Cooperative self-propulsion of active and passive rotors

Abstract

Reynolds number passive and active rotors in a fluid, we characterize the hydrodynamic interactions among rotors and the resulting dynamics of a pair of interacting rotors. This allows us to treat in a common framework passive or externally driven rotors, such as magnetic colloids driven by a rotating magnetic field, and active or internally driven rotors, such as sperm cells confined at boundaries. The hydrodynamic interaction of passive rotors is known to contain an azimuthal component ∼ 1/r 2 to dipolar order that can yield the recently discovered "cooperative self-propulsion" of a pair of rotors of opposite vorticity. While this interaction is identically zero for active rotors as a consequence of torque balance, we show that a ∼ 1/r 4 azimuthal component of the interaction arises in active systems to octupolar order. Cooperative self-propulsion, although weaker, can therefore also occur for pairs of active rotors.

Spiral and never-settling patterns in active systems

“…These authors did not, however, include cell reproduction which is essential to explain length selection in experimental patterns forming on the timescales of hours or days. In models of self-propelled particles with density conservation (α = 0) and no alignment (γ = 0) motility suppression can yield true phase separation whenλ > 1 [11,12]. A finite growth/death rate can arrest phase separation yielding concentric rings and high density bacterial "dots" not unlike those observed in Salmonella typhimurium [9].…”

“…Motility suppression has been further explored theoretically in models of self-propelled particles with density conservation [10][11][12][13][14]. With only steric repulsion and no alignment, motility suppression yields macroscopic phase separation, with large pretransitional density fluctuations [11,12]. In Vicsektype models with aligning interactions [13], the interplay of self-trapping and alignment yields a rich collection of traveling patterns, including bands, clumps and lanes [13].…”

“…It was recently demonstrated [7][8][9] that effective models of reproducing organisms that do not explicitly include chemotaxis can also yield stable patterns, as a result of the interplay between bacterial reproduction and death and the suppression of cell motility, which may arise from local crowding or biochemical signaling such as quorum sensing [4,10]. Motility suppression has been further explored theoretically in models of self-propelled particles with density conservation [10][11][12][13][14]. With only steric repulsion and no alignment, motility suppression yields macroscopic phase separation, with large pretransitional density fluctuations [11,12].…”

“…The rate s + becomes positive for D sp < −D α + r 2 . Motility suppression then promotes phase separation in regions of high and low density [11], which is in turn arrested by the density-dependent birth/death, as bacteria tend to grow in low density regions and die in high density regions, hence must migrate from high density to low density regions to obtain a steady state. The interplay of these two mechanisms ultimately yields For a fixed value ofα, the region ofλ where the system is unstable grows as alignment increases.…”

Colloidal Microworms Propelling via a Cooperative Hydrodynamic Conveyor Belt

“…Recent theoretical works [28][29][30] have addressed the rich dynamics of active rotors lying and spinning in the same plane. Here we rotate our particles perpendicular to the bounding plane and use real time and space experiments to elucidate the mechanism underlying the collective propulsion.…”