Effects of the intrinsic curvature of elastic filaments on the propulsion of a flagellated microrobot

Abstract

Understanding the propulsion mechanism of swimming microorganisms will facilitate the development of synthetic microswimmers for active cargo deliveries. Herein, we studied, theoretically and numerically, inertialess locomotion of a microswimmer—a spherical body propelled by two symmetrically actuated elastic filaments in the shape of a circular arc at rest, focusing on the effects of their uniform intrinsic curvature κ¯c. Combining the resistive force theory for viscous flow and Euler–Bernoulli beam theory for elastic filaments, the elasto-hydrodynamics was solved asymptotically. Our theory was verified by simulations using regularized Stokeslets posed on the filament centerlines, with and without considering hydrodynamic interactions (HIs) between the body and filaments. The asymptotic and numerical results showed qualitative agreement. Reasonable quantitative agreement between the asymptotic results and the numerical predictions neglecting body–filament HIs was observed, especially for small |κ¯c|. However, they deviated quantitatively from the numerical results with body–filament HIs, especially at a large κ¯c when the HIs became important owing to the short body–filament distance. The propulsive force generated by two arc-shaped filaments significantly depend on their uniform intrinsic curvature κ¯c. An appreciable increase in the thrust can be achieved by adjusting κ¯c, which qualitatively confirms and explains the experimentally reported propulsive enhancement facilitated by intrinsically curved appendages [Z. Ye, S. Régnier, and M. Sitti, “Rotating magnetic miniature swimming robots with multiple flexible flagella,” IEEE Trans. Rob. 30, 3–13 (2014)]. The increase in κ¯c can even change the sign of the thrust, leading to counter-intuitive, backward propulsion. The flow field reveals the hydrodynamic signature of the swimmer that shifts with time between a neutral swimmer, a pusher, and a puller.