Optimal Length of Low Reynolds Number Nanopropellers

Locomotion in fluids at the nanoscale is dominated by viscous drag. One efficient propulsion scheme is to use a weak rotating magnetic field that drives a chiral object. From bacterial flagella to artificial drills, the corkscrew is a universally useful chiral shape for propulsion in viscous environments. Externally powered magnetic micro- and nanomotors have been recently developed that allow for precise fuel-free propulsion in complex media. Here, we combine analytical and numerical theory with experiments on nanostructured screw-propellers to show that the optimal length is surprisingly short-only about one helical turn, which is shorter than most of the structures in use to date. The results have important implications for the design of artificial actuated nano- and micropropellers and can dramatically reduce fabrication times, while ensuring optimal performance.