Breaking the left‐right symmetry in fluttering artificial cilia that perform nonreciprocal oscillations

Recent investigations on active materi- als have introduced a new paradigm for soft robotics by showing that a complex response can be obtained from simple stimuli by harnessing dynamic instabili- ties. In particular, polyelectrolyte hydrogel filaments actuated by a constant electric field have been shown to exhibit self-sustained oscillations as a consequence of flutter instability. Owing to the nonreciprocal nature of the emerging oscillations, these artificial cilia are able to generate flows along the stimulus. Building upon these findings, in this paper we pro- pose a design strategy to break the left-right symme- try in the generated flows, by endowing the filament with a natural curvature at the fabrication stage. We develop a mathematical model based on morphoe- lastic rod theory to characterize the stability of the equilibrium configurations of the filament, proving the persistence of flutter instability. We show that the emerging oscillations are nonreciprocal and gener- ate thrust at an angle with the stimulus. The results we find at the level of the single cilium open new perspectives on the possible applications of artificial ciliary arrays in soft robotics and microfluidics.