Generic Long-Range Interactions Between Passive Bodies in an Active Fluid

Abstract

Because active particles break time-reversal symmetry, a single non-spherical body placed in an active fluid generates currents. We show that when two or more passive bodies are placed in an active fluid these currents lead to long-range interactions. Using a multipole expansion we characterize their leading-order behaviors in terms of single-body properties and show that they decay as a power law with the distance between the bodies, are anisotropic, and do not obey an action-reaction principle. The interactions lead to rich dynamics of the bodies, illustrated by the spontaneous synchronized rotation of pinned non-chiral bodies and the formation of traveling bound pairs. The occurrence of these phenomena depends on tunable properties of the bodies, thus opening new possibilities for self-assembly mediated by active fluids.Active matter is a class of nonequilibrium systems in which energy is converted into systematic motion on a microscopic scale [1]. They have attracted much attention [2,3] due to a host of interesting physical phenomena [4][5][6][7][8][9], their relevance to many biological systems [10][11][12][13], and their potential use for self-assembly applications [14]. They have also been suggested as tools for novel engineering applications -for example, active fluids have been used to power microscopic gears [15][16][17][18][19][20][21]. This results from the fact that, when an asymmetric body is immersed in a fluid with broken time-reversal symmetry, it experiences a net force [22][23][24] which is coupled to the generation of ratchet-like currents [25,26].In this Letter we study passive bodies immersed in an active fluid. We show that the ratchet-like currents generated by each body give rise to forces and torques which decay as a power law with distance, are anisotropic, and do not obey an action-reaction principle. Using a multipole expansion, the leading-order behavior of the interactions can be expressed in terms of single-body quantities that can be measured independently in experiments or numerical simulations. Moreover, by designing the two bodies one can control the amplitude and polarity of the interactions between them. This leads to a host of interesting dynamical phenomena of which we illustrate two: the spontaneous synchronized rotations of pinned rotors and the formation of traveling bound pairs. Our results suggest a new method for self-assembly by embedding passive bodies in an active fluid.We stress that the interactions studied here exist even between non-moving bodies and are therefore distinct from usual hydrodynamic interactions [27]. They are also different from thermal Casimir interactions [28,29], because they do not rely on correlations between the fluid particles and are present even in a dilute active fluid.Model. -We base our study on a common model of an active fluid consisting of N point-like particles, which * y.baek@damtp.cam.ac.uk do not interact among themselves and self-propel at a constant speed v in two dimensions. The position r i and the orientation θ i of acti...

Response of active Brownian particles to boundary driving

“…For example, the active Brownian particle (ABP) model describes spheres or discs that self-propel at constant velocity and whose direction of propulsion evolves diffusively [18]. Despite their simplicity, such self-propelled particle models exhibit striking emergent phenomena, including athermal phase separation [19][20][21][22][23][24][25][26][27][28][29], spontaneous flows [30][31][32][33][34][35], and long-range density variations [36][37][38][39][40]. However, researchers have only recently begun to study these models in the presence of external driving.…”

“…It has been established that boundaries have dramatic * email:kswag@brandeis.edu † email:hagan@brandeis.edu ‡ email:aparna@brandeis.edu and long-ranged effects in active systems, which make active systems non-extensive (i.e. their behaviors are not independent of system size) [37,39,40,[47][48][49][50]. However, the consequences of boundary driving have yet to be addressed in the literature of active particles.…”

Stabilization in the Eye of a Cyclone

“…Applications vary from the induced force on probes in contact with biological tissue or filaments to the motion of dust in atmospheric dynamics. While the context of probes in contact with nonequilibrium media is clearly physically interesting there are very few mathematical treatments and even less rigorous results [1][2][3][4][5][6][7][8][9]. The present paper presents a mathematical study about the stabilization of a probe (the slow particle) which interacts with (fast) medium particles that are subject to a vortex-shaped force-field.…”

Enhanced Orientational Ordering Induced by an Active yet Isotropic Bath

“…The polarisation field of the polar rods is described by the two-dimensional vector p, while that of AOUPs by m. We assume that the number density of the AOUPs is not conserved (i.e., they can move in and out of the system) to eliminate the effect of long-range interaction that such a conservation law could mediate [17]. Further, we also do not explicitly consider the dynamics of the density of the polar rods since even in the presence of m, the coupling between density and polarisation cannot change the mean-field critical point [18].…”

“…For the purpose of this experiment, passive polar rods will consist of particles with a polar top surface and a circular base instead of a polar base and circular top surface that constitutes active discs. However, care must be taken to isolate our fluctuation-driven effect from the flow-driven one described by [17] (alternatively, the flow-driven effect may be eliminated by randomly adding and removing isotropic active particles). Furthermore, the system of apolar particles in an isotropic momentum conserved active fluid that we consider, can model microtubules in a disordered actomyosin fluid or passive colloidal rods in a solution of spherical bacteria [28].…”