Elasto-Hydrodynamic Propulsion of a Magnetically Actuated Filament

Abstract

We investigate the low-Reynolds-number propulsion of a slender elastic filament with a dipolar magnetic head actuated by an oscillating field in a viscous fluid by studying its strokes and net forward motion. To capture these dynamics, we employ an elasto-hydrodynamic (EH) framework that couples Euler-Bernoulli beam mechanics with resistive force theory. Unlike prescribed-kinematics models, filament shapes here emerge self-consistently from the actuation and the force and torque boundary conditions (BCs). We demonstrate that viscous boundary contributions are crucial for quantitative agreement and show that the swimming dynamics are governed by the EH length and a magneto-viscous-elastic stroke amplitude introduced here. The swimming speed is non-monotonic with increasing ratio of the swimmer length to the EH length, and is shown to reach a maximum when the swimmer length is on the order of the EH length. We further discuss the analytical limit in which the tail BCs can be described as free, and the limitations that arise when viscous contributions to the BCs are ignored.