Rototaxis: Localization of active motion under rotation

Yuanjian Zheng,Hartmut Löwen

doi:10.1103/physrevresearch.2.023079

Yuanjian Zheng, Hartmut Löwen

Open Access

https://doi.org/10.1103/physrevresearch.2.023079

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Abstract

The ability to navigate in complex, inhomogeneous environments is fundamental to survival at all length scales, giving rise to the rapid development of various subfields in bio-locomotion such as the well established concept of chemotaxis. In this work, we extend this existing notion of taxis to rotating environments and introduce the idea of roto-taxis to bio-locomotion. In particular, we explore both overdamped and inertial dynamics of a model synthetic self-propelled particle in the presence of constant global rotation, focusing on the particle's ability to localize near a rotation center as a survival strategy. We find that in the overdamped regime, the swimmer is in general able to generate a self restoring active torque that enables it to remain on stable epicyclical-like trajectories. On the other hand, for underdamped motion with inertial effects, the intricate competition between self-propulsion and inertial forces, in conjunction with the rototactic torque leads to complex dynamical behavior with non-trivial phase space of initial conditions which we reveal by numerical simulations. Our results are relevant for a wide range of setups, from vibrated granular matter on turntables to microorganisms or animals swimming near swirls or vortices.

Highlights

Microorganisms and artificial microswimmers alike [1,2,3], are highly capable of adapting their motion in response to gradients present in external stimuli
For underdamped motion with inertial effects, the intricate competition between self-propulsion and inertial forces, in conjunction with the rotation-induced torque, leads to complex dynamical behavior with nontrivial phase space of initial conditions which we reveal by numerical simulations
An expression for the radius of the limit cycle m2ω04 + γ 2(ω − ω0 )2. Note that these equations imply that the periodic circular trajectory is not a solution to the equations of motion in the absence of activity, and the dynamics discussed here cannot be achieved by a passive rotor

Summary

INTRODUCTION

Microorganisms and artificial microswimmers alike [1,2,3], are highly capable of adapting their motion in response to gradients present in external stimuli. Despite its survival advantages as a taxis strategy, generating negative rototaxis is a considerably difficult task for microswimmers This is due to the centrifugal force in the rotating frame of the system that tends to expel the particle or organism away from its rotation center. We introduce a model 2D microswimmer capable of generating a tunable torque that sustains both negative and positive rototaxis by altering its initial swim orientation with respect to its position in the flow field. This is made possible in the presence of inertia that is increasingly being recognized to play a pivotal role in the dynamics of microswimmers [54,55,56,57,58]. We remark that a torque T ∼ R sin (θ − φ) that plays the same essential role as τ in orientating the swimmer towards the rotation center Oin the present model can be physically realized by placing a light source at the rotation center for phototactic particles [15,16,17,18,19,20,21,22,23,24,25] or by placing a pole of a magnetic field at Ofor magnetotactic swimmers [26,27,28,29,30,31]

OVERDAMPED DYNAMICS

INERTIAL DYNAMICS

Findings

CONCLUSION