diffusiophoretic interactions with hydrodynamics may significantly enrich the dynamics. The interplay between phase synchronization and spatial organization has the potential to achieve a new form of self-organization, without equilibrium counterparts, and not observed for collections of translational self-propelled particles 40 .…”