Nonlinear parametric excitation effect induces stability transitions in swimming direction of flexible superparamagnetic microswimmers

Microscopic artificial swimmers have recently become highly attractive due to their promising potential for biomedical microrobotic applications. Previous pioneering work has demonstrated the motion of a robotic microswimmer with a flexible chain of superparamagnetic beads, which is actuated by applying an oscillating external magnetic field. Interestingly, they have shown that the microswimmer's orientation undergoes a 90°-transition when the magnetic field's oscillation amplitude is increased above a critical value. This unexpected transition can cause severe problems in steering and manipulation of flexible magnetic microrobotic swimmers. Thus, theoretical understanding and analysis of the physical origins of this effect are of crucial importance. In this work, we investigate this transition both theoretically and experimentally by using numerical simulations and presenting a novel flexible microswimmer with an anisotropic superparamagnetic head. We prove that this effect depends on both frequency and amplitude of the oscillating magnetic field, and demonstrate existence of an optimal amplitude achieving maximal swimming speed. Asymptotic analysis of a minimal two-link model reveals that the changes in the swimmer's direction represent stability transitions, which are induced by a nonlinear parametric excitation.