Dynamics of Purcell-type microswimmers with active-elastic joints

TL;DR

This paper investigates a more realistic model of Purcell's microswimmer with elastic joints and periodic torques, revealing complex nonlinear behaviors such as multiple solutions, bifurcations, and stability changes.

Contribution

It introduces an extended microswimmer model with elastic joints and dynamic actuation, analyzing its nonlinear dynamics and stability properties.

Findings

Multiple periodic solutions depending on input parameters

Swimmer's direction can reverse due to bifurcations

Elastic joints induce rich nonlinear behaviors and symmetry breaking

Abstract

Purcell's planar three-link microswimmer is a classic model of swimming in low-Reynolds-number fluid, inspired by motion of flagellated microorganisms. Many works analyzed this model, assuming that the two joint angles are directly prescribed in phase-shifted periodic inputs. In this work, we study a more realistic scenario by considering an extension of this model which accounts for joints' elasticity and mechanical actuation of periodic torques, so that the joint angles are dynamically evolving. Numerical analysis of the swimmer's dynamics reveals multiplicity of periodic solutions, depending on parameters of the inputs - frequency and amplitude of excitation, joints' stiffness ratio, as well as joint's activation. We numerically study swimming direction reversal, as well as bifurcations, stability transitions, and symmetry breaking of the periodic solutions, which represent the effect of buckling instability observed in swimming microorganisms. The results demonstrate that this variant of Purcell's simple model displays rich nonlinear dynamic behavior with actuated-elastic joints. Similar results are also obtained when studying an extended model of a six-link microswimmer.