Optimizing an undulating magnetic microswimmer for cargo towing

One of the promising capabilities of magnetic microswimmers is towing a cargo, which can be used for targeted drug delivery or performing tissue biopsy. A key question is what should be the optimal size ratio between the cargo and the swimmer's flexible tail. This question is addressed here for the simplest theoretical model of a magnetic microswimmer undergoing planar undulations - a spherical load connected by a torsion spring to a rigid slender link. The swimmer's dynamic is formulated and leading-order expressions for its motion are obtained explicitly under small-amplitude approximation. Optimal combinations of magnetic actuation frequency, torsion stiffness, and tail length for maximizing displacement, average speed, or energetic efficiency are obtained. The theoretical results are compared with reported experiments in several types of cargo-towing magnetic microswimmers.