Micro-Tug-of-War: A Selective Control Mechanism for Magnetic Swimmers

Abstract

One of the aspirations for artificial microswimmers is their application in noninvasive medicine. For any practical use, adequate mechanisms enabling control of multiple artificial swimmers will be of paramount importance. Here we theoretically propose a multihelical, freely jointed motor as a selective control mechanism. We show that the nonlinear step-out behavior of a magnetized helix driven by a rotating magnetic field can be exploited when used in conjunction with other helices to obtain a velocity profile that is non-negligible only within a chosen interval of operating frequencies. Specifically, the force balance between the competing opposite-handed helices is tuned to give no net motion at low frequencies (tug-of-war), while in the middle-frequency range, the magnitude and, potentially, the sign of the swimming velocity can be adjusted by varying the driving frequency. We illustrate this idea on a two-helix system and demonstrate how to generalize to $\textit{N}$ helices, both numerically and theoretically. We then explain how to solve the inverse problem and design an artificial swimmer with an arbitrarily complex velocity vs frequency relationship. We finish by discussing potential experimental implementation.